We provide straight lines practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on straight lines skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of straight lines Questions

Question No | Questions | Class |
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1 | The lengths of the perpendicular from the points ( left(boldsymbol{m}^{2}, boldsymbol{2 m}right),left(boldsymbol{m m}^{prime}, boldsymbol{m}+boldsymbol{m}^{prime}right) ) and ( left(m^{prime 2}, 2 m^{prime}right) ) to the line ( x+y+1=0 ) form ( cos alpha+y sin alpha+sin alpha tan alpha=0 ) are in ( A ). an A.P. B. a G.P. c. а н.Р. D. none of these | 11 |

2 | Find the coordinates of points on the ( x ) axis which are at a distance of 17 units from the point (11,-8) | 11 |

3 | If ( P ) is (-3,4) and ( M y M x(P) ) shows the reflection ofthe point ( P ) in the ( x ) -axis and then the reflection of the image in the ( y ) – axis, then ( M_{y} M_{x}(P) ) is ( A cdot(3,4) ) B. (-3,-4) c. (-3,4) D. (3,-4) | 11 |

4 | If the vertices of a triangle are ( (1,-3),(4, p) ) and (-9,7) and its area is 15 sq. units, find the value(s) of ( p ) | 11 |

5 | If three points ( (h, 0),(a, b) ) and ( (0, k) ) lie on a line, show that ( frac{a}{h}+frac{b}{k}=1 ) | 11 |

6 | Find the inclination of the line ( ( ) in degrees ) whose slope is 1 | 11 |

7 | Let ( A B C ) be a triangle with ( A B=A C ) and ( D ) is mid-point of ( B C, E ) is the foot of perpendicular drawn from ( D ) to ( A C ) and ( F ) the mid point of ( D E . ) Angle between the line ( A F ) and ( B E ) is ( theta ). Then the value of ( 4 sin theta ) is A .4 B. 3 c. ( frac{3}{2} ) D. ( frac{4}{3} ) | 11 |

8 | Find inclination (in degrees) of a line perpendicular to x-axis. | 11 |

9 | Slope ( =-4 ) and ( y ) -intercept ( =2, ) then the equation of line is ( m x+y=c . ) Find ( boldsymbol{m}+boldsymbol{c} ) | 11 |

10 | Find the slope of a line passing through the points (-5,2) and (6,7) ( mathbf{A} cdot mathbf{9} ) B. 5 ( c .-5 ) D. ( frac{5}{11} ) ( E cdot-frac{5}{11} ) | 11 |

11 | Find the distance between parallel lines ( (i) 15 x+8 y-34=0 ) and ( 15 x+8 y+ ) ( mathbf{3 1}=mathbf{0} ) ( (text { ii })(x+y)+p=0 ) and ( (x+y)-r=0 ) | 11 |

12 | Find the locus of a variable point which is at a distance of 2 units from the ( y- ) axis A . ( x=pm 2 ) B . ( y=pm 2 ) c. ( x=pm 4 ) D. ( y=pm 4 ) | 11 |

13 | If the lines ( y=3 x+1 ) and ( 2 y=x+3 ) are equally inclined to the line ( y= ) ( m x+4 . ) Find the values of ( m ) | 11 |

14 | Which of the following is/are true regarding the following linear equation: ( boldsymbol{y}=mathbf{2} boldsymbol{x}+mathbf{3} ) A ( cdot ) It passes through (3,0) and ( m=frac{1}{2} ) B. It passes through (3,0) and ( m=-2 ) c. It passes through (0,3) and ( m=2 ) D. It passes through (0,3) and ( m=frac{1}{2} ) | 11 |

15 | 13. The incentre of the triangle with vertices (1, 3), (0,0) and (2,0) is (2000) 1 | 11 |

16 | If the slop of one of the lines represented by ( a x^{2}-6 x y+y^{2}=0 ) is the square of the other,then the value of a is A. -27 or 8 B. -3 or 2 c. -64 or 27 D. -4 or 3 | 11 |

17 | 15. Aline cuts the x-axis at A (7,0) and the y-axis at B(0,-5). A variable line PQ is drawn perpendicular to AB cutting the x- axis in Pand the y-axis in Q. IfAQ and BP intersect at R, find the locus of R. (1990 – 4 Marks) | 11 |

18 | The line ( y+7=0 ) is parallel to ( mathbf{A} cdot x=2 ) B. ( x=1 ) c. ( x=5 ) D. ( x ) -axis | 11 |

19 | ( A ) is a point on ( x- ) axis with abscissa -8 and ( B ) is point on ( y- ) axis with coordinate ( 15 . ) Find distance ( A B ) | 11 |

20 | If the equation ( a x^{2}-6 x y+y^{2} 2 g x+ ) ( 2 f y+c=0 ) represents a pair of line whose slopes are ( m ) and ( m^{2}, ) then sum of all possible values of ( a ) is- A . 17 в. -19 c. 19 D. -17 | 11 |

21 | The line making an angle ( left(-120^{circ}right) ) with ( x ) -axis is situated in the : A. First quandrant B. Second quandrant c. Third quandrant D. Fourth quandrant | 11 |

22 | In the given figure, ( boldsymbol{A B} | boldsymbol{C D}, angle boldsymbol{A B E}= ) ( 120^{circ}, angle E C D=100^{circ} ) and ( angle B E C=x^{o} ) Find the value of ( x ) | 11 |

23 | If the area of the ( triangle A B C ) is 68 sq.units and the vertices are ( boldsymbol{A}(boldsymbol{6}, boldsymbol{7}), boldsymbol{B}(-boldsymbol{4}, boldsymbol{1}) ) and ( C(a,-9) ) taken in order, then find the value of ( a ). | 11 |

24 | Given a triangle with unequal sides, if is the set of all points which are equidistant from ( mathrm{B} ) and ( mathrm{C} ), and ( mathrm{Q} ) is the set of all points which are equidistant from sides ( A B ) and ( A C, ) then what is the intersection with ( mathrm{Q} ) equal to? | 11 |

25 | The equations of ( L_{1} ) and ( L_{2} ) are ( y=m x ) and ( boldsymbol{y}=boldsymbol{n} boldsymbol{x}, ) respectively. Suppose ( boldsymbol{L}_{mathbf{1}} ) makes twice as large of an angle with the horizontal(measured counterclockwise from the positive ( x- ) axis) as does ( L_{2} ) and that ( L_{1} ) has 4 times the slope of ( L_{2} . ) If ( L_{1} ) is not horizontal, then the value of the product(mn) equals. ( A cdot frac{sqrt{2}}{2} ) B. ( -frac{sqrt{2}}{2} ) c. 2 D. -2 | 11 |

26 | 20. Orthocentre of triangle with vertices (0,0), (3, 4) and (4.0) (20035 (33) 0,12 0,3 (3,12) m) 69 d) (3.9) | 11 |

27 | less than 212 . Then (a) a +b-c> 0 (c) a-b+c>0 a>b>c>0, the distance between (1, 1) and the point of ersection of the lines ax +by+c= 0 and bx + ay+c=0 is (JEE Adv. 2013) (b) a-b+c<o (d) a+b-c<0 | 11 |

28 | 15. If a vertex of a triangle is (1, 1) and the mid points of two sides through this vertex are (-1, 2) and (3, 2) then the centroid of the triangle is [2005] | 11 |

29 | A straight line L through the origin meets the lines x+y=1 and x+y=3 at P and Q respectively. Through P and Qtwo straight lines L, and L, are drawn, parallel to 2x -y=5 and 3x+y=5 respectively. Lines L, and L, intersect at R. Show that the locus of R, as L varies, is a straight line. | 11 |

30 | 23. A straight line L through the point (3,-2) is inclined at an angle 60° to the line 3x + y = 1. If L also intersects the x-axis, then the equation of Lis (2011) (a) y+ 3x+2–313 = 0 (b) y-V3x+2+373 = 0 (c) V3y=x+3+2+3 =0 (d) V3y+x-3+2+3 = 0 | 11 |

31 | Find the inclination of a line whose slope is (i) 1 (ii) -1 (iii) ( sqrt{mathbf{3}} ) (iv) ( -sqrt{mathbf{3}} ) ( (v) frac{1}{sqrt{3}} ) | 11 |

32 | IX, X, X, as well as y, y..are in GP, with the same common ratio, then the points (x,y),(x, y,) and (x2, Yz). (1999 – 2 Marks) (a) lie on a straight line (6) lie on an ellipse (c) lie on a circle (d) are vertices of a triangle | 11 |

33 | Using determinent, if area of triangle is 4, whose vertices are ( (2,2),(6,6),(5, k) ) then ( mathrm{k}= ) A . 5 B. ( c cdot 7 ) D. 3 | 11 |

34 | The angle between the lines ( x cos alpha+ ) ( boldsymbol{y} sin boldsymbol{alpha}=boldsymbol{p}_{1} ) and ( boldsymbol{x} cos boldsymbol{beta}+boldsymbol{y} sin beta=boldsymbol{p}_{2} ) where ( boldsymbol{alpha}>boldsymbol{beta} ) is ( mathbf{A} cdot alpha+beta ) B. ( alpha-beta ) ( c cdot alpha beta ) D. ( 2 alpha-beta ) | 11 |

35 | Find the distance between each of the following pairs of points. ( boldsymbol{L}(mathbf{5},-mathbf{8}), boldsymbol{M}(-mathbf{7},-mathbf{3}) ) | 11 |

36 | The ( x ) -coordinate of a point ( P ) is twice its y-coordinate. If ( boldsymbol{P} ) is equidistant from ( Q(2,-5) ) and ( R(-3,6), ) then find the coordinates of ( boldsymbol{P} ) | 11 |

37 | Using section formula. show that the points (-3,-1),(1,3) and (-1,1) are collinear. | 11 |

38 | The distance between the points ( (mathbf{0}, mathbf{0}) ) and ( left(5, tan ^{-1} frac{4}{3}right) ) is ( mathbf{A} cdot mathbf{3} ) B. 4 c. 5 D. 7 | 11 |

39 | The distance between (3,5) and (5,3) A ( cdot 2 sqrt{2} ) B. ( sqrt{2} ) ( c cdot 2 ) D. None | 11 |

40 | Find the acute angle between the lines ( sqrt{3 x}+y=1 ) and ( x+sqrt{3 y}=1 ) | 11 |

41 | The distance between the lines ( y= ) ( 2 x+4 ) and ( 3 y=6 x-5 ) is equal to A . B. ( 3 / sqrt{5} ) c. ( frac{17 sqrt{5}}{15} ) D. ( frac{17}{sqrt{3}} ) | 11 |

42 | The angle between the lines ( x cos 30^{circ}+ ) ( y sin 30^{circ}=3 ) ( x cos 60^{circ}+y sin 60^{circ}=5 ) is A ( cdot 90^{circ} ) B. ( 30^{circ} ) ( c cdot 60^{circ} ) D. None of these | 11 |

43 | If the inclination of a line is ( 45^{circ}, ) then the slope of the line is? A . 0 B. – ( c cdot 1 ) D. 2 | 11 |

44 | Find the distances between the following pair of parallel lines: ( mathbf{3} boldsymbol{x}+mathbf{4} boldsymbol{y}+mathbf{9}=mathbf{0}, mathbf{6} boldsymbol{x}+mathbf{8} boldsymbol{y}+mathbf{1 5}=mathbf{0} ) A ( cdot frac{3}{10} ) B. ( frac{3}{5} ) c. ( frac{33}{10} ) D. ( frac{24}{5} ) | 11 |

45 | LE POR be a right angled isosceles triangle, right angled at P (2, 1). If the equation of the line OR is 2x+y=3, then the equation representing the pair of lines PQ and PR is (1999-2 Marks) (a) 3.×2-3y2 + &xy + 20x+10y +25=0 (b) 3×2 – 3y2 + 8xy – 20x – 10y + 25 =0 (c) 3×2 – 3y2 + &xy + 10x +15y +20=0 (d) 3×2 -3y2 – 8xy – 10x – 15y-20=0 | 11 |

46 | Calculate the angles marked with small etters in the following diagram. (iii) Rhombus | 11 |

47 | In the figures given below, write which lines form a pair of parallel lines and write them in the form of symbols: (1) (2) (3) (4) | 11 |

48 | The co-ordinates of the point of intersection of the diagonals of the square ABCD is (1,7) If true then enter 1 and if false then | 11 |

49 | Find an equation of the line perpendicular to the line ( 3 x+6 y=5 ) and passing through the point (1,3) Write the equation in the standard form. | 11 |

50 | For the equation given below, find the slope and the y-intercept: ( boldsymbol{x}=mathbf{5} boldsymbol{y}-boldsymbol{4} ) A ( cdot frac{1}{5} ) and ( frac{4}{5} ) B. ( frac{4}{5} ) and ( frac{4}{5} ) c. ( frac{4}{5} ) and ( frac{1}{5} ) D. ( frac{1}{5} ) and ( frac{1}{5} ) | 11 |

51 | In the diagram MN, is a straight line. The distance between ( mathrm{M} ) and ( mathrm{N} ) is: A. 6 units B. 8 units c. 9 units D. 10 units | 11 |

52 | For the angle in standard position if the Initial arm rotates ( 130^{circ} ) in anticlockwise direction, then state the quadrant in which terminal arm lies. (Draw the figure and write the answer). | 11 |

53 | Find the slope of the line passing through the points ( A(-2,1) ) and ( boldsymbol{B}(mathbf{0}, boldsymbol{3}) ) | 11 |

54 | Find the equation of a straight line: with slope -2 and intersecting the ( x- ) axis at a distance of 3 units to the left of origin. | 11 |

55 | The slope of any line which is parallel to the ( x ) -axis is ( mathbf{A} cdot mathbf{0} ) B. ( c cdot-1 ) ( D ) | 11 |

56 | The angle between the lines ( r cos (theta- ) ( boldsymbol{alpha})=boldsymbol{p}, boldsymbol{r} sin (boldsymbol{theta}-boldsymbol{alpha})=boldsymbol{q} ) is A ( cdot frac{pi}{4} ) в. c. ( frac{pi}{2} ) D. ( frac{5 pi}{12} ) | 11 |

57 | on 01 LU . 21. 2. and venele Pole chat on the link to south and x = **, A rectangle PQRS has its side PQ parallel to the line y=mx and vertices P, Q and S on the lines y=a, x=b and x=-b, respectively. Find the locus of the vertex R. (1996-2 Marks) | 11 |

58 | Find the angle between the ( x ) -axis and the line joining the points (3,-1) and (4,-2) A ( .115^{circ} ) B . ( 120^{circ} ) ( mathbf{c} cdot 135 ) D. ( 140^{circ} ) | 11 |

59 | Find the area of the triangle whose vertices are: ¡) (2,3),(-1,0),(2,-4) ii) (-5,-1),(3,-5),(5,2) | 11 |

60 | The axes being inclined at an angle of ( 60^{circ}, ) the angle between the two straight lines ( y=2 x+5 ) and ( 2 y+x+7=0 ) is ( mathbf{A} cdot 90 ) B. ( tan ^{-1} frac{5}{3} ) ( ^{mathrm{C}} cdot tan ^{-1} frac{sqrt{3}}{2} ) D. ( tan ^{-1} frac{5}{sqrt{3}} ) | 11 |

61 | If two vertices of an equilateral triangle ( operatorname{are}(3,0) ) and ( (6,0), ) find the third vertex. | 11 |

62 | 12. Lines 4 = ax + by+c = 0 and L2 = Ix+my+n=0 intersect at the point Pand make an angle o with each other. Find the equation of a line L different from L, which passes through P and makes the same angle o with L. (1988 – 5 Marks) | 11 |

63 | The angle between the lines ( y-x+ ) ( mathbf{5}=mathbf{0} ) and ( sqrt{mathbf{3}} x-boldsymbol{y}+mathbf{7}=mathbf{0} ) is/are: A ( cdot 15^{circ} ) В. ( 60^{circ} ) ( mathbf{c} cdot 165^{circ} ) D. ( 75^{circ} ) | 11 |

64 | If ( boldsymbol{A}left(mathbf{1}, boldsymbol{p}^{2}right) ; boldsymbol{B}(mathbf{0}, mathbf{1}) ) and ( boldsymbol{C}(boldsymbol{p}, boldsymbol{0}) ) are the co ordinates of three points then the value of ( p ) for which the area of triangle ABC is minimum, is A ( cdot frac{1}{sqrt{3}} ) B. ( -frac{1}{sqrt{3}} ) c. ( frac{1}{sqrt{3}} ) or ( -frac{1}{sqrt{3}} ) D. None | 11 |

65 | Find the distance between the lines ( mathbf{3} boldsymbol{x}+mathbf{4} boldsymbol{y}=mathbf{9} ) and ( boldsymbol{6} boldsymbol{x}+mathbf{8} boldsymbol{y}=mathbf{1 5} ) | 11 |

66 | If the points (2,1),(3,-2) and ( (a, b) ) are collinear then ( A cdot a+b=7 ) B. 3a+b=7 c. a-b=7 D. 3a-b=7 | 11 |

67 | Let ( mathbf{P}left(mathbf{x}_{1}, mathbf{y}_{1}right) ) be any point on the cartesian plane then match the following lists: LIST – I | 11 |

68 | 28. The area of the triangle fol ca of the triangle formed by the intersection 01 d me Parallel to x-axis and passing through P(h, k) with the lines Vexand x+y=2 is 4h2. Find the locus of the point P. (2005 – 2 Marks) | 11 |

69 | 61. The x-intercept of the graph of 7x – 3y = 2 is (4) | 11 |

70 | Find the value of ( x ) so that the points ( (x,-1),(2,1) ) and (4,5) are collinear. | 11 |

71 | Determine the distance from (5,10) to the line ( x-y=0 ) A . 3.86 в. 3.54 c. 3.68 D. 3.72 E. none of these | 11 |

72 | Find the slope of the line, which makes an angle of ( 30^{circ} ) with the positive direction of ( y ) -axis measured anticlockwise | 11 |

73 | If ( a, b, c ) and ( d ) are points on a number line such that ( a<b<c<d, b ) is twice as far from ( c ) as from ( a ), and ( c ) is twice as far from ( b ) as from ( d ), then what is the value of ( frac{c-a}{d-b} ? ) A ( cdot frac{1}{3} ) B. ( frac{2}{3} ) ( c cdot frac{1}{2} ) ( D ) | 11 |

74 | The points ( boldsymbol{A}(mathbf{2}, mathbf{9}), boldsymbol{B}(boldsymbol{a}, mathbf{5}), boldsymbol{C}(mathbf{5}, mathbf{5}) ) are the vertices of a triangle ( A B C ) right angled at B. find the value of ( ^{prime} a^{prime} ) and hence the area of ( Delta A B C ) | 11 |

75 | ( A(1,3) ) and ( B(7,5) ) are two opposite vertices of a square. The equation of a side through ( boldsymbol{A} ) is A. ( x+2 y-7=0 ) В. ( x-2 y+5=0 ) c. ( 2 x+y-5=0 ) D. None of these | 11 |

76 | Find the values of ( p ) for which the straight lines ( 8 p x+(2-3 p) y+1=0 ) and ( p x+8 y-7=0 ) are perpendicular to each other. A ( . p=1,2 ) в. ( p=2,2 ) c. ( p=1,3 ) D. None of these | 11 |

77 | Identify without plotting, the lines parallel to the ( x ) or ( y ) axis: ( 3-7 y=0 ) | 11 |

78 | In what ratio is the line segment joining (-3,-1) and (-8,-9) is divided at the point ( left(-5, frac{-21}{5}right) ? ) | 11 |

79 | If the equation for the line shown in the following graph is ( y=frac{1}{3} x+3, ) what is the value of ( k cdot n ? ) A . 9 B. 12 c. 15 D. 18 E . 24 | 11 |

80 | Distance of origin from line ( (1+ ) ( sqrt{3}) y+(1-sqrt{3}) x=10 ) along the line ( boldsymbol{y}=sqrt{mathbf{3}} boldsymbol{x}+boldsymbol{k} ) is A ( cdot frac{5}{sqrt{2}} ) B. ( 5 sqrt{2}+k ) c. 10 D. 5 | 11 |

81 | Let ( r ) be the distance from the origin to a point ( boldsymbol{P} ) with coordinates ( boldsymbol{x} ) and ( boldsymbol{y} ) Designate the ratio ( frac{y}{r} ) by ( s ) and the ratio ( frac{x}{r} ) by ( c . ) Then the values of ( s^{2}-c^{2} ) are limited to the numbers: A. less than -1 and greater than +1 , both excluded B. less than -1 and greater than +1 , both included c. between -1 and ( +! ), both excluded D. between -1 and ( +1, ) both included E. -1 and +1 only | 11 |

82 | Two roads are represented by the equations ( boldsymbol{y}-boldsymbol{x}=boldsymbol{6} ) and ( boldsymbol{x}+boldsymbol{y}=mathbf{8} ) An inspection bungalow has to be so constructed that it is at a distance of 100 from each of the roads. Possible location of the bungalow is given by : This question has multiple correct options A ( cdot(100 sqrt{2}+1,7) ) в. ( (1-100 sqrt{2}, 7) ) c. ( (1,7+100 sqrt{2}) ) D. ( (1,7-100 sqrt{2}) ) | 11 |

83 | The distance between the lines ( 5 x- ) ( 12 y+2=0 ) and ( 5 x-12 y-3=0, ) is A . 5 B. c. ( frac{5}{13} ) D. ( frac{1}{13} ) | 11 |

84 | Gradient of a line perpendicular to the line ( 3 x-2 y=5 ) is ( A cdot frac{-2}{3} ) B. ( c cdot-frac{3}{2} ) ( D cdot-frac{5}{2} ) | 11 |

85 | An equation of a line through the point (1,2) whose distance from the point (3,1) has the greatest value is A ( y=2 x ) ( x ) B. ( y=x+1 ) c. ( x+2 y=5 ) D. ( y=3 x-1 ) | 11 |

86 | 23. For points P = (x1, Yı) ww) of the for points P = (x.. .) and 0 = (x, y) OI co-ordinate plane, a new distance ) is defined by plane, a new distance d(P, d(P, Q)=x; -xz/+ V1-y2l. Leto ‘1*21+ Wi-yol. Let O=(0,0) and A=(3, 2). Prove that the set of points in the first quadrant equidistant (with respect to the new distance) Dom consists of the union of a line segment of finite an infinite ray. Sketch this set in a labelled diagram. ts in the first quadrant which are e new distance) from O and A | 11 |

87 | If ( p ) is the length of the perpendicular from the origin to the line ( frac{x}{a}+frac{y}{b}=1 ) then which of the following is true? A ( cdot frac{1}{a^{2}}+frac{1}{b^{2}}+frac{1}{p^{2}}=0 ) B . ( a^{2}+b^{2}-p^{2}=0 ) c. ( frac{1}{a^{2}}-frac{1}{b^{2}}=frac{1}{p^{2}} ) D. ( frac{1}{a^{2}}+frac{1}{b^{2}}-frac{1}{p^{2}}=0 ) | 11 |

88 | The distance of the point ( left(x_{1}, y_{1}right) ) from the origin A ( cdot x_{1}^{2}+y_{1}^{2} ) B. ( sqrt{x_{1}^{2}+y_{1}^{2}} ) c. ( frac{1}{sqrt{x_{1}^{2}+y_{1}^{2}}} ) D. ( frac{1}{x_{1}^{2}+y_{2}^{2}} ) | 11 |

89 | The distance from ( (mathbf{9}, mathbf{0}) ) to ( (mathbf{3}, mathbf{4}) ) | 11 |

90 | If (-4,3) and (4,3) are two vertices of an equilateral triangle, find the coordinates that the origin lies in the interior, (ii) exterior of the triangle. | 11 |

91 | Find the distance between the following pair of points. (5,7) and the origin A ( cdot sqrt{74} ) B. ( sqrt{64} ) c. ( sqrt{34} ) D. None of these | 11 |

92 | If the tangent to the curve ( y=x log x ) at ( (c, f(x)) ) is parallel to the line-segment joining ( boldsymbol{A}(mathbf{1}, boldsymbol{0}) ) and ( boldsymbol{B}(boldsymbol{e}, boldsymbol{e}), ) then ( mathbf{c}=ldots ) A ( cdot frac{e-1}{e} ) B. ( log frac{e-1}{e} ) c. ( frac{1}{e^{1-e}} ) D. ( frac{1}{e^{e-1}} ) | 11 |

93 | The area of a traingle is 5 square units, two of its verices are (2,1) and ( (3,-2) . ) The third vertex lies on ( y=x+3 ).The third vertex is ( ^{mathbf{A}} cdotleft(frac{7}{2}, frac{3}{2}right) ) в. ( left(-frac{3}{2}, frac{3}{2}right) ) c. ( left(-frac{3}{2}, frac{13}{2}right) ) D ( cdotleft(frac{7}{2}, frac{5}{2}right) ) | 11 |

94 | 8. The coordinates of A, B, C are (6, 3), (-3, 5), (4, – 2) respectively, and Pis any point (x, y). Show that the ratio of xty- 2 the area of the triangles A PBC and AABC is (1983 – 2 Marks) | 11 |

95 | What type of a quadrilateral do the points ( boldsymbol{A}(mathbf{2}, mathbf{2}), boldsymbol{B}(mathbf{7}, mathbf{3}), boldsymbol{C}(mathbf{1 1}, mathbf{1}) ) and ( D(6,6) ) taken in that order, form? A. Scalene quadrilateral B. Square c. Rectangle D. Rhombus | 11 |

96 | The line ( 2 x-3 y=4 ) A . passes through origin and ( m=-frac{2}{3} ) B. passes through (2,0) and ( m=frac{2}{3} ) c. passes through (0,2) and ( m=frac{2}{3} ) D. passes through (0,-2) and ( m=-frac{2}{3} ) | 11 |

97 | Coordinates of a point at unit distance from the lines ( 3 x-4 y+1=0 ) and ( 8 x+6 y+1=0 ) are This question has multiple correct options ( ^{A} cdotleft(frac{6}{5},-frac{1}{10}right) ) в. ( left(-frac{2}{5},-frac{13}{10}right) ) c. ( left(0, frac{3}{2}right) ) D. ( left(-frac{8}{5}, frac{3}{10}right) ) | 11 |

98 | The equation ( 9 x^{3}+9 x^{2} y-45 x^{2}= ) ( 4 y^{3}+4 x y^{2}-20 y^{2} ) represents 3 straight lines, two of which passes through origin. Then find the area of the triangle formed by these lines. | 11 |

99 | Find the slope of the line passing through the points ( C(3,5) ) and ( boldsymbol{D}(-mathbf{2},-mathbf{3}) ) | 11 |

100 | The angle between the pair of lines whose equation is ( 4 x^{2}+10 x y+ ) ( m y^{2}+5 x+10 y=0 ) is A ( cdot tan ^{-1}left(frac{3}{8}right) ) B. ( tan ^{-1} frac{2 sqrt{25-4 m}}{m+4} ) ( ^{mathbf{c}} cdot tan ^{-1}left(frac{3}{4}right) ) D. ( tan ^{-1} frac{sqrt{25-4 m}}{m+4} ) | 11 |

101 | If ( P(1,4), Q(9,-2), ) and ( R(5,1) ) are collinear then A. P lies between ( Q ) and ( R ) B. Q lies between P and R c. R lies between P and Q D. none of these | 11 |

102 | The distance between the points ( left(frac{1}{2}, frac{3}{2}right) ) and ( left(frac{3}{2}, frac{-1}{2}right) ) is | 11 |

103 | The vertices of a triangle ( A B C ) are ( A(2,3, ) 1), ( B(-2,2,0) ) and ( C(0,1,-1) ).Find the magnitude of the line joining mid points of the sides ( A C ) and ( B C ). A ( cdot frac{1}{sqrt{2}} ) unit B. 1 unit c. ( frac{3}{sqrt{2}} ) unit D. 2 unit | 11 |

104 | How many equilateral triangles of side 2a with one vertex at origin and side along the ( x ) -axis is possible. | 11 |

105 | One diagonal of a square is along the line ( 8 x-15 y=0 ) and one of its vertices is ( (1,2) . ) Then the equations of the sides of the square passing through this vertex are A ( .23 x+7 y=9,7 x+23 y=53 ) в. ( 23 x-7 y+9=0,7 x+23 y+53=0 ) c. ( 23 x-7 y-9=0,7 x+23 y-53=0 ) D. None of these | 11 |

106 | Trapezoid ( A B C D ) is graphed as shown above. Find the slope of ( overline{C D} ) A. -3 B. -1 ( c ) D. ( frac{5}{21} ) ( E cdot frac{3}{2} ) | 11 |

107 | If the straight lines ( frac{y}{2}=x-p ) and ( boldsymbol{a} boldsymbol{x}+mathbf{5}=boldsymbol{3} boldsymbol{y} ) are parallel, then find ( boldsymbol{a} ) | 11 |

108 | Find distance of point ( boldsymbol{A}(2,3) ) measured parallel to the line ( x-y=5 ) from the line ( 2 x+y+6=0 ) ( ^{mathrm{A}} cdot frac{13 sqrt{2}}{3} ) units B. ( frac{13}{3} ) units ( ^{mathrm{C}} cdot frac{13 sqrt{2}}{6} ) units D. None of these | 11 |

109 | The two lines ( boldsymbol{x}=boldsymbol{m} boldsymbol{y}+boldsymbol{n}, boldsymbol{z}=boldsymbol{p} boldsymbol{y}+boldsymbol{q} ) and ( boldsymbol{x}=boldsymbol{m}^{prime} boldsymbol{y}+boldsymbol{n}^{prime}, boldsymbol{z}=boldsymbol{p}^{prime} boldsymbol{y}+boldsymbol{q}^{prime} ) are perpendicular to each other, if ( mathbf{A} cdot m m^{prime}+p p^{prime}=1 ) В ( cdot frac{m}{m^{prime}}+frac{p}{p^{prime}}=-1 ) c. ( frac{m}{m^{prime}}+frac{p}{p^{prime}}=1 ) D. ( m m^{prime}+p p^{prime}=-1 ) | 11 |

110 | If X.X2, X3 and V1, V2,Y3 are both in G.P. with the same common ratio, then the points (X1,Y1),(x2,92) and (x3, V) [2003] (a) are vertices of a triangle lie on a straight line lie on an ellipse (d) lie on a circle. ditont from the | 11 |

111 | Find the length of the medians of a ( triangle A B C ) having vertices at ( boldsymbol{A}(mathbf{0},-mathbf{1}), boldsymbol{B}(mathbf{2}, mathbf{1}) ) and ( boldsymbol{C}(mathbf{0}, mathbf{3}) ? ) | 11 |

112 | (0) 20 (0) 100 33. Two sides of a rhombus are along the lines, X-y+1= 0 and 7x-y-5=0.Ifits diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus? [JEEM 2016 (10 7 © (-3,-9) (d) (-3,-8) 4 A atrial | 11 |

113 | 0 MULTUMULOU Slope of a line passing through P(2, 3) and intersecting the linex+y=7 at a distance of 4 units from P, is: [JEE M 2019-9 April (M) 1 – 15 1-√7 1+ 15 (b) 1+ 17 √5-1 17 – 1 17+1 (d) 15+1 | 11 |

114 | The points ( boldsymbol{A}(-4,1) ) ( B(-2,-2), C(4,0), D(2,3) ) are the vertices of A. parallelogram B. rectangle c. rhombus D. None of these | 11 |

115 | Obtain the equations of the lines passing through the intersection of ( operatorname{lines} 4 x-3 y-1=0 ) and ( 2 x-5 y+ ) ( mathbf{3}=mathbf{0} ) and equally inclined to the axes | 11 |

116 | Find the distance of the point (-1,1) from the line ( 12(x+6)=5(y-2) ) | 11 |

117 | ffigure ( square A B C D A B C D ) is a parallelogram, what is the ( x ) -coordinate of point B? 4 B. ( c ) ( D ) | 11 |

118 | What is the ( Y ) – intercept for the straight line ( 2 x-3 y=5 ? ) A ( cdot frac{2}{5} ) в. ( -frac{5}{3} ) c. ( -frac{5}{2} ) D. ( frac{1}{2} ) | 11 |

119 | Find the equation of the line perpendicular to ( boldsymbol{x}-mathbf{7} boldsymbol{y}+mathbf{5}=mathbf{0} ) and having ( boldsymbol{x} ) -intercept 3 | 11 |

120 | Prove that the line ( 5 x-2 y-1=0 ) is mid-parallel to the lines ( 5 x-2 y-9= ) 0 and ( 5 x-2 y+7=0 ) | 11 |

121 | The end A, B of a straight line segment of constant length c slide upon the fixed rectangular axes OX, OY respectively. If the rectangle OAPB be completed, then show that the locus of the foot of the perpendicular drawn from P to AB is 2 2 2 x3 + 3 = 63 (1983 – 2 Marks) | 11 |

122 | If the equation of the locus of a point equidistant from the point ( left(a_{1}, b_{1}right) ) and ( left(a_{2}, b_{2}right) ) is ( left(a_{1}-a_{2}right) x+left(b_{1}-b_{2}right) y+ ) ( c+0, ) then the value of ( c ) is A ( cdot a_{1}^{2}-a_{2}^{2}+b_{1}^{2}-b_{2}^{2} ) в. ( sqrt{a_{1}^{2}+b_{1}^{2}-a_{2}^{2}-b_{2}^{2}} ) c. ( frac{1}{2}left(a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2}right. ) D ( cdot frac{1}{2}left(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2}right. ) | 11 |

123 | n fig. ( 2, ) lines ( l_{1} | l_{2} . ) The value of ( x ) is : ( A cdot 70 ) B. 30 ( c cdot 40 ) D. 50 | 11 |

124 | Find the angle between the lines represented by ( 3 x^{2}+4 x y-3 y^{2}=0 ) | 11 |

125 | The line ( x+y=a ) meets the axis of ( x ) and ( y ) at ( A ) and ( B ) respectively. ( A ) triangle ( triangle A M N ) is inscribed in the ( triangle O A B, O ) being the origin, with right angle at ( N . M ) and ( N ) lie respectively on ( O B ) and ( A B . ) If the area of the triangle ( triangle A M N ) is ( frac{3}{8} ) of the area of the ( triangle O A B ) then ( frac{A N}{B N} ) is equal to A. B. 2 ( c .3 ) ( D ) | 11 |

126 | In the diagram, ( ell ) and ( m ) are parallel line. The sum of the angles ( A ), Band ( C ) marked in the diagram is- A ( cdot 180^{circ} ) B ( .270^{circ} ) ( c cdot 360^{circ} ) D. ( 300^{circ} ) | 11 |

127 | Find the radius of the circle whose centre is (3,2) and passes through (-5,6) A ( .4 sqrt{5} ) B. ( 2 sqrt{5} ) c. ( 4 sqrt{2} ) D. None of these | 11 |

128 | Tow consecutive sides of a parallelogram are ( 4 x+5 y=0 ) and ( 7 x+2 y=0 . ) If the equation to one diagonal is ( 11 x+7 y=9 ), then the equation of the other diagonal is A. ( x+y=0 ) в. ( 2 x+y=0 ) c. ( x-y=0 ) D. None of these | 11 |

129 | A circle that has its center at the origin and passes through (-8,-6) will also pass through the point B. (4,7) c. (7,7) (年. ( (7,7)) ) D. ( (9, sqrt{19}) ) | 11 |

130 | Find that point on y axis which as equidistant from point (6,5) and (-4,3) | 11 |

131 | It is given that ( angle X Y Z=64^{circ} ) and ( X Y ) is produced to point P.Draw a figure from the given information If ray y objects ( angle Z Y P, ) find ( angle X Y Q ) | 11 |

132 | Find the equation of the line perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive ( x ) -axis is ( 30^{circ} ) | 11 |

133 | There are two possible values of ( p & ) if the distance of ( (p, 4) ) and (5,0) is 5 then the two value difference of p is ( mathbf{A} cdot mathbf{4} ) B. 5 ( c cdot 6 ) D. 2 | 11 |

134 | The area of a triangle is 5. Two of its vertices are A (2, 1) and B (3,-2). The third vertex C lies on y=x+3. Find C. (1978) 15. | 11 |

135 | Find the slope of the line joining the points ( (2 a, 3 b) ) and ( (a,-b) ) | 11 |

136 | 1919) 5. A straight line L is perpendicular to the line 5x -y= 1. The area of the triangle formed by the line L and the coordinate axes is 5. Find the equation of the line L. (1980) | 11 |

137 | The three vertices of a parallelogram ( A B C D, ) taken in order are ( A(1,-2) ) ( B(3,6) ) and ( C(5,10) . ) Find the coordinates of the fourth vertex D. A. ( D(3,2) ) в. ( D(-3,2) ) c. ( D(3,-2) ) D. ( D(3,3) ) | 11 |

138 | Is the line through (-2,3) and (4,1) perpendicular to the line ( mathbf{3} boldsymbol{x}=boldsymbol{y}+mathbf{1} ? ) Does the line ( 3 x=y+1 ) bisect the line joining of (-2,3) and (4,1)( ? ) | 11 |

139 | The vertices of ( Delta A B C ) are (-2,1),(5,4) and (2,-3) respectively Find the area of triangle | 11 |

140 | Find the equation of the straight line which passes through the origin and making angle ( 60^{circ} ) with the line ( x+ ) ( sqrt{3} y+3 sqrt{3}=0 ) | 11 |

141 | Find the area of a triangle ( : boldsymbol{y}=boldsymbol{x}, boldsymbol{y}= ) ( 2 x ) and ( y=3 x+4 ? ) | 11 |

142 | ( p_{1}, p_{2} ) are the lengths of the perpendiculars from any point on ( 2 x+ ) ( 11 y=5 ) upon the lines ( 24 x+7 y= ) ( mathbf{2 0}, mathbf{4 x}-mathbf{3 y}=mathbf{2}, ) then ( boldsymbol{p}_{mathbf{1}}= ) ( A cdot p_{2} ) B . ( 2 mathrm{p}_{2} ) c. ( frac{1}{2} p_{2} ) D. ( frac{1}{3} p_{2} ) | 11 |

143 | In figure, write another name for ( angle 1 ) | 11 |

144 | The line ( 3 x+2 y=0 ) A ( cdot ) passes through (3,2) and ( m=-frac{3}{2} ) B. passes through (0,0) and ( m=frac{3}{2} ) c. passes through (2,3) and ( m=-frac{3}{2} ) D. passes through (0,0) and ( m=-frac{3}{2} ) | 11 |

145 | * If (P(1, 2), 2(4, 6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS, then (1998 – 2 Marks) (a) a=2, b=4 . (b) a=3, b=4 (c) a=2, b=3 (d) a=3, b=5 | 11 |

146 | Area of a triangle whose vertices are 0), (2,3),(5,8) is A ( .1 / 2 ) B. ( c cdot 2 ) D. 3/2 | 11 |

147 | The diagonals of a parallelogram ( P Q R S ) are along the lines ( x+3 y=4 ) and ( 6 x-2 y=7, ) then ( P Q R S ) must be ( a ) A. rectangle B. square c. cyclic quadrilateral D. rhombus | 11 |

148 | If the equations of the hypotenuse and a side of a right-angled isosceles triangle be ( boldsymbol{x}+boldsymbol{m} boldsymbol{y}=mathbf{1} ) and ( boldsymbol{x}=boldsymbol{k} ) respectively then This question has multiple correct options ( mathbf{A} cdot m=1 ) в. ( m=k ) c. ( m=-1 ) D. ( m+k=0 ) | 11 |

149 | If ( boldsymbol{A}(boldsymbol{y}, mathbf{2}), boldsymbol{B}(mathbf{1}, boldsymbol{y}) ) and ( boldsymbol{A} boldsymbol{B}=mathbf{5}, ) then the possible values are A .6,2 B. 5,-2 c. -2,-6 D. 2,0 | 11 |

150 | The two adjacent sides of a rectangle ( operatorname{are} 5 p^{2}-2 p+3 ) and ( 7 p^{2}-14 p+2 ) find the perimeter. | 11 |

151 | ( P(4,3) ) and ( Q ) lies on the same straight line which is parallel to the ( x ) -axis. If ( Q ) is 3 units from the ( x ) -axis, the possible coordinates of Q are: A ( .(4,0) ) в. (2,4) c. (-4,3) D. (8,4) | 11 |

152 | A value of ( k ) such that the straight lines ( boldsymbol{y}-boldsymbol{3} boldsymbol{x}+boldsymbol{4}=boldsymbol{0} ) and ( (boldsymbol{2} boldsymbol{k}-mathbf{1}) boldsymbol{x}-(boldsymbol{8} boldsymbol{k}- ) 1) ( y-6=0 ) are perpendicular is A ( cdot frac{2}{7} ) B. ( -frac{2}{7} ) c. D. | 11 |

153 | Equation of straight line ( boldsymbol{a} boldsymbol{x}+boldsymbol{b} boldsymbol{y}+boldsymbol{c}= ) ( 0, ) where ( 3 a+4 b+c=0, ) which is at maximum distance from ( (1,-2), ) is A. ( 3 x+y-17=0 ) B. ( 4 x+3 y-24=0 ) c. ( 3 x+4 y-25=0 ) D. ( x+3 y-15=0 ) | 11 |

154 | What is the value of ( k, ) if the line ( 2 x- ) ( 3 y=k ) passes through the origin. A . B. 1 ( c cdot 3 ) D. – | 11 |

155 | One vertex of the equilateral triangle with centroid at the origin and one side as ( boldsymbol{x}+boldsymbol{y}-mathbf{2}=mathbf{0} ) is: A ( cdot(-1,-1) ) в. (2,2) c. (-2,-2) D. (2,-2) | 11 |

156 | Line through the points (-2,6) and (4,8) is perpendicular to the line through the points (8,12) and ( (x, 24) . ) Find the value of ( x ) | 11 |

157 | The number of straight lines which are equally inclined to both the axes is ; A . 4 B. ( c cdot 3 ) ( D ) | 11 |

158 | Prove that the general equation ( a x^{2}+ ) ( 2 h x y+b y^{2}+2 g x+2 f y+c=0 ) will represent two parallel straight lines if ( h^{2}=a b ) and ( b g^{2}=a f^{2} . ) Also prove that the distance between them is ( 2 sqrt{left{frac{g^{2}-a c}{a(a+b)}right}} ) Also prove that ( frac{a}{h}=frac{h}{b}=frac{g}{f} ) | 11 |

159 | The axes being inclined at an angle of ( 60^{circ}, ) the inclination of the straight line ( boldsymbol{y}=2 boldsymbol{x}+mathbf{5} ) with ( mathbf{x} ) -axis is ( A cdot 30 ) B . ( tan ^{-1}(sqrt{3} / 2) ) ( c cdot tan ^{-1} 2 ) D. ( 60^{circ} ) | 11 |

160 | If the line ( (2 x+y+1)+lambda(x-y+ ) 1) ( =0 ) is parallel to ( y-a x i s ) then value of ( lambda ) is ( ? ) A . B. – ( c cdot frac{1}{2} ) ( D ) | 11 |

161 | Find the distance between the points (0,8) and (6,0) | 11 |

162 | Which of the following is/are true regarding the following linear equation: ( y=frac{3}{2} x+frac{2}{3} ) A ( cdot ) It passes through ( left(0, frac{2}{3}right) ) and ( m=frac{3}{2} ) B. It passes through ( left(0, frac{3}{2}right) ) and ( m=frac{2}{3} ) ( ^{mathbf{c}} cdot ) it passes through ( left(0,-frac{2}{3}right) ) and ( m=-frac{3}{2} ) D. It passes through ( left(0,-frac{3}{2}right) ) and ( m=-frac{2}{3} ) | 11 |

163 | The owner of a milk store finds that he can sell 980 liters of milk each week at Rs. 14 per lit. and 1220 liters of milk each week at Rs. 16 per lit. Assuming a liner relationship between selling price and demand, how many liters could you sell weakly at Rs. 17 per liter? | 11 |

164 | A point on the line ( y=x ) whose perpendicular distance from the line ( frac{x}{4}+frac{y}{3}=1 ) is 4 has the coordinates This question has multiple correct options ( mathbf{A} cdotleft(-frac{8}{7},-frac{8}{7}right) ) B ( cdotleft(frac{32}{7}, frac{32}{7}right) ) ( ^{mathrm{c}} cdotleft(frac{3}{2}, frac{3}{2}right) ) D. none of these | 11 |

165 | Which point on y-axis is equidistant from (2,3) and (-4,1)( ? ) | 11 |

166 | Find the areas of the triangles the coordinates of whose angular points ( operatorname{are}left(1,30^{circ}right),left(2,60^{circ}right) ) and ( left(3,90^{circ}right) ) | 11 |

167 | In the adjoining figure, ( angle A P O=42^{circ} ) and ( angle C Q O=38^{circ} . ) Find the value of ( angle ) POQ. ( mathbf{A} cdot 68^{circ} ) B. ( 72^{circ} ) ( c cdot 80^{circ} ) D. ( 126^{circ} ) | 11 |

168 | If ( A(-1,3), B(1,-1) ) and ( C(5,1) ) are the vertices of a triangle ( A B C ) find the length of the median passing through the vertex ( A ). A. 5 units B. 6 units c. 15 units D. None of these | 11 |

169 | The equation of the line passing through ( (-4,3), ) parallel to the ( 3 x+ ) ( mathbf{7} boldsymbol{y}+mathbf{6}=mathbf{0} ) A. ( 3 x+7 y-9=0 ) B. 3x+7y+9=0 c. ( 3 x+7 y+3=0 ) D. 3x+7y+12=0 | 11 |

170 | The co-ordinates of the vertices ( P, Q, R ) ( & S ) of square ( P Q R S ) inscribed in the ( triangle A B C ) with vertices ( A equiv(0,0), B equiv ) (3,0)( & C equiv(2,1) ) given that two of its vertices ( P, Q ) are on the side ( A B ) are respectively ( ^{mathbf{A}} cdotleft(frac{1}{4}, 0right),left(frac{3}{8}, 0right),left(frac{3}{8}, frac{1}{8}right) &left(frac{1}{4}, frac{1}{8}right) ) в. ( left(frac{1}{2}, 0right),left(frac{3}{4}, 0right),left(frac{3}{4}, frac{1}{4}right) &left(frac{1}{2}, frac{1}{4}right) ) c. ( (1,0),left(frac{3}{2}, 0right),left(frac{3}{2}, frac{1}{2}right) &left(1, frac{1}{2}right) ) D. ( left(frac{3}{2}, 0right),left(frac{9}{4}, 0right),left(frac{9}{4}, frac{3}{4}right) &left(frac{3}{2}, frac{3}{4}right) ) | 11 |

171 | Draw the graph of the equation ( frac{x}{4}+ ) ( frac{y}{3}=1 . ) Also, find the area of the triangle formed by the line and the coordinate axes. | 11 |

172 | What loci are represented by the equations: ( (x+y)^{2}-c^{2}=0 ) | 11 |

173 | Prove that the straight line ( x+y= ) touches the parabola ( y=x-x^{2} ) | 11 |

174 | If the points (1,0),(0,1) and ( (x, 8) ) are collinear, then the value of ( x ) is equal to ( mathbf{A} cdot mathbf{5} ) B. -6 ( c cdot 6 ) D. – | 11 |

175 | The distance between which two points is 2 units ? A ( cdot(-2,-3) ) and (-2,-4) B. (0,4) and (6,0) c. (7,2) and (6,2) D. (4,-3) and (2,-3) | 11 |

176 | The slopes of two line segments are equal. Which of the following is correct? A. The line segments are parallel. B. The end points of the line segments are collinear c. The line segments are perpendicular. D. The ends points of the line segments are n | 11 |

177 | Find the angles between the lines ( sqrt{3} x+y=1 ) and ( x+sqrt{3} y=1 ) | 11 |

178 | 9. The orthocentre of the triangle formed by the lines xy = 0 and x+y=1 is (1995S) @ (6) 6 (5) © (,0) (a (24) | 11 |

179 | If one side of an equiateral triangle is ( 3 x+4 y=7 ) and its vertex is (1,2) then the length of the side of the triangle is A ( cdot frac{4 sqrt{3}}{17} ) B. ( frac{3 sqrt{3}}{16} ) ( c cdot frac{8 sqrt{3}}{15} ) D. ( frac{4 sqrt{3}}{15} ) | 11 |

180 | Find the area of triangle having vertices ( operatorname{are} boldsymbol{A}(mathbf{3}, mathbf{1}), boldsymbol{B}(mathbf{1} mathbf{2}, mathbf{2}) ) and ( boldsymbol{C}(mathbf{0}, mathbf{2}) ) A . 4 B. 6 c. 12 D. 18 | 11 |

181 | 14. Straight lines 3x + 4y = 5 and 4x – 3y = 15 intersect at the point A. Points B and C are chosen on these two lines such that AB = AC. Determine the possible equations of the line BC passing through the point (1,2). (1990 – 4 Marks) | 11 |

182 | Find the distance between the following pairs of point. ( boldsymbol{P}(-mathbf{5}, mathbf{7}), boldsymbol{Q}(-mathbf{1}, mathbf{3}) ) | 11 |

183 | In the above figure ( boldsymbol{A B} | boldsymbol{C D} ) ( angle A B E=120^{circ}, angle D C E=110^{circ} ) and ( angle B E C=x^{circ} ) then ( x^{circ} ) will be ( A cdot 60 ) B. 50 ( c cdot 4 ) D. 70 | 11 |

184 | In the adjoining figure, if line ( l | m ) and line ( n ) is the transversal, what is the value of ( x ) ( A cdot 65 ) в. ( 50^{circ} ) ( c cdot 41^{0} ) D. ( 130^{circ} ) | 11 |

185 | A line ( P Q ) makes intercepts of length 2 units between the lines ( y+2 x=3 ) and ( boldsymbol{y}+mathbf{2} boldsymbol{x}=mathbf{5} . ) If the coordinates of ( boldsymbol{P} ) are ( (2,3), ) coordinates of ( Q ) can be This question has multiple correct options в. (2,3) c. ( left(0, frac{9}{2}right) ) D. (3,2) | 11 |

186 | Points ( P, Q, R ) and ( S ) divide the line segment joining the points ( A(1,2) ) and ( B(6,7) ) in 5 equal parts. Find the coordinates of the points ( P, Q ) and ( R ) | 11 |

187 | The slope and ( y ) -intercept of the following line are respectively ( mathbf{5} boldsymbol{x}-mathbf{8} boldsymbol{y}=-mathbf{2} ) A ( cdot ) slope ( =m=-frac{5}{8} ) and ( y ) -intercept ( =frac{1}{4} ) B. slope ( =m=frac{5}{8} ) and ( y ) -intercept ( =-frac{1}{4} ) c. slope ( =m=-frac{5}{8} ) and ( y ) -intercept ( =-frac{1}{4} ) D. slope ( =m=frac{5}{8} ) and ( y ) -intercept ( =frac{1}{4} ) | 11 |

188 | In the adjoining figure, ( A B | C D ) and ( E F ) is transversal. the value of ( x-y ) is A ( cdot 75^{circ} ) B . ( 40^{circ} ) ( c cdot 35^{circ} ) Don | 11 |

189 | ( A(2,6) ) and ( B(1,7) ) are two vertices of a triangle ( A B C ) and the centroid is (5,7) The coordinates of ( C ) are A. (8,12) B. (12,8) c. (-8,12) D. (10,8) | 11 |

190 | In the adjoining figure, ( A B ) and ( C D ) are parallel lines. The transversals ( P Q ) and ( R S ) intersect at ( U ) on the line ( A B . ) Given that ( angle D W U=110^{circ} ) and ( angle C V P=70^{circ} ) find the measure of ( angle Q U S ) | 11 |

191 | Find the slope and ( y ) -intercept of the line ( 2 x+2 y=-2 ) A. slope ( =1, ) y-intercept ( =-3 ) B. slope = -1, y-intercept = -1 c. slope ( =1, y ) -intercept ( =3 ) D. slope ( =1, y ) -intercept ( =1 ) | 11 |

192 | Find the slope and ( y ) -intercept of the line ( boldsymbol{x}-boldsymbol{y}=mathbf{3} ) A. slope ( =2, y ) -intercept ( =-3 ) B. slope ( =0, y ) -intercept ( =-3 ) c. slope ( =1, y ) -intercept ( =-3 ) D. slope ( =1, y ) -intercept ( =3 ) | 11 |

193 | Write the slope of the line whose inclination is ( 45^{circ} ) | 11 |

194 | Find the inclination of the line ( ( ) in degrees ) whose slope is ( frac{mathbf{1}}{sqrt{mathbf{3}}} ) | 11 |

195 | In the given figure, if ( boldsymbol{A B} | boldsymbol{C D} ) ( angle A P Q=50^{circ} ) and ( angle P R D=127^{circ}, ) find and ( y ) | 11 |

196 | Find the distance of the point (6,8) and the origin. | 11 |

197 | Find the slope of the line whose inclination is ( mathbf{1 0 5}^{circ} ) | 11 |

198 | A point ( P ) is such that its perpendicular distance from the line ( boldsymbol{y}-mathbf{2 x + 1}=mathbf{0} ) is equal to its distance from the origin,then the locus of the point ( boldsymbol{P} ) A ( cdot x^{2}+4 y^{2}+4 x y+4 x-2 y-1=0 ) B. ( x^{2}+y^{2}+4 x y+x-y-1=0 ) c. ( x^{2}+4 y^{2}-1=0 ) D. None of these | 11 |

199 | If sum of the distances of a point from two perpendicular lines in a plane is 1 then its locus is A. a square B. a circle c. a straight line D. two intersecting lines | 11 |

200 | Find the coordinates of the point ( boldsymbol{P} ) which divides line segment ( Q R ) internally in the ratio ( m: n ) in the following example: ( Q equiv(-5,8), R equiv(4,-4) ) and ( m: n=2: 1 ) is (1,0) If true then enter 1 and if false then enter 0 | 11 |

201 | The number of points on the line ( x+ ) ( boldsymbol{y}=mathbf{4} ) which are unit distance apart from the line ( 2 x+2 y=5 ) is ( mathbf{A} cdot mathbf{0} ) B. 1 c. 2 D. ( infty ) | 11 |

202 | ( a x+b y+c=0 ) does not represent an equation of line if A. ( a=c=0, b neq 0 ) B. ( b=c=0, a neq 0 ) c. ( a=b=0 ) D. ( c=0, a neq 0, b neq 0 ) | 11 |

203 | Show that the product of perpendiculars on the line ( frac{x}{a} cos theta+ ) ( frac{y}{b} sin theta=1 ) from the points ( (pm sqrt{a^{2}-b^{2}}, 0) ) is ( b^{2} ) | 11 |

204 | n Fig ( 6.23, ) if ( A B | C D, angle A P Q=50^{circ} ) and ( angle P R B=127^{circ}, ) find ( a ) and ( y ) | 11 |

205 | 11. Two sides of a rhombus ABCD are parallel to the lines y = x+2 and y = 7x +3. If the diagonals of the rhombus intersect at the point (1, 2) and the vertex A is on the y-axis, find possible co-ordinates of A. (1985 – 5 Marks) | 11 |

206 | The area of triangle formed by the lines ( 18 x^{2}-9 x y+y^{2}=0 ) and the line ( y=9 ) is A. ( frac{27}{4} ) в. ( frac{27}{2} ) c. ( frac{27}{8} ) D. 27 | 11 |

207 | The triangle with vertices ( A(4,4), B(-2, ) -6) and ( mathrm{C}(4,-1) ) is shown in the diagram The area of ( Delta ) ABC is A . 5 sq. units B. 12 sq. units c. 15 sq. units D. 20 sq. units | 11 |

208 | Given the system of equation ( boldsymbol{p} boldsymbol{x}+boldsymbol{y}+ ) ( boldsymbol{z}=mathbf{1}, boldsymbol{x}+boldsymbol{p} boldsymbol{y}+boldsymbol{z}=boldsymbol{p}, boldsymbol{x}+boldsymbol{y}+boldsymbol{p} boldsymbol{z}=boldsymbol{p}^{2} ) then for what value of ( p ) does this system have no solution A . -2 B. – 1 ( c .1 ) D. | 11 |

209 | ( A B ) is parallel to ( Q R, ) such that ( frac{P A}{A Q}= ) ( frac{P B}{B R} cdot P B=2 mathrm{cm}, E C=4 mathrm{cm} ) and ( Q R=9 mathrm{cm}, ) then find the length of ( A B ) | 11 |

210 | If the line joining the points ( left(a t_{1}^{2}, 2 a t_{1}right),left(a t_{2}^{2}, 2 a t_{2}right) ) is parallel to ( mathbf{y}= ) ( mathbf{x}, ) then ( mathbf{t}_{mathbf{1}}+mathbf{t}_{mathbf{2}}= ) A ( cdot frac{1}{2} ) B. 4 ( c cdot frac{1}{4} ) D. 2 | 11 |

211 | For what value of ( lambda ) is the line ( (8 x+3 y-15)+lambda(3 x-8 y+12)=0 ) parallel to the X-axis? | 11 |

212 | Prove that the area of triangle with vertices ( (boldsymbol{t}, boldsymbol{t}-mathbf{2}),(boldsymbol{t}+mathbf{2}, boldsymbol{t}+mathbf{2}),(boldsymbol{t}+ ) ( mathbf{3}, boldsymbol{t} ) ) is independent of ( mathbf{t} ) | 11 |

213 | The sum of the abscissa of all the points on the line ( x+y=4 ) that lie at a unit distance from the line ( 4 x+3 y- ) ( mathbf{1 0}=mathbf{0} ) is A .4 B. -4 ( c .3 ) D. – 3 | 11 |

214 | What is the perimeter of the triangle with vertices ( boldsymbol{A}(-mathbf{4}, mathbf{2}), boldsymbol{B}(mathbf{0},-mathbf{1}) ) and ( C(3,3) ? ) A. ( 7+3 sqrt{2} ) B. ( 10+5 sqrt{2} ) c. ( 11+6 sqrt{2} ) D. ( 5+10 sqrt{2} ) | 11 |

215 | The coordinates of two consecutive vertices ( A ) and ( B ) of a regular hexagon ( A B C D E F ) are (1,0) and (2,0) respectively. The equation of the diagonal ( C E ) is A. ( sqrt{3} x+y=4 ) B . ( x+sqrt{3} y+4=0 ) c. ( x+sqrt{3} y=4 ) D. None of these | 11 |

216 | The condition that the slope of one of the lines represented by ( a x^{2}+2 h x y+ ) ( b y^{2}=0 ) is twice that of the other is A ( cdot h^{2}=a b ) B ( cdot 2 h^{2}=3 a b ) D. ( 4 h^{2}=9 a b ) | 11 |

217 | In the given figure ( boldsymbol{P Q} | boldsymbol{R S}, angle boldsymbol{R} boldsymbol{S F}= ) ( 40^{circ}, angle P Q F=35^{circ} ) and ( angle Q F P=x^{o} ) What is the value of ( x ? ) A . ( 75^{circ} ) В. 105 с. 135 D. ( 140^{circ} ) | 11 |

218 | Find the distance between the following pairs of points:(-5,7),(-1,3) | 11 |

219 | The distance between two parallel lines ( 3 x+4 y+10=0 ) and ( 3 x+4 y-10= ) ( mathbf{0} ) is A . в. ( -4 sqrt{5} ) ( c cdot 2 sqrt{5} ) D. 4 | 11 |

220 | The line ( b x+a y=3 a b ) cuts the coordinate axes at ( A ) and ( B ), then centroid of ( triangle O A B ) is – ( mathbf{A} cdot(b, a) ) B ( cdot(a, b) ) c. ( left(frac{a}{3}, frac{b}{3}right) ) D cdot ( (3 a, 3 b) ) | 11 |

221 | The point on the ( x ) -axis which is equidistant from the points (5,4) and (-2,3) is A. (-2,0) в. (2,0) D. (2,2) | 11 |

222 | The line represented by the equation ( boldsymbol{y}=-boldsymbol{2} boldsymbol{x}+boldsymbol{6} ) is the perpendicular bisector of the line segment AB. If A has the coordinates ( (7,2), ) what are the coordinates for B ? A. (3,0) (年) (3,0),(0,0) в. (4,0) c. (6,2) (年. ( 6,2,2,6) ) D. (5,6) | 11 |

223 | If ( p ) is the length of the perpendicular from the origin on the line ( frac{x}{a}+frac{y}{b}=1 ) and ( a^{2}, p^{2}, b^{2} ) are in A.P. then ( a b ) is equal to This question has multiple correct options A ( cdot p^{2} ) B ( cdot sqrt{2} p^{2} ) c. ( -sqrt{2} p^{2} ) D. ( 2 p^{2} ) | 11 |

224 | The distance between the lines ( 3 x+ ) ( mathbf{4} boldsymbol{y}=mathbf{9} ) and ( mathbf{6} boldsymbol{x}+mathbf{8} boldsymbol{y}-mathbf{1 5}=mathbf{0} ) is ( A cdot frac{3}{10} ) в. ( frac{33}{10} ) ( c cdot frac{33}{5} ) D. none of these | 11 |

225 | The equation of the line parallel to ( 5 x- ) ( 12 y+26=0 ) and at a distance of 4 units from it, is This question has multiple correct options A. ( 5 x-12 y-26=0 ) в. ( 5 x-12 y+26=0 ) c. ( 5 x-12 y-78=0 ) D. ( 5 x-12 y+78=0 ) | 11 |

226 | If P=(1,0), Q=(-1,0) and R=(2,0) are three given points, then locus of the point S satisfying the relation sQ2 + SR2=2SP2, is (1988-2 Marks) (a) a straight line parallel to x-axis (b) a circle passing through the origin c) a circle with the centre at the origin (d) a straigth line parallel to y-axis. | 11 |

227 | ( text { Four points }boldsymbol{A}(mathbf{6}, mathbf{3}), boldsymbol{B})-mathbf{3}, mathbf{5}) ) ( C(4,-2) ) and ( D(x, 3 x) ) are given such that ( frac{Delta D B C}{Delta A B C}=frac{1}{2}, ) find ( x ) | 11 |

228 | n Figure, ( boldsymbol{B A} | boldsymbol{E} boldsymbol{D} ) and ( boldsymbol{B C} | boldsymbol{E F} ). Show that ( angle A B C+angle D E F=180^{circ} ) | 11 |

229 | The ratio in which the line ( 3 x+4 y+ ) ( 2=0 ) divides the distance between ( 3 x+4 y+5=0 ) and ( 3 x+4 y-5=0 ) A .7: 3 B. 3: 7 ( c cdot 2: 3 ) D. None of these | 11 |

230 | If vertices of a triangle are (0,4),(4,1) and ( (7,5), ) find its perimeter. | 11 |

231 | The co-ordinates of the vertices of a rectangle are (0,0),(4,0),(4,3) and ( (0,3) . ) The length of its diagonal is ( mathbf{A} cdot mathbf{4} ) B. 5 ( c cdot 7 ) D. 3 | 11 |

232 | 16. Let 0<a« be fixed angle. If P =(cos 0, sin ) and Q = (cos(a-0), sin(a -0)), then Q is obtained from P by (2002) (a) clockwise rotation around origin through an angle a (b) anticlockwise rotation around origin through an angle a © reflection in the line through origin with slope tan a (d) reflection in the line through origin with slope tan (a/2) | 11 |

233 | 18. Determine all values of a for which the point (a, a?) lies inside the triangle formed by the lines 2x+3y-1=0 (1992 – 6 Marks) x +2y-3 = 0 5x – 6y_1=0 | 11 |

234 | ( left(a m_{1}^{2}, 2 a m_{1}right),left(a m_{2}^{2}, 2 a m_{2}right) ) and ( left(a m_{3}^{2}, 2 a m_{3}right) ) | 11 |

235 | The condition for the points ( (x, y),(-2,2) ) and (3,1) to be collinear is A. ( x+5 y=8 ) B. x+5y=6 c. ( 5 x+y=8 ) D. 5x+y=6 | 11 |

236 | evaluate: ( mathbf{3} boldsymbol{x}-mathbf{5} boldsymbol{y}=mathbf{1 6} ; boldsymbol{x}-mathbf{3} boldsymbol{y}=mathbf{8} ) | 11 |

237 | Find the direction in which a straight line must be drawn through the point ( (1,2), ) so that its point of intersection with the line ( x+y=4 ) may be at a distance of 3 units from this point. | 11 |

238 | Find the angles of a triangle whose sides are ( boldsymbol{x}+mathbf{2} boldsymbol{y}-mathbf{8}=mathbf{0}, mathbf{3} boldsymbol{x}+boldsymbol{y}- ) ( mathbf{1}=mathbf{0} ) and ( boldsymbol{x}-mathbf{3} boldsymbol{y}+mathbf{7}=mathbf{0} ) | 11 |

239 | 2. The points (0,3), (1, 3) and (82, 30) are vertices of (1986 – 2 Mar (a) an obtuse angled triangle an acute angled triangle (C) a right angled triangle an isosceles triangle (e) none of these. (b) | 11 |

240 | 14. The line parallel to the x- axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx – 2ay – 3a=0, where (a,b) (0,0) is [2005] (a) below the x – axis at a distance of – from it (b) below the x – axis at a distance from it (©) above the x – axis at a distance of from it (d) above the x – axis at a distance of – from it | 11 |

241 | The angle of inclination of a straight line parallel to ( x ) -axis is equal to A ( cdot 0^{circ} ) В. ( 60^{circ} ) ( c cdot 45^{circ} ) D. ( 90^{circ} ) | 11 |

242 | Lines ( L_{1}: x+sqrt{3} y=2, ) and ( L_{2}: a x+ ) ( b y=1 ) meet at ( P ) and enclose an angle of ( 45^{circ} ) between them. A line ( L_{3}: y= ) ( sqrt{3} x, ) also passes through ( P ) then ( mathbf{A} cdot a^{2}+b^{2}=1 ) B ( cdot a^{2}+b^{2}=2 ) c. ( a^{2}+b^{2}=3 ) ( mathbf{D} cdot a^{2}+b^{2}=4 ) | 11 |

243 | The area between the curves ( x^{2}=4 y ) and line ( boldsymbol{x}+mathbf{2}=mathbf{4} boldsymbol{y} ) is A ( cdot frac{9}{8} ) в. ( frac{9}{4} ) ( c cdot frac{9}{2} ) D. | 11 |

244 | Find the areas of the triangles the whose coordinates of the points are respectively. (5,2),(-9,-3) and (-3,-5) | 11 |

245 | The equations of the lines through (1,1) and making angles of ( 45^{circ} ) with the line ( boldsymbol{x}+boldsymbol{y}=mathbf{0} ) are A ( . x-1=0, x-y=0 ) В. ( x-y=0, y-1=0 ) c. ( x+y-2=0, y-1=0 ) D. ( x-1=0, y-1=0 ) | 11 |

246 | ff ( P(x, y) ) is equidistant from ( A(a+ ) ( boldsymbol{b}, boldsymbol{b}-boldsymbol{a}) ) and ( boldsymbol{B}(boldsymbol{a}-boldsymbol{b}, boldsymbol{a}+boldsymbol{b}), ) show that ( boldsymbol{b} boldsymbol{x}=boldsymbol{a} boldsymbol{y} ) | 11 |

247 | ( triangle A B C ) is an isosceles triangle. If the coordinates of the base are ( boldsymbol{B} equiv(mathbf{1}, mathbf{3}) ) and ( C equiv(-2,7), ) the coordinates of vertex ( A ) can be This question has multiple correct options A. (1,6) (年) (1,66) в. ( left(-frac{1}{2}, 5right) ) ( ^{c} cdotleft(frac{5}{6}, 6right) ) D. ( left(-7, frac{1}{8}right) ) | 11 |

248 | If a line makes angles ( 90^{circ}, 60^{circ} ) and ( 30^{circ} ) with the positive direction of ( x, y ) and ( z ) axis respectively find its direction cosines. | 11 |

249 | The equation ot the line passing through the point (1,-2,3) and paralle to the ( operatorname{linex}-y+2 z=5 ) and ( 3 x+y+ ) ( z=6 ) is A ( cdot frac{x-1}{-3}=frac{y+2}{5}=frac{z-3}{4} ) B. ( frac{x-1}{1}=frac{y+2}{-1}=frac{z-3}{2} ) ( mathbf{c} cdot frac{x-1}{3}=frac{y+2}{1}=frac{z-3}{6} ) D. ( frac{x-1}{3}=frac{y+2}{-1}=frac{z-3}{2} ) | 11 |

250 | Find the value of ( k ) if line PQ is parallel to line RS where ( boldsymbol{P}(mathbf{2}, boldsymbol{4}), boldsymbol{Q}(boldsymbol{3}, boldsymbol{6}), boldsymbol{R}(boldsymbol{8}, boldsymbol{1}) ) and ( S(10, k) ) | 11 |

251 | Vyum 22. Let 0(0,0), P(3,4), (6,0) be the vertices of the triangles OPQ. The point Rinside the triangle OPQ is such that the triangles OPR, POR, OQR are of equal area. The coordinates of Rare (2007-3 marks) m (3) a) (3) (29(a), (2) | 11 |

252 | A line passing through ( mathbf{P}(-2,3) ) meets the axes in ( A ) and ( B ). If ( P ) divides ( A B ) in the ratio of 3: 4 then the perpendicular distance from (1,1) to the line is A ( cdot frac{9}{sqrt{5}} ) B. ( frac{7}{sqrt{5}} ) c. ( frac{8}{sqrt{5}} ) D. ( frac{6}{sqrt{5}} ) | 11 |

253 | The slope and y-intercept of the following line are respectively ( 5 x-2 y=3 ) A ( cdot ) slope ( =m=-frac{5}{2} quad ) and ( quad y- ) intercept ( =-frac{3}{2} ) B ( cdot ) slope ( =m=frac{5}{2} quad ) and ( quad y- ) intercept ( =frac{3}{2} ) C ( cdot ) slope ( =m=frac{5}{2} quad ) and ( quad y- ) intercept ( =-frac{3}{2} ) D. slope ( =m=-frac{5}{2} quad ) and ( quad y- ) intercept ( =frac{3}{2} ) | 11 |

254 | The area of the triangle formed by the points ( (a, b+c),(b, c+a) ) and ( (c, a+b) ) is ( A ) B. ( a+b+c ) ( c cdot a b c ) D. | 11 |

255 | 74. The area of the triangle formed by the straight line 3x + 2y = 6 and the co-ordinate axes is (1) 3 square units (2) 6 square units (3) 4 square units (4) 8 square units | 11 |

256 | Given lines ( : 4 x+3 y=3 ) and ( 4 x+ ) ( 3 y=12 ) The other possible equation of straight line passing through (-2,-7) and making an intercept of length 3 between the given lines. A. ( 7 x+24 y+182=0 ) в. ( 5 x-7 y=39 ) c. ( 3 y-11 x=1 ) D. ( 7 x+16 y=-126 ) | 11 |

257 | ( J(4,-5), L(-6,7), m: n=3: 5 ) is (19,-23) If true then enter 1 and if false then enter ( mathbf{0} ) | 11 |

258 | If the lines ( y=m_{1} x+c ) and ( y= ) ( boldsymbol{m}_{2} boldsymbol{x}+boldsymbol{c}_{2} ) are parallel, then A. ( m_{1}=m_{2} ) в. ( m_{1} m_{2}=1 ) c. ( m_{1} m_{2}=-1 ) D. ( m_{1}=m_{2}=0 ) | 11 |

259 | f ( boldsymbol{P Q} | boldsymbol{S T}, angle boldsymbol{P Q R}=mathbf{1 1 0}^{boldsymbol{o}} ) and ( angle R S T=130^{circ}, ) find ( angle Q R S(text { Indegrees }) ) | 11 |

260 | Find the slope of the line perpendicular to the line joining the points (2,-3) and ( (mathbf{1}, mathbf{4}) ) | 11 |

261 | The value of ( k ) when the distance between the points ( (3, k) ) and (4,1) is ( sqrt{10} ) is A . ( 30 r 4 ) B. ( -4 o r-2 ) c. ( -4 o r 2 ) D. ( 4 o r-2 ) | 11 |

262 | The ( x ) and ( y ) intercepts of the line ( 2 x- ) ( mathbf{3} boldsymbol{y}+mathbf{6}=mathbf{0}, ) respectively are : A .2,3 B. 3,2 c. -3,2 D. 3,-2 | 11 |

263 | 32. The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0,41) and (41, 0) is: JEEM 2015] (a) 820 (b) 780 (c) 901 (d) 861 | 11 |

264 | Prove that the points (-3,0),(1,-3) and (4,1) are the vertices of an isosceles right-angled triangle. Find the area of this triangle | 11 |

265 | f point ( (x, y) ) is equidistant from points (7,1) and (3,5) show that ( y=x-2 ) | 11 |

266 | Find the slope of the line passing through the points ( G(-4,5) ) and ( boldsymbol{H}(-mathbf{2}, mathbf{1}) ) | 11 |

267 | The line ( frac{x}{3}+frac{y}{4}=1 ) meets the ( y- ) axis and ( x- ) axis at ( A ) and ( B, ) respectively. square ( A B C D ) is constructed on the line segment ( A B ) away from the origin. the coordinates of the vertex of the square farthest from the origin are A ( .(7,3) ) в. (4,7) c. (6,4) (年. ( 6,4,4) ) D. (3,8) | 11 |

268 | If (-6,-4),(3,5),(-2,1) are the vertices of a parallelogram, then remaining vertex can be This question has multiple correct options в. (7,10) c. (-1,0) D. (-11,-8) | 11 |

269 | The point on the line ( 4 x-y-2=0 ) which is equidistant from the points (-5,6) and (3,2) is A . (2,6) в. (4,14) c. (1,2) D. (3,10) | 11 |

270 | If four points are ( boldsymbol{A}(boldsymbol{6}, boldsymbol{3}), boldsymbol{B}(-boldsymbol{3}, boldsymbol{5}), boldsymbol{C}(boldsymbol{4},-boldsymbol{2}) ) and ( boldsymbol{P}(boldsymbol{x}, boldsymbol{y}) ) then the ratio of the areas of ( triangle P B C ) and ( triangle A B C ) is A ( cdot frac{x+y-2}{7} ) в. ( frac{x-y-2}{7} ) c. ( frac{x-y+2}{2} ) D. ( frac{x+y+2}{2} ) | 11 |

271 | 16. Find the equation of the line passing through the point (2, 3) and making intercept of length 2 units between the lines y + 2x = 3 and y + 2x=5. (1991.- 4 Marks) (2, 3) AC 2 y+2x=5 y + 2x = 3 | 11 |

272 | Find the slope and ( y ) -intercept of the line ( 0.2 x-y=1.2 ) A. slope ( =0.2, y ) -intercept ( =-1.2 ) B. slope ( =1.2, y ) -intercept ( =-1.2 ) c. slope ( =0.2, y ) -intercept ( =-2.2 ) D. slope ( =0.2, y ) -intercept ( =-1.3 ) | 11 |

273 | The distance between the straight lines ( mathbf{y}=mathbf{m} mathbf{x}+mathbf{c}_{1}, mathbf{y}=mathbf{m} mathbf{x}+mathbf{c}_{2} ) is ( left|mathbf{c}_{1}-mathbf{c}_{2}right| ) then ( mathbf{m}= ) ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) D. 3 | 11 |

274 | The area of the triangle whose vertices ( operatorname{are}(3,8),(-4,2) ) and (5,-1) is : A. 75 sq.units в. 37.5 sq.units c. 45 sq.units D. 22.5 sq.units | 11 |

275 | The perpendicular distance from the point of intersection of the lines ( 3 x+ ) ( 2 y+4=0,2 x+5 y-1=0 ) to the line ( 7 x+24 y-15=0 ) is A ( cdot frac{2}{3} ) B. ( c cdot frac{1}{5} ) D. | 11 |

276 | Slope of the line that is perpendicular to the line whose equation ( 4 x+5 y=14 ) is A ( -frac{4}{5} ) в. ( c cdot frac{4}{5} ) D. ( -frac{5}{4} ) | 11 |

277 | If the point ( A(2,4) ) is equidistant from ( P(3,8) ) and ( Q(7, y), ) find the values of ( y ) ( mathbf{A} cdot 6 & 4 ) B. ( 12 & 2 ) c. ( 10 & 4 ) D. None of these | 11 |

278 | The angle made by the line ( sqrt{mathbf{3}} boldsymbol{x}-boldsymbol{y}+ ) ( mathbf{3}=mathbf{0} ) with the positive direction of ( mathbf{X} ) axis is ( A cdot 30 ) B . 45 ( c cdot 60 ) D. ( 90^{circ} ) | 11 |

279 | Find whether the lines drawn through the two pairs of points are parallel or perpendicular ( (boldsymbol{3}, boldsymbol{3}),(boldsymbol{4}, boldsymbol{6}) ) and (4,1),(6,7) | 11 |

280 | 7. The locus of a variable point whose distance from (-2, 0) is (1994) 2/3 times its distance from the line x= – is (a) ellipse (b) parabola (c) hyperbola d) none of these | 11 |

281 | Find the value of ( a ) when the distance between the points ( (3, a) ) and (4,1) is ( sqrt{10} . ) The points (2,1) and (1,-2) are equidistant from the point ( (x, y), ) Find locus of point | 11 |

282 | The equation of a straight line which passes through the point (1,-2) and cuts off equal intercept from axes will be: A. ( x+y=1 ) B. ( x-y=1 ) c. ( x+y+1=0 ) D. ( x-y-2=0 ) | 11 |

283 | Find the distance between the following pair of points. (-5,7) and (-1,3) | 11 |

284 | Find the distances between the following pair of points. ( $ $(4,-7) ) and ( (-1, ) 5)( $ $ ) | 11 |

285 | Draw the graph for the linear equation ( boldsymbol{x}=-2 boldsymbol{y} ) A. passes through (0,0) and ( m=2 ) B. passes through (0,0) and ( m=-2 ) c. passes through (1,2) and ( m=-frac{1}{2} ) D. passes through (0,0) and ( m=-frac{1}{2} ) | 11 |

286 | Without using distance formula, show that points (-2,-1),(4,0),(3,3) and (-3,2) are the vertices of a parallelogram | 11 |

287 | The points ( boldsymbol{A}(boldsymbol{a}, boldsymbol{b}+boldsymbol{c}), boldsymbol{B}(boldsymbol{b}, boldsymbol{c}+boldsymbol{a}) ) and ( boldsymbol{C}(boldsymbol{c}, boldsymbol{a}+boldsymbol{b}) ) are: A. collinear B. doesn’tt lie in the same plane c. doesn’t lie on the same line D. nothing can be said | 11 |

288 | If ( p ) and ( p^{prime} ) are the perpendiculars from the origin upon the ( operatorname{lines} x sec theta+ ) ( boldsymbol{y} csc boldsymbol{theta}=boldsymbol{a} ) and ( boldsymbol{x} cos boldsymbol{theta}-boldsymbol{y} sin boldsymbol{theta}= ) ( a cos 2 theta ) respectively then A ( cdot 4 p^{2}+p^{prime 2}=a^{2} ) B cdot ( p^{2}+4 p^{prime 2}=a^{2} ) C ( cdot p^{2}+p^{prime 2}=a^{2} ) D. none of these | 11 |

289 | A point P lies on the x-axis and has abscissa 5 and a point ( Q ) lies on ( y ) -axis and has ordinate ( -12 . ) Find the distance ( mathrm{PQ} ) A. 13 units B. 8 units c. 15 units D. 11 units | 11 |

290 | What is the slope of the line parallel to the equation ( 2 y-3 x=4 ? ) ( A cdot frac{3}{2} ) B. ( frac{1}{2} ) ( c cdot frac{4}{2} ) D. ( frac{-3}{2} ) | 11 |

291 | The coordinate of the point dividing internally the line joining the points (4,-2) and (8,6) in the ratio 7: 5 is A ( .(16,18) ) в. (18,16) ( ^{C} cdotleft(frac{19}{3}, frac{8}{3}right) ) D. ( left(frac{8}{3}, frac{19}{3}right) ) E . (7,3) | 11 |

292 | What is the angle between the straight ( operatorname{lines}left(m^{2}-m nright) y=left(m n+n^{2}right) x+n^{3} ) and ( left(boldsymbol{m} boldsymbol{n}+boldsymbol{m}^{2}right) boldsymbol{y}=left(boldsymbol{m} boldsymbol{n}-boldsymbol{n}^{2}right) boldsymbol{x}+boldsymbol{m}^{3} ) where ( boldsymbol{m}>boldsymbol{n} ? ) ( ^{mathbf{A}} cdot tan ^{-1}left(frac{2 m n}{m^{2}+n^{2}}right) ) B. ( tan ^{-1}left(frac{4 m^{2} n^{2}}{m^{4}-n^{4}}right) ) ( ^{mathbf{C}} cdot tan ^{-1}left(frac{4 m^{2} n^{2}}{m^{4}+n^{4}}right) ) D. ( 45^{circ} ) | 11 |

293 | For the equation given below, find the the slope and the y-intercept ( : 3 y=7 ) A ( cdot 0 ) and ( frac{7}{3} ) B. ( _{0} ) and ( -frac{7}{3} ) c. ( -frac{7}{3} ) and 0 D. ( frac{7}{3} ) and 0 | 11 |

294 | The value of “c” if the line ( boldsymbol{x}+mathbf{4} boldsymbol{y}=mathbf{9} ) pases through ( (mathbf{5}, boldsymbol{c}) ) ( mathbf{A} cdot mathbf{1} ) B. – 1 c. 0 D. None of these | 11 |

295 | The centre of a square is at the origin and vertex is ( A(2,1) . ) Find the ( c 0 ) ordinates of other vertices of the square A. ( B(1,-2), C(-2,-1), D(-1,-2) ) B. ( B(-1,-2), C(-2,-1), D(-1,-2) ) c. ( B(-1,2), C(-2,-1), D(1,-2) ) D. ( (-1,-2), C(-2,-1), D(1,2) ) | 11 |

296 | A straight line L through the point (3,-2) is inclined at an angle 60 to the line ( sqrt{mathbf{3}} x+y=1 . ) If ( L ) also intersects the ( x ) -axis, the equation of ( L ) is A ( cdot y+sqrt{3} x+2-3 sqrt{3}=0 ) B . ( y-sqrt{3} x+2+3 sqrt{3}=0 ) c. ( sqrt{3} y-x+3+2 sqrt{3}=0 ) D. ( sqrt{3} y+x-3+2 sqrt{3}=0 ) | 11 |

297 | The slope of a line is double of the slope of another line. If the tangent of the angle between them is ( frac{1}{3} ) find the slopes of the lines. | 11 |

298 | 1. Three lines px + q + r = 0, qx + ry + P rx+py +9=0 are concurrent if (1985 – 2 Marks) (a) p+q+r=0 (b) p2 + q2 + y2 = qr+rp + pq p3 + q3 + p3 = 3pqr (d) none of these. | 11 |

299 | The area of the triangle formed by the ( operatorname{lines} y=a x, x+y-a=0 ) and the ( y-a x i s ) is equal to A ( cdot frac{1}{2|1+a|} ) в. ( frac{a^{2}}{|1+a|} ) c. ( frac{1}{2} mid frac{a}{1+a} ) D. ( frac{a^{2}}{2|1+a|} ) | 11 |

300 | A circle that has its center its center at the origin and passes through (-8,-6) will also pass through the point: A ( cdot(1,10) ) B. (4,7) ( c cdot(7,7) ) D. ( (9, sqrt{19}) ) | 11 |

301 | 20. 1,2,30turou 2394 A line through A (-5, 4) meets ough A (-5, 4) meets the line x + 3y + 2 = 0, 2x + y + 4 = 0 and x – y – 5 = 0 at the points B, respectively. If (15/AB)2 + (10/AC)2 = (6/ AD)’, find the equation of the line. (1993 – 5 Marks) – 5 = 0 at the points B, C and D | 11 |

302 | The distance of point (4,4) from ( Y ) -axis is A . 4 units B. ( sqrt{32} ) units c. -4 units D. None of the above | 11 |

303 | 24. Let ABC and PQR be any two triangles in the same plane. Assume that the prependiculars from the points A, B, C to the sides QR, RP, PQ respectively are concurrent. Using vector methods or otherwise, prove that the prependiculars from P, Q, R to BC, CA, AB respectively are also concurrent. (2000- 10 Marks) | 11 |

304 | A family of lines is given by ( (1+ ) ( 2 lambda) x+(1-lambda) y+lambda=0, lambda ) being the parameter. The line belonging to this family at the maximum distance from the point (1,4) is A. ( 4 x-y+1=0 ) B. ( 33 x+12 y+7=0 ) c. ( 12 x+33 y=7 ) D. none of these | 11 |

305 | 19. Tagent at a point P, other than (0,0)) on the curve y=x meets the curve again at P. The tangent at P, meets the curve at Pg, and so on. Show that the abscissae of P.P.P………..Po, form a GP. Also find the ratio. [area (AR,P3,B)]/[area(P, P2, P.)] (1993 – 5 Marks) | 11 |

306 | The distance between the parallel lines ( boldsymbol{y}=mathbf{2} boldsymbol{x}+mathbf{4} ) and ( mathbf{6} boldsymbol{x}=mathbf{3} boldsymbol{y}+mathbf{5} ) is A ( cdot frac{17}{sqrt{3}} ) B. c. ( frac{3}{sqrt{5}} ) D. ( frac{17 sqrt{5}}{15} ) | 11 |

307 | Investigate for what values of ( lambda, mu ) the simultaneous equation ( boldsymbol{x}+boldsymbol{y}+boldsymbol{z}= ) ( mathbf{6} ; boldsymbol{x}+mathbf{2} boldsymbol{y}+mathbf{3} boldsymbol{z}=mathbf{1 0} & boldsymbol{x}+mathbf{2} boldsymbol{y}+boldsymbol{lambda} boldsymbol{z}= ) ( mu ) have a unique solution A. ( lambda neq 3 ) в. ( lambda neq 5 ) c. ( lambda neq 1 ) D. ( lambda neq 2 ) | 11 |

308 | Let ( P(2,-4) ) and ( Q(3,1) ) be two given points. Let ( R(x, y) ) be a point such that ( (x-2)(x-3)+(y-1)(y+4)=0 ) area of ( triangle P Q R ) is ( frac{13}{2}, ) then the number of possible positions of ( boldsymbol{R} ) are A .2 B. 3 ( c cdot 4 ) D. None of these | 11 |

309 | Find the equation of the line that passes through the points (-1,0) and (-2,4) | 11 |

310 | Find the equation of the line that passes through the points (-1,0) and (-4,12) A ( . y+4 x=-1 ) B. ( y+4 x=-4 ) c. ( -y+4 x=-8 ) D. ( y-8 x=-12 ) | 11 |

311 | Prove that the points (-7,-3),(5,10),(15,8) and (3,-5) taken in order are the corners of a parallelogram. | 11 |

312 | Line ( A B ) passes through point (1,2) and intersects the positive ( x ) and ( y ) axes at ( boldsymbol{A}(boldsymbol{a}, boldsymbol{0}) ) and ( boldsymbol{B}(boldsymbol{0}, boldsymbol{b}) ) respectively. If the area of ( triangle A O B ) is 1 unit the value of ( (2 a-b)^{2} ) is A .220 в. 240 c. 248 D. 284 | 11 |

313 | If the point ( P(k-1,2) ) is equidistant from the points ( boldsymbol{A}(boldsymbol{3}, boldsymbol{k}) ) and ( boldsymbol{B}(boldsymbol{k}, boldsymbol{5}) ) then how many values of ( k ) are obtained? Write ( 0, ) if the value cannot be | 11 |

314 | Prove that the points ( (0,0),left(3, frac{pi}{2}right), ) and ( left(3, frac{pi}{6}right) ) form an equilateral triangle. | 11 |

315 | Find the distance between the lines ( 3 x+ ) ( y-12=0 ) and ( 3 x+y-4=0 ) A ( cdot frac{16}{sqrt{10}} ) в. ( frac{12}{sqrt{10}} ) c. ( frac{4}{sqrt{10}} ) D. ( frac{8}{sqrt{10}} ) E. Answer Required | 11 |

316 | If one of the diagonals of a square is along the line ( x=2 y ) and one of its vertices is ( (3,0), ) then its sides through this vertex are given by the equations A. ( y-3 x+9=0,3 y+x-3=0 ) в. ( y-3 x-9=0,3 y+x-3=0 ) c. ( y-3 x+9=0,3 y-x+3=0 ) D. ( y-3 x+3=0,3 y+x+9=0 ) | 11 |

317 | ( l, m, n ) are parallel lines. If ( p ) intersects them at ( A, B, C ) and ( q ) at ( D, E, F, ) then A. ( A B=D E ) and ( B C=E F ) always B. At least one of the pairs ( A B, D E ) and ( B C, E F ) are necessarily equal c. At least one of the pairs ( A B, B C ) and ( D E, E F ) are necessarily equal D. ( frac{A B}{B C}=frac{D E}{E F} ) | 11 |

318 | 20. If one of the lines of my2 + (1-m2) xy-mx2=0 is a bisector of the angle between the lines xy=0, then m is [2007] (a) 1 (b) 2 (C) -1/2 (d) -2 | 11 |

319 | 34. A straight the through a fixed point (2, 3) intersec coordinate axes at distinct points Pand 0. Ifo is the origin and the rectangle OPRQ is completed, then the locus OI KIS: (JEEM 2018] (a) 2x+3y = xy (b) 3x +2y = xy (C) 3x +2y =6xy (d) 3x +2y=6 | 11 |

320 | If in triangles ( boldsymbol{X} boldsymbol{Y} boldsymbol{Z}, boldsymbol{X} boldsymbol{Y}=boldsymbol{X} boldsymbol{Z} ) and ( M, N ) are the midpoints of ( X Y, Y Z ) and which one of the following is correct? ( mathbf{A} cdot M N=Y Z ) в. ( N Y=N Z=M N ) c. ( M X=M Y=N Y ) D. ( M N=M X=M Y ) | 11 |

321 | Find the equation of all lines having slope 2 and being tangent to the curve ( boldsymbol{y}+frac{mathbf{2}}{boldsymbol{x}-mathbf{3}}=mathbf{0} ) | 11 |

322 | The line ( L_{1} ) given by ( frac{x}{5}+frac{y}{b}=1 ) passes through the point ( M(13,32) . ) The line ( L_{2} ) is parallel to ( L_{1} ) and has the equation ( frac{x}{c}+frac{y}{3}=1 . ) Then the distance between ( L_{1} ) and ( L_{2} ) is A. ( sqrt{17} ) в. ( frac{17}{sqrt{15}} ) c. ( frac{23}{sqrt{17}} ) D. ( frac{23}{sqrt{15}} ) | 11 |

323 | f ( x_{1}, x_{2}, x_{3} ) and ( y_{1}, y_{2}, y_{3} ) are in GP with same common ratio, then ( left(x_{1}, y_{1}right),left(x_{2}, y_{2}right),left(x_{3}, y_{3}right) ) A. lie on an ellipse B. lie on a circle c. are vertices of triangle D. lie on a straight line | 11 |

324 | The lines ( pleft(p^{2}+1right) x-y+q=0 ) and ( left(p^{2}+1right)^{2} x+left(p^{2}+1right) y+2 q=0 ) are perpendicular to a common line for: A. exactly one value of B. exactly two values of ( mathrm{p} ) C. more than two values of ( mathrm{p} ) D. no value of | 11 |

325 | Which of the following is true for a line ( l ) lying in the same plane and intersecting ( triangle A B C ) but not perpendicular to ( overline{B C} ? ) A. ( l ) intersects ( overline{A B} ) or ( overline{A C} ) B. ( l ) intersects ( overline{A C} ) c. ( l ) does not intersects ( overline{A B} ) or ( overline{A C} ) D. ( l ) intersects ( overline{A B} ) | 11 |

326 | Find the slope of the line which make the following angle with the positive direction of ( x- ) axis : ( frac{2 pi}{3} ) | 11 |

327 | In the diagram, ( P Q R ), is an isosceles triangle and ( Q R=5 ) units. The coordinates of ( Q ) are: A ( .(4,5) ) B. (3,4) ( c cdot(2,4) ) D. (1,4) | 11 |

328 | In the figure above, line ( iota ) (not shown) is perpendicular to segment ( A B ) and bisects segment ( A B ). Which of the following points lies on line ( iota ) ? A ( cdot(0,2) ) В ( cdot(1,3) ) ( c .(3,1) ) D. (3,3) E. 6,6 | 11 |

329 | 52. What will be the distance of in- tersection point of x + y -3 = 0 and 3x – 2y = 4 from the point which lies at x-axis at a distance 2 units from origin ? (1) 3 unit (2) 1 unit (3) 2 unit (4) O unit | 11 |

330 | If ( A ) is the area of a triangle whose vertices are ( (1,2,3),(-2,1,-4),(3,4,-2), ) then the value of ( 4 A^{2} ) is A . 1098 B. 1056 c. 1218 D. 1326 | 11 |

331 | The area of the triangle formed by ( (0,0),left(a^{x^{2}}, 0right),left(0, a^{6 x}right) ) is ( frac{1}{2 a^{5}} s q ) unit then ( x ) is equal to ( mathbf{A} cdot 1 ) or 5 B. -1 or 5 c. 1 or -5 D. -1 or -5 | 11 |

332 | Equation of two equal sides of a triangle are the lines ( 7 x-y+3=0 ) and ( x+ ) ( y-3=0 ) and the third side passes through the point ( (1,-10), ) then the equation of the third side can be This question has multiple correct options A . ( x-3 y=31 ) B. ( 3 x+y+7=0 ) c. ( x+3=0 ) ( mathbf{D} cdot y=3 ) | 11 |

333 | The slope and y-intercept of the following line are respectively ( 2 y+2 x-5=0 ) A ( cdot ) slope ( =m=1 quad ) and ( quad y- ) intercept ( =c=frac{5}{2} ) B. slope ( =m=1 / 5 ) and ( y- ) intercept ( =c=frac{2}{5} ) C ( cdot ) slope ( =m=-1 ) and ( y- ) intercept ( =c=frac{5}{2} ) D. slope ( =m=-1 / 5 ) and ( y- ) intercept ( =c=frac{2}{5} ) | 11 |

334 | f ( p, q ) and ( r ) are three points with coordinates (1,4) and (4,5) and ( (m, m) ) respectively, are collinear then value of ( 2 m ) is | 11 |

335 | Find the slope of the line whose inclination is ( 5 pi / 6 ) | 11 |

336 | ( operatorname{Let} A(a cos theta, 0), B(0, a sin theta) ) be any two points then the distance between two points is A. ( |a| ) units B . ( a^{2} ) units c. ( sqrt{a} ) units D. ( sqrt{2} a ) units | 11 |

337 | Let ( S ) be the set of points whose abscissas and ordinates are natural numbers. Let ( boldsymbol{P} in boldsymbol{S} ) such that the sum of the distance of ( boldsymbol{P} ) from (8,0) and (0,12) is minimum among all elements in S. Then the number of such points ( P ) in ( boldsymbol{S} ) is ( A cdot 1 ) B. 3 ( c .5 ) D. 11 | 11 |

338 | Let ( A B ) and ( C D ) be two parallel lines and ( stackrel{leftrightarrow}{P Q} ) be a transversal. Let ( stackrel{leftrightarrow}{P Q} ) intersect ( A^{leftrightarrow} B ) in ( L . ) Suppose the bisector of ( angle A L P ) intersect ( C D ) in ( R ) and the bisector of ( angle P L B ) intersect ( stackrel{leftrightarrow}{C D} ) in ( mathrm{S} ) Prove that ( angle boldsymbol{L} boldsymbol{R} boldsymbol{S}+angle boldsymbol{R} boldsymbol{S} boldsymbol{L}=boldsymbol{9} boldsymbol{0}^{boldsymbol{o}} ) | 11 |

339 | Let ( P Q R ) be a right angled isosceles traingle, right angled at ( P(2,1) . ) If the equation of the line ( Q R ) is ( 2 x+y=3 ) then the equation represnting the pair of lines ( P Q ) and ( P R ) is A ( cdot 3 x^{2}-3 y^{2}+8 x y+2 x+10 y+25=0 ) B . ( 3 x^{2}-3 y^{2}+8 x y-20 x-10 y+25=0 ) c. ( 3 x^{2}-3 y^{2}+8 x y+10 x+15 y+20=0 ) D. ( 3 x^{2}-3 y^{2}-8 x y-10 x-15 y-20=0 ) | 11 |

340 | ( A, B, C ) are the points ( (-2,-1),(0,3),(4,0) . ) Then the co- ordinates of the point ( D ) such that ( A B C D ) is a parallelogram are A. (2,-4) в. (2,4) c. (-2,-4) D. None of these | 11 |

341 | Three points ( (0,0),(3, sqrt{3}),(3, lambda) ) form an equilateral triangle, then ( lambda ) is equal to ( A cdot 2 ) B. -3 ( c .-4 ) D. ( sqrt{3} ) | 11 |

342 | Find the angle which the straight line ( y=sqrt{3} x-4 ) makes with y-axis. | 11 |

343 | f the line ( left(frac{x}{2}+frac{y}{3}-1right)+lambda(2 x+y- ) 1) ( =0 ) is parallel to ( x ) -axis then ( lambda= ) ( A cdot-frac{1}{2} ) B. ( frac{1}{2} ) ( c cdot-frac{1}{4} ) D. | 11 |

344 | n figure, ( A B | C D ) and a transversal ( P Q ) cuts them at ( L ) and ( M ) respectively. f ( angle Q M D=100^{circ} ), find all other angles | 11 |

345 | The equation of the line farthest from (-5,-4) belonging to the family of ( operatorname{lines}(2+lambda) x+(3 lambda+1) y+2(2+ ) ( lambda)=0, ) where ( lambda ) is a variable parameter is A. ( 3 x+4 y+6=0 ) в. ( 3 x+4 y+3=0 ) c. ( 4 x+3 y+3=0 ) D. ( 4 x+3 y-3=0 ) | 11 |

346 | If ( (x, y) ) is equidistant from ( P(-3,2) ) and ( Q(2,-3), ) then A ( .2 x=y ) в. ( x=-y ) c. ( x=2 y ) D. ( x=y ) | 11 |

347 | Find the distance between (8,-8) from the origin. | 11 |

348 | The line ( x cos theta+y sin theta=p ) meets the axes of co-ordinates at ( A ) and ( B ) respectively. Through A and B lines are drawn parallel to axes so as to meet the perpendicular drawn from origin to given line in ( P ) and ( Q ) respectively; then show that ( |P Q|=frac{4 p|cos 2 theta|}{sin ^{2} 2 theta} ) | 11 |

349 | Find a point on ( boldsymbol{y}-boldsymbol{a} boldsymbol{x} boldsymbol{i} boldsymbol{s} ) which is equidistant from (-5,-2) and (3,2) | 11 |

350 | Prove that: ( mathbf{3} boldsymbol{x}-mathbf{5} boldsymbol{y}=mathbf{1 6} ; boldsymbol{x}-mathbf{3} boldsymbol{y}=mathbf{8} ) | 11 |

351 | The line through point ( (boldsymbol{m},-mathbf{9}) ) and ( (7, m) ) has slope ( m . ) The ( y ) -intercept of this line, is? A . -18 B. -6 ( c .6 ) D. 18 | 11 |

352 | If the equation to the locus of points equidistant from the points (-2,3),(6,-5) is ( a x+b y+c=0 ) where ( a>0 ) then, the ascending order of ( a, b, c ) is A. ( a, b, c ) в. ( c, b, a ) c. ( b, c, a ) D. ( a, c, b ) | 11 |

353 | The perimeter of triangle with vertices ( boldsymbol{A}(mathbf{0}, mathbf{0}), boldsymbol{B}(mathbf{5}, mathbf{7}) ) and ( boldsymbol{C}(mathbf{9}, mathbf{5}) ) B. ( sqrt{74}+sqrt{106} ) c. ( sqrt{74}+sqrt{20}+sqrt{106} ) D. None of the above | 11 |

354 | Find the area of the triangle formed by the midpoints of the sides of ( Delta A B C ) where ( boldsymbol{A}=(mathbf{3}, mathbf{2}), boldsymbol{B}=(-mathbf{5}, mathbf{6}) ) and ( boldsymbol{C}= ) (8,3) | 11 |

355 | Find the distance of the line ( 4 x+7 y+ ) ( 5=0 ) from the point (1,2) along the line ( 2 x-y=0 ) | 11 |

356 | The distance of the point (1,3) from the line ( 2 x+3 y=6, ) measured parallel to the line ( 4 x+y=4, ) is A ( cdot frac{5}{sqrt{13}} ) units B. ( frac{3}{sqrt{17}} ) units c. ( sqrt{17} ) units D. ( frac{sqrt{17}}{2} ) units | 11 |

357 | Find the area of the triangle whose vertices are (-5,7),(4,5) and (-4,-5) | 11 |

358 | What is the distance of points ( boldsymbol{A}(mathbf{5},-mathbf{7}) ) from ( y ) -axis. | 11 |

359 | The distance between the lines ( 4 x+ ) ( 3 y=11 ) and ( 8 x+6 y=15, ) is ( A cdot frac{7}{2} ) B. 4 ( c cdot frac{7}{10} ) D. None of these | 11 |

360 | Find the equation of the straight line equally inclined to the lines, ( 3 x=4 y+ ) 7 and ( 5 y=12 x+6 ) | 11 |

361 | Show that the tangent of an angle between the lines ( frac{x}{a}+frac{y}{b}=1 a n d frac{x}{a}- ) ( frac{y}{b}=1 i s frac{2 a b}{a^{2}-b^{2}} ) | 11 |

362 | 15. Area of the parallelogram formed by the me y=mx+1, y=nx and y=mx+ 1 equals (a) Im+n/(m -n2 (6) 2/m + nl (@’1/(m+n) (d) 1/(m-nl) rallelogram formed by the lines y = mx, (20015) | 11 |

363 | Find the distance between ( (x+3, x-3) ) from the origin. | 11 |

364 | Slope of the line passing through the points ( boldsymbol{P}(1,-1) ) and ( boldsymbol{Q}(-2,5) ) is ( A cdot 2 ) B. 6 c. -2 D. – 3 | 11 |

365 | 52. What will be the distance of in- tersection point of x + y – 3 = 0 and 3x – 2y = 4 from the point which lies at x-axis at a distance 2 units from origin? (1) 3 unit (2) 1 unit (3) 2 unit (4) O unit | 11 |

366 | Using section formula, show that the points ( boldsymbol{A}(mathbf{2},-mathbf{3}, mathbf{4}), boldsymbol{B}(-mathbf{1}, mathbf{2}, mathbf{1}) ) and ( Cleft(0, frac{1}{3}, 2right) ) are collinear. | 11 |

367 | ( (p, q) ) is a point such that ( p ) and ( q ) are integers ( p geq 50 ) and the equation ( p x^{2}+q x+1=0 ) has real roots. The square of the least distance of the point from the origin is ( S ) Find ( frac{boldsymbol{S}-mathbf{2 2 5}}{mathbf{5 0 0}} ) | 11 |

368 | A variable line is such that its distance from origin always remains 2 units. Minimum value of the length of intercept made by it between coordinate axis is A . 2 B. 4 c. 8 D. 16 | 11 |

369 | If the slope of a line through ( (-2,3),(4, a) ) is ( frac{-5}{3} ) then equation of the line is. A. ( 5 x-3 y-1=0 ) B. ( 5 x+3 y+1=0 ) c. ( 3 x-5 y+1=0 ) D. ( 5 x+3 y=0 ) | 11 |

370 | If the line ( sqrt{5} x=y ) meets the lines ( x= ) ( mathbf{1}, boldsymbol{x}=mathbf{2}, ldots, boldsymbol{x}=boldsymbol{n}, ) at points ( boldsymbol{A}_{mathbf{1}}, boldsymbol{A}_{mathbf{2}}, dots ) ( A_{n} ) respectively then ( left(O A_{1}right)^{2}+ ) ( left(O A_{2}right)^{2}+ldots+left(O A_{n}right)^{2} ) is equal to ( (0 ) is the origin) A ( cdot 3 n^{2}+3 n ) B. ( 2 n^{3}+3 n^{2}+n ) ( mathbf{c} cdot 3 n^{3}+3 n^{2}+2 ) D. ( left(frac{3}{2}right)left(n^{4}+2 n^{3}+n^{2}right) ) | 11 |

371 | Write the inclination of a line which is Perpendicular to y-axis | 11 |

372 | ( a, b, c ) are in A.P. and the points ( boldsymbol{A}(boldsymbol{a}, mathbf{1}), boldsymbol{B}(boldsymbol{b}, mathbf{2}) ) and ( boldsymbol{C}(boldsymbol{c}, boldsymbol{3}) ) are such that ( (O A)^{2},(O B)^{2} ) and ( (O C)^{2} ) are also in A.P; ( O ) being the origin, then This question has multiple correct options A ( cdot a^{2}+c^{2}=2 b^{2}-2 ) B. ( a c=b^{2}+1 ) c. ( (a+c)^{2}=4 b^{2} ) D. ( a+b+c=3 b ) | 11 |

373 | The coordinate of vertices of triangles are given. Identify the types of triangles (3,-3)(3,5)(11,-3) | 11 |

374 | If the relation between the cost charged by a game shop is shown by the given graph, then the ( y- ) intercept of this graph represents A. The cost of playing 5 games B. The cost per game, which is ( $ 5 ) C. The entrance fee to enter the arcade D. The number of games that are played | 11 |

375 | If the each of the vertices of a triangle has integral coordinates, then the triangle may be This question has multiple correct options A. right angled B. equilateral c. isosceles D. none of these | 11 |

376 | The distance between the parallel lines ( 5 x-12 y-14=0 ) and ( 5 x-12 y+ ) ( 12=0 ) is equal to A ( cdot frac{1}{13} ) B. 2 c. ( frac{2}{13} ) D. 4 E ( cdot frac{4}{13} ) | 11 |

377 | Which of the following points are the vertices of an equilateral triangle? A ( cdot(a, a),(-a,-a),(2 a, a) ) В ( cdot(a, a),(-a,-a),(-a sqrt{3}, a sqrt{3}) ) c. ( (sqrt{2} a,-a),(a, sqrt{2} a),(a,-a) ) D. ( (0,0),(a,-a),(a, sqrt{2} a) ) | 11 |

378 | In the adjoining figure line ( mathrm{p} | ) line ( mathrm{q} ) Line ( t ) and line ( s ) are transversals. Find measure of ( angle mathbf{x} ) and ( angle mathbf{y} ) using the measures of angles given in the figure | 11 |

379 | Let the opposite angular points of a square be (3,4) and ( (1,-1) . ) Find the coordinates of the remaining angular points. | 11 |

380 | A straight line is drawn through the point ( p(2,3) ) and is inclined at an angle of ( 30^{circ} ) with the ( x- ) axis, the co-ordinates of two points on it at a distance of 4 from ( p ) is/are A ( cdot(2+2 sqrt{3}, 5),(2-2 sqrt{3}, 1) ) B . ( (2+2 sqrt{3}, 5),(2+2 sqrt{3}, 1) ) c. ( (2-2 sqrt{3}, 5),(2-2 sqrt{3}, 1) ) D. none of these | 11 |

381 | If three points (0,0),(3,45) and ( (3, lambda) ) form en equilateral triangle, then the value of ( lambda, ) is A . 96 B. 18 c. 50 D. No possible value of ( lambda ) to make an equilateral triangle | 11 |

382 | Column II gives the area of triangles whose vertices are given in column I match them correctly. | 11 |

383 | The coordinates of the vertices of a triangle are ( left(x_{2}, y_{2}right) ) and ( left(x_{3}, y_{3}right) . ) The line joining the first two is divided in the ratio I : ( k ), and the line joining this point of division to the opposite angular point is then divided in the ratio ( mathrm{m}: mathrm{k}+ ) I. Find the coordinates of the latter point of section. | 11 |

384 | In the diagram ( M N ) is a straight line on a Cartesian plane. The coordinates of ( N ) ( operatorname{are}(12,13) ) and ( M N^{2}=9 ) units. The coordinates of ( M ) are: A ( .(21,13) ) B. (12,22) c. (12,4) D. (3,13) | 11 |

385 | 18. Let A (h, k), B(1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which ‘k’ can take is given by [2007] (a) {-1,3} () {-3,-2} (c) {1,3} (d) {0,2} | 11 |

386 | 29. The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0,1) (1, 1) and (1,0) [JEE M 2013] (a) 2+V2 (6) 2-3 (c) 1+ V2 (d) 1-2 is : PO | 11 |

387 | Prove that the angle between the straight lines joining the origin to the intersection of the straight line ( y= ) ( 3 x+2 ) with the curve ( x^{2}+2 x y+ ) ( 3 y^{2}+4 x+8 y-11=0 ) is ( tan ^{-1} frac{2 sqrt{2}}{3} ) | 11 |

388 | If the coordinates of the points ( A, B, C, D ) be (1,2,3),(4,5,7),(-4,3,-6) and (2,9,2) respectively, then find the angle between the lines ( A B ) and ( C D ) | 11 |

389 | Show that the following points are collinear. (3,-2),(-2,8) and (0,4) | 11 |

390 | The distance between the points (5,-9) and ( (11, y) ) is 10 units. Find the values of ( y ) A. -2,-17 в. -1,-17 c. -1,-27 D. -1,17 | 11 |

391 | Find the area of the shaded region in PQRSPQRS is an equilateral triangle A ( cdot(6 pi-9 sqrt{3}) mathrm{cm}^{2} ) в. ( (4 pi-9 sqrt{3}) ) ст ( ^{2} ) c. ( (3 pi-9 sqrt{3}) c m^{2} ) D・ ( (2 pi-9 sqrt{3}) ) с ( m^{2} ) E. None of thes | 11 |

392 | The line represented by the equation ( y= ) ( x ) is the perpendicular bisector of line segment AB. If A has the coordinates ( (-3,3), ) what are the coordinates of ( mathrm{B} ) ? A ( cdot(6,-3) ) в. (3,-6) c. (3,-3) D. (6,3) | 11 |

393 | The vertices of ( triangle A B C ) are ( boldsymbol{A}(mathbf{1}, mathbf{8}), boldsymbol{B}(-mathbf{2}, mathbf{4}), boldsymbol{C}(mathbf{8},-mathbf{5}) . ) If ( boldsymbol{M} ) and ( boldsymbol{N} ) are the midpoints of ( A B ) and ( A C ) respectively, find the slope of ( M N ) and hence verify that ( M N ) is parallel to ( B C ). A ( cdot-frac{9}{10} ) в. ( frac{9}{10} ) ( c cdot-frac{9}{5} ) D. None of these | 11 |

394 | If the line ( p x-q y=r ) intersects the co ordinate axes at ( (a, 0) ) and ( (0, b), ) then value of atb is equal to A ( cdot_{r}left(frac{q+p}{q p}right) ) В ( cdot_{r}left(frac{q-p}{p q}right) ) c. ( _{r}left(frac{p-q}{p q}right) ) D. ( rleft(frac{p+q}{p-q}right) ) E ( cdot rleft(frac{p-q}{p+q}right) ) | 11 |

395 | Find the ratio in which the ( y- ) axis divides the line segment joining the points (5,-6) and ( (-1,-4) . ) Also find the point of intersection. | 11 |

396 | Find the area of a parallelogram ( boldsymbol{A B C D} ) if three of its vertices are ( boldsymbol{A}(mathbf{2}, mathbf{4}), boldsymbol{B}(mathbf{2}+sqrt{mathbf{3}}, mathbf{5}) ) and ( boldsymbol{C}(mathbf{2}, mathbf{6}) ) | 11 |

397 | Find the slope of the line passing through the points ( A(2,3) ) and ( B(4,7) ) | 11 |

398 | State the following statement is True or False ( A ) line passing through (3,4) meets the axes ( O X ) and ( O Y ) at ( A ) and ( B ) respectively. The minimum area of the triangle ( O A B ) in square units is 34 A . True B. False | 11 |

399 | Distance of the point (2,5) from the line ( mathbf{3} boldsymbol{x}+boldsymbol{y}+mathbf{4}=mathbf{0} ) measured parallel to the line ( 3 x-4 y+8=0 ) is A ( cdot frac{15}{2} ) B. ( frac{9}{2} ) c. 5 D. None of the above | 11 |

400 | The equation of lines parallel to ( 3 x- ) ( 4 y-5=0 ) at a unit distance from it is A. ( 3 x-4 y-10=0 ) в. ( 5 x+3 y-5=0 ) c. ( 3 x+4 y+10=0 ) D. ( 6 x+2 y+4=0 ) | 11 |

401 | Solve the following question: Find the slope of the line passing through the points ( A(2,3) ) and ( B(4,7) ) | 11 |

402 | Find the value of ( k, ) if the points ( A(7,-2), B(5,1) ) and ( C(3,2 k) ) are collinear. | 11 |

403 | A parallel line is drawn from point ( P(5,3) ) to ( y ) -axis, what is the distance between the line and ( y ) -axis. | 11 |

404 | There are two parallel lines,one of which has the equation ( 3 x+4 y=2 . ) If the lines cut an intercept of length 5 on the line ( x+y=1 ) then the equation of the other line is A ( cdot_{3 x+y}=frac{sqrt{6}-2}{2} ) в. ( 3 x+4 y=frac{sqrt{6}-2}{2} ) c. ( 3 x+4 y=7 ) D. none of these | 11 |

405 | In the figure, ( A C=9, B C=3 ) and ( D ) is 3 times as far from ( A ) as from ( B ). What is ( B D ? ) A. 6 B. 9 c. 12 D. 15 E. 18 | 11 |

406 | If the points ( boldsymbol{A}(mathbf{1}, mathbf{2}), boldsymbol{B}(mathbf{4}, boldsymbol{6}), boldsymbol{C}(boldsymbol{3}, mathbf{5}) ) are the vertices of a ( Delta A B C ), find the equation of the line passing through the midpoints of ( A B ) and ( B C ) | 11 |

407 | ( boldsymbol{A}(boldsymbol{p}, boldsymbol{0}), boldsymbol{B}(boldsymbol{4}, boldsymbol{0}), boldsymbol{C}(boldsymbol{5}, boldsymbol{6}) ) and ( boldsymbol{D}(1, boldsymbol{4}) ) are the vertices of a quadrilateral ( A B C D . ) If ( angle A D C ) is obtuse, the maximum integral value of ( p ) is : ( mathbf{A} cdot mathbf{1} ) B . 2 ( c .3 ) D. | 11 |

408 | The diagonals of a parallelogram PQRS are along the lines x +3y=4 and 6x – 2y= 7. Then PQRS must be a. (1998 – 2 Marks) (a) rectangle (b) square (c) cyclic quadrilateral (d) rhombus. | 11 |

409 | The equation of a line through (2,-3) parallel to y-axis is A. ( y=-3 ) B. ( y=2 ) c. ( x=2 ) D. ( x=-3 ) | 11 |

410 | Area of right triangle ( M O B ) is 16 sq.units. If ( boldsymbol{O} ) is the origin and the coordinates of ( A ) are ( (8,0), ) what are the coordinates of B ? ( A cdot(0,4) ) B. (0, 2) ( c cdot(-1,1) ) ( mathbf{D} cdotleft(0, frac{1}{2}right) ) | 11 |

411 | 10. Let A(2, -3) and B(-2, 3) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line (a) 3x – 2y = 3 (b) 2x – 3y = 7 [2004] (c) 3x+2y=5 (d) 2x+3y=9 | 11 |

412 | The value of ( x ) in the figure given below is ( A cdot 2 mathrm{cm} ) ( B .1 mathrm{cm} ) ( c .2 .5 mathrm{cm} ) D. 3 cm | 11 |

413 | Point ( P(2,3) ) lines on the ( 4 x+3 y=17 ) Then find the co-ordinated of points farthest from the line which are at 5 units distance from the P. A. (6,6) (年) 6,6,6 в. (6,-6) D. (-2,0) | 11 |

414 | Find the slope of the line, which makes an angle of ( 30^{circ} ) with the positive direction of ( y- ) axis measured anticlockwise. | 11 |

415 | Find a relationship between ( x ) and ( y ) so that the distance between the points ( (x, y) ) and (-2,4) is equal to 5 A ( cdot x^{2}+y^{2}+4 x-8 y-4=0 ) B . ( x^{2}+y^{2}+4 x-8 y-5=0 ) c. ( x^{2}+y^{2}+4 x-8 y-6=0 ) D. ( x^{2}+y^{2}+4 x-8 y-53=0 ) | 11 |

416 | Int he given figure ( l|boldsymbol{m}| boldsymbol{n} ). If ( boldsymbol{x}=boldsymbol{y} ) and ( a=b, ) then ( mathbf{A} cdot l | n ) B. ( ln ) D. ( D | n ) | 11 |

417 | The equations of line ( A B ) and line ( P Q ) are ( y=-frac{1}{2} x ) and ( y=2 x ) respectively. Find the measure of angle ( angle mathrm{BOQ} ) which is formed by intersection of line ( A B ) and line PQ. (Point P and point A are in first and second quadrant respectively) A ( cdot 60^{circ} ) B. ( 150^{circ} ) ( c cdot 90^{circ} ) D. ( 120^{circ} ) | 11 |

418 | Triangle is formed by the lines ( boldsymbol{x}+boldsymbol{y}= ) ( mathbf{0}, boldsymbol{x}-boldsymbol{y}=mathbf{0} ) and ( ell boldsymbol{x}+boldsymbol{m} boldsymbol{y}=mathbf{1 .} ) If ( ell ) and ( m ) follow the condition ( ell^{2}+ ) ( m^{2}=1 ; ) then the locus of its circumcentre is A ( cdotleft(x^{2}-y^{2}right)^{2}=x^{2}+y^{2} ) B . ( left(x^{2}+y^{2}right)^{2}=left(x^{2}-y^{2}right) ) C ( cdotleft(x^{2}+y^{2}right)=4 x^{2} y^{2} ) D. ( left(x^{2}-y^{2}right)^{2}left(x^{2}+y^{2}right)=1 ) | 11 |

419 | The equation of line perpendicular to ( x-2 y+1=0 ) and passing through (1,2) is. A. ( 3 x-8 y+6=0 ) B. ( 2 x+y=4 ) c. ( 3 x-5 y+1=0 ) D. ( 5 x+3 y=0 ) | 11 |

420 | Prove that the product of the lengths of the perpendiculars drawn from the points ( (sqrt{a^{2}-b^{2}}, 0) ) and ( (-sqrt{a^{2}-b^{2}}, 0) ) to the line ( frac{x}{a} cos theta+ ) ( frac{y}{b} sin theta=1 ) is ( b^{2} ) | 11 |

421 | Find the slope and ( y ) -intercept of the line ( 2 x+5 y=1 ) A ( cdot ) slope ( =-frac{2}{5}, y ) -intercept ( =frac{1}{5} ) B. slope ( =-frac{1}{5}, y ) -intercept ( =frac{1}{5} ) c. slope ( =-frac{2}{3}, y ) -intercept ( =frac{1}{5} ) D. slope ( =-frac{2}{5}, y ) -intercept ( =frac{2}{5} ) | 11 |

422 | Given lines ( : 4 x+3 y=3 ) and ( 4 x+ ) ( 3 y=12 . ) One of the possible equations of straight line passing through (-2,-7) and making an intercept of length 3 between the given lines is A . ( y=-7 ) В. ( 4 x+3 y=-29 ) c. ( 3 x-4 y=22 ) D. ( 7 x+24 y+182=0 ) | 11 |

423 | The value of ‘ ( a ) ‘ so that the curves ( y= ) ( 3 e^{x} ) and ( y=frac{a}{3} e^{-x} ) are perpendicular to each other: A ( cdot frac{1}{3} ) B. – 1 ( c .3 ) D. | 11 |

424 | ( boldsymbol{A}(boldsymbol{3}, boldsymbol{2}, boldsymbol{0}), boldsymbol{B}(boldsymbol{5}, boldsymbol{3}, boldsymbol{2}), boldsymbol{C}(-boldsymbol{9}, boldsymbol{6},-boldsymbol{3}) ) are three points forming a triangle and ( A D ) is the bisectors of the ( angle B A C ) meet BC at ( D, ) then co-ordinates of ( D ) are: ( ^{mathbf{A}} cdotleft(frac{17}{16}, frac{57}{16}, frac{28}{16}right) ) в. ( left(frac{38}{16}, frac{57}{16}, frac{17}{16}right) ) ( ^{mathbf{C}} cdotleft(frac{38}{16}, frac{17}{16}, frac{57}{166}right) ) D. ( left(frac{57}{16}, frac{38}{16}, frac{17}{16}right) ) | 11 |

425 | Find the slope of line having inclination ( mathbf{6 0}^{circ} ) | 11 |

426 | Find he point of intersection of ( mathrm{AB} ) and CD, where ( boldsymbol{A}(boldsymbol{6},-boldsymbol{7}, boldsymbol{0}), boldsymbol{B}(boldsymbol{1 6},-boldsymbol{1 9},-boldsymbol{4}), boldsymbol{C}(boldsymbol{0}, boldsymbol{3},-boldsymbol{6}) ) | 11 |

427 | If the perpendicular distance of a point ( P ) from the ( x ) -axis is 5 units and the foot of the perpendicular lines on the negative direction of ( x ) -axis, then the point P has? A. ( x ) coordinate ( =5 ) B. ( y ) coordinate ( =5 ) only c. ( y ) coordinate ( =-5 ) only D. ( y ) coordinate ( =5 ) or -5 | 11 |

428 | Find the distance of the point (-1,1) from the line ( 12(x+6)=5(y-2) ) | 11 |

429 | Which of these equations represents a line parallel to the line ( 2 x+y=6 ? ) A. ( y=2 x+3 ) в. ( y-2 x=4 ) c. ( 2 x-y=8 ) D. ( y=-2 x+1 ) | 11 |

430 | Srivani walks ( 12 m ) due East and turns left and walks another 5 m, how far is she from the place she started? | 11 |

431 | The distance between the lines ( 5 x- ) ( 12 y+65=0 ) and ( 5 x-12 y-39=0 ) is ( A cdot 4 ) B. 16 ( c cdot 2 ) D. | 11 |

432 | Points ( A & B ) are in the first quadrant:Point ‘o’ isthe origin. If the slope of ( mathrm{OA} ) is ( 1, ) slope of ( mathrm{OB} ) is 7 and OA=OB, then the slope of AB is- A. ( -1 / 5 ) B . ( -1 / 4 ) c. ( -1 / 3 ) D. ( -1 / 2 ) | 11 |

433 | Which of the following points is equidistant from (3,2) and (-5,-2)( ? ) в. (0,-2) D. (2,-2) | 11 |

434 | Find the centre of the circle passing through (6,-6),(3,-7) and (3,3) | 11 |

435 | If the point ( (x, y) ) is equidistant from the points ( (a+b, b-a) ) and ( (a- ) ( b, a+b), ) prove that ( b x=a y ) | 11 |

436 | If ( A D ) and ( overline{B C} ) are parallel, then calculate the value of ( x ) ( mathbf{A} cdot 60^{circ} ) B. ( 70^{circ} ) ( c cdot 80^{circ} ) D. 110 | 11 |

437 | Find inclination (in degrees) of a line parallel to ( y ) -axis. | 11 |

438 | The points (-2,5) and (3,-5) are plotted in xy planes. Find the slope and ( y ) intercept of the line joining the points. | 11 |

439 | The line joining the points (-6,8) and (8,-6) is divided into four equal parts; find the coordinates of the points of section | 11 |

440 | 6. If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is (1992 – 2 Marks) (a) square (b) circle (c) straight line (d) two intersecting lines | 11 |

441 | Line ( L ) passes through the points (4,-5) and ( (3,7) . ) Find the slope of any line perpendicular to line ( boldsymbol{L} ) A ( cdot frac{1}{2} ) B. ( frac{1}{4} ) ( c cdot frac{1}{8} ) D. ( frac{1}{12} ) | 11 |

442 | The distance or origin from the point ( P(3,2) ) is : A ( cdot sqrt{2} ) B. ( sqrt{15} ) c. ( sqrt{13} ) D. ( sqrt{11} ) | 11 |

443 | Find the valueof ( c ) if the point (4,5) pases through ( boldsymbol{y}=mathbf{5} boldsymbol{x}+boldsymbol{c} ) A . -15 B. 15 ( c .5 ) ( D cdot-5 ) | 11 |

444 | Find the distance between ( boldsymbol{x}+boldsymbol{y}+mathbf{1}= ) 0 and ( 2 x+2 y+5=0 ) | 11 |

445 | Points on the line ( y=x ) whose perpendicular distance from the line ( 3 x+4 y=12 ) is 4 have the coordinates ( ^{A} cdotleft(-frac{8}{7},-frac{8}{7}right),left(-frac{32}{7},-frac{32}{7}right) ) в. ( left(frac{8}{7}, frac{8}{7}right),left(frac{32}{7}, frac{32}{7}right) ) ( ^{mathbf{c}} cdotleft(-frac{8}{7},-frac{8}{7}right),left(frac{32}{7}, frac{32}{7}right) ) D. None of these | 11 |

446 | If ( A(3, y) ) is equidistant from points ( P(8,-3) ) and ( Q(7,6), ) find the value of ( y ) and find the distance ( boldsymbol{A} boldsymbol{Q} ) | 11 |

447 | n figure, ( l, m ) and ( n ) are parallel lines intersected by transversal ( boldsymbol{p} ) at ( boldsymbol{X}, boldsymbol{Y} ) and ( Z ) respectively. Find ( angle 1, angle 2 ) and ( angle 3 ) | 11 |

448 | ( P ) is the point (-5,3) and ( Q ) is the point ( (-5, m) . ) If the length of the straight line PQ is 8 units, the the possible value of “m”‘ is: A ( .-5 ) and 5 B. – 5 or 11 c. -5 or -11 D. 5 or 11 | 11 |

449 | ( boldsymbol{A}(mathbf{3}, mathbf{4}) ) and ( boldsymbol{B}(mathbf{5},-mathbf{2}) ) are two given points. If ( boldsymbol{A P}=boldsymbol{P B} ) and area of ( triangle P A B=10, ) then ( P ) is A. (7,1) () B. (7,2) c. (-7,2) D. (-7,-1) | 11 |

450 | Equation of the line through the point of intersection of the lines ( 3 x+2 y+4= ) 0 and ( 2 x+5 y-1=0 ) whose distance from (2,-1) is ( 2, ) is A. ( 2 x-y+5=0 ) B. ( 4 x+3 y+5=0 ) c. ( x+2=0 ) D. ( 3 x+y+5=0 ) | 11 |

451 | Plot the points ( A(1,-1), B(-1,4) ) and ( C(-3, ) -1) on a graph paper to obtain the triangle ABC. Give a special name to the triangle ( A B C ) and, if possible, find its area. | 11 |

452 | Find the distance between the parallel lines ( 3 x+2 y=7 ) and ( 9 x+6 y=5 ) | 11 |

453 | Find the slope of a line passing through the following points: ( left(a t_{1}^{2}, 2 a t_{1}right) ) and ( left(a t_{2}^{2}, 2 a t_{2}right) ) A. ( frac{2}{t_{2}-t_{1}} ) в. ( frac{2}{t_{2}+t_{1}} ) c. ( frac{1}{t_{2}+t_{1}} ) D. None of these | 11 |

454 | Let ( alpha ) be the distance between the lines ( -x+y=2 ) and ( x-y=2, ) and ( beta ) be the distance between the lines ( 4 x-3 y=5 ) and ( 6 y-8 x=1, ) then find ( alpha ) and ( beta ) | 11 |

455 | If ( theta ) is the angle between the pair of straight lines ( x^{2}-5 x y+4 y^{2}+3 x- ) ( 4=0, ) then ( tan ^{2} theta ) is equal to ( A cdot frac{9}{16} ) в. ( frac{16}{25} ) c. ( frac{9}{25} ) D. ( frac{21}{25} ) E ( cdot frac{25}{9} ) | 11 |

456 | The line L given by ( frac{x}{5}+frac{y}{b}=1 ) passes through the point ( (13,32) . ) The line ( mathrm{K} ) is parallel to L and has the equation ( frac{x}{e}+ ) ( frac{y}{3}=1 . ) Then the distance between L and K is A. ( frac{23}{sqrt{15}} ) в. ( sqrt{17} ) c. ( frac{17}{sqrt{15}} ) D. ( frac{23}{sqrt{17}} ) | 11 |

457 | Show that the points ( A(2,-2), B(8,4), C(5,7), D(-1,1) ) are the vertices of a rectangle. | 11 |

458 | Let ( A B C D ) be a square of side ( 2 a . ) Find the coordinates of the vertices of this square when (i) A coincides with the origin and ( A B ) and ( A D ) are along ( O X ) and ( O Y ) respectively. (ii) The centre of the square is at the origin and coordinate axes are parallel to the sides ( A B ) and ( A D ) respectivey. | 11 |

459 | Find the distances between the following pair of parallel lines: ( mathbf{3} boldsymbol{x}+mathbf{4} boldsymbol{y}=mathbf{1 3}, mathbf{3} boldsymbol{x}+mathbf{4} boldsymbol{y}=mathbf{3} ) | 11 |

460 | Find the ratio in which the line ( 2 x+ ) ( 3 y-5=0 ) divides the line segment joining the points (8,9) and ( (2,1) . ) Also, find the coordinates of the point of division. | 11 |

461 | ( A ) line cuts the ( x ) -axis at ( A(7,0) ) and the y-axis at ( B(0,-5), ) A variable line ( P Q ) is drawn perpendicular to ( A B ) cutting the x-axis at ( boldsymbol{P} ) and the ( y ) -axis at in ( boldsymbol{Q} ) If ( A Q ) and ( B P ) intersect at ( R, ) the locus | 11 |

462 | I : Length of the perpendicular from ( left(x_{1}, y_{1}right) ) to the line ( a x+b y+c=0 ) is ( left|frac{boldsymbol{a} boldsymbol{x}_{1}+boldsymbol{b} boldsymbol{y}_{1}+boldsymbol{c}}{sqrt{boldsymbol{a}^{2}+boldsymbol{b}^{2}}}right| ) II : The equation of the line passing through (0,0) and perpendicular to ( a x+b y+c=0 ) is ( b x-a y=0 . ) Then which of the following is true? A. only I B. only II c. both 18 ॥ D. neither I nor II | 11 |

463 | If the segments joining the points ( A(a, b) ) and ( B(c, d) ) studends an angle at the origin, prove that ( cos theta= ) ( frac{boldsymbol{a c}+boldsymbol{b} boldsymbol{d}}{sqrt{left(boldsymbol{a}^{2}+boldsymbol{b}^{2}right)left(boldsymbol{c}^{2}+boldsymbol{d}^{2}right)}} ) | 11 |

464 | Find the equation of a straight line: with slope 2 and ( y- ) intercept 3 | 11 |

465 | The perpendicular distance of the origin from the lines ( 2 x+5 y=20 ) and ( 5 x+ ) ( 2 y=20 ) are same. A. True B. False | 11 |

466 | The area of the triangle formed by the ( operatorname{lines} x+y=3, x-3 y+9=0 ) and ( 3 x-2 y+1=0 ) is A ( -frac{16}{7} ) sq. units B ( cdot frac{10}{7} ) sq. units c. 4 sq. units D. 9 sq. units | 11 |

467 | Determine the ratio in which the point ( P(3,5) ) divides the join of ( A(1,3) & ) ( boldsymbol{B}(mathbf{7}, mathbf{9}) ) | 11 |

468 | If the two lines represented by ( x^{2}left(tan ^{2} theta+cos ^{2} thetaright)-2 x y tan theta+ ) ( boldsymbol{y}^{2} sin ^{2} boldsymbol{theta}=mathbf{0} ) make angles ( boldsymbol{alpha}, boldsymbol{beta} ) with the ( x ) -axis, then This question has multiple correct options ( A cdot tan alpha+tan beta=4 operatorname{cosec} 2 theta ) ( mathbf{B} cdot tan alpha tan beta=sec ^{2} theta+tan ^{2} theta ) c. ( tan alpha-tan beta=2 ) D. ( frac{tan alpha}{tan beta}=frac{2+sin 2 theta}{2-sin 2 theta} ) | 11 |

469 | Find the distance between (2,3,-5) and (1,6,3) | 11 |

470 | Find the cosine of the angle ( A ) of the triangle with vertices ( boldsymbol{A}(mathbf{1},-mathbf{1}), boldsymbol{B}(boldsymbol{6}, mathbf{1 1}) ) and ( boldsymbol{C}(mathbf{1}, boldsymbol{2}) ) | 11 |

471 | Find the equation of a straight line: with slope ( -1 / 3 ) and ( y- ) intercept -4 | 11 |

472 | 9. (1983 – 2 Marks) Two equal sides of an isosceles triangle are given by the equations 7x – y + 3 = 0 and x + y – 3 = 0 and its third side passes through the point (1, -10). Determine the equation of the third side. (1984 – 4 Marks) | 11 |

473 | 12. Let PS be the median of the triangle with vertices 96,-1) and R(7,3). The equation of the line passing through (1,-1) and parallel to PS is (2000) (a) 2x -9y-7=0 (b) 2x – 9y-11 = 0 (c) 2x+91-11=0 (d) 2x+9y+7=0 | 11 |

474 | The graph of the line ( y=6 ) is a line that is: A. Parallel to x-axis at a distance of 6 units from the origin B. Parallel to y-axis at a distance of 6 units from the origin c. Making an intercept of 6 units on the x-axis D. Making an intercept of 6 units on both the axes. | 11 |

475 | VII 26. – V15 ne lines L, :y- x = 0 and L, : 2x + y=0 intersect the line 3.+ 2 = 0 at P and respectively. The bisector of the acute angle between L, and L, intersects L3 at R. tatement-1: The ratio PR:RQ equals 212:15 ement-2: In any triangle, bisector of an angle divides the triangle into two similar triangles. [2011] (a) Statement-1 is true. Statement-2 is true; Statement-2 15 not a correct explanation for Statement-1. (6) Statement-1 is true, Statement-2 is false. Statement-1 is false, Statement-2 is true. (d) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Iftbe 1 | 11 |

476 | Find the co-ordinate of points on ( x ) -axis which are at a distance of 5 units form the point ( (mathbf{6},-mathbf{3}) ) | 11 |

477 | Find the distance between the points (2,1) and (3,2) | 11 |

478 | Two rails are algebraically represented by the equations ( 3 x-5 y-20=0 ) and ( 6 x- ) ( 10 y+40=0 ) | 11 |

479 | Find the slope of the line that passes through the points (7,4) and (-9,4) ( A cdot O ) B. ( c cdot-1 ) ( D cdot 2 ) | 11 |

480 | Find the perimeter of the triangles whose vertices have the following coordinates ( (mathbf{3}, mathbf{1 0}),(mathbf{5}, mathbf{2}),(mathbf{1 4}, mathbf{1 2}) ) | 11 |

481 | Find the inclination of a line whose slope is (i) 1 (ii) -1 (iii) ( sqrt{3} ) ( (i v)-sqrt{3} ) ( (v) frac{1}{sqrt{3}} ) | 11 |

482 | Classify the following pair of line as coincident, parallel or intersecting ( boldsymbol{x}-mathbf{2} boldsymbol{y}+mathbf{3}=mathbf{0} ) & ( mathbf{3} boldsymbol{x}-mathbf{6} boldsymbol{y}+mathbf{9}=mathbf{0} ) A. Parallel B. Intersecting c. coincident D. None of these | 11 |

483 | Find the slope of the line passing the two given points ( (a, 0) ) and ( (0, b) ) | 11 |

484 | A line passes through ( left(x_{1}, y_{1}right) ) and ( (h, k) ) If slope of the line is ( m ), show that ( k- ) ( boldsymbol{y}_{1}=boldsymbol{m}left(boldsymbol{h}-boldsymbol{x}_{1}right) ) | 11 |

485 | If the distances of ( boldsymbol{P}(boldsymbol{x}, boldsymbol{y}) ) from ( boldsymbol{A}(-1,5) ) and ( boldsymbol{B}(mathbf{5}, 1) ) are equal, then A ( .2 x=y ) в. ( 3 x=2 y ) c. ( 3 x=y ) D. ( 2 x=3 y ) | 11 |

486 | Given ( f(x) ) is a linear function and ( boldsymbol{f}(mathbf{2})=mathbf{3} ) and ( boldsymbol{f}(-mathbf{6})=-mathbf{1 3} . ) Find ( boldsymbol{y} ) intercept of ( boldsymbol{f}(boldsymbol{x}) ) A . -1 B. c. 1 D. | 11 |

487 | Write the inclination of a line which is parallel to x-axis. | 11 |

488 | Find the distance between the following pair of points. (-2,-3) and (3,2) | 11 |

489 | find the acute angle between ( y=5 x+ ) 6 and ( y=x ) | 11 |

490 | Find the area of the triangle whose vertices are (10,-6),(2,5) and (-1,3) | 11 |

491 | The equation of an altitude of an equilateral triangle is ( sqrt{mathbf{3}} x+y=2 sqrt{3} ) and one of the vertices is ( (3, sqrt{3}), ) then the possible number of triangles are, ( mathbf{A} cdot mathbf{1} ) B . 2 ( c cdot 3 ) D. 4 | 11 |

492 | The diagonals of a parallelogram ( P Q R S ) are along the lines ( x+3 y=4 ) and ( 6 x-2 y=7 . ) Then ( P Q R S ) must be ( a ) A. rectangle B. square c. cyclic quadrilateral D. rhombus | 11 |

493 | Find the point on the curve ( y=x^{3}- ) ( 2 x^{2}-x, ) where the tangents are parallel to ( 3 x-y+1=0 ) | 11 |

494 | Consider the points ( boldsymbol{A}(mathbf{0}, mathbf{1}) ) and ( boldsymbol{B}(mathbf{2}, mathbf{0}) ) and the ( P ) be a point on the line ( 4 x+ ) ( 3 y+9=0 . ) Coordinates of ( P ) such that ( |boldsymbol{P} boldsymbol{A}-boldsymbol{P} boldsymbol{B}| ) is maximum are ( mathbf{A} cdotleft(-frac{12}{5}, frac{17}{5}right) ) B ( cdotleft(-frac{18}{5}, frac{9}{5}right) ) ( ^{mathbf{C}} cdotleft(-frac{6}{5}, frac{17}{5}right) ) D ( cdot(0,-3) ) | 11 |

495 | The coordinates of the point ( P(x, y) ) which divides the line segment joining the points ( boldsymbol{A}left(boldsymbol{x}_{1}, boldsymbol{y}_{1}right) ) and ( boldsymbol{B}left(boldsymbol{x}_{2}, boldsymbol{y}_{2}right) ) internally in the ratio ( m_{1}: m_{2} ) are ( left(frac{m_{1} x_{2}-m_{2} x_{1}}{m_{1}+m_{2} 1}, frac{m_{1} y_{2}-m_{2} y_{1}}{m_{1}+m_{2}}right) ) A . True B. False c. Ambiguous D. Data insufficient | 11 |

496 | Find the value ( k ). for which the point ( (-1, ) 3) lies on the graph of the equation ( 2 x- ) ( y+k=0 ) | 11 |

497 | Find the area of the triangle with vertices at the points: (0,0),(6,0) and (4,3) | 11 |

498 | ху 25. The line L given by + = 1 passes through the point (13, 32). The line K is parallel to L and has the equation – + =1. Then the distance between L and Kis [2010] c3 | 11 |

499 | A triangle has vertices at ( (mathbf{6}, mathbf{7}),(mathbf{2},-mathbf{9}) ) and ( (-4,1) . ) Find the slope of its sides. A ( cdot frac{11}{7},-13,-frac{1}{4} ) в. ( frac{11}{7}, 13,-frac{1}{4} ) c. ( frac{11}{7},-13, frac{1}{4} ) D. None of these | 11 |

500 | The angle between the lines ( 2 x+ ) ( 11 y-7=0 ) and ( x+3 y+5=0 ) is equal to A ( cdot tan ^{-1}left(frac{17}{31}right) ) B. ( tan ^{-1}left(frac{11}{35}right) ) ( ^{mathbf{c}} cdot tan ^{-1}left(frac{1}{7}right) ) D ( cdot tan ^{-1}left(frac{33}{35}right) ) E ( cdot tan ^{-1}left(frac{7}{33}right) ) | 11 |

501 | 35. Consider the set of Consider the set of all lines px + ay+r=0 such that 3p + 2q + 4r = 0. Which one of the following statements is true? JJEEM 2019-9 Jan (M) (a) The lines are concurrent at the point (6) Each line passes through the origin. (c) The lines are all parallel. (d) The lines are not concurrent. | 11 |

502 | If the point ( P(2,1) ) lies on the segment joining Points ( A(4,2) ) and ( B(8,4) ) then ( ^{mathbf{A}} cdot A P=frac{1}{3} A B ) B. AB = PB ( c cdot p B=frac{1}{3} A B ) D. ( A P=frac{1}{2} A B ) | 11 |

503 | On an xy-graph, what is the length of a line segment drawn from (3,7) to (6,5) ( ? ) A ( cdot sqrt{13} ) B . 16 c. 17 D. 18 E . 20 | 11 |

504 | The slope and y-intercept of the following line are respectively ( mathbf{7} boldsymbol{x}-boldsymbol{y}+mathbf{3}=mathbf{0} ) A. slope ( =m=7 / 3 ) and ( y- ) intercept ( =1 ) B. slope ( =m=-7 ) and ( y- ) intercept ( =3 ) c. slope ( =m=-7 / 3 ) and ( y- ) intercept ( =1 ) D. slope ( =m=7 ) and ( y- ) intercept ( =3 ) | 11 |

505 | If the angle between two lines is ( pi / 4 ) and slope of one of the line is ( 1 / 2, ) find the slope of the other line. | 11 |

506 | Two straight lines ( u=0 ) and ( v=0 ) pass through the origin and angle between them is ( tan ^{-1}left(frac{7}{9}right) . ) If the ratio of the slope of ( v=0 ) and ( u=0 ) is ( frac{9}{2} ) then their equations are This question has multiple correct options A. ( y+3 x=0 ) and ( 3 y+2 x=0 ) B. ( 2 y+3 x=0 ) and ( 3 y+x=0 ) c. ( 2 y=3 x ) and ( 3 y=x ) D. ( y=3 x ) and ( 3 y=2 x ) | 11 |

507 | (a) What is the slope of the line joining the points ( A(2,-3) ) and ( B(6,3) ? ) Find the equation of this line. (b) Find the co-ordinates of the point ( C ) at which the line cuts the ( x ) -axis. (c) Show that ( C ) is the mid-point of the line ( boldsymbol{A B} ) | 11 |

508 | The ends of a quadrant of a circle have the coordinates (1,3) and ( (3,1) . ) Then the centre of such a circle is A. (2, 2) B. (1,1) ( c cdot(4,4) ) ( D cdot(2,6) ) | 11 |

509 | Find the vertices of the triangle whose mid point of sides are (3,1),(5,6) and (-3,2) A ( cdot(-1,7)(-5,-3)(6,5) ) B . (7,1)(2,3)(4,1) c. (-1,7)(-5,-3)(11,5) D. (1,7)(5,3)(-11,5) | 11 |

510 | The ratio which divides the line joining the points (2,3) and ( (4,2), ) also divides the segment joining the point (1,2) and (4,3) is A .1: 2 B. ( (3: 1) ) c. ( (1: 4) ) D. 1: 1 | 11 |

511 | The number of lines which pass through point (2,-3) and are at a distance 8 from point (-1,2) is ( A cdot infty ) B. 4 ( c cdot 2 ) D. | 11 |

512 | The distance from origin to (5,12) is A . 13 B. 17 c. 10 D. 7 | 11 |

513 | Find the distance between (8,3) and (3,2) | 11 |

514 | ( left(2,30^{circ}right) ) and ( left(4,120^{circ}right) ) | 11 |

515 | If one diagonal of a square is along the line ( x=2 y ) and one of its vertices is ( (3,0), ) then its sides through this vertex are given by the equations A. ( y-3 x+9=0,3 y+x-3=0 ) B. ( y+3 x+9=0,3 y+x-3=0 ) c. ( y+3 x+9=0,3 y-x+3=0 ) D. ( y-3 x+3=0,3 y+x+9=0 ) | 11 |

516 | Two points ( (a, 3) ) and ( (5, b) ) are the opposite vertices of a rectangle. If the other two vertices lie on the line ( y= ) ( 2 x+c ) which also passes through the point ( (boldsymbol{a} / boldsymbol{c}, boldsymbol{b} / boldsymbol{c}) ) then what is the value of c? This question has multiple correct options A ( cdot 2 sqrt{2}+1 ) B. ( 2 sqrt{2}-1 ) c. ( 1-2 sqrt{2} ) D. ( -1-2 sqrt{2} ) | 11 |

517 | Find the coordinates of the points of trisection of the line segment joining (1,-2) and (-3,4) | 11 |

518 | Find, if possible, the slope of the line through the points (2,5) and (-4,5) | 11 |

519 | In the given figure, ( m | n ) and ( angle 1=50^{circ} ) then find ( angle mathbf{5} ) A ( cdot 130^{circ} ) В. ( 60^{circ} ) ( c cdot 70^{circ} ) D. ( 180^{circ} ) | 11 |

520 | Consider a triangle ( A B C, ) whose vertical ( operatorname{are} A(-2,1), B(1,3) ) and ( C(x, y) ).ff ( C ) is a moving point such that area of ( Delta A B C ) is constant,then locus of ( C ) is: A. staight line B. Circle c. Ray D. Parabola | 11 |

521 | Find a point on the ( x ) -axis which is equidistant from the points (7,6) and (3,4) | 11 |

522 | (5,-2),(6,4) and (7,-2) are the vertices of a – m…. triangle. A. equilateral B. right angle c. scalene D. isosceles | 11 |

523 | If the lines ( frac{x-1}{2}=frac{y+1}{3}=frac{z}{5 t-1} ) and ( frac{boldsymbol{x}+mathbf{1}}{mathbf{2} boldsymbol{s}+mathbf{1}}=frac{boldsymbol{y}}{mathbf{2}}=frac{boldsymbol{z}}{mathbf{4}} ) are parallel to each other, then value of s,t will be A ( cdot_{6,} frac{5}{7} ) B. ( frac{1}{2}, 1 ) c. ( _{3,} frac{5}{7} ) D. ( 4, frac{7}{10} ) | 11 |

524 | Three sides ( A B, B C ) and ( C A ) of a triangle ( A B C ) are ( 5 x-3 y+2=0, x- ) ( 3 y-2=0 ) and ( x+y-6=0 ) respectively. Find the equation of the altitude through the vertex ( boldsymbol{A} ) | 11 |

525 | A straight line through origin 0 meets the lines ( 3 y=10-4 x ) and ( 8 x+6 y+ ) ( 5=0 ) at points ( A ) and ( B ) respectively Then 0 divides the segment ( A B ) in the ratio: A .2: 3 B. 1: 2 c. 4: 1 D. 3: 4 | 11 |

526 | n Fig 3.13 line ( D E | ) line ( G F ) ray ( E G ) and ray ( F G ) are bisectors of ( angle D E F ) and ( angle D F M ) respectively. Prove that. (i) ( angle D E G=frac{1}{2} angle E D F ) (ii) ( boldsymbol{E} boldsymbol{F}=boldsymbol{F} boldsymbol{G} ) | 11 |

527 | The portion of a line intercepted between the coordinate axes is divided by the point (2,-1) in the ration ( 3: 2 . ) The equation of the line is : A. ( 5 x-2 y-20=0 ) В. ( 2 x-y+7=0 ) c. ( x-3 y-5=0 ) D. ( 2 x y+y-4=0 ) | 11 |

528 | If the lines ( x+2 y+3=0, x+2 y- ) ( mathbf{7}=mathbf{0} ) and ( mathbf{2} boldsymbol{x}-boldsymbol{y}-mathbf{4}=mathbf{0} ) are the sides of a square, then equation of the remaining sides of the square can be This question has multiple correct options A. ( 2 x-y+6=0 ) В. ( 2 x-y+8=0 ) c. ( 2 x-y-10=0 ) D. ( 2 x-y-14=0 ) | 11 |

529 | Find the area of the triangle whose vertices are: ( (mathrm{i})(2,3),(-1,0),(2,-4) ) ( (i i)(-5,-1),(3,-5),(5,2) ) This question has multiple correct options A. (i) 32 sq. units B. (ii) 32 sq. units c. (ii) 10.5 sq. units D. (i) 10.5 sq. units | 11 |

530 | Show that ( boldsymbol{A}(mathbf{2}, mathbf{3}), boldsymbol{B}(mathbf{4}, mathbf{5}) ) and ( boldsymbol{C}(mathbf{3}, mathbf{2}) ) can be the vertices of a rectangle. Find the coordinates of the fourth vertex | 11 |

531 | (u) trombus. Tethe vertices P, Q, R of a triangle PQR are rational points. which of the following points of the triangle PQR is (are) always rational point(s)? (1998 – 2 Marks) (a) centroid (b) incentre (c) circumcentre (d) orthocentre A rational point is a point both of whose co-ordinates are rational numbers.) | 11 |

532 | ( A(3,-4), B(5,-2), C(-1,8) ) are the vertices of ( triangle A B C . D, E, F ) are the midpoints of sides ( overline{B C}, overline{C A} ) and ( overline{A B} ) respectively. Find area of ( triangle A B C . ) Using coordinates of ( D, E, F, ) find area of ( triangle D E F . ) Hence show that the ( A B C= ) ( mathbf{4}(D E F) ) | 11 |

533 | In the given figure, if line ( A B | ) line ( C F ) and line BC || line ED then prove that ( angle A B C=angle F D E ) | 11 |

534 | Let the perpendiculars from any point on the line ( 2 x+11 y=5 ) upon the lines ( 24 x+7 y-20=0 ) and ( 4 x-3 y-2= ) 0 have the lengths ( p_{1} ) and ( p_{2} ) respectively. Then, A ( cdot 2 p_{1}=p_{2} ) B . ( p_{1}=p_{2} ) ( mathbf{c} cdot p_{1}=2 p_{2} ) D. None of these | 11 |

535 | The area of a triangle is 5 sq.unit. If two vertices of the triangle are (2,1),(3,-2) and the third vertex is ( (x, y) ) where ( y=x+3, ) then find the coordinates of the third vertex. | 11 |

536 | A line through (-5,2) and (1,-4) is perpendicular to the line through ( (x,-7) ) and (8,7) Find the ( x ) A . -4 B. -5 ( c .-6 ) D. ( frac{-19}{3} ) E. none of these | 11 |

537 | ( left{boldsymbol{a} boldsymbol{m}_{1} boldsymbol{m}_{2}, boldsymbol{a}left(boldsymbol{m}_{1}+boldsymbol{m}_{2}right)right},left{boldsymbol{a} boldsymbol{m}_{2} boldsymbol{m}_{3}, boldsymbol{a}(boldsymbol{m}right. ) | 11 |

538 | Find the slope of a line which is parallel to the line ( 8 x+9 y=3 ) A. -8 в. ( -frac{8}{9} ) ( c cdot frac{8}{3} ) D. 3 E . 8 | 11 |

539 | In the given figure, ( angle B=65^{circ} ) and ( angle C=45^{circ} ) in ( triangle A B C ) and ( D A E | B C . ) If ( angle D A B=x^{o} ) and ( angle E A C=y^{o} ) and ( angle E A C=y^{o}, ) find the values of ( x ) and ( y ) | 11 |

540 | Find the slope of line ( l ), which is the perpendicular bisector of the line segment with endpoints (2,0) and (0,-2) A . 2 B. c. 0 D. – E. -2 | 11 |

541 | Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0,-1),(2,1) and ( (0,3) . ) Find the ratio of this area to the area of the given triangle. | 11 |

542 | In what ratio does the point ( P(p,-1) ) divide the line segment joining the points ( A(1,-3) ) and ( B(6,2) ? ) Hence, find the value of ( mathrm{p} ) | 11 |

543 | ( 21-3(b-7)=b+20 ) | 11 |

544 | 27. A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinate axes at points Pand Q. Find the absolute minimum value of OP+0Q, as L varies, where O is the origin. (2002 – 5 Marks) | 11 |

545 | Show that ( A B C D ) is a square where ( A, B, C, D ) are the points (0,4,1),(2,3,-1),(4,5,0) and (2,6,2) respectively. | 11 |

546 | 17. If (a,a?) falls inside the angle made by the lines y = x>0 and y = 3x, x > 0, then a belong to [2006] (a) (0,5) (6) (3,00) | 11 |

547 | Find the equation of line equally inclined to coordinate axes and passes through (-5,1,-2) | 11 |

548 | Find the area of square whose one pair of the opposite vertices are (3,4) and ( (5, ) 6) | 11 |

549 | The area of a triangle is 5 and its two vertices are ( boldsymbol{A}(mathbf{2}, mathbf{1}) ) and ( boldsymbol{B}(mathbf{3},-mathbf{2}) . ) The third vertex lies on ( y=x+3 . ) Then third vertex is This question has multiple correct options A ( cdotleft(frac{7}{2}, frac{13}{2}right) ) в. ( left(frac{5}{2}, frac{5}{2}right) ) ( ^{c} cdotleft(-frac{3}{2}, frac{3}{2}right) ) D. (0,0) | 11 |

550 | The distance of the point (1,2) from the line ( x+y+5=0 ) measured along the line parallel to ( 3 x-y=7 ) is equal to A ( cdot frac{4}{sqrt{10}} ) B. 40 c. ( sqrt{40} ) D. ( 10 sqrt{2} ) | 11 |

551 | Find the length of the perpendicular from the point (4,-7) to the line joining the origin and the point of intersection of the ( 2 x-3 y+14=0 ) and ( 5 x+5 y- ) ( mathbf{7}=mathbf{0} ? ) | 11 |

552 | The distance between (-4,-5) and (-4,-10) is units. A . 15 B. 10 ( c .5 ) D. | 11 |

553 | If the straight line ( a x+b y+p=0 ) and ( x cos alpha+y sin alpha=p ) enclosed an angle of ( frac{pi}{4} ) and the line ( x sin alpha-y cos alpha=0 ) meets them at the same point, the ( a^{2}+b^{2} ) is A .4 B. 3 ( c cdot 2 ) D. | 11 |

554 | The distance formula between two points ( Aleft(x_{1}, y_{1}right) ) and ( Bleft(x_{2}, y_{2}right) ) is given by A ( cdotleft(x_{1}-x_{2}right)^{2}+left(y_{1}-y_{2}right)^{2} ) B . ( left(x_{2}-x_{1}right)^{2}+left(y_{2}-y_{1}right)^{2} ) c. ( sqrt{left(x_{2}-x_{1}right)^{2}+left(y_{2}-y_{1}right)^{2}} ) D. None of the above | 11 |

555 | Find the coordinates of the points where the graph of the equation ( 3 x+4 y=21 ) intersect ( x- ) axis and ( y- ) axis. | 11 |

556 | Find the angle between the curves given below: ( boldsymbol{y}^{2}=boldsymbol{4} boldsymbol{x}, boldsymbol{x}^{2}+boldsymbol{y}^{2}=mathbf{5} ) | 11 |

557 | Find the slope of the line that passes through the points (2,0) and (2,4) | 11 |

558 | If ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{2} boldsymbol{h} boldsymbol{x} boldsymbol{y}+boldsymbol{b} boldsymbol{y}^{2}+boldsymbol{2} boldsymbol{g} boldsymbol{x}+boldsymbol{2} boldsymbol{f} boldsymbol{y}+ ) ( c=0 ) represents a pair of parallel lines, then ( sqrt{frac{g^{2}-a c}{f^{2}-b c}}= ) A. B. ( sqrt{frac{a}{b}} ) ( c cdot sqrt{frac{b}{a}} ) ( D cdot frac{b}{a} ) | 11 |

559 | Find ( k ) if ( P Q | ) RS and ( boldsymbol{P}(mathbf{2}, boldsymbol{4}) boldsymbol{Q}(boldsymbol{3}, boldsymbol{6}), boldsymbol{R}(boldsymbol{3}, boldsymbol{1}), boldsymbol{S}(boldsymbol{5}, boldsymbol{k}) ) | 11 |

560 | Find the angles of inclination of straight lines whose slopes are ( sqrt{mathbf{3}} ) | 11 |

561 | Find the angle between the lines whose direction cosines satisfy the equation ( ell+boldsymbol{m}+boldsymbol{n}=mathbf{0}, ell^{2}+boldsymbol{m}^{2}-boldsymbol{n}^{2}=mathbf{0} ) | 11 |

562 | The line segment joining the points ( (-3, ) -4 ) and (1,-2) is divided by the ( y ) -axis in the ratio ( A cdot 1: 3 ) B. 3:1 ( c cdot 2: 3 ) D. 3:2 | 11 |

563 | A line passing through the points ( (a, 2 a) ) and (-2,3) is perpendicular to the line ( 4 x+3 y+5=0, ) find the value of a. | 11 |

564 | Find the inclination of the line whose slope is 0 | 11 |

565 | An equilateral triangle is constructed between two parallel line ( sqrt{mathbf{3}} x+boldsymbol{y}- ) ( 6=0 ) and ( sqrt{3} x+y+9=0 ) with base on one and vertex on the other. Then the area of triangle is ? | 11 |

566 | The line through (1,5) parallel to ( x ) -axis is A. ( x=1 ) B. ( y=5 ) c. ( y=1 ) D. x = 5 | 11 |

567 | If the distance between the points ( (k,-1) ) and (3,2) is ( 5, ) then the value of k is A . 2 B. -2 ( c cdot-1 ) D. | 11 |

568 | 28. A ray of light along x + V3y = 13 gets reflected upon reaching x-axis, the equation of the reflected ray is [JEEM 2013 (a) y=x+ 13 (b) V3y = x – 13 (C) y= V3x – 13 (d) V3y = x-1 | 11 |

569 | Find the distance between the following pair of points: ( (a, 0) ) and ( (0, b) ) | 11 |

570 | Find what straight lines are represented by the following equation and determine the angles between them. ( boldsymbol{x}^{2}+2 boldsymbol{x} boldsymbol{y} cot boldsymbol{theta}+boldsymbol{y}^{2}=mathbf{0} ) | 11 |

571 | The distance between the points ( (0,0),left(x_{1}, y_{1}right) ) is units A ( cdot sqrt{x_{1}^{2}+y_{1}^{2}} ) в. ( sqrt{x_{1}+y_{1}} ) ( mathbf{c} cdot sqrt{x_{1}^{2}+y_{1}} ) ( mathbf{D} cdot sqrt{x_{1}+y_{1}^{2}} ) | 11 |

572 | Equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of ( 120^{circ} ) with ( x- ) axis is A ( . x sqrt{3}+y+8=0 ) в. ( x+sqrt{3} y=8 ) c. ( x sqrt{3}-y=8 ) D. ( x-sqrt{3} y+8=0 ) | 11 |

573 | The equation of the bisector of the angle between the lines ( 3 x-4 y+7=0 ) and ( 12 x+5 y-2=0 ) A. ( 11 x+3 y-9=0 ) B. ( 3 x-11 y+9=0 ) c. ( 11 x-3 y-9=0 ) D. ( 11 x-3 y+9=0 ) | 11 |

574 | The area of the triangle formed by the points (2,6),(10,0) and ( (0, k) ) is zero square units. Find the value of ( k ) A ( cdot frac{15}{2} ) B. ( frac{3}{2} ) ( c cdot frac{7}{2} ) D. ( frac{13}{2} ) | 11 |

575 | The lines represented by ( 3 x+4 y=8 ) and ( p x+2 y=7 ) are parallel. Find the value of ( p ) | 11 |

576 | The distance between the lines ( 4 x+ ) ( 3 y=11 ) and ( 8 x+6 y=15 ) is : ( A cdot frac{7}{2} ) B. ( frac{7}{3} ) ( c cdot frac{7}{5} ) D. ( frac{7}{10} ) | 11 |

577 | The distance between the pair of parallel lines ( x^{2}+2 x y+y^{2}-8 a x- ) ( 8 a y-9 a^{2}=0 ) is A ( .2 sqrt{5} a ) an в. ( sqrt{10} a ) ( c cdot 10 a ) D. ( 5 sqrt{2} a ) | 11 |

578 | Find the shortest distance of (3,4) from origin. | 11 |

579 | The equations to a pair of opposite sides of parallelogram are x2 – 5x + 6 = 0 and y2 – 6y + 5 = 0, the equations to its diagonals are (1994) (a) x+4y=13, y = 4x-7 (b) 4x+y=13, 4y=x-7 (c) 4x+y=13, y=4x-7 (d) y – 4x = 13, y + 4x=7 | 11 |

580 | 64. The equation of a line perpendie ular to x – 4y = 6 and passing through the intersection point of x-axis and y-axis, will be (1) x + 4y = 0 (2) 4x + y = 0 (3) x + 4y = 4 (4) 4x + y = 4 | 11 |

581 | The straight lines ( 4 x-3 y-5=0, x- ) ( 2 y-10=0,7 x+y-40=0 ) and ( x+ ) ( 3 y+10=0 ) form the sides of a A. plain quadrilateral B. cyclic quadrilateral c. rectangle D. parallelogram | 11 |

582 | Find the areas of the triangles the whose coordinates of the points are respectively. ( (a, b+c),(a, b-c) ) and ( (-a, c) ) | 11 |

583 | Find the slope of a line passing through the following points: ( (3-5) ) and (1,2) | 11 |

584 | Find the length of the perpendicular from the point (5,4) on the straight line. | 11 |

585 | A line ( 4 x+y=1 ) passes through the point ( boldsymbol{A}(mathbf{2},-mathbf{7}) ) and meets line ( boldsymbol{B} boldsymbol{C} ) at ( boldsymbol{B} ) whose equation is ( 3 x-4 y+1=0, ) the equation of line ( A C ) such that ( A B= ) ( boldsymbol{A C} ) is A ( .52 x+89 y+519=0 ) В. ( 52 x+89 y-519=0 ) c. ( 82 x+52 y+519=0 ) D. ( 89 x+52 y-519=0 ) | 11 |

586 | The straight line ( 3 x+4 y-12=0 ) meets the coordinate axes at ( A ) and ( B ). An equilateral triangle ( A B C ) is constructed. The possible coordinates of vertex ( C ) are This question has multiple correct options ( ^{mathbf{A}} cdotleft(2left(1-frac{3 sqrt{3}}{4}right), frac{3}{2}left(1-frac{4}{sqrt{3}}right)right) ) B ( cdotleft(-2(1+sqrt{3}), frac{3}{2}(1-sqrt{3})right) ) ( left(2(1+sqrt{3}), frac{3}{2}(1+sqrt{3})right) ) ( left(2left(1+frac{3 sqrt{3}}{4}right), frac{3}{2}left(1+frac{4}{sqrt{3}}right)right) ) | 11 |

587 | Show that the triangle whose vertices ( operatorname{are}(8,-4),(9,5) ) and (0,4) is an isosceles triangle. | 11 |

588 | Find the slope of the line having its inclination ( 60^{circ} ) | 11 |

589 | The vertices of triangle ( A B C ) are ( boldsymbol{A}(mathbf{1},-mathbf{2}), boldsymbol{B}(-mathbf{7}, mathbf{6}) ) and ( boldsymbol{C}(mathbf{1 1} / mathbf{5}, mathbf{2} / mathbf{5}) ) | 11 |

590 | Find the slope of line which passes through the point (7,11) and (9,15) | 11 |

591 | Find the angle subtended at the origin by the line segment whose end points ( operatorname{are}(0,100) ) and (10,0) | 11 |

592 | The equation of the line which is parallel to ( 3 cos theta+4 sin theta+frac{5}{r}=0 ) ( cos theta+4 sin theta+frac{10}{r}=0 ) and equidistant from these lines is ( ^{mathbf{A}} cdot_{3 cos theta}+4 sin theta-frac{5}{r}=0 ) B. ( 3 cos theta+4 sin theta+frac{15}{r}=0 ) c. ( 6 cos theta+8 sin theta+frac{15}{r}=0 ) D. ( 6 cos theta+8 sin theta-frac{15}{r}=0 ) | 11 |

593 | Find the angle of inclination of straight line whose slope is ( frac{1}{sqrt{3}} ) | 11 |

594 | Find the slope of the line passing through the following points ( M(4,0) ) and ( Q(-3,-2) ) A ( cdot frac{2}{7} ) B. ( frac{7}{3} ) ( c cdot frac{1}{2} ) D. ( frac{8}{5} ) | 11 |

595 | ( P ) and ( Q ) are two points whose coordinates are ( left(a t^{2}, 2 a tright) a n dleft(frac{a}{t^{2}}, frac{-2 a}{t}right) ) respectively and ( mathrm{S} ) in the point ( (mathrm{a}, 0) . ) show that ( frac{1}{S P}+frac{1}{S Q} ) is independent of ( t ) | 11 |

596 | PULP Three distinct points A, B and C are given in the 2-dimensional coordinates plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (–1, 0) is equal to . Then the circumcentre of the triangle ABC is at the point: [2009] (a) 6.0) (> 65,0) (0) () (0,0) | 11 |

597 | The equation of the base of an equilateral triangle is ( mathbf{x}+mathbf{y}-mathbf{2}=mathbf{0} ) and the vertex is ( (2,-1), ) then the length of side is A . 1 в. 2 ( c .3 ) D. ( sqrt{frac{2}{3}} ) | 11 |

598 | The slope of a line perpendicular to ( mathbf{5} boldsymbol{x}+mathbf{3} boldsymbol{y}+mathbf{1}=mathbf{0} ) is A ( -frac{5}{3} ) в. ( frac{5}{3} ) c. ( -frac{3}{5} ) D. | 11 |

599 | Find the angle between two diameters of the ellipse ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1 ) Whose extremities have eccentricity angle a and ( beta=a+frac{pi}{2} ) | 11 |

600 | For the equation given below, find the slope and the y-intercept: ( boldsymbol{x}+mathbf{3} boldsymbol{y}+mathbf{5}=mathbf{0} ) A ( cdot frac{1}{3} ) and ( frac{5}{3} ) в. ( -frac{1}{3} ) and ( -frac{5}{3} ) ( mathrm{c} cdot_{-3} ) and ( frac{3}{5} ) D. 3 and ( -frac{5}{3} ) | 11 |

601 | In the given diagram(not drawn to scale), if ( A B | C D, A F|| B D ) and ( angle F C D=58^{circ}, ) then ( angle A F C= ) A ( cdot 108^{circ} ) B ( .126^{circ} ) ( c cdot 162^{circ} ) D. ( 98^{circ} ) | 11 |

602 | ( A B C D ) is a rectangle with ( A(-1,2) ) ( B(3,7) ) and ( A B: B C=4: 3 . ) If ( P ) is the centre of the rectangle then the distance of ( P ) from each corner is equal to A ( cdot frac{sqrt{41}}{2} ) B. ( frac{3 sqrt{41}}{4} ) c. ( frac{2 sqrt{41}}{3} ) D. ( frac{5 sqrt{41}}{8} ) | 11 |

603 | The value of ( k ) for which the lines ( 2 x+ ) ( mathbf{3} boldsymbol{y}+boldsymbol{a}=mathbf{0} ) and ( mathbf{5} boldsymbol{x}+boldsymbol{k} boldsymbol{y}+boldsymbol{a}=mathbf{0} ) represent family of parallel lines is ( A cdot 3 ) в. 4.5 ( c .7 .5 ) D. 15 | 11 |

604 | Prove that the points (3,0)(6,4) and (-1,3) are the vertices of a right angled isosceles triangle. | 11 |

605 | The point ( F ) has the co-ordinates (0,-8) IF the distance EF is 10 units, then the co-ordinates of E will be A. (-6,0) B. (6,0) c. (6,8) (年. ( 6,8,8) ) D. Either 1 or 2 | 11 |

606 | Identify the equation of a straight line passing through the point of intersection of ( boldsymbol{x}-boldsymbol{y}+mathbf{1}=mathbf{0} ) and ( mathbf{3} boldsymbol{x}+ ) ( boldsymbol{y}-mathbf{5}=mathbf{0} ) and perpendicular to one of them. A. ( x+y+3=0 ) в. ( x+y-3=0 ) c. ( x-3 y-5=0 ) D. ( x-3 y+5=0 ) | 11 |

607 | Find the slope of the line perpendicular to ( A B ) if ( A=(0,-5) ) and ( B=(-2,4) ) | 11 |

608 | If the coordinates of the one end of a diameter of a circle are (2,3) and the coordinates of its centre are (-2,5) then the coordinates of the other end of the diameter are: A. (-6,7) в. (6,-7) c. (6,7) (は) D. (-6,-7) | 11 |

609 | The angle made by the line joining the points (2,0) and ( (-4,2 sqrt{3}) ) with ( x ) axis is – A ( .120^{circ} ) В . ( 60^{circ} ) ( mathbf{c} cdot 150^{circ} ) D. ( 135^{circ} ) | 11 |

610 | Consider the following population and year graph, find the slope of the line ( A B ) and using it, find what will be the population in the year ( 2010 ? ) | 11 |

611 | If the straight line ( a x+b y+p=0 ) and ( x cos alpha+y sin alpha=p ) enclosed an angle of ( frac{pi}{4} ) and the line ( x sin alpha-y cos alpha=0 ) meets them at the same point, then ( a^{2}+b^{2} ) is A .4 B. 3 ( c cdot 2 ) D. | 11 |

612 | If the point ( left(boldsymbol{x}_{1}+boldsymbol{t}left(boldsymbol{x}_{2}-boldsymbol{x}_{1}right), boldsymbol{y}_{1}+right. ) ( left.tleft(y_{2}-y_{1}right)right) ) divides the join of ( left(x_{1}, y_{1}right) ) and ( left(x_{2}, y_{2}right) ) internally, then A. ( t<0 ) B. ( 0<t1 ) D. ( t=1 ) | 11 |

613 | The distance of the point ( P(6,8) ) from the origin is ( mathbf{A} cdot mathbf{8} ) B. ( 2 sqrt{7} ) c. 10 D. 6 | 11 |

614 | During the month of July, the number of units, ( y ), of a certain product sold per day can be modeled by the function ( y=-3.65 x+915, ) where ( x ) is the average daily temperature in degrees Fahrenheit. Find the statement which directly follows from the above equation. A. As the temperature increases, the number of units sold decreases. B. As the temperature increases, the number of units sold remains constant C. As the temperature increases, the number of units sold increases D. There is no linear relationship between temperature and the number of units sold | 11 |

615 | A rectangular hyperbola whose cente is C is cut by any circle of radius ( r ) in four point ( P, Q, R, ) S. The value of ( C P^{2}+ ) ( C Q^{2}+C R^{2}+C S^{2} ) is equal to: A ( cdot r^{2} ) B . ( 2 r^{2} ) ( c cdot 3 r^{2} ) D. ( 4 r^{2} ) | 11 |

616 | Find slope if ( theta=150^{circ} ) | 11 |

617 | The lines ( 3 x-4 y=4 ) and ( 6 x-8 y- ) ( mathbf{7}=mathbf{0} ) are tangents to the same circle. Then is radius is ? A ( cdot frac{1}{4} ) B. ( frac{1}{2} ) ( c cdot frac{3}{4} ) D. ( frac{3}{2} ) | 11 |

618 | Find an equation of the line through the points (-3,5) and (9,10) and write it in standard form ( A x+B y=C, ) with ( A> ) 0 A ( .6 x-10 y=-75 ) B. ( 5 x-12 y=-75 ) c. ( 4 x-11 y=-65 ) D. ( x-6 y=-15 ) | 11 |

619 | ( X, Y, Z, U ) are four points in a straight line. If distance from ( X ) to ( Y ) is ( 15, Y ) to ( Z ) is ( 5, Z ) to ( U ) is 8 and ( X ) to ( U ) is ( 2, ) what is the correct sequence of the points? A. ( X-Y-Z-U ) в. ( X-Z-Y-U ) c. ( X-U-Z-Y ) D. ( X-Z-U-Y ) | 11 |

620 | Find the distance between the two parallel straight lines ( boldsymbol{y}=boldsymbol{m} boldsymbol{x}+boldsymbol{c} ) and ( boldsymbol{y}=boldsymbol{m} boldsymbol{x}+boldsymbol{d} ) | 11 |

621 | A and ( mathrm{B} ) are the centres of two circles that just touch each other at ( P ) If ( A ) is ( (4,1), B ) is (2,2) and the radii of the circles are 2 and 3 respectively then ( P ) has coordinates ( A cdot(4,3) ) B. (3,3) ( c cdot(16 / 5,7 / 5) ) D. ( (4 / 5,4 / 5) ) | 11 |

622 | If a line ( A B ) makes an angle ( theta ) with ( O X ) and is at a distance of ( p ) units from the origin, then the equation of ( A B ) is A ( . x sin theta-y cos theta=p ) B. ( x cos theta+y sin theta=p ) ( mathbf{c} . x sin theta+y cos theta=p ) D. ( x cos theta-y sin theta=p ) | 11 |

623 | Find the length of the straight line joining the pairs of points whose polar coordinates are ( left(a, frac{pi}{2}right) ) and ( left(3 a, frac{pi}{6}right) ) | 11 |

624 | State whether the following statement is true or false. If ( P ) divides ( O A ) internally in the ratio | 11 |

625 | If in ( triangle A B C, A equiv(1,10), ) circumcentre ( equivleft(-frac{1}{3}, frac{2}{3}right) ) and orthocentre ( equiv ) ( left(frac{11}{3}, frac{4}{3}right), ) then the coordinates of midpoint of side opposite to ( A ) is A ( cdotleft(1,-frac{11}{3}right) ) в. (1,5) c. (1,-3) D. (1,6) | 11 |

626 | Find the point on the straight line ( 3 x+ ) ( boldsymbol{y}+mathbf{4}=mathbf{0} ) which is equidistant from the points (-5,6) and (3,2) | 11 |

627 | A straight line drawn through (1,2) intersects ( x+y=4 ) at a distance ( frac{sqrt{6}}{3} ) from ( (1,2) . ) The angle made by the line with the positive direction of ( x ) -axis is ( alpha . ) Find the greater of the two values of ( boldsymbol{alpha} ) A . ( 105^{circ} ) B ( cdot 75^{circ} ) ( c cdot 60^{0} ) D. ( 15^{circ} ) | 11 |

628 | Write the formula for area of a triangle where ( Aleft(x_{1}, y_{1}right), Bleft(x_{x}, y_{2}right) ) and ( Cleft(x_{3}, y_{3}right) ) are the vertices of a triangle ( A B C ) | 11 |

629 | The graph of ( x=5 ) is perpendicular to A. x-axis B. y-axis c. Line ( y=x ) D. Line ( y=-x ) | 11 |

630 | The angle between the lines ( k x+y+ ) ( 9=0, y-3 x=4 ) is ( 45^{circ}, ) then the value of ( k ) is : A. 2 only B. 2 or ( -frac{1}{2} ) c. -2 only D. -2 or ( -frac{1}{2} ) | 11 |

631 | Find the distance between the following pair of points: (-6,7) and (-1,-5) | 11 |

632 | Perpendicular distance between ( 2 x+ ) ( 2 y-z+1=0 ) and ( 2 x+2 y-x+4= ) 0 is | 11 |

633 | The slope of the line joining the points (-21,11) and (15,-7) is A . -2 B. ( frac{1}{2} ) ( c cdot 2 ) D. ( frac{-1}{2} ) | 11 |

634 | If the points ( (a, 0),(0, b) ) and (1,1) are collinear, which of the following is true? A ( cdot frac{1}{a}+frac{1}{b}=2 ) B. ( frac{1}{a}-frac{1}{b}=1 ) c. ( frac{1}{a}-frac{1}{b}=2 ) D. ( frac{1}{a}+frac{1}{b}=1 ) | 11 |

635 | Choose the correct answer from the alternative given. Area of triangle formed by straight lines ( boldsymbol{x}-boldsymbol{y}=mathbf{0}, boldsymbol{x}+boldsymbol{y}=mathbf{0} ) and ( mathbf{2} boldsymbol{x}=mathbf{5} ) is A . 25 в. ( frac{25}{2} ) c. ( frac{25}{4} ) D. None of these | 11 |

636 | A line a passes through (3,-4) and is parallel to y – axis find its equation. | 11 |

637 | What is the distance between the ( operatorname{lines} 3 x+4 y=9 ) and ( 6 x+8 y=18 ? ) A. B. 3 units c. 9 units D. 18 units | 11 |

638 | 21. Area of the triangle formed by the line x+y=3 and angle bisectors of the pair of straight lines x2 – y2 + 2y=1 is (20045 (a) 2 sq. units (b) 4 sq. units (C) 6 sq. units (d) 8 sq. units | 11 |

639 | 38. If non zero numbers a, b, c are in H.P., then the straight line -+-+-=0 always passes through a fixed point. The a b c point is [2005] (a) (-1,2) (b) (-1,-2) (a) (1) (c) (1, -2) (1,-2) | 11 |

640 | Find the area of the triangle ( P Q R ) if coordinates of ( Q ) are (3,2) and the coordinates of mid-points of the sides through ( Q ) are (2,-1) and (1,2) | 11 |

641 | In what ratio does the point ( left(frac{1}{2}, 6right) ) divide the line segment joining the points (3,5) and (-7,9)( ? ) | 11 |

642 | PQRS is a parallelogram and PA, SB, RC, QD are angle bisectors. If ( P Q=Q D=6 ) units, find ( boldsymbol{m} angle boldsymbol{P Q R} ) ( A cdot 30^{circ} ) B. 60 ( c cdot 120 ) D. Indeterminate | 11 |

643 | Find the value of ( x ) in the diagram below | 11 |

644 | The diagonal passing through origin of a quadrilateral formed by ( boldsymbol{x}=mathbf{0}, boldsymbol{y}= ) ( mathbf{0}, boldsymbol{x}+boldsymbol{y}=mathbf{1} ) and ( boldsymbol{6} boldsymbol{x}+boldsymbol{y}=mathbf{3} ) is A ( .3 x-2 y=0 ) в. ( 2 x-3 y=0 ) c. ( 3 x+2 y=0 ) D. None of these | 11 |

645 | Find the angle of inclination (in degrees) of the line passing through the points (1,2) and (2,3) A ( cdot 60^{circ} ) B . ( 45^{circ} ) ( c cdot 30^{0} ) D. ( 90^{circ} ) | 11 |

646 | If the points (2,5),(4,6) and ( (a, a) ) are collinear, then find the value of ( a ) A . 4 B. -4 ( c .-8 ) D. | 11 |

647 | 30. Let PS be the median of the triangle with vertices P(2, 2), 96,-1) and R(7,3). The equation of the line passing through (1,-1) and parallel to PS is: (JEE M 2014] (a) 4x+ 7y+3=0 (b) 2x– 9y-11=0 (c) 4x – 7y-11=0 (d) 2x +9y+7=0 | 11 |

648 | Find the distance between the points (0,0) and ( (36,15) . ) Can you now find the distance between the two towns ( A ) and ( boldsymbol{B} ) | 11 |

649 | The distance between points ( (5 sin 90,0) ) and ( (0,6 cos 90) ) is A. 5 units B. 6 units c. 1 units D. None of the above | 11 |

650 | Find the equation of a straight line cutting off an intercept -1 from ( y- ) axis and being equally inclined to the axes. | 11 |

651 | If the straight line joining two points ( P(5,8) ) and ( Q(8, k) ) is parallel to ( x- ) axis, then write the value of ( k ) | 11 |

652 | The slope of the line, ( l_{1} ) is ( frac{-3}{5} ) and ( l_{1} ) and ( l_{2} ) are parallel. Find the slope of ( l_{2} ) A ( cdot frac{-5}{3} ) в. ( frac{-1}{5} ) c. ( frac{-3}{5} ) D. ( frac{3}{5} ) | 11 |

653 | Find the acute angle the line ( x / 1= ) ( boldsymbol{y} / mathbf{3}=boldsymbol{z} / mathbf{0} ) and plane ( mathbf{2} boldsymbol{x}+boldsymbol{y}=mathbf{5} ) | 11 |

654 | The angle between the lines ( 3 x+y- ) ( mathbf{7}=mathbf{0} ) and ( boldsymbol{x}+mathbf{2} boldsymbol{y}+mathbf{9}=mathbf{0} ) is A ( cdot frac{pi}{3} ) в. ( c cdot frac{pi}{2} ) D. | 11 |

655 | In the figure the arrow head segments are parallel then find the value of ( x ) and ( y ) | 11 |

656 | Find the equation of a line passing through the points ( A(3,-5) ) and (4,-8) A. ( 3 x+y=4 ) B. ( 3 x+2 y=5 ) ( c cdot x+3 y=4 ) ( D cdot 4 x=3 y ) | 11 |

657 | A light ray emerging from the point source placed at ( boldsymbol{P}(2,3) ) is reflected at a point ( Q ) on the ( y ) -axis. It then passes through the point ( R(5,10) ). The coordinates of ( Q ) are A ( .(0,3) ) B. (0,2) c. (0,5) (年. ( 0,5,5) ) D. None of these | 11 |

658 | Te 9. If the equation of the locus of a point equidistant from the point (a1, b) and (az, b2) is (a – b2)x+ (Q1 – 12)y+c = 0 , then the value of cis (a) Var? +62 – az? –by? [2003] (6) }(az2 +622 – az? -42) 22 – az2 +672 – bz? (d) {(az? +az? +672 +632). | 11 |

659 | The diagonals of a parallelogram ( P Q R S ) are along the lines ( x+3 y=4 ) and ( 6 x-2 y=7, ) then ( P Q R S ) must be ( a ) A. rectangle B. square c. cyclic quadrialtaral D. rhombus | 11 |

660 | Find the coordinate of point which divides ( A(5,6) ) and (5,10) in 2: 3 | 11 |

661 | Find the distance of the point (36,15) from origin. | 11 |

662 | What is the slope of a line whose inclination with the positive direction of ( x ) axis is ( 120^{circ} ? ) | 11 |

663 | A Line is of length 10 and one end is ( (2,-3) . ) If the abscissa of the other end is ( 10, ) then find its ordinate. | 11 |

664 | Show that the product of perpendiculars on the line ( frac{x}{a} cos theta+ ) ( frac{y}{b} sin theta=1 ) from the points ( (pm sqrt{a^{2}-b^{2}}, 0) ) is ( b^{2} ) | 11 |

665 | Equation(s) or the straight line(s), inclined at ( 30^{circ} ) to the ( x ) -axis such that the length of its (each of their) line segment(s) between the coordinate axes is 10 units is/are This question has multiple correct options A. ( x+sqrt{3} y+5 sqrt{3}=0 ) в. ( x-sqrt{3} y+5 sqrt{3}=0 ) c. ( x+sqrt{3} y-5 sqrt{3}=0 ) D. ( x-sqrt{3} y-5 sqrt{3}=0 ) | 11 |

666 | Find the acute angle between the lines ( 3 x+y-7=0 ) and ( x+2 y-9=0 ) A ( cdot 45^{circ} ) B . ( 135^{circ} ) ( c cdot 60^{circ} ) D. ( 120^{circ} ) | 11 |

667 | Find the point on the X-axis, which are at a distance of ( 2 sqrt{5} ) from the point ( (7,-4) . ) How many such point are there? | 11 |

668 | Find the slope and ( y ) -intercept of the line ( -mathbf{5 x}+boldsymbol{y}=mathbf{5} ) A. slope ( =5, y ) -intercept ( =-5 ) B. slope ( =5, y ) -intercept ( =-4 ) c. slope ( =5, y ) -intercept ( =5 ) D. slope ( =5, y ) -intercept ( =-1 ) | 11 |

669 | Find the equation of the line intersecting the ( x ) -axis at a distance of 3 units to the left of origin with slope -2 | 11 |

670 | Find the areas of the triangles the coordinates of whose angular points are respectively. ( left{begin{array}{c}a m_{1}, frac{a}{m_{1}} \ a m_{3}, frac{a}{m_{3}}end{array}right},left{a m_{2}, frac{a}{m_{2}}right} ) and | 11 |

671 | If ( boldsymbol{A}left(mathbf{1}, boldsymbol{p}^{2}right), boldsymbol{B}(mathbf{0}, mathbf{1}) ) and ( boldsymbol{C}(boldsymbol{p}, mathbf{0}) ) are the coordinates of three points, then the value of ( p ) for which the area of the triangle ( A B C ) is minimum is A ( cdot frac{1}{sqrt{3}} ) B. ( -frac{1}{sqrt{3}} ) c. ( frac{1}{sqrt{2}} ) or ( -frac{1}{sqrt{3}} ) D. none | 11 |

672 | Write the equation of line passing through ( boldsymbol{A}(-mathbf{3}, mathbf{4}) ) and ( boldsymbol{B}(mathbf{4}, mathbf{5}) ) in the form of ( a x+b y+c=0 ) | 11 |

673 | Find the distance between (4,5) and (5,6) A ( cdot sqrt{2} ) B. ( sqrt{3} ) ( c cdot sqrt{6} ) D. ( sqrt{7} ) | 11 |

674 | 7. The vertices of a triangle are [at,t2 alt, + t2)], [atztz, aſt2 +t3)], [atztı, altz + tı)]. Find the orthocentre of the triangle. (1983 – 3 Marks) | 11 |

675 | Which of the following is/are true regarding the following linear equation: ( frac{boldsymbol{x}-mathbf{1}}{mathbf{3}}-frac{boldsymbol{y}+mathbf{2}}{mathbf{2}}=mathbf{0} ) A ( cdot ) It passes through ( left(0,-frac{2}{3}right) ) and ( m=frac{8}{3} ) B. It passes through ( left(0, frac{8}{3}right) ) and ( m=-frac{2}{3} ) c. ( _{text {It passes through }}left(0,-frac{8}{3}right) ) and ( m=frac{2}{3} ) D . It passes through ( left(0,-frac{2}{3}right) ) and ( m=-frac{8}{3} ) | 11 |

676 | Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points ( boldsymbol{P}(mathbf{0},-mathbf{4}) ) and ( boldsymbol{B}(mathbf{8}, mathbf{0}) ) | 11 |

677 | Find the area of the triangle formed by tangents from the point (4,3) to the circle ( x^{2}+y^{2}=9 ) and the length of the line joining their points to contact.? | 11 |

678 | 16. A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is (a) x + y = 7 (b) 3x – 4y + 7 = 0 [2006] (c) 4x + 3y = 24 (d) 3x + 4y = 25 | 11 |

679 | The medians AD and BE of a triangle with vertices ( boldsymbol{A}(mathbf{0}, boldsymbol{b}), boldsymbol{B}(mathbf{0}, boldsymbol{0}) ) and ( C(a, 0) ) are perpendicular to each other if | 11 |

680 | Find what straight lines are represented by the following equation and determine the angles between them. ( boldsymbol{x}^{2}+2 boldsymbol{x} boldsymbol{y} sec boldsymbol{theta}+boldsymbol{y}^{2}=mathbf{0} ) | 11 |

681 | For two parallel lines and a transversal ( angle 1=74^{circ} . ) For which pair of angle measures is the sum the least? A. ( angle 1 ) and a corresponding angle B. ( angle 1 ) and the corresponding co-interior angle C. ( angle 1 ) and its supplement D. ( angle 1 ) and its complement | 11 |

682 | State the following statement is True or False The area (in sq. units) of the triangle formed by the points with polar coordinates (1,0)( left(2, frac{pi}{3}right) ) and ( left(3, frac{2 pi}{3}right) ) is ( frac{5 sqrt{3}}{4} ) A. True B. False | 11 |

683 | Find the area of triangle formed by the points (8,-5),(-2,-7) and (5,1) | 11 |

684 | If one of the diagonals of a square is along the line ( 4 x=2 y ) and one of its vertices is ( (3,0), ) then its side through this vertex nearer to the origin is given by the equation. A. ( y-3 x+9=0 ) В. ( 3 y+x-3=0 ) c. ( x-3 y-3=0 ) D. ( 3 x+y-9=0 ) | 11 |

685 | The perpendicular bisector of the line segment joining P (1, 4) and Q(k, 3) has y-intercept-4. Then a possible value of k is [2008] (a) 1 (6) 2 (c) 2 (d) -4 1 and the | 11 |

686 | The point ( (p, p+1) ) lies on the locus of the point which moves such that its distance from the point (1,0) is twice the distance from ( (0,1) . ) The value of ( frac{1}{2 p^{2}}+frac{1}{2 p^{4}} ) is equal to | 11 |

687 | 14 cus of centroid of the triangle whose vertices are o cost, a sin t), (b sint, -b cost) and (1, 0), where t is a parameter, is [2003] (a) (3x + 1)2 + (3y)2 = a? – 62 (b) (3x – 1)2 + (3y)2 = a? – 62 (c) (3x – 1)2 + (3y)2 = a? +62 (d) (3x + 1)2 + (3y)2 = a2 +62. both i n 1 | 11 |

688 | The distance of point ( X(1,1) ) from origin 0 is A ( cdot sqrt{2} ) B. ( 2 sqrt{1} ) c. ( 1 sqrt{1} ) D. None | 11 |

689 | If one of the diagonals of a square is along the line ( x=2 y ) and one of its verices is ( (3,0), ) then its side through this vertex nearer to the origin is given by the equation. A. ( y-3 x+9=0 ) В. ( 3 y+x-3=0 ) c. ( x-3 y-3=0 ) D. ( 3 x+y-9=0 ) | 11 |

690 | The equation of the straight line passing through the point of intersection of the straight lines ( frac{x}{a}= ) ( frac{boldsymbol{y}}{boldsymbol{b}}=1 ) and ( frac{boldsymbol{x}}{boldsymbol{b}}+frac{boldsymbol{y}}{boldsymbol{a}}=mathbf{1} ) and having infinite slopes is | 11 |

691 | The radius of any circle touching the ( operatorname{lines} 3 x-4 y+5=0 ) and ( 6 x-8 y- ) ( mathbf{9}=mathbf{0} ) is A . 1.9 B. 0.95 c. 2.9 D. 1.45 | 11 |

692 | The line joining the points ( boldsymbol{A}(mathbf{0}, mathbf{5}) ) and ( B(4,2) ) is perpendicular to the line joining the points ( C(-1,-2) ) and ( D(5, b) . ) Find the value of ( b ) | 11 |

693 | The distance between a pair of parallel ( operatorname{lines} 9 x^{2}-24 x y+16 y^{2}-12 x+ ) ( mathbf{1 6} boldsymbol{y}-mathbf{1 2}=mathbf{0} ) A . 5 B. 8 ( c cdot 8 / 5 ) D. ( 5 / 8 ) | 11 |

694 | The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is ( A cdot 1: 2 ) B. 1:3 ( c .3: 2 ) D. None of these | 11 |

695 | Find the distance between the points (1,5) and (5,8) | 11 |

696 | Find the slope of the line passing through the following pairs: ( (-1,2 sqrt{3}) ) and ( (-2, sqrt{3}) ) A. ( sqrt{3} ) B. ( 3 sqrt{3} ) c. ( frac{1}{sqrt{3}} ) D. ( frac{sqrt{3}}{3} ) | 11 |

697 | The coordinates of a point on the line ( boldsymbol{x}+boldsymbol{y}+mathbf{3}=mathbf{0} ) whose distance from ( x+2 y+2=0 ) is ( sqrt{5} ) is equal to в. (-9,6) c. (-9,-6) (年 (-9,-6),(-6) D. none of these | 11 |

698 | A rectangle has two opposite vertices at the points (1,2) and ( (5,5) . ) If the other vertices lie on the line ( x=3 ), then the coordinates of the other vertices are ( mathbf{A} cdot(3,-1),(3,-6) ) в. (3,1),(3,5) C . (3,2),(3,6) D. (3,1),(3,6) | 11 |

699 | the slant height of a right cone is given as ( 10 mathrm{cm} . ) if the volume of cone is maximum, then the semi- vertical angle is: A ( cdot_{-cos frac{1}{sqrt{3}}} ) B. ( tan ^{-1} sqrt{2} ) c. D. | 11 |

700 | The two straight lines ( a_{1} x+b_{2} y+ ) ( c_{2}=0 ) and ( a_{2} x+b_{2} y+c_{2} z=0 ) will be parallel to each other, if A ( cdot frac{a_{1}}{b_{1}}=frac{a_{2}}{b_{2}} ) В ( cdot frac{a_{1}}{a_{2}}=frac{b_{1}}{b_{2}} ) c. ( a_{1} b_{1}=a_{2} b_{2} ) D. ( a_{1} a_{2}=b_{1} b_{2} ) | 11 |

701 | How many points are there on the ( x- ) axis whose distance from the point (2,3) is less than 3 units? | 11 |

702 | 5. Line Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q, then (1990-2 Marks) (a) a² +6² = p² + q² + 02 © d+p?=b+q? (a) | 11 |

703 | Find the slope of the line with inclination ( 60^{circ} ) | 11 |

704 | Find if possible, the slope of the line through the points ( (1 / 2,3 / 4) ) and ( (-1 / 3,5 / 4) ) | 11 |

705 | 18. A straight line through the origin on ne through the origin O meets the parallel lines 9 and 2x+y+6=0 at points P and respectively. Then the point o divides the segemnt PQ in to (2002) (a) 1:2 (6) 3:4 (c) 2:1 (d) 4:3 | 11 |

706 | 19. The number of intergral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0,0),(0,21) and (21,0), is (2003 (a) 133 (b) 190 (C) 233 (d) 105 | 11 |

707 | Find what straight lines are represented by the following equation and determine the angles between them. ( boldsymbol{y}^{3}-boldsymbol{x} boldsymbol{y}^{2}-mathbf{1 4} boldsymbol{x}^{2} boldsymbol{y}+boldsymbol{2 4} boldsymbol{x}^{3}=mathbf{0} ) | 11 |

708 | Find the slope of the straight line passing through the points (3,-2) and (-1,4) | 11 |

709 | Say true or false. The distance of the point (5,3) from the ( X ) -axis is 5 units. A . True B. False | 11 |

710 | If ( P, Q, R ) are collinear points such that ( boldsymbol{P}(boldsymbol{3}, boldsymbol{4}), boldsymbol{Q}(boldsymbol{7}, boldsymbol{7}) ) and ( boldsymbol{P} boldsymbol{R}=mathbf{1 0}, ) find ( boldsymbol{R} ) | 11 |

711 | Find the slope of the line which make the following angle with the positive direction of ( x- ) axis ( -frac{pi}{4} ) | 11 |

712 | For points ( boldsymbol{A}(mathbf{1},-mathbf{1}, mathbf{1}), boldsymbol{B}(mathbf{1}, boldsymbol{3}, mathbf{1}), boldsymbol{C}(mathbf{4}, boldsymbol{3}, mathbf{1}) ) and ( D(4,-1,1) ) taken in order are the vertices of A. a parallelogram which is neither a square nor a rhombus B. rhombus c. as isosceles trapezium D. a cyclic quadrilateral | 11 |

713 | Find the slope of the line passing through the points (3,-2)( &(7,-2) ) | 11 |

714 | If the distance between the parallel lines given by ( x^{2}+2 x y+y^{2}-9 a^{2}=0 ) is ( 90 sqrt{2} ) then ( a ) is equal to | 11 |

715 | Three lines ( boldsymbol{x}+mathbf{2} boldsymbol{y}-mathbf{7}=mathbf{0}, boldsymbol{x}+mathbf{2} boldsymbol{y}+ ) ( mathbf{3}=mathbf{0} ) and ( mathbf{2} boldsymbol{x}-boldsymbol{y}+mathbf{4}=mathbf{0} ) form ( mathbf{3} ) sides of two squares then equation of remaining side of these squares is A. ( 2 x+y+14=0 ) В. ( 2 x-y-14=0 ) c. ( 2 x-y+6=0 ) D. ( 2 x-y+14=0 ) | 11 |

716 | pouvoiy.1 100 ml Us 01 22. Using co-ordinate geometry, prove that the three ant of any triangle are concurrent. (1998 -8 Marks) 1. | 11 |

717 | ( boldsymbol{p} boldsymbol{t}(boldsymbol{5},-boldsymbol{2}) ) is the mid pt of line segment joining the ( p t sleft(frac{x}{2}, frac{y+1}{2}right) ) and ( (x+ ) ( mathbf{1}, boldsymbol{y}-mathbf{3}) ) then find the value of ( boldsymbol{x} ) & ( boldsymbol{y} ) | 11 |

718 | A line in the ( x y ) -plane passes through the origin and has a slope of ( frac{1}{7} . ) Which of the following points lies on the line? ( mathbf{A} cdot(0,7) ) В ( cdot(1,7) ) c. (7,7) D cdot (14,2) | 11 |

719 | A point ( P(2,-1) ) is equidistant from the points ( (a, 7) ) and ( (-3, a) . ) Find ‘a’ | 11 |

720 | If the distance between (8,0) and ( A ) is 7 then coordinates of the point ( A ) can not be A. (8,-7) B. (8,7) ( c cdot(1,0) ) ( D cdot(0,-8) ) | 11 |

721 | Find the distance between the origin and the point (5,12) | 11 |

722 | Which of the following lines is parallel to the line ( 3 x-2 y+6=0 ? ) A. ( 3 x+2 y-12=0 ) в. ( 4 x-9 y=6 ) c. ( 12 x+18 y=15 ) D. ( 15 x-10 y-9=0 ) | 11 |

723 | ( A ) and ( B ) are the points (2,0) and (0,2) respectively. The coordinates of the point ( P ) on the line ( 2+3 y+1=0 ) are A. (7,-5) if |PA – PBl is maximum B. ( left(frac{1}{5}, frac{1}{5}right) ) if ( |P A-P B| ) is maximun c. (7,-5) if ( mid P A-P B / ) is minimum D. ( left(frac{1}{5}, frac{1}{5}right) ) if ( mid ) PA – PB l is minimun | 11 |

724 | 27. OUL CAPlllllUIT IUI lalu If the line 2rtu the line segment joining the points (1,1) and (4 3:2, then k equals: 29 (b) 5 (c) 6 (d) k passes through the point which divides ning the points (1,1) and (2,4) in the ratio [2012] (a) | 11 |

725 | Find the angle between ( y-sqrt{3} x=5 & ) ( sqrt{mathbf{3}} boldsymbol{y}-boldsymbol{x}+boldsymbol{6}=mathbf{0} ) | 11 |

726 | If vertices of a triangle are represented by complex numbers ( z, i z, z+i z, ) then area of triangle is ( A cdot|z|^{2} ) B. ( frac{1}{2}|z|^{2} ) c ( cdot 2|z|^{3} ) D・ ( 3|z|^{2} ) | 11 |

727 | The perimeter of a triangle formed by points ( (mathbf{0}, mathbf{0}),(mathbf{6}, mathbf{0}),(mathbf{0}, mathbf{6}) ) is A. ( 6(2+sqrt{2}) ) units B. ( 2+sqrt{2} ) units c. ( 6 sqrt{2} ) units D. None of the above | 11 |

728 | Find the distance between two complex nymbers ( z_{1}=2+3 i ) and ( z_{2}=7-9 i ) on the complex plane. | 11 |

729 | Find the slope of the inclination of the line of the following: ( boldsymbol{theta}=mathbf{6 0}^{circ} ) A ( cdot frac{1}{sqrt{3}} ) B. ( sqrt{3} ) c. ( frac{2}{sqrt{3}} ) D. ( frac{sqrt{3}}{2} ) | 11 |

730 | If ( P(2,-1), Q(3,4), R(-2,3) ) and ( S(-3,-2) ) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus. | 11 |

731 | Using slope concept show that the points ( P(-2,3), Q(7,-4) ) and ( R(2,1) ) A. are not collinear B. cannot be plotted c. are not defined D. are collinear | 11 |

732 | The distance between the lines ( 3 x+ ) ( mathbf{4} boldsymbol{y}=mathbf{9} ) and ( mathbf{6} boldsymbol{x}+mathbf{8} boldsymbol{y}+mathbf{1 5}=mathbf{0} ) is ( A cdot frac{3}{10} ) в. ( frac{33}{10} ) ( c cdot frac{33}{5} ) D. none of these | 11 |

733 | Four points ( A(6,3), B(-3,5), C(4,-2) ) and ( D(x, 3 x) ) are given in such a way that ( frac{A r e a(Delta D B C)}{A r e a(Delta A B C)}=frac{1}{2} ) find ( x ) This question has multiple correct options A ( cdot frac{11}{8} ) B. ( frac{3}{8} ) ( c cdot frac{9}{8} ) D. None of these | 11 |

734 | If the distance between the points ( boldsymbol{A}(mathbf{4}, boldsymbol{p}) ) and ( boldsymbol{B}(mathbf{1}, mathbf{0}) ) is 5 units, then the value(s) of ( p ) is are A. 4 only B. – 4 only y ( c .pm 4 ) only D. 0 | 11 |

735 | The distance between the straight lines ( 9 x+40 y-50=0,9 x+40 y+32=0 ) is ( A cdot 1 ) B . 2 ( c cdot 82 ) D. 41 | 11 |

736 | Find the slope and ( y ) -intercept of line ( boldsymbol{y}-mathbf{3} boldsymbol{x}=mathbf{5} ) | 11 |

737 | If points ( (h, k)(1,2) ) and (-3,4) lie on line ( L_{1} ) and points ( (h, k) ) and (4,3) lie on ( L_{2} . ) If ( L_{2} ) is perpendicular to ( L_{1}, ) then value of ( frac{boldsymbol{h}}{boldsymbol{k}} ) is? A. ( -frac{1}{7} ) B. ( frac{1}{3} ) ( c cdot 3 ) D. | 11 |

738 | The slope and the y-intercept of the given line, ( 2 x-3 y=7 ) are respectively A ( cdot frac{3}{2}, frac{-3}{7} ) B. ( frac{2}{3}, frac{-7}{3} ) ( c cdot frac{3}{2}, frac{3}{7} ) D. ( frac{2}{3}, frac{7}{3} ) | 11 |

739 | The slope of the line, ( l_{2} ) is 5 and ( l_{1} ) and ( l_{2} ) are parallel. Find the slope of ( l_{1} ) A . – B. 5 ( c ) D. – | 11 |

740 | Say true or false Points (1,7),(4,2),(-1,-1) and (-4,4) are the vertices of a square A. True B. False | 11 |

741 | Find the slope of the straight line passing through the points (3,-2) and (7,2) | 11 |

742 | Value of a when the distance between the points ( (3, a) ) and (4,1) is ( sqrt{10} ) is A. 4 or -2 B . -2 or 4 c. 6 or 2 D. None | 11 |

743 | ( A B | D E ). Find the measure of ( angle A O D ) | 11 |

744 | Find the inclination of the line whose slope is ( frac{mathbf{1}}{sqrt{mathbf{3}}} ) | 11 |

745 | If the straight line, ( 2 x-3 y+17=0 ) is perpendicular to the line passing through the points (7,17) and ( (15, beta) ) then ( beta ) equals:- A . -5 B. ( -frac{35}{3} ) c. ( frac{35}{3} ) D. 5 | 11 |

746 | The points (5,1),(1,-1) and (11,4) are A. Collinear B. Vertices of right angled triangle c. vertices of equilateral triangle D. Vertices of isosceles triangle | 11 |

747 | 31. Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay+c=0 and 5bx +2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then [JEE M 2014] (a) 3bc-2ad=0 (b) 3bc +2ad=0 (c) 2bc – 3ad=0 (d) 2bc + 3ad=0 | 11 |

748 | Find the ordinate of point whose abcissa is 4 and which is at a distance 5 from (0,5) A .1,2 B. 2,4 c. 2,8 D. None | 11 |

749 | 13. Let ABC be a triangle with AB= AC. If D is the midpoint of BC, E is the foot of the perpendicular drawn from D to AC and F the mid-point of DE, prove that AF is perpendicular to BE. (1989 – 5 Marks) | 11 |

750 | Find the area of the triangle formed by joining the mid points of the sides of the triangle, whose vertices are (0,1)( ;(2,1) ) and ( (0,3) . ) Find the ratio of this area to the area of the given triangle | 11 |

751 | The shortest distance between the line ( y ) ( -x=1 ) and the curve ( x=y^{2} ) is : A ( cdot frac{2 sqrt{3}}{8} ) B. ( frac{3 sqrt{5}}{8} ) c. ( frac{sqrt{3}}{4} ) D. ( frac{3 sqrt{2}}{8} ) | 11 |

752 | (9,2),(5,-1) and (7,-5) are the vertices of the triangle. Find its area. A . 10 B. 1 c. 12 D. 13 | 11 |

753 | The slope and y-intercept of the following line are respectively ( 8 x-4 y-1=0 ) A ( cdot )slope( =m=frac{-1}{2} ) and ( y- ) intercept ( =frac{1}{4} ) B . slope ( =m=2 ) and ( y- ) intercept ( =-frac{1}{4} ) c. slope ( =m=-frac{1}{2} ) and ( y- ) intercept ( =-frac{1}{4} ) D. slope ( =m=frac{1}{2} ) and ( y- ) intercept ( =frac{1}{4} ) | 11 |

754 | The perpendicular distance between the straight lines ( 6 x+8 y+15=0 ) and ( mathbf{3} boldsymbol{x}+mathbf{4} boldsymbol{y}+mathbf{9}=mathbf{0} ) is A. ( 3 / 2 ) units B. 3/10 units c. ( 3 / 4 ) units D. 2/7units | 11 |

755 | Find the value of ( k ) for which the area of the triangle with vertices ( (2,-2),(-3,3 k) ) and (-2,3) is 20 sq.units. | 11 |

756 | Find the acute angle between the two lines: ( A B ) and ( C D ) passing through the points ( boldsymbol{A} equiv(mathbf{3}, mathbf{1},-mathbf{2}), boldsymbol{B} equiv(mathbf{4}, mathbf{0},-mathbf{4}) ) and ( boldsymbol{C} equiv ) ( (4,-3,3), D equiv(6,-2,2) ) | 11 |

757 | Which of the following is/are true regarding the following linear equation: ( boldsymbol{y}=mathbf{4} boldsymbol{x}-frac{mathbf{5}}{mathbf{2}} ) A . It passes through (2.5,0) and ( m=-4 ) B. It passes through (2.5,0) and ( m=4 ) C. It passes through (0,2.5) and ( m=-4 ) D. It passes through (0,-2.5) and ( m=4 ) | 11 |

758 | 17. Let P=(-1,0), (0.0) and R=(3, 373 ) be three points. Then the equation of the bisector of the angle PQR is -X+ y = 0 (6) x + 13y = 0 (2002) (0) √3x + y = 0 (2 x + 3y = 0 | 11 |

759 | 3. The straight lines x+y=0,3x+y-4=0,x+3y-4=0 form a triangle which is (1983-1 Mark) (a) isosceles (b) equilateral (c) right angled (d) none of these | 11 |

760 | The quadrilateral ( A B C D ) formed by the point ( boldsymbol{A}(mathbf{0}, mathbf{0}) ; boldsymbol{B}(mathbf{3}, mathbf{4}) ; boldsymbol{C}(mathbf{7}, mathbf{7}) ) and ( D(4,3) ) is a A. rectangle B. rhombus c. square D. parallelogram | 11 |

761 | The distance between the parallel lines ( 8 x+6 y+5=0 ) and ( 4 x+3 y-25=0 ) is ( A cdot frac{7}{2} ) B. ( frac{9}{2} ) c. ( frac{11}{2} ) D. | 11 |

762 | The line ( 3 x-4 y+8=0 ) is rotated through an angle ( frac{pi}{4} ) in the clockwise direction about the point ( (0,2) . ) The equation of the line in its new position is A. ( 7 y+x-14=0 ) в. ( 7 y-x-14=0 ) c. ( 7 y+x-2=0 ) D. ( 7 y-x=0 ) | 11 |

763 | The line ( (a+2 b) x+(a-3 b) y=a-b ) for different values of ( a ) and ( b ) passes through the fixed point ( ^{mathrm{A}} cdotleft(frac{3}{5}, frac{7}{5}right) ) в. ( left(frac{7}{2}, frac{5}{2}right) ) ( ^{mathrm{c}} cdotleft(frac{6}{5}, frac{6}{5}right) ) D ( cdotleft(frac{2}{5}, frac{3}{5}right) ) | 11 |

764 | f ( boldsymbol{pi} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{2 5}, ) write ( boldsymbol{y} ) in terms of ( boldsymbol{x} ) | 11 |

765 | A student moves ( sqrt{2 x} k m ) east from his residence and then moves ( x ) km north. He then goes ( x ) km north east and finally he takes a turn of ( 90^{circ} ) towards right and moves a distance ( x mathrm{km} ) and reaches his school. What is the shortest distance of the school from his residence? A. ( (2 sqrt{2}+1) x k m ) B. ( 3 x ) km ( mathbf{c} cdot 2 sqrt{2} x k m ) D. ( 3 sqrt{2} x ) km | 11 |

766 | Find the area of the triangle formed by joining the midpoints of the sides of a triangle whose vertices are (0,-1),(2,1) and ( (0,3) . ) Write the ratio of the area fo the given triangle to the area of the new triangle. | 11 |

767 | The points with co-ordinates ( (2 a, 3 a) ) (3b, 2b) and (c,c) are collonear? A. For no value of ( a, b, c ) B. For all values of ( a, b, c ) c. If a ( , c / 5 ) b are in ( mathrm{H.P} ) D. ( 5 a=c ) | 11 |

768 | Find the slope of a line parallel to the line ( boldsymbol{y}=frac{mathbf{2}}{mathbf{3}} boldsymbol{x}-mathbf{4} ) A . -4 в. ( -frac{3}{2} ) ( c cdot 2 ) D. ( frac{3}{2} ) ( E cdot frac{2}{3} ) | 11 |

769 | If the angle between the lines ( k x-y+ ) ( 6=0,3 x-5 y+7=0 ) is ( frac{pi}{4}, ) then one of the value of ( k= ) ( mathbf{A} cdot mathbf{1} ) B . 2 ( c cdot 3 ) D. | 11 |

770 | Find the slope of a non-vertical line ( boldsymbol{a} boldsymbol{x}+boldsymbol{b} boldsymbol{y}+boldsymbol{c}=mathbf{0} ) | 11 |

771 | If ( p_{1}, p_{2}, p_{3} ) are lengths of perpendiculars from points ( left(boldsymbol{m}^{2}, mathbf{2 m}right) ) ( left(m m^{prime}, m+m^{prime}right) ) and ( left(m^{prime}^{2}, 2 m^{prime}right) ) to the line ( x cos alpha+y sin alpha+frac{sin ^{2} alpha}{cos alpha}=0 ) then ( boldsymbol{p}_{1}, boldsymbol{p}_{2}, boldsymbol{p}_{3} ) are in A. A.P в. G…P c. н.P D. A.G.P.P | 11 |

772 | If (4,3) and (-4,3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle. A ( cdot(0,-3-4 sqrt{3}) ) В. ( (0,3+4 sqrt{3}) ) c. ( (0,3-4 sqrt{3}) ) D. ( (0,-3+4 sqrt{3}) ) | 11 |

773 | The distance between the straight lines ( 5 x+12 y+11=0,5 x+12 y+37=0 ) is A .2 B. 3 ( c cdot 26 ) D. 48 | 11 |

774 | For what value of ( boldsymbol{x} ) will ( l_{1} ) and ( l_{2} ) be parallel lines ( mathbf{A} cdot 32^{circ} ) B ( cdot 12^{circ} ) ( c cdot 42^{circ} ) D. None of these | 11 |

775 | The line through ( A(-2,3) ) and ( B(4, b) ) is perpendicular to the line ( 2 x-4 y=5 ) Find the value of ( |boldsymbol{b}| ) | 11 |

776 | The points (6,2),(2,5) and (9,6) form the vertices of a ( _{–} ) triangle. A . right B. equilateral c. right isosceles D. scalene | 11 |

777 | f ( boldsymbol{A}=(-mathbf{3}, mathbf{4}), boldsymbol{B}=(-mathbf{1},-mathbf{2}), boldsymbol{C}= ) ( (mathbf{5}, mathbf{6}), boldsymbol{D}=(boldsymbol{x},-mathbf{4}) ) are vertices of ( mathbf{a} ) quadrilateral such that ( Delta A B D= ) ( 2 Delta A C D . ) Then ( x, ) is equal to: ( mathbf{A} cdot mathbf{6} ) B. 9 ( c cdot 69 ) D. 96 | 11 |

778 | Find inclination (in degrees) of a line perpendicular to y-axis. | 11 |

779 | 3. One side of a rectangle lies along the line 4x + 7y+5=0. Two of its vertices are (-3,1) and (1,1). Find the equations of the other three sides. (1978) | 11 |

780 | If ( M(x, y) ) is equidistant from ( A(a+ ) ( b, b-a) ) and ( B(a-b, a+b), ) then A. ( b x+a y=0 ) В. ( b x-a y=0 ) ( mathbf{c} cdot a x+b y=0 ) D. ( a x-b y=0 ) | 11 |

781 | Find the inclination of the line passing through (-5,3) and (10,7) A. 14.73 B . 14.93 ( c cdot 14.83 ) D. 14.63 E. none of these | 11 |

782 | Find the areas of the triangles the coordinates of whose angular points ( operatorname{are}left(-3,-30^{circ}right),left(5,150^{circ}right) ) and ( left(7,210^{circ}right) ) | 11 |

783 | The angle between the lines ( y-x+ ) ( mathbf{5}=mathbf{0} ) and ( sqrt{mathbf{3}} boldsymbol{x}-boldsymbol{y}+mathbf{7}=mathbf{0} ) is/are This question has multiple correct options A ( cdot 15^{circ} ) B. ( 60^{circ} ) ( mathbf{c} cdot 165^{circ} ) D. ( 75^{circ} ) | 11 |

784 | If 0 is the origin and ( A_{n} ) is the point with coordinates ( (boldsymbol{n}, boldsymbol{n}+mathbf{1}) ) then ( left(O A_{1}right)^{2}+left(O A_{2}right)^{2}+ldots+left(O A_{7}right)^{2} ) is equal to | 11 |

785 | The slope of a straight line passing through ( A(-2,3) ) is ( -4 / 3 . ) The points on the line that are 10 units away from ( A ) are A ( .(-8,11),(4,-5) ) B. (-7,9), (17-1) c. (7,5)(-1,-1) D. (6,10),(3,5) | 11 |

786 | The slope of the line joining the point (-8,-3) and (8,3) is A ( cdot frac{8}{3} ) в. ( frac{3}{8} ) ( c cdot 0 ) D. – | 11 |

787 | There is a pair of points, one on each of the lines, whose combined equation is ( (4 x-3 y+5)(6 x+8 y+5)=0 . ) If they are such that the distance of the point on one line is 2 units from the other line then the points are ( ^{mathbf{A}} cdotleft(frac{1}{10}, frac{9}{5}right)left(frac{1}{2},-1right) ) в. ( left(frac{1}{2},-1right)left(-frac{23}{10}, frac{7}{3}right) ) ( ^{mathbf{C}} cdotleft(frac{1}{10}, frac{9}{5}right)left(-frac{23}{10},-frac{7}{5}right) ) D. none of these | 11 |

788 | A point ( A(p, q) ) is 2 units away from ( x- ) axis and 5 units from ( y- ) axis. What would be its coordinate? | 11 |

789 | Find the locus of the point equidistant from (-1,2) and (3,0) | 11 |

790 | Solve for ( x ) and ( y ) ( frac{boldsymbol{a} boldsymbol{x}}{boldsymbol{b}}-frac{boldsymbol{b} boldsymbol{y}}{boldsymbol{a}}=boldsymbol{a}+boldsymbol{b}, boldsymbol{a} boldsymbol{x}-boldsymbol{b} boldsymbol{y}=boldsymbol{2} boldsymbol{a} boldsymbol{b} ) | 11 |

791 | A line through ( boldsymbol{A}(-mathbf{5},-mathbf{4}) ) meets the line ( boldsymbol{x}+mathbf{3} boldsymbol{y}+mathbf{2}=mathbf{0}, mathbf{2} boldsymbol{x}+boldsymbol{y}+mathbf{4}=mathbf{0} ) and ( x-y-5=0 ) at the point ( B, C ) and ( D ) respectively. If ( left(frac{15}{A B}right)^{2}+ ) ( left(frac{10}{A C}right)^{2}=left(frac{6}{A D}right)^{2} . ) Find the equation of the line. | 11 |

792 | Find the area of the triangle with vertices at the points: (3,8),(-4,2) and ( (5,-1) . ) If the area is ( left(frac{a}{2}right) ) sq. units, then what will be the value of ( boldsymbol{a} ? ) | 11 |

793 | The ratio in which (2,3) divides the line segment joining (4,8),(-2,-7) is A. 2: 1 externally B. 2: 3 c. 4: 3 externally D. 1: 2 | 11 |

794 | Starting at the origin, a beam of light hits a mirror(in the form of a line) at the point ( A(4,8) ) and reflected line passes through the point ( B(8,12) . ) Compute the slope of the mirror. | 11 |

795 | Find the joint equation of lines passing through the origin, each of which making angle of measure ( 150^{circ} ) with the line ( boldsymbol{x}-boldsymbol{y}=mathbf{0} ) | 11 |

796 | A straight line segment of length l moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio 1:2. (1978) . | 11 |

797 | The distance between the lines ( 3 x+ ) ( mathbf{4} boldsymbol{y}=mathbf{9} ) and ( mathbf{6} boldsymbol{x}+mathbf{8} boldsymbol{y}+mathbf{1 5}=mathbf{0} ) is: ( A cdot frac{3}{10} ) в. ( frac{33}{10} ) ( c cdot frac{33}{5} ) D. None of these | 11 |

798 | Find the equation of straight lines passing through (1,1) and which are at a distance of 3 units from (-2,3) | 11 |

799 | A square or side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle al 0<a< with the positive direction of x-axis. The equation of its diagonal not passing through the origin is (a) y(cosa + sin a) + x(cos a – sin a) = a [2003] (b) y(cosa -sin a)- x(sin a – cos a) = a (c) y(cosa + sin a) + x(sin a – cos a) = a (d) y(cos a + sin a) + x(sin a + cos a) = a. | 11 |

800 | In the figure, if line ( l ) has a slope of -2 what is the ( y ) -intercept of ( l ) ? ( A cdot 7 ) B. 8 ( c ) D. 10 | 11 |

801 | Locus of a point that is equidistant from the lines ( x+y-2 sqrt{2}=0 ) and ( boldsymbol{x}+boldsymbol{y}-sqrt{mathbf{2}}=mathbf{0} ) is A ( . x+y-5 sqrt{2}=0 ) B . ( x+y-3 sqrt{2}=0 ) c. ( 2 x+2 y-3 sqrt{2}=0 ) D. ( 2 x+2 y-5 sqrt{2}=0 ) | 11 |

802 | The coordinates of a point on the line ye where perpendicular from the line ( 3 x+4 y=12 ) is 4 units, are A ( cdotleft(frac{3}{7}, frac{5}{7}right) ) в. ( left(frac{3}{2}, frac{3}{2}right) ) ( c cdotleft(-frac{8}{7},-frac{8}{7}right) ) D. ( left(frac{32}{7},-frac{32}{7}right) ) | 11 |

803 | The angle between the line ( x+y=3 ) and the line joining the points (1,1) and (-3,4) is A ( cdot tan ^{-1}(7) ) B ( cdot tan ^{-1}(-1 / 7) ) ( mathbf{c} cdot tan ^{-1}(1 / 7) ) D. None of these | 11 |

804 | Consider the points ( boldsymbol{A}(boldsymbol{a}, boldsymbol{b}+boldsymbol{c}) ) ( B(b, c+a), ) and ( C(c, a+b) ) be the vertices of ( triangle mathrm{ABC} ). The area of ( triangle mathrm{ABC} ) is: A ( cdot 2left(a^{2}+b^{2}+c^{2}right) ) B . ( a^{2}+b^{2}+c^{2} ) c. ( 2(a b+b c+c a) ) D. None of these | 11 |

805 | A point ( P ) divides the line segment joining the points ( boldsymbol{A}(mathbf{3},-mathbf{5}) ) and ( B(-4,8) ) such that ( frac{A P}{P B}=frac{K}{1} . ) If ( P ) lies on the line ( x+y=0, ) then find the value of ( k ) | 11 |

806 | The straight lines ( 7 x+y+1=0 ) and ( 7 x+y-9=0 ) are tangents to the same circle.Then the area of this circle is | 11 |

807 | Find the slope and ( y ) -intercept of the line given by the equation ( 2 y+3 x=-2 ) | 11 |

808 | If equation of line is ( (boldsymbol{y}-mathbf{2} sqrt{mathbf{3}})= ) ( frac{sqrt{3}+1}{sqrt{3}-1}(x-2), ) then find the slope | 11 |

809 | Prove that the straight lines ( x+2 y+ ) ( mathbf{1}=mathbf{0} ) and ( mathbf{2} boldsymbol{x}-boldsymbol{y}+mathbf{5}=mathbf{0} ) are perpendicular to each other. | 11 |

810 | The line joining the points ( left(x_{1}, y_{1}right) ) and ( left(x_{2}, y_{2}right) ) subtends a right angle This question has multiple correct options ( mathbf{A} cdot ) at the point (1,-1) if ( x_{1} x_{2}+y_{1} y_{2}+2=x_{1}-y_{1}+x_{2}- ) ( y_{2} ) B. at the point (-1,1) if ( x_{1} x_{2}+y_{1} y_{2}+2=y_{1}-x_{1}+y_{2}- ) ( x_{2} ) C ( . ) at the point (1,1) if ( x_{1} x_{2}+y_{1} y_{2}+2=x_{1}+y_{1}+x_{2}+ ) ( y_{2} ) D. at the point (-1,-1) if ( x_{1} x_{2}+y_{1} y_{2}+2=x_{1}+y_{1}+ ) ( x_{2}+y_{2} ) | 11 |

811 | Find the points on the ( x ) -axis such that their perpendicular distance from the ( operatorname{line} frac{x}{a}+frac{y}{b}=1 ) is ( a b>0 ) A ( cdotleft(frac{a}{b}(b pm sqrt{a^{2}+b^{2}}), 0right) ) в. ( left(frac{a}{b}(-b pm sqrt{a^{2}+b^{2}}), 0right) ) c. ( left(frac{b}{a}(a pm sqrt{a^{2}+b^{2}}), 0right) ) D ( cdotleft(frac{b}{a}(-a pm sqrt{a^{2}+b^{2}}), 0right) ) | 11 |

812 | Prove that the general equation ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{2} boldsymbol{h} boldsymbol{x} boldsymbol{y}+boldsymbol{b} boldsymbol{y}^{2}+boldsymbol{2} boldsymbol{g} boldsymbol{x}+boldsymbol{2} boldsymbol{f} boldsymbol{y}+boldsymbol{c}= ) 0 represents two parallel straight lines if ( h^{2}=a b ) and ( b g^{2}=a f^{2} ) Prove also that the distance between them is ( frac{2 sqrt{g^{2}-a c}}{a(a+b)} ) | 11 |

813 | The slope and y-intercept of the following line are respectively ( 4 x-y=0 ) A. slope ( =m=4 ) and ( y- ) intercept ( =0 ) B. slope ( =m=-4 quad ) and ( quad y- ) intercept ( =0 ) C ( . ) slope ( =m=1 / 4 ) and ( y- ) intercept ( =0 ) D. slope ( =m=0 ) and ( y- ) intercept ( =1 / 4 ) | 11 |

814 | U TUN UI these. All points lying inside the triangle formed by the poms (1,3), (5,0) and (-1,2) satisfy (1986 – 2 Marks) (a) 3x + 2y > 0 (b) 2x + y-13 > 0 (C) 2x – 3y – 12 S 0 (d) -2x + y 2 0 (e) none of these. | 11 |

815 | Find the point ( (0, y) ) that is equidistant from (4,-9) and (0,-2) A ( cdotleft(0,-frac{93}{14}right) ) в. ( left(frac{93}{14}, 0right) ) ( ^{c} cdotleft(0,-frac{14}{93}right) ) D. ( left(frac{14}{93}, 0right) ) | 11 |

816 | If a straight line makes angles ( boldsymbol{alpha}, boldsymbol{beta}, boldsymbol{gamma} ) with the ( x, y, z ) axes respectively, then show that ( sin ^{2} alpha+sin ^{2} beta+sin ^{2} gamma=2 ) | 11 |

817 | Find the shortest distance between the ( x^{2}+y^{2}=9 ) and (6,8) is | 11 |

818 | Prove that (4,0),(-2,-3),(3,2),(-3,-1) coordinates are not the vertices of parallelogram. | 11 |

819 | If the slope of the line passing through the points ( (2, sin theta) ) and ( (1, cos theta) ) is 0 then the general solution of ( theta ), is A ( cdot n pi+frac{pi}{4}, forall n in Z ) B ( cdot n pi-frac{pi}{4}, forall n in Z ) c. ( _{n pi pm} frac{pi}{4}, forall n in Z ) D. ( n pi, forall n in Z ) | 11 |

820 | AP and BQ are the bisectors of two alternate interior angles formed by the intersection of a transversal t with parallel lines ( l ) and ( m . ) If ( angle P A B= ) ( boldsymbol{x} angle boldsymbol{Q} boldsymbol{B} boldsymbol{A} . ) Find ( boldsymbol{x} ) | 11 |

821 | Which of the following is/are true regarding the following linear equation: ( boldsymbol{x}+mathbf{5} boldsymbol{y}+mathbf{2}=mathbf{0} ) A. It passes through (0,-0.4) and ( m=-0.2 ) B. It passes through (0,0.4) and ( m=0.2 ) C. It passes through (0,-0.2) and ( m=-0.4 ) D. It passes through (0,0.2) and ( m=0.4 ) | 11 |

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