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

#### List of pair of linear equations in two variables Questions

Question No | Questions | Class |
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1 | A number consist of two digits whose sum is ( 11 . ) The number formed by reversing the digits is 9 less than the original number. Find the number. | 10 |

2 | Solve the following pair of simultaneous equations: ( frac{a}{4}-frac{b}{3}=0 ; frac{3 a+8}{5}=frac{2 b-1}{2} ) A ( . a=-4.5, b=12 ) в. ( a=4, b=-5 ) c. ( a=14, b=10.5 ) D. ( a=12, b=11.5 ) | 10 |

3 | Two straight lines passing through the point ( A(3,2) ) cut the line ( 2 y=x+3 ) and x-axis perpendicularly at ( P ) and ( Q ) respectively. The equation of the line PQ is A. ( 7 x+y-21=0 ) B. ( x+7 y+21=0 ) ( mathbf{c} cdot 2 x+y-8=0 ) D. ( x+2 y+8=0 ) | 10 |

4 | If ( 7 x+13 y=27 ) and ( 13 x+7 y=33 ) find ( x+y ) | 10 |

5 | Reduce the equation ( 2 x+3 y-4=0 ) to slope-intercept form and find its slope and ( y- ) intercept | 10 |

6 | A rectangular ( A 4 ) size paper is kept on cartesian plane coinciding the points ( (3,0),(-1,0),(0,-2) . ) Find the area of the paper in sq. units. A . 12 B. 8 c. 16 D. 10 | 10 |

7 | Solve the following pair of linear (simultaneous) equations by the method of elimination: ( boldsymbol{x}+mathbf{8} boldsymbol{y}=mathbf{1 9}, mathbf{2} boldsymbol{x}+mathbf{1 1} boldsymbol{y}=mathbf{2 8} ) A. ( x=3 ) and ( y=2 ) B. ( x=12 ) and ( y=5 ) c. ( x=1 ) and ( y=6 ) D. ( x=9 ) and ( y=-6 ) | 10 |

8 | Solve graphically the following pairs of equations ( boldsymbol{y}=mathbf{2} boldsymbol{x}+mathbf{1} ; boldsymbol{y}+mathbf{3} boldsymbol{x}-mathbf{6}=mathbf{0} ) ( mathbf{A} cdot(1,3) ) B ( cdot(2,3) ) ( mathbf{c} cdot(4,3) ) D. None of these | 10 |

9 | The equations ( a x+b y+c=0 ) and ( boldsymbol{d} boldsymbol{x}+boldsymbol{e} boldsymbol{y}+boldsymbol{f}=boldsymbol{0} ) represent the same straight line if and only if A ( cdot frac{a}{d}=frac{b}{c} ) в. ( c=f ) c. ( frac{a}{d}=frac{b}{e}=frac{c}{f} ) D. ( a=d, b=e, c=f ) | 10 |

10 | Solve for ( boldsymbol{x}, boldsymbol{y} ) ( (a+2 b) x+(2 a-b) y=2,(a- ) 2b) ( x+(2 a+b) y=3 ) A. ( x=(5 b-2 a), y=10 a b ) в. ( x=frac{5 b-2 a}{10 a b}, y=frac{a+10 b}{10 a b} ) c. ( x=frac{5 b-2 a}{10 a b}, y=frac{5 a+10 b}{10 a b} ) D. ( x=frac{5 b+2 a}{10 a b}, y=frac{a+10 b}{10 a b} ) | 10 |

11 | Solve the following pair of simultaneous equations: ( frac{mathbf{3}}{mathbf{a}}+frac{mathbf{4}}{mathbf{b}}=mathbf{2} ; frac{mathbf{9}}{mathbf{a}}-frac{mathbf{4}}{mathbf{b}}=mathbf{2} ) A ( . a=3, b=4 ) в. ( a=1, b=-2 ) c. ( a=5, b=-3 ) D. ( a=0, b=6 ) 6 | 10 |

12 | Find the value of ( ^{prime} x^{prime} ) and ( ^{prime} y^{prime} ) for the equations ( frac{a^{2}}{x}-frac{b^{2}}{y}=0 ; frac{a^{2} b}{x}+frac{b^{2} a}{y}= ) ( boldsymbol{a}+boldsymbol{b} ) where ( boldsymbol{x}, boldsymbol{y} neq mathbf{0} ) A . ( x=a^{2}, y=b^{2} ) B . ( x=b^{2}, y=a^{2} ) c. ( x=frac{b}{a}, y=frac{a}{b} ) D. ( x=frac{1}{b}, y=frac{1}{a} ) | 10 |

13 | Solve the following pair of equations: ( frac{5 y}{2}-frac{x}{3}=8 ) ( frac{y}{2}+frac{5 x}{3}=12 ) ( mathbf{A} cdot x=2 ; y=7 ) B. ( x=4 ; y=3 ) ( mathbf{c} cdot x=6 ; y=4 ) D. ( x=7 ; y=3 ) | 10 |

14 | Draw the graph of the above linear equation having Celsius on X-axis and Fahrenheit on Y-axis. | 10 |

15 | If the point (3,2) lies on the graph of the equation ( 5 x+a y=19, ) then find ( a ) ( mathbf{A} cdot mathbf{5} ) B. 7 ( c . ) D. 2 | 10 |

16 | If ( mathrm{I}, mathrm{m}, mathrm{n} & mathrm{I}^{prime}, mathrm{m}^{prime}, mathrm{n}^{prime} ) be the direction cosines of two lines which include an angle ( boldsymbol{theta} ) then ( mathbf{A} cdot cos theta=l l^{prime}+m m^{prime}+n n^{prime} ) B . ( sin theta=l l^{prime}+m m^{prime}+n n^{prime} ) ( mathbf{c} cdot cos theta=m n^{prime}+m^{prime} n+n l+n^{prime} l+l m^{prime}+l^{prime} m ) ( mathbf{D} cdot sin theta=m n^{prime}+m^{prime} n+n l+n^{prime} l+l m^{prime}+l^{prime} m ) | 10 |

17 | toppr Q Type your questiò (i) ( frac{-}{2 x}+frac{-}{3 y}=2 ; frac{-}{3 x}+frac{-}{2 y}=frac{-}{6} ) (ii) ( frac{mathbf{2}}{sqrt{boldsymbol{x}}}+frac{mathbf{3}}{sqrt{boldsymbol{y}}}=mathbf{2} ; frac{mathbf{4}}{sqrt{boldsymbol{x}}}-frac{mathbf{9}}{sqrt{boldsymbol{y}}}=-mathbf{1} ) (iii) ( frac{4}{x}+3 y=14 ; frac{3}{x}-4 y=23 ) (iv) ( frac{mathbf{5}}{boldsymbol{x}-mathbf{1}}+frac{mathbf{1}}{boldsymbol{y}-mathbf{2}}=mathbf{2} ; frac{mathbf{6}}{boldsymbol{x}-mathbf{1}}- ) ( frac{3}{y-2}=1 ) ( (v) frac{7 x-2 y}{x y}=5 ; frac{8 x+7 y}{x y}=15 ) (vi) ( 6 x+3 y=6 x y ; 2 x+4 y=5 x y ) (vii) ( frac{mathbf{1 0}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{2}}{boldsymbol{x}-boldsymbol{y}}=mathbf{4} ; frac{mathbf{1 5}}{boldsymbol{x}+boldsymbol{y}}- ) ( frac{5}{x-y}=-2 ) (viii) ( frac{1}{3 x+y}+frac{1}{3 x-y}= ) ( frac{3}{4} ; frac{1}{2(3 x+y)}-frac{1}{2(3 x-y)}=frac{-1}{8} ) | 10 |

18 | A man starts his job with a certain monthly salary and a fixed increment every year. If his salary will be Rs. 11000 after 2 years and Rs. 14000 after 4 years of his service. What is his starting salary and what is the annual increment? A. Starting salary is Rs. 7500 and increment is Rs. 2500 B. Starting salary is Rs.5000 and increment is Rs. 1800 C. Starting salary is Rs. 8000 and increment is Rs. 1500 D. Starting salary is Rs. 7000 and increment is Rs. 1300 | 10 |

19 | A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs 1500 after 4 year of service and Rs 1800 after 10 years of service, what was his starting salary and what is the annual increment? | 10 |

20 | Solve the simultaneous equations by substitution method. ( -boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{0} ; mathbf{1 0} boldsymbol{x}+mathbf{1 5} boldsymbol{y}=mathbf{1 0 5} ) | 10 |

21 | No. of Solutions for: ( frac{4}{3} x+2 y=8 ) [ 2 x+3 y=12 ] | 10 |

22 | Solve the following equations by substitution method. ( boldsymbol{x}=mathbf{2} boldsymbol{y}-mathbf{1} ; boldsymbol{y}=mathbf{2} boldsymbol{x}-mathbf{7} ) A. ( x=8, y=3 ) в. ( x=2, y=3 ) c. ( x=5, y=3 ) D. ( x=1, y=3 ) | 10 |

23 | Solve the equations ( frac{5}{x-1}+frac{1}{y-2}=2 ) and ( frac{6}{x-1}- ) ( frac{3}{y-2}=1 ) | 10 |

24 | The pair of equations ( boldsymbol{y}=mathbf{0} ) and ( boldsymbol{y}=-mathbf{7} ) have : A. one solution B. two solutions c. infinitely many solutions D. no solution | 10 |

25 | For what value of ” ( c^{prime prime} ) will the equations ( 3 x-4 y=7 ) and ( x+c y=13 ) have no solution? A ( cdot frac{3}{4} ) B. ( frac{4}{3} ) ( c .-4 ) D. ( frac{-4}{3} ) | 10 |

26 | If ( 2 x+3 y=6 sqrt{3} ) and ( 2 x-3 y=6, ) find the value of ( x y ? ) A. ( x y=3 ) в. ( x y=2 ) c. ( x y=1 ) D. ( x y=7 ) | 10 |

27 | Solve the following system of equation for ( x ) and ( y ) ( frac{5}{x-1}+frac{1}{y-2}=2, frac{6}{x-1}-frac{3}{y-2}=1 ) | 10 |

28 | Solve the equations using elimination method: ( x-y=2 ) and ( -x y=-10 ) A. (6,-4) () в. (6,4) c. (-6,-4) D. (-6,4) | 10 |

29 | Reduce the equation ( 4 x+6 y-7=0 ) to intercept form.Hence find the length of the segment intercepted between the axes. | 10 |

30 | Determine the value of ( k ) so that the following linear equations has no solution: ( (3 k+1) x+3 y-2=0 ) and ( left(k^{2}+right. ) 1) ( boldsymbol{x}+(boldsymbol{k}-mathbf{2}) boldsymbol{y}-mathbf{5}=mathbf{0} ) A. ( k=-1 ) B. ( k=3 ) c. ( k=-7 ) D. ( k=8 ) | 10 |

31 | ( frac{boldsymbol{x} boldsymbol{y}}{boldsymbol{x}+boldsymbol{y}}=frac{boldsymbol{6}}{mathbf{5}} ) ( frac{x y}{y-x}=6 ) A. ( x=-2, y=3 ) в. ( x=3, y=2 ) c. ( x=2, y=3 ) D. ( x=-3, y=-2 ) | 10 |

32 | Solve: ( 37 x+29 y=45 ; 29 x+37 y=21 ) | 10 |

33 | Graph ( ( i v ) ) is represented by which equation? ( (i) ) (i) (iii) (iv) A ( cdot y=2 x ) B. ( y+x=2 ) ( mathbf{c} cdot y=2+x ) D. ( x=y+22 ) | 10 |

34 | Equation of a straight line passing through the point (2,3) and inclined at an angle of ( tan ^{-1} frac{1}{2} ) with the line ( y+ ) ( 2 x=5, ) is: ( mathbf{A} cdot y=3 ) B. ( x=2 ) c. ( 3 x+4 y-18=0 ) D. ( 4 x+3 y-17=0 ) | 10 |

35 | Determine the values of a and ib for which the given system of equations has infinitely many solutions: ( (2 a-1) x-3 y=5 ) and ( 3 x+(b- ) 2) ( y=3 ) | 10 |

36 | Find ( p ) for which given equation has unique solution ( 4 x+p y+8=0 ) ( 2 x+2 y+2=0 ) | 10 |

37 | Solve the following system of equations ( frac{mathbf{6}}{boldsymbol{x}+boldsymbol{y}}=frac{mathbf{7}}{boldsymbol{x}-boldsymbol{y}}+mathbf{3}, frac{mathbf{1}}{mathbf{2}(boldsymbol{x}+boldsymbol{y})}= ) ( frac{1}{3(x-y)} ) where ( x+y neq 0 ) and ( x ) ( boldsymbol{y} neq mathbf{0} ) | 10 |

38 | Draw the graph of the straight line given by the equation ( 4 x-3 y+36=0 ) Calculate the area of the triangle formed by the line drawn and the coordinate axes. A. Area ( =45 ) sq. units B. Area = 54 sq. units c. Area ( =48 ) sq. units D. Area = 58 sq. units | 10 |

39 | Find the equations of the lines for which ( cot theta=frac{1}{2}, ) where ( theta ) is the angle of inclination of the line and ( y- ) intercept is ( frac{-3}{2} ) | 10 |

40 | Solve the following puzzles using the equations: The present age of Beena is 2 years | 10 |

41 | Solve: ( 3 x-5=x-5 ) | 10 |

42 | Solve ( boldsymbol{x}+mathbf{4} boldsymbol{y}=mathbf{2 4} boldsymbol{x} boldsymbol{y}, boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{2} mathbf{1} boldsymbol{x} boldsymbol{y} ) | 10 |

43 | The cost of 7 erasers and 5 pencils is Rs ( mathbf{5 8} ) and the cost of 5 erasers and 6 pencils is Rs.56. Formulate this problem algebraically and solve it graphically. | 10 |

44 | Reduce the equation ( 3 x+4 y-5=0 ) to intercept form.Hence find the length of the segment intercepted between the axes. | 10 |

45 | Solve the following pair of equations by cross multiplication rule. ( boldsymbol{x}+boldsymbol{y}=boldsymbol{a}+boldsymbol{b}, boldsymbol{a} boldsymbol{x}-boldsymbol{b} boldsymbol{y}=boldsymbol{a}^{2}-boldsymbol{b}^{2} ) A . ( x=1, y=a b ) в. ( x=a+b, y=b ) c. ( x=a, y=b ) D. ( x=b, y=1 ) | 10 |

46 | The number of solutions for ( 2 x+3 y= ) 10 and ( 4 x+6 y=25 ) are | 10 |

47 | Intersection point of lines ( boldsymbol{x}=mathbf{2}, boldsymbol{x}= ) -2 is A. (0,0) (年) ( 0,0,0,0,0,1, ) в. (1,1) c. It does not exist D. None | 10 |

48 | A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number A . 25 B. 45 c. 75 D. None of these | 10 |

49 | ( a, b, c(a>c) ) are the three digits, from left to right of a three digit number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digit 4 in its unit’s place. The other two digits from left to right are – A. 5 and 4 B. 5 and 9 c. 4 and 5 D. 9 and 5 | 10 |

50 | Find the point of intersection of the lines represented by ( 3 x-2 y=6 ) and the y-axis. | 10 |

51 | If the lines given by ( 3 x+2 k y=2 ) and ( mathbf{2} boldsymbol{x}+mathbf{5} boldsymbol{y}+mathbf{1}=mathbf{0} ) are parallel, then the value of ( k ) is A ( cdot frac{-5}{4} ) B. ( frac{2}{5} ) c. ( frac{15}{4} ) D. ( frac{3}{2} ) | 10 |

52 | ( A ) and ( B ) each have a certain number of mangoes. A says to B “If you give me 30 of your mangoes, I will have twice as many as left with you.” B replies, “If you give me ( 10, ) I will have thrice as many as left with you.” How many mangoes does each have? | 10 |

53 | If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order, we get 4 as a quotient and 3 as a remainder. Now if we divide the required number by the sum of its digits, we get 8 as a quotient and 7 as a remainder. Find the number. | 10 |

54 | Represent the following pair of equations graphically and write the coordinates of points where the line intersects ( boldsymbol{y} ) -axis ( boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{6} ) ( 2 x-3 y=12 ) | 10 |

55 | ( A ) and ( B ) are friends and their ages differ by 2 years. A’s father D is twice as old as A and B is twice as old as his sister ( C ). The age of ( D ) and ( C ) differ by 40 years. Find the ages of ( A ) and ( B ) | 10 |

56 | For which value of the given system of equations have infinitely many solution ( (k-3) x+3 y=k ) and ( k x+k y=12 ) A . -6 B. 6 ( c cdot 0 ) D. 3 | 10 |

57 | 11. The ratio of the present ages of Sunita and Vinita is 4 : 5. Six years hence, the ratio of their ages will be 14 : 17. What will be the ratio of their ages 12 years hence ? (1) 17:19 (2) 15 : 19 (3) 13:15 (4) 16:19 | 10 |

58 | Solve the following simultaneous equations by substitution method and find the value of ( x 3 x-2 y=4 ; 6 x+ ) ( 7 y=19 ) | 10 |

59 | Solve the simultaneous equations: ( frac{1}{x}+frac{1}{y}=12, frac{3}{x}-frac{2}{y}=1 ) | 10 |

60 | Reduce the equation ( 9 x+7 y-3=0 ) to intercept form.Hence find the length of the segment intercepted between the axes. | 10 |

61 | Solve ( : boldsymbol{x}+boldsymbol{y}=mathbf{1 1 0}, boldsymbol{y}=boldsymbol{x}+mathbf{4} ) | 10 |

62 | A pair of linear equations in two variables ( x ) and ( y ) is ( a_{1} x+b_{1} y+c_{1}=0 ) and ( a_{2} x+b_{2} y+c_{2}=0, ) such that ( frac{a_{1}}{a_{2}} neq frac{c_{1}}{c_{2}}, ) then it has A. Unique solution B. No solution c. Infinitely many solutions D. Can’t say | 10 |

63 | Solve the following pair of linear (simultaneous) equations by the method of elimination: ( boldsymbol{y}=boldsymbol{4} boldsymbol{x}-mathbf{7} ) ( 16 x-5 y=25 ) A ( cdot x=frac{3}{2}, y=6 ) B・ ( x=frac{5}{2}, y=3 ) c. ( _{x}=frac{7}{4}, y=2 ) D. ( x=frac{9}{2}, y=0 ) | 10 |

64 | 64. If 32x – y = 3*+y = 27. then the value of 3x-y will be (1) 3 (2) ja | 10 |

65 | Solve: ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}= ) ( mathbf{1 4} ) A. ( x=2 ; y=3 ) В. ( x=3 ; y=2 ) c. ( x=1 ; y=5 ) D. ( x=4 ; y=1 ) | 10 |

66 | Solve the given pair of equations by substitution method: ( boldsymbol{x}+boldsymbol{y}=mathbf{0} ) ( boldsymbol{y}-boldsymbol{x}=boldsymbol{6} ) A. (2,7) (i) в. (-3,3) c. (4,9) (年. (4,9) D. (-6,2) | 10 |

67 | f we write equation as ( a x+b y+c=0 ) then ( a=? ) 4 B. ( c ) ( D ) | 10 |

68 | Use the graphical method to find the value of ( k, ) if ( (5, k-2) ) lies on the straight line ( boldsymbol{x}-mathbf{2} boldsymbol{y}+mathbf{1}=mathbf{0} ) A .2 B. 3 ( c cdot 4 ) D. 5 | 10 |

69 | Given ( 3 x-4 y=7 ) and ( x+c y=13 ) for what value of “c” will the two equation not have a solution? A ( cdot frac{3}{4} ) B. ( frac{4}{3} ) ( c cdot-4 ) D. ( frac{-4}{3} ) | 10 |

70 | Find the equations to the straight lines which pass through the origin and are inclined at ( 75^{circ} ) to the straight line ( (x+y) sqrt{3}+y-x=a ) | 10 |

71 | Equation of a straight line passing through the point (2,3) and inclined at an angle of ( tan ^{-1}left(frac{1}{2}right) ) with the line ( y+ ) ( 2 x=5 ) is This question has multiple correct options ( mathbf{A} cdot y=3 ) B. ( x=2 ) c. ( 3 x+4 y-18-0 ) D. ( 4 x+3 y-17=0 ) | 10 |

72 | Write the equation of a line which is parallel to ( x- ) axis at a distance of 5 units from it, and another line parallel to ( y- ) axis at a distance of 7 units from it. Draw the graphs and write the coordinates of point of intersection. | 10 |

73 | Solve the following systems of equations graphically: ( boldsymbol{x}+boldsymbol{y}=boldsymbol{6} ) ( boldsymbol{x}-boldsymbol{y}=mathbf{2} ) | 10 |

74 | Identify the system of equations: ( 2 x- ) ( 2 y=2 ) and ( x-y=1 ) A. inconsistent B. consistent c. dependent D. non-linear | 10 |

75 | In the system of equations ( boldsymbol{x}+boldsymbol{y}=mathbf{4} boldsymbol{x} boldsymbol{y} ) and ( frac{1}{x}+frac{2}{y}=10, ) the value of ( x ) and ( y ) will be A ( cdot-frac{1}{3} ) and ( frac{1}{6} ) B ( cdot frac{1}{5} ) and ( frac{1}{6} ) c. ( -frac{1}{2} ) and ( frac{1}{6} ) D. ( +frac{1}{3} ) and ( -frac{1}{2} ) | 10 |

76 | Write a pair of linear equations which has the unique solution ( x=-1, y=3 . ) How many such pairs can you write? A. ( x+y=2 & x-y=-4 ; ) infinite B. ( 2 x+y=6 & 2 x-3 y=6 ; 3 ) c. ( 5 x-8 y=13 ) & ( x+3 y=7 ; 8 ) D. Cannot be determined | 10 |

77 | Find the common solution: ( 2 x+y=8 ) ( boldsymbol{x}-boldsymbol{y}=mathbf{1} ) | 10 |

78 | What is the nature of the graphs of a system of linear equations with exactly one solution? A. Parallel lines B. Perpendicular lines c. coincident lines D. Intersecting lines | 10 |

79 | The graph of ( 2 x+3 y=6 ) is represented by ( A ) 3 c. ॥ D. IV | 10 |

80 | A member of these family with positive gradient making an angle of ( frac{pi}{4} ) with the line ( 3 x-4 y=2, ) is A. ( 7 x-y-5=0 ) B. ( 4 x-3 y+2=0 ) c. ( x+7 y=15 ) D. ( 5 x-3 y-4=0 ) | 10 |

81 | Rohit says to Ajay “Give me a hundred, I shall then become twice as rich as you.” Ajay replies “If you give me ten, I shall be six times as rich as you.” How much does each have originally? A. Rohit has Rs. 20 and Ajay has Rs. 90 B. Rohit has Rs. 50 and Ajay has Rs. 200 c. Rohit has Rs. 40 and Ajay has Rs. 170 D. Rohit has Rs. 56 and Ajay has Rs. 190 | 10 |

82 | Solve the following pairs of equations by reducing them to a pair of linear equations: ( frac{7 x-2 y}{x y}=5 ) ( frac{8 x+7 y}{x y}=15 ) | 10 |

83 | Solve the simultaneous equation: ( frac{2}{x}+frac{2}{3 y}=frac{1}{6} ; frac{3}{x}+frac{2}{y}=0 ) | 10 |

84 | What is the value of ( x ) for the following equations: ( x-5 y=10 ) and ( x+y=4 ? ) (Use cross multiplication method) ( mathbf{A} cdot x=5 ) B. ( x=4 ) c. ( x=3 ) D. ( x=2 ) | 10 |

85 | Draw the graph of straight line ( y= ) ( -2 x+3 . ) Use your graph to find the area between the line and co-ordinate axes. A. 4.66 sq.units B. 3.25 sq.units c. 2.25 sq.units D. 5.66 sq.units | 10 |

86 | Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is ( 3 x+4 y=4 ) and the opposite vertex of the hypotenuse is ( (2,2), ) will be ( ? ) A. ( x-7 y+12=0 ) в. ( 7 x+y-12=0 ) c. ( x-7 y+16=0 ) D. ( 7 x+y+16=0 ) | 10 |

87 | Find the equations of the lines for which ( tan theta=frac{1}{sqrt{2}}, ) where ( theta ) is the angle of inclination of the line and ( x- ) intercept is 3 | 10 |

88 | solve the equation using substitution method: ( 2 x+3 y=13 ) and ( 4 x+5 y=23 ) A ( cdot(-2,3) ) B. (2,3) c. (2,-3) D. (-2,-3) | 10 |

89 | ( A equiv(1,2) ) and ( B equiv(7,10) ) are two points. If ( boldsymbol{P}(boldsymbol{x}, boldsymbol{y}) ) is a point such that ( angle A P B=60^{circ} ) and area of ( Delta A P B ) is maximum, then which of the following is (are) TRUE? This question has multiple correct options A. ( P ) lies on any line perpendicular to ( A B ) B. ( P ) lies on the perpendicular bisector of ( A B ) c. ( P ) lies on the line ( 3 x+4 y=36 ) D. Radius of circumcircle of ( Delta P A B ) is 10 units | 10 |

90 | If we divide a two-digit number by the sum of its digits, we get 6 as a quotient and 2 as a remainder. Now if we divide it by the product of its digits, we get 5 as a quotient and 2 as a remainder. Find the number. | 10 |

91 | Find the equations of the lines for which ( tan theta=frac{1}{3}, ) where ( theta ) is the angle of inclination of the line and ( y- ) intercept is ( frac{-1}{2} ) | 10 |

92 | Solve : ( frac{4}{x}+frac{5}{y}=7 ; frac{3}{x}+frac{4}{y}=5 ) | 10 |

93 | If the line ( 2 x+3 y+12=0 ) cuts the axes at ( A ) and ( B ), then the equation of the perpendicular bisector of ( A B ) is A. ( 3 x-2 y+5=0 ) B. ( 3 x-2 y+7=0 ) c. ( 3 x-2 y+9=0 ) D. ( 3 x-2 y+8=0 ) | 10 |

94 | If ( boldsymbol{y}=boldsymbol{a}+frac{boldsymbol{b}}{boldsymbol{x}}, ) where ( boldsymbol{a} ) and ( boldsymbol{b} ) are constants and if ( boldsymbol{y}=mathbf{1} ) when ( boldsymbol{x}=-mathbf{1} ) and ( y=5 ) when ( x=-5, ) what is the value of ( a+b ? ) A. -1 B. 0 ( c cdot 1 ) D. 11 | 10 |

95 | Solve the systems of equations: ( frac{boldsymbol{x}-mathbf{2}}{mathbf{4}}+frac{boldsymbol{y}+mathbf{1}}{mathbf{3}}=mathbf{2} ; frac{boldsymbol{x}+mathbf{1}}{mathbf{7}}+frac{boldsymbol{y}-mathbf{3}}{mathbf{2}}= ) ( frac{1}{2} ) A ( cdot(6,2) ) в. (2,2) c. (2,3) (年. (2,3,3) D. (3,4) | 10 |

96 | A two-digit number is thrice as large as the sum of its digits, and the square of that sum is equal to the trippled required number. Find the number | 10 |

97 | Through the point (3,4) are drawn two straight lines each inclined at ( 45^{circ} ) to the straight line ( x-y=2 . ) Find their equations and find also the area included by the three lines. | 10 |

98 | Solve ( : frac{3}{x+y}+frac{2}{x-y}=2 ) and ( frac{9}{x+y}-frac{4}{x-y}=1 ) A. ( x=frac{2}{5} ; y=frac{7}{2} ) B. ( x=frac{5}{2} ; y=frac{1}{2} ) c. ( x=frac{6}{7} ; y=frac{4}{3} ) D. ( x=frac{7}{3} ; y=frac{1}{2} ) | 10 |

99 | Solve ( frac{33}{u+2}+frac{12}{v-3}=123 ) and ( frac{12}{u+2}+frac{33}{v-3}=102 ) | 10 |

100 | Given that both ( x ) and ( y ) are positive integers. Solve the following systems of equations. ( boldsymbol{x}^{2}+boldsymbol{x} boldsymbol{y}=mathbf{1 5}, boldsymbol{y}^{2}+boldsymbol{x} boldsymbol{y}=mathbf{1 0} ) | 10 |

101 | Solve the following pairs of equations, graphically: ( 2 x-3 y=-6 ) and ( x-frac{y}{2}=1 ) ( mathbf{A} cdot(3,2) ) в. (3,3) c. (4,4) D. (3,4) | 10 |

102 | The perpendicular bisector of the line segment joining ( boldsymbol{P}(1,4) ) and ( boldsymbol{Q}(boldsymbol{k}, boldsymbol{3}) ) has ( boldsymbol{y}- ) intercept ( -4 . ) Then a possible value of ( k ) is ( ? ) A . -2 B. -4 c. D. 2 | 10 |

103 | f we write equation as ( a x+b y+c=0 ) then ( b=? ) 4 B. ( c ) ( D ) | 10 |

104 | Yamini and Fatima, two students of Class IX of a school, together contributed Rs 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which the given data will satisfy and also plot its graph. A. ( x+y=100 ) в. ( x+y=112 ) c. ( x+y=50 ) D. ( x+2 y=100 ) | 10 |

105 | Find the equations of the lines for which ( tan theta=frac{1}{4}, ) where ( theta ) is the angle of inclination of the line and ( y- ) intercept is ( frac{-3}{2} ) | 10 |

106 | Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method? ( 3 x-5 y=20,6 x-10 y=40 ) A. No solutions B. Unique solutions, ( x=0 ) and ( y=1 ) c. Infinitely many solutions D. Data insufficient | 10 |

107 | Solve the following pairs of equations by reducing them to a pair of linear equations: ( frac{4}{x}+3 y=14, frac{3}{x}-4 y=23 ) | 10 |

108 | Solve the following pair of equation by the elimination method. ( boldsymbol{x}+boldsymbol{y}=mathbf{1 4}, boldsymbol{x}-boldsymbol{y}=mathbf{4} ) | 10 |

109 | Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: ( 2 x+ ) ( mathbf{3} boldsymbol{y}=mathbf{8}, mathbf{2} boldsymbol{x}=mathbf{2}+mathbf{3} boldsymbol{y} ) A ( cdot x=2, y=frac{3}{2} ) в. ( x=3, y=5 ) c. ( _{x}=frac{5}{2}, y=1 ) D. ( x=frac{3}{2}, y=4 ) | 10 |

110 | Solve ( boldsymbol{x}+boldsymbol{y}=mathbf{3} ) ( boldsymbol{x}-boldsymbol{y}=mathbf{1} ) | 10 |

111 | ( frac{1}{3} x-frac{1}{6} y=4 ) ( 6 x-a y=8 ) In the system of equations above, ( a ) is a constant. If the system has no solution, what is the value of ( boldsymbol{a} ) A ( cdot frac{1}{3} ) B. ( c .3 ) D. | 10 |

112 | Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years.Four years ago, the product of their ages in years was 48 | 10 |

113 | Solve the following equations graphically [ begin{array}{l} mathbf{2 x}+boldsymbol{y}=mathbf{6} \ mathbf{2 x – y}+mathbf{2}=mathbf{0} end{array} ] | 10 |

114 | Based on equations reducible to linear equations Solve for ( x ) and ( y: 9+25 x y=53 x ) and | 10 |

115 | The equation of the straight line cutting off an intercept 8 on ( x ) -axis and making an angle of ( 60^{circ} ) with the positive direction of ( y- ) axis is A ( . x-sqrt{3} y-8=0 ) B. ( x+sqrt{3} y=8 ) c. ( y-sqrt{3} x=8 ) D. ( y+sqrt{3} x=8 ) | 10 |

116 | The equation of the straight line which passes through (1,1) and making angle ( 60^{circ} ) with the line ( x+sqrt{3} y+2 sqrt{3}=0 ) is/are. A. ( y=1 ) B. ( x=1 ) c. ( x+y=2 ) D. ( x+sqrt{3} y-sqrt{3}-1=0 ) | 10 |

117 | The equation of perpendicular bisector of the line segment joining the points (1,2) and (-2,0) is- A ( .5 x+2 y=1 ) B. ( 4 x+6 y=1 ) c. ( 6 x+4 y=1 ) D. None of these | 10 |

118 | Using substitution method find the value of ( x ) and ( y: ) ( 4 x+9 y=5 ) and ( -5 x+3 y=8 ) A. -1 and ( frac{-2}{5} ) B. -1 and ( frac{2}{5} ) c. -1 and 1 D. 1 and ( frac{2}{5} ) | 10 |

119 | If the equations ( 4 x+7 y=10 ) and ( 10 x+k y=25 ) represent coincident lines, then the value of ( k ) is A . 5 в. ( frac{17}{2} ) c. ( frac{27}{2} ) D. ( frac{35}{2} ) | 10 |

120 | Find the equation to, and the length of the perpendicular drawn from the point (1,1) upon the straight line ( 3 x+4 y+ ) ( 5=0, ) the angle between the axes being ( 120^{circ} ) | 10 |

121 | Solve the following simultaneous equations: ( frac{27}{x-2}+frac{31}{y+3}=85 ; quad frac{31}{x-2}+ ) ( frac{27}{y+3}=89 ) A ( cdot x=frac{3}{4}, y=4 ) B. ( x=frac{5}{2}, y=-2 ) c. ( _{x}=frac{4}{3}, y=3 ) D. ( x=frac{7}{2}, y=6 ) | 10 |

122 | Find the value of ( p, ) if ( p q+12=3 p+ ) ( p r ) and ( q-r=7 ) A . -3 B. -4 ( c cdot frac{1}{3} ) D. E. ( -frac{6}{5} ) | 10 |

123 | If ( boldsymbol{x}+boldsymbol{y}=mathbf{2 5} ) and ( frac{mathbf{1 0 0}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{3 0}}{boldsymbol{x}-boldsymbol{y}}=mathbf{6} ) then the value of ( x-y ) is A . 18 B . 20 c. 15 D. 10 | 10 |

124 | Two perpendicular lines are intersecting at ( (4,3) . ) One meeting coordinate axis at ( (4,0), ) find the coordinates of the intersection of other line with the cordinate axes. A ( .(0,3) ) B. (1,3) D. None of these | 10 |

125 | Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a ring on the items kept in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla half the number of rides she had on the Giant Wheel. Each ride costs ( R s .3 ), and a game Hoopla costs ( R s .4 . ) If she spent Rs.20 in the fair, represent this situation algebraically | 10 |

126 | Solve the following pairs of equations by reducing them to a pair of linear equations: ( frac{2}{sqrt{x}}+frac{2}{sqrt{y}}=2, frac{4}{sqrt{x}}-frac{9}{sqrt{y}}=-1 ) | 10 |

127 | Find the values of ( x ) and ( y, ) if ( frac{mathbf{2}}{boldsymbol{x}}+frac{mathbf{6}}{boldsymbol{y}}=mathbf{1 3} ; quad frac{mathbf{3}}{boldsymbol{x}}+frac{boldsymbol{4}}{boldsymbol{y}}=mathbf{1 2} ) A ( cdot x=frac{1}{6}, y=frac{2}{3} ) B. ( x=frac{1}{3}, y=frac{2}{3} ) c. ( x=frac{1}{7}, y=frac{2}{3} ) D. ( x=frac{1}{2}, y=frac{2}{3} ) | 10 |

128 | The number of solutions for the system of equations ( 2 x+y=4,3 x+2 y=2 ) and ( boldsymbol{x}+boldsymbol{y}=-boldsymbol{2} ) is ( mathbf{A} cdot mathbf{1} ) B . 2 ( c cdot 3 ) D. infinitely many E . | 10 |

129 | A line passes through the origin and makes an angle of ( pi / 4 ) with the line ( boldsymbol{x}-boldsymbol{y}+mathbf{1}=mathbf{0} . ) Then This question has multiple correct options A. Equation of the line is ( x=0 ) B. The equation of the line is ( y=0 ) C. The point of intersection of the line with the given line ( s(-1,0) ) D. The point of intersection of the line with the given line is (0,1) | 10 |

130 | Solve the following pair of simultaneous equations: ( 4 x+frac{3}{y}=1 ; 3 x-frac{2}{y}=5 ) A. ( x=-6, y=7 ) в. ( x=-3, y=1 ) c. ( x=1, y=-1 ) D. ( x=2, y=0 ) | 10 |

131 | Kate and Nora each have a sum of money. The ratio of the amount of money Kate has to that of Nora is 3: 5 After Nora gives Rs. 150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes ( 7: 9 . ) Find the sum of money Kate had initially. | 10 |

132 | Solve: ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}=14 ) Hence find the value of ( k, ) if ( y=k x-2 ) A ( cdot x=4, y=1 ) and ( k=frac{2}{3} ) в. ( x=5, y=3 ) and ( k=frac{3}{5} ) c. ( _{x}=3, y=2 ) and ( k=frac{4}{3} ) D. ( x=1, y=2 ) and ( k=frac{9}{2} ) | 10 |

133 | On comparing the ratios ( frac{boldsymbol{a}_{1}}{boldsymbol{a}_{2}}, frac{boldsymbol{b}_{1}}{boldsymbol{b}_{2}} ) and ( frac{boldsymbol{c}_{1}}{boldsymbol{c}_{2}} ) find out whether the following pairs of linear equations are consistent, or inconsistent. ( mathbf{5} boldsymbol{x}-mathbf{3} boldsymbol{y}=mathbf{1 1} ;-mathbf{1 0} boldsymbol{x}+mathbf{6} boldsymbol{y}=mathbf{2 2} ) A. Consistent B. Inconsistent c. Ambiguous D. Data insufficient | 10 |

134 | Find the value of ( a, ) so that the following system of equations bears no solution ( 2 y-6 x=28 ) ( 4 y-a x=28 ) A . -12 B. – – ( c cdot 3 ) D. 6 ( E cdot 12 ) | 10 |

135 | The equation of perpendicular bisector of the line segment joining the points (-1,-2) and (2,0) is A ( .5 x+2 y=1 ) в. ( 4 x+6 y=-1 ) c. ( 6 x+4 y=-1 ) D. none of these | 10 |

136 | Solve for ‘u’ and ‘v’, 2 ( (3 u-v)=5 u v ) and ( 2(u+3 v)=5 u v ) | 10 |

137 | Solve the equations ( 2 x-3 y=9 ) ( 4 x+6 y=18 ) | 10 |

138 | If ( 2 x=t+sqrt{t^{2}+4} ) and ( 3 y=t- ) ( sqrt{t^{2}+4} ) then the value of ( y ) when ( x=frac{2}{3} ) is A . -2 B. 1 ( c cdot-1 ) D. | 10 |

139 | Reduce the equation ( x+2 y-6=0 ) to slope-intercept form and find its slope and ( boldsymbol{y}- ) intercept. | 10 |

140 | A particular work can be completed by 6 men and 6 women in 24 days; whereas the same work can be completed by 8 men and 12 women in 15 days, according to the amount of work done one man is equivalent to how many women? A ( cdot_{frac{1}{2}} ) women в. ( 5 frac{1}{3} ) women ( ^{mathrm{c}} cdot_{5} frac{2}{3} ) women D. ( frac{3}{2} ) women | 10 |

141 | Coordinates of a square are: ( (2,2),(-2,2),(-2,-2) . ) Find the length of the side of square A .4 B . 2 ( c cdot 6 ) D. None of these | 10 |

142 | Solve: ( 8 x-7=6 ) | 10 |

143 | If ( boldsymbol{y}=boldsymbol{a}+frac{boldsymbol{b}}{boldsymbol{x}}, ) where ( boldsymbol{a} ) and ( boldsymbol{b} ) are constants, and if ( boldsymbol{y}=mathbf{1} ) when ( boldsymbol{x}=-mathbf{1} ) and ( y=5 ) when ( x=-5, ) then ( a+b ) equals. A . -1 B. c. D. 10 E. 11 | 10 |

144 | If one line of the pair of lines ( a x+ ) ( 2 b x y+b y^{2}=0 ) bisects the angle bet. Co-ordinates axes in the quadrant ( A cdot a-b=12 b ) B. ( a+b=-2 b ) ( c cdot a+b=2 b ) D. ( (a-b)^{2}=4 b^{2} ) | 10 |

145 | If ( 2 x+y=23 ) and ( 4 x-y=19 ; ) find the values of ( x-3 y ) and ( 5 y-2 x ) A. The values of ( x-3 y ) and ( 5 y-2 x ) are -20 and 31 respectively B. The values of ( x-3 y ) and ( 5 y-2 x ) are 0 and 3 respectively c. The values of ( x-3 y ) and ( 5 y-2 x ) are 14 and -9 respectively D. The values of ( x-3 y ) and ( 5 y-2 x ) are 5 and 23 respectively | 10 |

146 | Reduce the equation ( x+2 y-3=0 ) to slope-intercept form and find its slope and ( boldsymbol{y}- ) intercept. | 10 |

147 | A line passing through the origin and making an angle ( frac{pi}{4} ) with the line ( y- ) ( mathbf{3} boldsymbol{x}=mathbf{5} ) has the equation This question has multiple correct options A. ( x+2 y=0 ) в. ( 2 x=y ) c. ( x=2 y ) ( mathbf{D} cdot y+2 x=0 ) | 10 |

148 | Draw a graph for the following pair of linear equations in two variables and find their solution from the graph. ( 2 x+y=5 ) ( 3 x-2 y=4 ) | 10 |

149 | Choose the correct options for the figure This question has multiple correct options A. Point A is substitute into the equation for line ( l_{2} ) B. Point A is substitute into the equation for line ( l_{1} ) C. Point ( C ) is substitute into the equation for line ( l_{1} ) D. Point ( C ) is substitute into the equation for line ( l_{2} ). | 10 |

150 | Solve the following pair of linear equations by the substitution method. (i) ( boldsymbol{x}+boldsymbol{y}=mathbf{1 4} ; boldsymbol{x}-boldsymbol{y}=mathbf{4} ) (ii) ( s-boldsymbol{t}=mathbf{3} ; frac{boldsymbol{s}}{mathbf{3}}+frac{boldsymbol{t}}{mathbf{2}}=mathbf{6} ) (iii) ( 3 x-y=3 ; 9 x-3 y=9 ) (iv) ( 0.2 x+0.3 y=1.3 ; 0.4 x+0.5 y= ) ( mathbf{2 . 3} ) (v) ( sqrt{mathbf{2}} boldsymbol{x}+sqrt{mathbf{3}} boldsymbol{y}=mathbf{0} ; sqrt{mathbf{3}} boldsymbol{x}-sqrt{mathbf{8}} boldsymbol{y}=mathbf{0} ) (vi) ( frac{mathbf{3} boldsymbol{x}}{mathbf{2}}-frac{mathbf{5} boldsymbol{y}}{mathbf{3}}=-mathbf{2} ; frac{boldsymbol{x}}{mathbf{3}}+frac{boldsymbol{y}}{mathbf{2}}=frac{mathbf{1 3}}{mathbf{6}} ) | 10 |

151 | The sum of the digits of a two digit number is ( 15 . ) If 9 is added to the number, the digit are reversed. Find the number. | 10 |

152 | Based on equations reducible to linear equations Solve for ( x ) and ( y: frac{2}{x-1}+frac{y-2}{4}= ) ( 2 ; frac{3}{2(x-1)}+frac{2(y-2)}{5}=frac{47}{20} ) A ( . x=3, y=6 ) в. ( x=1, y=5 ) c. ( x=2, y=-7 ) D. ( x=5, y=-9 ) | 10 |

153 | By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them. ( boldsymbol{x}+boldsymbol{y}=mathbf{3} ) and ( mathbf{3} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{9} ) | 10 |

154 | Solve the equations using graphical method: ( boldsymbol{x}-boldsymbol{y}=mathbf{3} ) and ( boldsymbol{x}+boldsymbol{y}=mathbf{1 1} ) A ( .(7,4) ) в. (-7,3) c. (7,-4) D. (-7,4) | 10 |

155 | 26. The number of values of k, for which the system of equations : [JEE M 2013] (k+1)x+8y=4k kox + (k+3) y = 3k-1 has no solution, is (a) infinite (b) 1 (c) 2 (d) 3 | 10 |

156 | The graph of ( x+2=0 ) is a line parallel to ( ldots ldots . . . ) axis. This question has multiple correct options A . ( x ) B. ( y ) c. ( x-2=0 ) D. None of these | 10 |

157 | Solve graphically: ( 2 x+y-7=0, x+ ) ( 3 y-11=0 ) | 10 |

158 | Find the equations of the straight lines which pass through (3,2) and make an angle of ( 45^{circ} ) with the line ( x=2 y+4 ) | 10 |

159 | Show graphically the given system of equations ( 2 x+4 y=10 ) and ( 3 x+6 y=12 ) has no solution. | 10 |

160 | Solve the equations using cross multiplication method: ( x-y=12 ) and ( boldsymbol{x}+boldsymbol{y}=mathbf{1 4} ) A . ( x=13, y=1 ) В. ( x=13, y=-1 ) c. ( x=-13, y=-1 ) D. ( x=-13, y=1 ) | 10 |

161 | Reduce the equation ( 2 x-3 y+5=0 ) to intercept form.Hence find the length of the segment intercepted between the axes. | 10 |

162 | Based on cross-multiplication method, solve the following pair of equations by cross multiplication rule ( mathbf{5} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{3 5}, mathbf{2} boldsymbol{x}+mathbf{4} boldsymbol{y}=mathbf{2 8} ) Then A. ( x=4, y=5 ) B. ( x=5, y=4 ) c. ( x=6, y=3 ) D. ( x=3, y=6 ) | 10 |

163 | Solve : ( frac{mathbf{5}}{boldsymbol{x}+boldsymbol{y}}-frac{mathbf{2}}{boldsymbol{x}-boldsymbol{y}}+mathbf{1}=mathbf{0} ) ( frac{15}{x+y}+frac{7}{x-y}-10=0 ) | 10 |

164 | A man sold two paintings at ( R s 924 ) each. On one he gains ( 20 % ) and on the other he loses ( 20 % ). How much does he gain or lose in the whole transaction? | 10 |

165 | Consider the following statements: The system of equations ( .2 x-y=4 ) and ( boldsymbol{p} boldsymbol{x}-boldsymbol{y}=boldsymbol{q} ) I. has a unique solution if ( y neq 2 ) Il. has infinitely many solutions if ( boldsymbol{p}= ) ( 2, q=4 ) Of these statements: A. I alone is correct B. II alone is correct c. I and II are correct D. I and II are false | 10 |

166 | Find the equation of the line passing through the point (2,3) and perpendicular to the straight line ( 4 x- ) ( mathbf{3} boldsymbol{y}=mathbf{1 0} ) A. ( 3 x+4 y=18 ) в. ( 3 x-4 y=18 ) c. ( 3 x+4 y=-18 ) D. ( 4 x-3 y=-18 ) | 10 |

167 | If ( frac{x+y-8}{2}=frac{x+2 y-14}{3}=frac{3 x-y}{4} ) then the values of ( x ) and ( y ) is A ( . x=1, y=3 ) B. ( x=5, y=2 ) c. ( x=3, y=3 ) D. ( x=2, y=6 ) | 10 |

168 | The graph of the linear equation ( 2 x- ) ( y=4 ) cuts ( x ) -axis at A ( .(2,0) ) в. (-2,0) c. (0,-4) D. (0,4) | 10 |

169 | Find the equation of the line having an inclination ( 60^{circ} ) with the positive direction of ( X ) axis and cut off an intercept of 4 on the positive side of ( Y ) axis. | 10 |

170 | A line is perpendicular to ( 3 x+y=3 ) and passes through a point ( (2,2) . ) Its ( y ) intercept is A ( cdot 2 / 3 ) в. ( 1 / 3 ) c. 1 D. ( 4 / 3 ) | 10 |

171 | The cost of ( 2 mathrm{kg} ) of apples and ( 1 mathrm{kg} ) of grapes on the day was found to be Rs. 160. After a month the cost of ( 4 mathrm{kg} ) of apples ( 2 mathrm{kg} ) of grapes is ( mathrm{Rs} .300 ) Represent the situation algebraically. | 10 |

172 | [ begin{array}{l} 2 x-5 y=8 \ 4 x+k y=17 end{array} ] For which of the following values of ( k ) will the system of equations above have no solution? A . -10 в. -5 c. 0 D. 5 E . 10 | 10 |

173 | Solve the following system of equations for ( boldsymbol{x} ) & ( boldsymbol{y} ) ( frac{5}{x-1}+frac{1}{y-2}=2, frac{3}{x-1}=1 ) | 10 |

174 | Solve: ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}= ) ( mathbf{1 4} ) Hence, find ‘a’ if ( boldsymbol{y}=boldsymbol{a} boldsymbol{x}-boldsymbol{2} ) A ( cdot x=1, y=6 ) and ( a=3 frac{2}{5} ) B. ( x=3, y=12 ) and ( a=7 frac{6}{5} ) c. ( _{x}=3, y=2 ) and ( a=1 frac{1}{3} ) D. ( x=12, y=16 ) and ( a=4 frac{31}{3} ) | 10 |

175 | Find the value of ( x ) and ( y ) using cross multiplication method: ( boldsymbol{x}+boldsymbol{y}=mathbf{0} ) and ( boldsymbol{x}-boldsymbol{y}=mathbf{2} ) ( A cdot(1,1) ) B . (-1,1) ( c cdot(1,-1) ) D. (-1,-1) | 10 |

176 | Solve the following simultaneous equations: ( 217 x+131 y=913 ) ( 131 x+217 y=827 ) A. ( x=7, y=3 ) В. ( x=2, y=1 ) c. ( x=3, y=2 ) D. ( x=1, y=5 ) | 10 |

177 | Solve the following simultaneous equations: ( frac{7}{2 x+1}+frac{13}{y+2}=27, frac{13}{2 x+1}+ ) ( frac{7}{y+2}=33 ) | 10 |

178 | ( f-2 x=4 y+6 ) and ( 2(2 y+3)=3 x- ) 5What is the solution ( (x, y) ) to the system of equation above? | 10 |

179 | A square paper is kept on cartesian plane coinciding the points ( (2,0),(4,0),(0,2) . ) Find the perimeter of the paper. A. 8 Units B. 12 Units c. 16 Units D. None of these | 10 |

180 | Draw the graph of ( 2 x+3 y=12 ) | 10 |

181 | Solve graphically the following pairs of equations ( 4 x-y-5=0 ; x+y-5=0 ) ( mathbf{A} cdot(2,3) ) B ( cdot(3,3) ) ( mathbf{c} cdot(4,3) ) D. None of these | 10 |

182 | The solution of the equations ( frac{boldsymbol{m}}{boldsymbol{x}}+ ) ( frac{n}{y}=a ) and ( frac{n}{x}+frac{m}{y}=b ) is given by A ( x=frac{n^{2}+m^{2}}{a m-b n}, y=frac{m^{2}-n^{2}}{b m-a n} ) B. ( _{x}=frac{m^{2}-n^{2}}{a m-b n}, y=frac{n^{2}-m^{2}}{b m-a n} ) c. ( _{x}=frac{m^{2}-n^{2}}{a m-b n}, y=frac{m^{2}-n^{2}}{b m-a n} ) D. ( x=frac{n^{2}-m^{2}}{a m-b n}, y=frac{n^{2}-m^{2}}{b m-a n} ) | 10 |

183 | Find whether the lines representing the following pair of linear equation intersect at a point, are parallel or coincident ( cdot frac{3 x}{2}-frac{5 y}{3}=-2 ; frac{x}{3}+frac{y}{2}= ) ( mathbf{1 3} ) ( mathbf{6} ) | 10 |

184 | Determine the values of ( mathrm{m} ) and ( n ) so that the following system of linear equations have infinite number of solutions: ( (2 m-1) x+3 y-5=0 ) ( 3 x+(n-1) y-2=0 ) | 10 |

185 | The equation of line bisecting perpendicularly the segment joining the points (-4,6) and (8,8) is ( mathbf{A} cdot y=7 ) в. ( 6 x+y-19=0 ) c. ( x+2 y-7=0 ) D. ( 6 x+2 y-19=0 ) | 10 |

186 | The equation of ( y ) axis is A ( . quad x=0 ) ( mathbf{B} cdot y=0 ) ( mathbf{c} cdot x=k ) D. None of these | 10 |

187 | Father says to son “I am 9 times as old as you were when i was as old as you are”. If the sum of their present ages is 50 years. What is the age of father? | 10 |

188 | A straight line passes through the points (2,4) and ( (5,-2) . ) Taking ( 1 c m= ) 1 units, mark these points on a graph paper and draw the straight line through these points. If points ( (boldsymbol{m},-mathbf{4}) ) and ( (3, n) ) lie on the drawn line, find the values of ( m ) and ( n ) A. ( m=1 ) and ( n=2 ) B. ( m=3 ) and ( n=2 ) c. ( m=6 ) and ( n=2 ) D. ( m=9 ) and ( n=2 ) | 10 |

189 | One says, “Give me a hundred, friend! shall then become twice as rich as you.”.” The other replies, “lf you give me ten, shall be six times as rich as you.” Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II] | 10 |

190 | The line joining two points ( A(2,0), B(3,1) ) is rotated about ( A ) in anti-clockwise direction through an angle of ( 15^{circ} . ) The equation of the line in the now position, is A ( cdot sqrt{3} x-y-2 sqrt{3}=0 ) B. ( x-3 sqrt{y}-2=0 ) c. ( sqrt{3} x+y-2 sqrt{3}=0 ) D. ( x+sqrt{3} y-2=0 ) | 10 |

191 | Solve ( 0.2 x+0.3 y=1.3 ) ( mathbf{0 . 4 x}+mathbf{0 . 5 y}=mathbf{2 . 3} ) A. ( x=-2 ) and ( y=3 ) B. ( x=3 ) and ( y=3 ) c. ( x=2 ) and ( y=3 ) D. None of these | 10 |

192 | Find the value of ( x ) and ( y ) using cross multiplication method: ( 5 x+y=15 ) and ( 2 x+6 y=34 ) A. (-2,5) в. (2,-5) ( c cdot(2,5) ) D. (-2,-5) | 10 |

193 | Solve the following pair of linear equation: ( frac{1}{3 x+y}+frac{1}{3 x-y}=frac{3}{4}, frac{1}{2(3 x+y)} ) ( frac{1}{2(3 x-y)}=frac{-1}{8}, 3 x+y neq 0,3 x- ) ( boldsymbol{y} neq 0 ) | 10 |

194 | The angle between lines joining the original to the point of intersection of the line ( sqrt{mathbf{3}} x+boldsymbol{y}=mathbf{2} ) and the curve ( y^{2}-x^{2}=4 ) is A ( cdot tan ^{-1} frac{2}{sqrt{3}} ) B. ( frac{pi}{6} ) ( ^{mathrm{c}} tan ^{-1}left(frac{sqrt{3}}{2}right) ) D. ( frac{pi}{2} ) | 10 |

195 | Draw the graph for the equation given below. Hence find the co-ordinates of the points where the graph drawn meets the co-ordinate axes: ( frac{1}{3} x+frac{1}{5} y=1 ) ( mathbf{A} cdot(6,3) ) and (5,0) B ( cdot(3,5) ) and (2,0) c. (3,0) and (0,5) ( mathbf{D} cdot(2,0) ) and (0,7) | 10 |

196 | Solve the following equation using the trial and error method. ( 2 x+4=8 ) | 10 |

197 | Solve ( : frac{2}{x}+frac{2}{3 y}=frac{1}{6} ) and ( frac{3}{x}+frac{2}{y}=0 ) Hence, find ‘ ( m^{prime} ) for which ( y=m x-4 ) A ( . x=3 ; y=-5 ) and ( m=2 ) B. ( x=6 ; y=-4 ) and ( m=0 ) c. ( x=2 ; y=-3 ) and ( m=0 ) D. ( x=4 ; y=-4 ) and ( m=2 ) | 10 |

198 | f ( x+y=6 ) and ( 3 x-y=4, ) then ( x-y ) is equal to: A . -1 B. ( c cdot 2 ) D. | 10 |

199 | Find the equation of the line passing through the point (-6,10) and perpendicular to the straight line ( 7 x+ ) ( 8 y=5 ) | 10 |

200 | The system of equation ( 3 x-4 y=12 ) and ( 6 x ) ( 8 y=48 ) A. 2 solution B. 1 solution c. infinite number of solutions D. no solutuion | 10 |

201 | Solve graphically the pair of equations ( x+3 y=6, ) and ( 3 x-5 y=18 . ) Hence find the value of ( boldsymbol{K} ) if ( mathbf{7} boldsymbol{x}+mathbf{3} boldsymbol{y}=boldsymbol{K} ) A. ( x=-3, y=1, K=13 ) В. ( x=-8, y=5, K=8 ) c. ( x=1, y=2, K=29 ) D. ( x=6, y=0, K=42 ) | 10 |

202 | Solve : ( (x+y-4)^{2}+(x-y-2)^{2}=0 ) A ( . x=1, y=1 ) в. ( x=4, y=1 ) c. ( x=3, y=1 ) D. ( x=5, y=1 ) | 10 |

203 | Fill in the blanks: The graph of line ( x+2 ) ( =0 ) is parallel to ( ldots ldots . . . . ) axis. | 10 |

204 | Solve the following equation ( 3 x-4 y=1 ) ( -2 x+frac{8}{3} y=5 ) | 10 |

205 | What is the value of ( a ) for the following equation: ( 3 a+4 b=13 ) and ( a+3 b=1 ) ( ? ) (Use cross multiplication method) ( mathbf{A} cdot a=5 ) B. ( a=6 ) ( mathbf{c} cdot a=mathbf{7} ) ( mathbf{D} cdot a=8 ) | 10 |

206 | The equation to a straight line referred to axes inclined at ( 30^{circ} ) to one another is ( y=2 x+1 . ) Find its equation referred to axes inclined at ( 45^{circ}, ) the origin and axis of ( x ) being unchanged. | 10 |

207 | Solve the following simultaneous linear equations by method of reduction. ( boldsymbol{x}+mathbf{2} boldsymbol{y}+boldsymbol{z}=mathbf{8} ) ( 2 x+3 y-z=11 ) ( 3 x-y-2 z=5 ) | 10 |

208 | Solve for ( x ) and ( y ) by using method of substitution: ( mathbf{0 . 2 x + 0 . 3 y}=mathbf{1 . 3 ; 0 . 4 x + 0 . 5 y}=mathbf{2 . 3} ) A. -2,-3 B. 2,-3 c. 2,3 D . -2,3 | 10 |

209 | Solve ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}=14 ) and hence find ‘p’, if ( boldsymbol{y}=boldsymbol{p} boldsymbol{x}-boldsymbol{2} ) | 10 |

210 | If ( 2 x+y=23 ) and ( 4 x-y=19, ) find the values of ( 5 y-2 x ) and ( frac{y}{x}-2 ) A ( cdot 36,-frac{1}{3} ) в. ( _{31,-frac{5}{7}} ) c. ( _{38, frac{6}{7}} ) D. None of these | 10 |

211 | Solve: ( frac{mathbf{2 0}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{3}}{boldsymbol{x}-boldsymbol{y}}=mathbf{7} ) and ( frac{8}{x-y}-frac{15}{x+y}=5 ) A. ( x=3 ) and ( y=2 ) B. ( x=2 ) and ( y=7 ) c. ( x=9 ) and ( y=4 ) D. ( x=1 ) and ( y=9 ) | 10 |

212 | Solve: ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}=14 ) Hence, find ( boldsymbol{a} ) if ( boldsymbol{y}=boldsymbol{a} boldsymbol{x}-boldsymbol{2} ) A ( cdot x=2 ; y=26 ) and ( a=2 frac{5}{3} frac{5}{3} ) B・ ( x=3 ; y=2 ) and ( a=1 frac{1}{3} ) c. ( _{x}=1 ; y=5 ) and ( a=2 frac{7}{3} ) D. ( x=5 ; y=1 ) and ( a=5 frac{1}{8} ) | 10 |

213 | Solve the following linear equations. ( boldsymbol{x}-boldsymbol{y}=mathbf{3} ; mathbf{4} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{0} ) | 10 |

214 | Find the equations of the lines for which ( tan theta=frac{3}{5}, ) where ( theta ) is the angle of inclination of the line and ( x- ) intercept is -8 | 10 |

215 | Draw the graph for the linear equation given below: ( mathbf{2} boldsymbol{x}-mathbf{7}=mathbf{0} ) Which of the following points lie on this line? This question has multiple correct options A. (3.5,0) в. (3,0) c. (-2,2) D. (3.5,2) | 10 |

216 | If a line passes through the point ( P(1,2) ) makes an angle of ( 45^{circ} ) with the x-axis and meets the line ( x+2 y-7= ) 0 in ( Q, ) then ( P Q ) equals- A. ( sqrt{3} ) B. ( frac{3 sqrt{2}}{2} ) ( c cdot frac{2 sqrt{2}}{3} ) D. ( sqrt{2} ) | 10 |

217 | Solve for ( x ) and ( y: 6 x+3 y=6 x y ) and ( 2 x+4 y=5 x y ) | 10 |

218 | Solve: ( a x+b=0 ) | 10 |

219 | Show that the equation of the line passing through the origin and making an angle ( theta ) with the line ( y=m x+c ) is ( frac{boldsymbol{y}}{boldsymbol{x}}=frac{boldsymbol{m} pm tan boldsymbol{theta}}{1 mp boldsymbol{m} tan boldsymbol{theta}} ) | 10 |

220 | One diagonal of a square is the portion of ( frac{x}{97}+frac{y}{79}=1 ) intercepted between the axes. ( boldsymbol{p}_{1}, boldsymbol{p}_{2} ) are the lengths of the perpendiculars from the vertices of the other diagonal on the axis of ( y ) then ( p_{1}^{2}+p_{2}^{2} ) is equal to | 10 |

221 | Solve the equations using graphical method: ( x+y=7 ) and ( 2 x-3 y=9 ) ( A cdot(6,-1) ) B. (-6, 1) ( c cdot(6,1) ) D. (-6,-1) | 10 |

222 | The equation of the line with inclination ( 45^{0} ) and passing through the point (-1,2) is A. ( x+y+3=0 ) в. ( x-y+3=0 ) c. ( x-y-3=0 ) D. ( x+y-3=0 ) | 10 |

223 | Differentiate the following function with respect to ( x ) ( sin ^{2} x ) ( A cdot cos x ) B. ( sin 2 x ) ( mathbf{c} cdot sin 3 x ) D. ( sin ^{2} x cos x ) | 10 |

224 | Is the point (0,3) lie on the graph of the linear equation ( 3 x+4 y=12 ? ) | 10 |

225 | Solve the following simultaneous equations: ( frac{mathbf{1 6}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{2}}{boldsymbol{x}-boldsymbol{y}}=mathbf{1} ; quad frac{mathbf{8}}{boldsymbol{x}+boldsymbol{y}}- ) ( frac{12}{x-y}=7 ) A ( . x=2, y=3 ) B. ( x=6, y=1 ) c. ( x=7, y=4 ) D. ( x=3, y=5 ) | 10 |

226 | Find the equation of the line passing through the point (2,3) and perpendicular to the straight line ( 4 x- ) ( mathbf{3} boldsymbol{y}=mathbf{1 0} ) | 10 |

227 | A piece of cloth costs rupees ( 75 . ) If the piece is four meters longer and each meter costs rupees 5 less, the cost remains unchanged. What is the length of the piece? A. 12 meters B. 8 meters c. 10 meters D. 6 meters | 10 |

228 | The solution of the equations ( 2 x- ) ( 3 y=7 ) and ( 4 x-6 y=20 ) is A. ( x=18, y=12 ) В. ( x=0, y=0 ) c. No solution D. ( x=8, y=5 ) | 10 |

229 | If the equations ( (boldsymbol{b}+boldsymbol{c}) boldsymbol{x}+(boldsymbol{c}+boldsymbol{a}) boldsymbol{y}+(boldsymbol{a}+boldsymbol{b})= ) ( mathbf{0}, boldsymbol{c} boldsymbol{x}+boldsymbol{a} boldsymbol{y}+boldsymbol{b}=mathbf{0} ) and ( boldsymbol{a} boldsymbol{x}+boldsymbol{b} boldsymbol{y}+boldsymbol{c}=mathbf{0} ) are consistent, then show that either ( boldsymbol{a}+boldsymbol{b}+boldsymbol{c}=boldsymbol{0} ) or ( boldsymbol{a}=boldsymbol{b}=boldsymbol{c} ) | 10 |

230 | The axes being inclined at an angle of ( 30^{circ}, ) find the equation to the straight line which passes through the point (-2,3) and is perpendicular to the straight line ( boldsymbol{y}+mathbf{3} boldsymbol{x}=mathbf{6} ) | 10 |

231 | Find all two-digit numbers such that the sum of the digits constituting the number is not less than ( 7 ; ) the sum of the squares of the digits is not greater than ( 30 ; ) the number consisting of the same digits written in the reverse order is not larger than half the given number | 10 |

232 | Find the value of ( k ) for which the given system of equations has infinite number of solutions. ( mathbf{5} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{2} boldsymbol{k} ) and ( mathbf{2}(boldsymbol{k}+mathbf{1}) boldsymbol{x}+boldsymbol{k} boldsymbol{y}= ) ( (3 k+4) ) A . 4 B. 7 ( c cdot 3 ) D. 6 | 10 |

233 | Find the equations to the straight lines which pass through the point ( (h, k) ) and are inclined at an angle ( tan ^{-1} m ) to the straight line ( boldsymbol{y}=boldsymbol{m} boldsymbol{x}+boldsymbol{c} ) | 10 |

234 | A rectangular ( A 4 ) size paper is kept on cartesian plane coinciding the points ( (3,0),(-1,0),(0,-2) . ) Find the perimeter of the paper. A. 10 Units B. 16 Units c. 9 units D. 12 Units | 10 |

235 | Based on cross-multiplication method, solve the following pairs of equations by cross multiplication rule. ( frac{x}{2}-frac{y}{3}+4=0, frac{x}{2}-frac{5 y}{3}+12=0 ) Then ( x+y ) is equal to | 10 |

236 | The values of and ( y ) satisfying the two equations ( 32 x+33 y=31,33 x+ ) ( 32 y=34 ) respectively will be A. -1,2 в. 2,-1 c. 0,0 D. 2,3 | 10 |

237 | One pendulum ticks 57 times in 58 seconds and another 608 times in 609 seconds. If they start simultaneously, find the time after which will they tick together? A ( cdot frac{211}{19} ) в. ( frac{1217}{19} s ) c. ( frac{1218}{19} s ) D. ( frac{1018}{19} s ) | 10 |

238 | The equations representing the given graph is A. ( 7 x+2 y=11 ; y-2 x=3 ) B. ( 2 x+7 y=11 ; 5 x+(35 y / 2)=25 ) c. ( 3 x-7 y=10 ; 8 y-6 x=4 ) D. ( 3 x-4 y=1 ; 3 x-4 y x+2=0 ) | 10 |

239 | A line passes through (5,-6) and it is parallel to ( y- ) axis.Find its equation. | 10 |

240 | A Father is four times as old as his son. The age of the father at the time of the birth of his son was ( 30 . ) Find the age of his son | 10 |

241 | Solve the set of equations: ( 3(2 u+v)= ) ( mathbf{7} boldsymbol{u} boldsymbol{v} ) and ( boldsymbol{3}(boldsymbol{u}+boldsymbol{3} boldsymbol{v})=mathbf{1 1} boldsymbol{u} boldsymbol{v} ) A ( cdot u=1 ; v=frac{3}{2} ) в. ( u=2 ; v=frac{1}{2} ) c. ( u=2 ; v=frac{5}{4} ) D. ( u=5 ; v=frac{7}{4} ) | 10 |

242 | If the equations ( k x+4 y+1=0, x+ ) ( k y+1=0 ) and ( 2 x-3 y+1=0 ) are consistent, then show that the value of ( k ) is not a real number. | 10 |

243 | The ages of ( A ) and ( B ) are in the ratio 8: 3 Six years hence, their ages will be in the ratio 9: 4 Find the sum of their present ages. | 10 |

244 | Solve graphically: ( 2 x-3 y=7 ) and ( 5 x+y=9 ) A. ( x=2, y=-6 ) в. ( x=8, y=-9 ) c. ( x=0, y=-3 ) D. ( x=2, y=-1 ) | 10 |

245 | A man is 24 years older than his son. 12 years ago, he was five times as old as his son. Find the present ages of both. A. Present age of father is 44 years and Present age of son is 20 years B. Present age of father is 42 years and Present age of son is 18 years c. Present age of father is 60 years and Present age of son is 36 years D. Present age of father is 48 years and Present age of son is 24 years | 10 |

246 | On comparing the ratios ( frac{a_{1}}{a_{2}}, frac{b_{1}}{b_{2}} ) and ( frac{c_{1}}{c_{2}} ) find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. ( mathbf{6} boldsymbol{x}-mathbf{3} boldsymbol{y}+mathbf{1 0}=mathbf{0} ; mathbf{2} boldsymbol{x}-boldsymbol{y}+mathbf{9}=mathbf{0} ) A. Intersect at a point B. Parallel c. coincident D. Data insufficient | 10 |

247 | Based on equations reducible to linear equations Solve for ( x ) and ( y frac{1}{3 x}-frac{1}{7 y}=frac{2}{3} ; frac{1}{2 x}- ) ( frac{1}{3 y}=frac{1}{6} ) A. ( x=1 / 8, y=1 / 2 ) в. ( x=1 / 3, y=1 / 6 ) c. ( x=1 / 7, y=1 / 8 ) D. ( x=1 / 5, y=1 / 7 ) | 10 |

248 | Solve the equation: ( -4 x+8 y=12 ) and ( -2 x+4 y=6 ) and then identify the system of equation. This question has multiple correct options A. Consistent B. Inconsistent c. Dependent D. None the above | 10 |

249 | Write the nature of the lines representing the linear equation ( 2 x- ) ( boldsymbol{y}=mathbf{3} ) and ( mathbf{4} boldsymbol{x}-boldsymbol{y}=mathbf{5} ) | 10 |

250 | The distance between two places is 900 km. An ordinary express train takes 5 hours more than a superfast express train to cover this distance. If the speed of the superfast express train is 15 km/hr more than that of the ordinary express train, find the speed of the trains. | 10 |

251 | Solve the following pair of linear (simultaneous) equations by the method of elimination: ( 8 x+5 y=9 ) ( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{4} ) A. ( x=1 ) and ( y=-2 ) B. ( x=1 ) and ( y=-5 ) c. ( x=3 ) and ( y=6 ) D. ( x=-2 ) and ( y=5 ) | 10 |

252 | Reduce the equation ( 2 x-3 y-5=0 ) to slope-intercept form and find its slope and ( y- ) intercept | 10 |

253 | Draw the graph of straight line ( y= ) ( -2 x+3 . ) Use graph to find the intercept on ( y ) -axis. A . 3 B . 2 c. 0 D. | 10 |

254 | Solve the following system of equations: ( boldsymbol{x}+boldsymbol{y}=boldsymbol{a}-boldsymbol{b} ) ( boldsymbol{a} boldsymbol{x}-boldsymbol{b} boldsymbol{y}=boldsymbol{a}^{2}+boldsymbol{b}^{2} ) | 10 |

255 | The line joining two points ( A(2,0) ) and ( B(3,1) ) ir rotated about ( A ) about in the anticlock wise direction through an angle of ( 15^{circ} . ) The equation of the line in the new position is: A ( . x-sqrt{3} y-2=0 ) В. ( x-2 y-2=0 ) c. ( sqrt{3} x-y-2 sqrt{3}=0 ) D. ( sqrt{2} x-y-2 sqrt{2}=0 ) | 10 |

256 | Solve the following pair of equations by reducing them to a pair of linear equations: ( frac{1}{(3 x+y)}+frac{1}{(3 x-y)}= ) ( frac{3}{4}, frac{1}{2(3 x+y)}-frac{1}{2(3 x-y)}=frac{-1}{8} ) A ( . x=2, y=7 ) в. ( x=5, y=0 ) c. ( x=1, y=1 ) D. ( x=2, y=3 ) | 10 |

257 | For what value of ( boldsymbol{K} ) will the following pair of linear equations have infinitely many solutions? ( boldsymbol{K} boldsymbol{x}+boldsymbol{3} boldsymbol{y}-(boldsymbol{K}-boldsymbol{3})=mathbf{0} ) ( mathbf{1 2} boldsymbol{x}+boldsymbol{K} boldsymbol{y}-boldsymbol{K}=mathbf{0} ) | 10 |

258 | Solve ( 8 x-2 y=28 ) and ( x+4 y=-5 ) | 10 |

259 | Based on equations reducible to linear equations Solve for ( x ) and ( y: frac{16}{x+3}+frac{3}{y-2}= ) ( mathbf{5} ; frac{mathbf{8}}{boldsymbol{x}+mathbf{3}}-frac{mathbf{1}}{boldsymbol{y}-mathbf{2}}=mathbf{0} ) A. ( x=5, y=3 ) В. ( x=7, y=2 ) c. ( x=1, y=5 ) D. None of these | 10 |

260 | The straight line passing through the point of intersection of the straight lines ( boldsymbol{x}-mathbf{3} boldsymbol{y}+mathbf{1}=mathbf{0} ) and ( mathbf{2} boldsymbol{x}+mathbf{5} boldsymbol{y}-mathbf{9}=mathbf{0} ) and having infinite slope and and at a distance 2 units from the origin has the equation ( mathbf{A} cdot x=2 ) В. ( 3 x+y-1=0 ) ( mathbf{c} cdot y=1 ) D. None of these | 10 |

261 | Solve the following equations: ( y+sqrt{x^{2}-1}=2 ) ( sqrt{boldsymbol{x}+mathbf{1}}-sqrt{boldsymbol{x}-mathbf{1}}=sqrt{boldsymbol{y}} ) This question has multiple correct options A. ( x=2 ; y=5 ) в. ( x=1 ; y=2 ) c. ( _{x}=frac{5}{3} ; frac{2}{3} ) D. ( x=3 ; y=3 ) | 10 |

262 | Show that the equations to the straight lines passing through the point (3,-2) and inclined at ( 60^{circ} ) to the line ( sqrt{3} x+ ) ( boldsymbol{y}=1 ) are ( boldsymbol{y}+boldsymbol{2}=boldsymbol{0} ) and ( boldsymbol{y}-sqrt{mathbf{3}} boldsymbol{x}+ ) ( mathbf{2}+mathbf{3} sqrt{mathbf{3}}=mathbf{0} ) | 10 |

263 | 54. ‘x number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men is (1) 6 (2) 10 (3) 12 (4) 15 | 10 |

264 | Find the equations of the lines for which ( tan theta=frac{2}{3}, ) where ( theta ) is the angle of inclination of the line and ( x- ) intercept is 5 | 10 |

265 | Find the value of ( mathrm{m} ) and ( mathrm{n} ) using cross multiplication method: ( 3 m+n=15 ) and ( m+2 n=10 ) ( A cdot(4,3) ) B. (-4,3) ( c cdot(-4,-3) ) D. (4,-3) | 10 |

266 | The length of the sides of a triangle are ( mathbf{2} boldsymbol{x}+frac{boldsymbol{y}}{mathbf{2}}, boldsymbol{5} frac{boldsymbol{x}}{mathbf{3}}+boldsymbol{y}+frac{mathbf{1}}{mathbf{2}}, boldsymbol{2} frac{boldsymbol{x}}{mathbf{3}}+mathbf{2} boldsymbol{y}+frac{mathbf{5}}{mathbf{2}} ) the triangle is equilateral. Then its perimeter is ( frac{m}{2} . ) Find ( m ) | 10 |

267 | Equation of a straight line passing through the origin and making with ( x- ) axis an angle twice the size of the angle made by the line ( y=0.2 x ) with the ( x- ) axis, is : A. ( y=4.0 x ) В. ( y=frac{5}{12} x ) c. ( 6 y-5 y=0 ) D. none of these | 10 |

268 | Solve ( 2 x+3 y=8 ) ( 2 x=2+3 y ) | 10 |

269 | For what value of ( alpha, ) the system of equations ( boldsymbol{alpha} boldsymbol{x}+mathbf{3} boldsymbol{y}=boldsymbol{alpha}-boldsymbol{3} ) ( 12 x+alpha y=alpha ) will have no solution ( mathbf{A} cdot alpha=5 ) B . ( alpha=-6 ) c. ( alpha=-4 ) D. ( alpha=2 ) | 10 |

270 | ff ( x+y=5 ) and ( x=3 ), then the value of ( boldsymbol{y} ) | 10 |

271 | Area of triangle formed by angle bisectors of coordinate axes and the line ( y=6 ) in sq.units is A . 36 B . 24 ( c cdot 72 ) D. 16 | 10 |

272 | Find the value of ( x ) and ( y ) using elimination method: ( frac{x}{2}+frac{y}{3}=1 ) and ( frac{x}{4}+frac{y}{7}=2 ) A. (44,-63) В . (-41,63) c. (44,63) D. (-44,-63 | 10 |

273 | Solve: ( frac{34}{3 x+4 y}+frac{15}{3 x-2 y}=5 ) and ( frac{25}{3 x-2 y}-frac{8.50}{3 x+4 y}=4.5 ) A. ( x=7 ; y=2 ) в. ( x=5 ; y=2 ) c. ( x=1 ; y=2 ) D. ( x=3 ; y=2 ) | 10 |

274 | The value of ( k ) for which the system of equations ( 3 x+5 y=0 ) and ( k x+ ) ( 10 y=0 ) has a non-zero solution, is ( A cdot 0 ) B . 2 ( c cdot 6 ) D. 8 | 10 |

275 | Based on equations reducible to linear equations Solve for ( x ) and ( y: frac{24}{2 x+y}-frac{13}{3 x+2 y}= ) ( 2 ; frac{26}{3 x+2 y}+frac{8}{2 x+y}=3 ) A. ( x=-2, y=6 ) в. ( x=-5, y=3 ) c. ( x=3, y=2 ) D. ( x=1, y=0 ) | 10 |

276 | Which option of linear equation is inconsistent? ( mathbf{A} cdot x+y=1 ) ( 2 x+y=0 ) B. ( x-y=2 ) ( 2 x-2 y=1 ) c. ( 2 x-3 y=0 ) ( 2 y+x=1 ) D. 2x – 4 ( y=19 ) ( -2 x+y=0 ) | 10 |

277 | State whether the given statement is true or false: A pair of linear equations is given by ( boldsymbol{a}_{1} boldsymbol{x}+boldsymbol{b}_{1} boldsymbol{y}+boldsymbol{c}_{1}=boldsymbol{0} ) and ( boldsymbol{a}_{2} boldsymbol{x}+boldsymbol{b}_{2} boldsymbol{y}+ ) | 10 |

278 | Fill in the blanks: The graph of line ( y+3 ) ( =0 ) is parallel to axis. | 10 |

279 | Solve the equations ( frac{mathbf{1 0}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{2}}{boldsymbol{x}-boldsymbol{y}}=4, frac{mathbf{1 5}}{boldsymbol{x}+boldsymbol{y}}-frac{mathbf{5}}{boldsymbol{x}-boldsymbol{y}}= ) -2 | 10 |

280 | Solve: ( 2 A-B=-2 C ) and ( boldsymbol{A}-boldsymbol{B}=-boldsymbol{C} ) Find ( A ) and ( B ). | 10 |

281 | Solve the following simultaneous equations using graphical method ( boldsymbol{x}+boldsymbol{y}=boldsymbol{6} ) ( boldsymbol{x}-boldsymbol{y}=mathbf{2} ) | 10 |

282 | If ( A=2 y^{2}+3 x-x^{2}, B=3 x^{2}-y^{2} ) and ( C=5 x^{2}-3 x y ) then find ( B-C ) | 10 |

283 | Solve: ( boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{4} ) ( 2 x-y=1 ) | 10 |

284 | If ( 2^{2 x-y}=32 ) and ( 2^{x+y}=16 ) then ( x^{2}+ ) ( y^{2} ) is equal to ( mathbf{A} cdot mathbf{9} ) B. 10 c. 11 D. 13 | 10 |

285 | The following pair of linear equations consistent. State true and false: ( boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{1 1} ; mathbf{2}(mathbf{2} boldsymbol{x}+mathbf{6} boldsymbol{y})=mathbf{2 2} ) A. True B. False | 10 |

286 | The equation ( a x^{2}+b y^{2}+c x+c y=0 ) represents a pair of straight lines, when This question has multiple correct options ( mathbf{A} cdot a+b=0 ) B . ( c=0 ) c. ( a+c=0 ) D. ( c(a+b)=0 ) | 10 |

287 | Solve each pair of equation by using the substitution method. ( boldsymbol{x}+frac{mathbf{6}}{boldsymbol{y}}=mathbf{6} ) ( mathbf{3} boldsymbol{x}-frac{mathbf{8}}{boldsymbol{y}}=mathbf{5} ) A ( . x=3 ) and ( y=-2 ) в. ( x=30 ) and ( y=2 ) c. ( x=3 ) and ( y=2 ) D. None of these | 10 |

288 | Two perpendicular lines are intersecting at ( (4,3) . ) One meeting coordinate axis at ( (4,0), ) find the distance between origin and the point of intersection of other line with the cordinate axes. A . 4 B. 7 ( c .3 ) D. 5 | 10 |

289 | Solve graphically the following pairs of equations. ( boldsymbol{y}-mathbf{2} boldsymbol{x}+mathbf{2}=mathbf{0} ; boldsymbol{y}=mathbf{4} boldsymbol{x}-mathbf{4} ) ( mathbf{A} cdot(1,0) ) B ( cdot(2,0) ) ( mathbf{c} cdot(3,0) ) D. None of these | 10 |

290 | ( frac{mathbf{2 2}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{1 5}}{boldsymbol{x}-boldsymbol{y}}=mathbf{5} ) ( frac{mathbf{5 5}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{4 5}}{boldsymbol{x}-boldsymbol{y}}=mathbf{1 4} ) A. ( x=-8, y=3 ) в. ( x=-3, y=8 ) c. ( x=8, y=3 ) D. ( x=8, y=-3 ) | 10 |

291 | Solve the equations using elimination method: ( 2 x+3 y=15 ) and ( 3 x+3 y=12 ) A ( cdot(-3,-7) ) в. (-3,7) c. (-3,6) D. (3,-7) | 10 |

292 | The sum of two numbers is 80 and the greater number exceed twice the smaller by 11. Find the larger numbers. | 10 |

293 | Draw the graphs of equations ( 2 x+y= ) 7 and ( 2 x+y=8 . ) If they intersect, write the co-ordinates of the point of their intersection. | 10 |

294 | Solve for ( x ) and ( y, ) if ( x+y=7 ) and ( 2 x+ ) ( 3 y=18 ) A ( . x=3, y=4 ) в. ( x=2, y=5 ) c. ( x=1, y=6 ) D. ( x=4, y=3 ) | 10 |

295 | Solve the following pair of equations: ( frac{a}{x}-frac{b}{y}=0 ) ( frac{a b^{2}}{x}+frac{a^{2} b}{y}=a^{2}+b^{2} ) A. ( x=a b ) and ( y=b ) B. ( x=a ) and ( y=b ) c. ( x=b ) and ( y=a ) D. ( x=b-a ) and ( y=a b ) | 10 |

296 | Draw the graph of each of the equations ( 2 x+3 y+5=0 ) and ( 5 x+4 y+1=0 ) and find the coordinates of the point where the lines meet. | 10 |

297 | If ( 2 a=b, ) the pair of equations ( x+ ) ( 2 y=2 a-6 b, a x+b y=2 a^{2}-3 b^{2} ) possess solution(s) A. No B. Only one c. only two D. An infinite number of slutions | 10 |

298 | The ratio of income of two persons is 9: 7 and the ratio of their expenditure is ( 4: 3 . ) If each of them manages to save Rs. 2000 per month, find their monthly income. A. ( R s .18,000, ) Rs.14, 000 B. ( R s .1,000, R s .14,000 ) c. ( R s .18,000, ) Rs.1, 000 D. None of these | 10 |

299 | f ( 3 x-2 y=5 ) and ( 3 y-2 x=3 ) then find the value of ( (boldsymbol{x}+boldsymbol{y}) ) | 10 |

300 | Solve the following system of equation: ( frac{1}{2 x}-frac{1}{y}=-1 ) ( frac{1}{x}+frac{1}{2 y}=8, ) where ( x neq 0, y neq 0 ) | 10 |

301 | If ( boldsymbol{x}=boldsymbol{m}+mathbf{1} ) and ( frac{mathbf{1}}{mathbf{3}}(mathbf{6} boldsymbol{x}-mathbf{3})-(mathbf{8}- ) ( mathbf{3} boldsymbol{x})=mathbf{1 1} ; ) find the value of ( mathbf{m} ) A ( . m=2 ) в. ( m=3 ) c. ( m=7 ) D. ( m=5 ) | 10 |

302 | Draw the graph of equation ( 3 x+2 y=6 ) Find the sum of the co-ordinates of the point where the graph intersects the ( Y ) axis. | 10 |

303 | Find the equations of the lines for which ( tan theta=sqrt{2}, ) where ( theta ) is the angle of inclination of the line and ( y- ) intercept is -1 | 10 |

304 | Find the value of ( k ) so that the line ( 2 x- ) ( k y-7=0 ) may be parallel to ( 3 x+ ) ( 4 y+7=0 ) | 10 |

305 | The value of ( k ) for which the system of equations ( 2 x+3 y=5 ) ( 4 x+k y=10 ) has an infinite number of solutions, is ( mathbf{A} cdot mathbf{1} ) B. 3 ( c cdot 6 ) D. 0 | 10 |

306 | Solve for ( x ) and ( y ) ( boldsymbol{m} boldsymbol{x}-boldsymbol{n} boldsymbol{y}=boldsymbol{m}^{2}+boldsymbol{n}^{2}, boldsymbol{x}-boldsymbol{y}=boldsymbol{2} boldsymbol{n} ) A. ( x=m+n ; y=m-n ) в. ( x=m-n ; y=m n-n ) c. ( x=m+m n ; y=m+n ) D. ( x=m n-n ; y=m-n ) | 10 |

307 | Find the values of ( alpha & beta ) for which the following system of linear equations has infinite number of solution. ( 2 x+3 y=7 ) ( 2 alpha x+(alpha+beta) y=28 ) | 10 |

308 | Solve the following pair of equations by cross multiplication rule. ( frac{x}{a}+frac{y}{b}=0, frac{x}{a}-frac{y}{b}=4 ) A. ( x=2 a, y=-2 b ) в. ( x=-3 a, y=-b ) c. ( x=a, y=2 b ) D. None of these | 10 |

309 | When a bucket is half full, the weight of the bucket and the water is 10 kg. When the bucket is two-thirds full, the total weight is 11 kg. What is the total weight, in kg, when the bucket is completely full? A . 12 в. ( 12 frac{1}{2} ) ( c cdot_{12} frac{2}{3} ) D. 13 | 10 |

310 | Solve the following pair of linear equations by the elimination method and the substitution method: (i) ( x+y=5 ) and ( 2 x-3 y=4 ) (ii) ( 3 x+4 y=10 ) and ( 2 x-2 y=2 ) (iii) ( 3 x-5 y-4=0 ) and ( 9 x=2 y+7 ) (iv) ( frac{x}{2}+frac{2 y}{3}=-1 ) and ( x-frac{y}{3}=3 ) | 10 |

311 | If ( 2 a=b, ) the pair of equations ( a x+ ) ( b y=2 a^{2}-3 b^{2}, x+2 y=2 a-6 b ) possess A. no solution B. only one solutions c. only two solutions D. an infinite number of solutions | 10 |

312 | The sum of the two digits of a two digit number is 12. The number obtained by interchanging the digits exceeds the given number by 18. Find the number. | 10 |

313 | If the product of two numbers is 10 and their sum is ( 7, ) which is the greatest of the two numbers? A . -2 B. 2 ( c .5 ) D. 4 | 10 |

314 | The equation of a straight line passing through the point of intersection of ( x- ) ( boldsymbol{y}+mathbf{1}=mathbf{0} ) and ( mathbf{3} boldsymbol{x}+boldsymbol{y}-mathbf{5}=mathbf{0} ) and perpendicular to one of them, is? A. ( x+y+3=0 ) в. ( x-y-3=0 ) c. ( x-3 y-5=0 ) D. ( x-3 y+5=0 ) | 10 |

315 | Show that the following system of linear equations is consistent and also find their solution: ( mathbf{5} boldsymbol{x}+mathbf{3} boldsymbol{y}+mathbf{7} boldsymbol{z}=mathbf{4} ) ( mathbf{3} boldsymbol{x}+mathbf{2 6} boldsymbol{y}+mathbf{2} boldsymbol{z}=mathbf{9} ) ( mathbf{7} boldsymbol{x}+mathbf{2} boldsymbol{y}+mathbf{1 0} boldsymbol{z}=mathbf{5} ) | 10 |

316 | In a factory, the cost of manufacturing ( x ) article is ( R s 20+2 x ) and the selling price of ( x ) articles is ( R s(2.5) x . ) Draw the graph and determine. (i) Number of articles to be manufactured and sold to reach break- even point (no profit and no loss situation); (ii) The profit made when 60 articles are manufactured and sold | 10 |

317 | Draw the graph of equation2 ( y+x=7 ) and ( 2 x+y=8 ) on the same ( c o ) ordination system. Write the pt of intersection. | 10 |

318 | Represent the solution of each of the following inequalities on the real number line: ( 7-x leq 2-6 x ) | 10 |

319 | The slope of one of the lines given by ( a x^{2}+2 h x y+b y^{2}=0 ) is ( k ) times the other, then A ( cdot 4 k^{2} h=a b(1+k) ) B . ( k h^{2}=4 a b(1+k)^{2} ) C. ( k h^{2}=2 a b(1+k)^{2} ) D. ( 4 k h^{2}=a b(1+k)^{2} ) | 10 |

320 | Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, shall be three times as old as you will be.” Is not this interesting? Represent this situation algebraically. | 10 |

321 | If the system of equations ( 2 x+3 y- ) ( mathbf{5}=mathbf{0}, mathbf{4} boldsymbol{x}+boldsymbol{k} boldsymbol{y}-mathbf{1 0}=mathbf{0} ) has an infinite number of solutions, then A ( cdot k=frac{3}{2} ) в. ( _{k neq frac{3}{2}} ) c. ( k neq 6 ) D. ( k=6 ) | 10 |

322 | A train covered a certain distance at a uniform speed. If the train would have been ( 6 mathrm{km} / mathrm{h} ) faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by ( 6 mathrm{km} / mathrm{h} ) it would have taken 6 hours more than the scheduled time. Find the length of the journey. | 10 |

323 | 11. For what values of m, does the system of equations 3x + my=m 2x-5x=20 has solution satisfying the conditions x > 0, y>0. (1980) | 10 |

324 | From Delhi station, if we buy 2 ticket for station ( A ) and 3 tickets for station ( B ), the total cost is Rs.77. But if we buy 3 tickets for station ( A ) and 5 tickets for station ( mathrm{B} ), the total cost is Rs. 124. What are the fares from Delhi to station ( A ) and to station B ? A. ( A=R s .12 ; B=R s .17 ) в. ( A=R s .13 ; B=R s .17 ) c. ( A=R s .18 ; B=R s .17 ) D. ( A=R s .19 ; B=R s .17 ) | 10 |

325 | Determine, graphically, the vertices of the triangle formed by the lines ( boldsymbol{y}=boldsymbol{x}, mathbf{3} boldsymbol{y}=boldsymbol{x}, boldsymbol{x}+boldsymbol{y}=mathbf{8} ) B . (0,0),(4,4),(0,2) D. (0,0),(4,4),(6,2) | 10 |

326 | Use graph paper for this question. Take ( 2 c m=2 ) units on ( x ) -axis and ( 1 c m=1 ) unit on ( y ) -axis. Solve graphically the following equations: ( 3 x+5 y=12 ; 3 x-5 y+18=0 ) (Plot only three points per line) A. ( x=-1 ; y=3 ) в. ( x=-1 ; y=7 ) c. ( x=-1 ; y=5 ) D. ( x=-1 ; y=2 ) | 10 |

327 | 1250 persons went to see a circus-show Each adult paid Rs. 75 and each child paid Rs. 25 for the admission ticket Find the number of adults and number of children, if the total collection from them amounts to Rs. 61,250 A. Adults ( =600 ) and children ( =650 ) B. Adults = 300 and children = 450 c. Adults ( =800 ) and children ( =700 ) D. Adults ( =640 ) and children ( =800 ) | 10 |

328 | Show graphically that the pair of equations ( 3 x+4 y=6,6 x+8 y=12 ) represents coincident lines | 10 |

329 | Solve the following equations by graphical method ( 2 x+3 y=0 ) | 10 |

330 | Solve: ( 3(2 x+y)=7 x y ) and ( mathbf{3}(boldsymbol{x}+mathbf{3} boldsymbol{y})=mathbf{1 1} boldsymbol{x} boldsymbol{y} ) where, ( boldsymbol{x} neq mathbf{0}, boldsymbol{y} neq mathbf{0} ) A ( cdot x=3 ; y=frac{1}{2} ) в. ( x=1 ; y=frac{3}{2} ) c. ( x=4 ; y=2 ) D. ( x=3 ; y=4 ) | 10 |

331 | If the system of equations ( 2 x+3 y=7 ) ( 2 a x+(a+b) y=28 ) has infinitely many solutions, then A ( . a=2 b ) B. ( b=2 a ) c. ( a+2 b=0 ) ( mathbf{D} cdot 2 a+b=0 ) | 10 |

332 | Solve the following system of equations by the method of substitution: ( mathbf{3} boldsymbol{x}-mathbf{4} boldsymbol{y}=mathbf{1 0}, mathbf{4} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{5} ) | 10 |

333 | Solve the following pair of equations graphically; ( 2 x-3 y=1, & 4 x-3 y+ ) ( mathbf{1}=mathbf{0} ) A. ( x=1 y=-1 ) В. ( x=-1 y=-1 ) c. ( x=-1 y=1 ) D. ( x=1 y=1 ) | 10 |

334 | Nitya and Satya have some marbles with them. Nitya says to Satya, “If you give one marble to me, we will have equal number of marbles. Satya says to Nitya, “If you give me one marble, I will have twice the number of marbles you have”. How many marbles do Nitya and Satya have respectively? A ( cdot 4,6 ) в. 5,7 ( c cdot 6,4 ) D. 7,5 | 10 |

335 | Solve: ( 3 x+4 y=10,2 x-2 y=2 ) by the method of elimination. | 10 |

336 | Find the equations of the straight line which passes through the point (-3,8) and cut positive intercepts on the coordinates axes whose sum is 7 . | 10 |

337 | The graph of ( x=2 ) is a line parallel to axis. ( A ) в. ( y=2 ) c. ( y ) D. None of these | 10 |

338 | Solve the following simultaneous equations using graphical method ( boldsymbol{x}+boldsymbol{y}=boldsymbol{6} ) ( boldsymbol{x}-boldsymbol{y}=boldsymbol{4} ) | 10 |

339 | Solve the following system of equations by the method of substitution: ( 3 x-7 y=7,11 x+5 y=87 ) | 10 |

340 | Solve the following pairs of equations. ( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{4} ; mathbf{9} boldsymbol{x}+mathbf{6} boldsymbol{y}-mathbf{1 2}=mathbf{0} ) A. Many solution B. No solution c. Unique solution D. None of these | 10 |

341 | A purse contains only 25 paise and 10 paise coins. The total amount in the purse is ( R s .8 .25 . ) If the number of 25 paise coins is one-third the number of 10 paise coins, then the total number of coins in the purse is: | 10 |

342 | Solve each of the following pairs of equations by the elimination method. ( 2 x+3 y=8 ) ( 4 x+6 y=7 ) | 10 |

343 | inflated with both helium and nitrogen gas. Between the two gases, the balloon can be inflated up to 8 liters in volume. The density of helium is 0.20 grams per liter, and the density of nitrogen is 1.30 grams per liter. The balloon must be filled so that the volumetric average density of the balloon is lower than that of air, which has a density of 1.20 grams per liter. Which of the following system of inequalities best describes how the balloon will be filled, if ( x ) represents the number of liters of helium and ( y ) represents the number of liters of nitrogen? A ( cdotleft{begin{array}{l}x+y>8 \ 20 x+130 y>120end{array}right. ) B. ( left{begin{array}{l}x+y=8 \ frac{0.2 x+1.30 y}{2}<1.20end{array}right. ) c. ( left{begin{array}{l}x+y leq 8 \ 0.20left(frac{x}{x+y}right)+1.30left(frac{y}{x+y}right)<1.20end{array}right. ) D ( cdotleft{begin{array}{l}x+y leq 8 \ 0.20 x+1.30 y<1.20end{array}right. ) | 10 |

344 | The coach of a cricket team buys 3 bats and 6 balls for ( c 3900 ). Later, she buys another bat and 3 more balls of the same kind for ( c 1300 . ) Represent this situation algebraically and geometrically | 10 |

345 | Find the equations of the lines for which ( tan theta=-1, ) where ( theta ) is the angle of inclination of the line and ( x- ) intercept is 4 | 10 |

346 | The sum of the present ages of the father and his son is 45 years. 5 years ago, the age of the father was 6 times that of son. What is the present age of the son? | 10 |

347 | Draw the graph of i) ( y=2 x+5, ) ii) ( boldsymbol{y}=mathbf{2} boldsymbol{x}-mathbf{5}, ) iii) ( boldsymbol{y}=mathbf{2} boldsymbol{x} ) and find the point of intersection on ( x ) -axis. Is the ( x ) coordinates of these points also the zero of the polynomial? | 10 |

348 | ( frac{5}{x+y}-frac{2}{x-y}=-1 ) ( frac{15}{x+y}+frac{7}{x-y}=10 ) | 10 |

349 | Solve: ( mathbf{3}(mathbf{2 u}+boldsymbol{v})=mathbf{7} boldsymbol{u} boldsymbol{v} ) and ( mathbf{3}(boldsymbol{u}+mathbf{3} boldsymbol{v})=mathbf{1 1} boldsymbol{u} boldsymbol{v} ) | 10 |

350 | If ( a m neq b l, ) then the system of equations ( a x+b y=c ) and ( l x+m y= ) ( n ) has: A. A unique solution B. No solution c. Infinitely many solutions D. May or may not have a solution | 10 |

351 | The difference of the slopes of the lines represented by ( 6 x^{2}-5 x y+y^{2}=0 ) is ( mathbf{A} cdot mathbf{1} ) B . 2 ( c .3 ) D. | 10 |

352 | f ( 2 x+y=9 ) and ( 3 x-y=6 ) then find the value of ( x ) | 10 |

353 | Find the value of ( p ) for which the given simultaneous equation has unique solution: ( mathbf{8} boldsymbol{x}-boldsymbol{p} boldsymbol{y}+mathbf{7}=mathbf{0} ; quad mathbf{4} boldsymbol{x}-mathbf{2} boldsymbol{y}+mathbf{3}= ) ( mathbf{0} ) A. All values of ( p ) except 4 в. ( p=7 ) ( mathbf{c} cdot p=6 ) D. All values of ( p ) except 5 | 10 |

354 | Given set of equations is ( mathbf{1} . mathbf{3} boldsymbol{g}+mathbf{1} . mathbf{7} boldsymbol{h}=mathbf{5} ) ( 3 h=20+13 g ) Based on the system of equations above, determine the value of ( h ) ( ^{A} cdot frac{7}{2} ) or 3.5 B. 3 c. ( frac{9}{2}=4.5 ) D. 4 | 10 |

355 | Find the value of ( x ) and ( y ) using elimination method: ( 2 x+3 y=-6 ) and ( b x+2 y=-10 ) A ( cdotleft(2, frac{-2}{3}right) ) B ( cdotleft(-2, frac{2}{3}right) ) c. ( left(2, frac{2}{3}right) ) D. ( left(-2, frac{-2}{3}right) ) | 10 |

356 | The equation of the straight line passing through the point (4,3) and making intercepts on the cordinate axes whose sum is ( -1, ) is : A ( cdot frac{x}{2}+frac{y}{3}=-1 ) and ( frac{x}{-2}+frac{y}{1}=-1 ) B. ( frac{x}{2}-frac{y}{3}=-1 ) and ( frac{x}{-2}+frac{y}{1}=-1 ) c. ( frac{x}{2}+frac{y}{3}=-1 ) and ( frac{x}{-2}+frac{y}{1}=1 ) D. ( frac{x}{2}-frac{y}{3}=1 ) and ( frac{x}{-2}+frac{y}{1}=1 ) | 10 |

357 | 62. The equations 3x + 4y = 10 – x + 2y = 0 have the solution (a, b). The val- ue of a + b is (1) 1 (2) 2 b y (3) 3 (4) 4 – | 10 |

358 | The work done by a body on application of a constant force is directly proportional to the distance traveled by the body. Express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Read from the graph, the work done when the distance traveled by the body is 0 units. A. 0 units B. 2 units c. 1 units D. 3 units | 10 |

359 | If the straight line draw through the point ( P(sqrt{3}, 2) ) and inclined at an angle ( frac{pi}{6} ) with the ( x ) -axis,meets the line ( sqrt{3} x- ) ( 4 y+8=0 ) at Q.Find the length ( P Q ? ) | 10 |

360 | Solve the following equations by substitution method. ( mathbf{5} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{2} mathbf{1} ; mathbf{2} boldsymbol{x}-boldsymbol{y}=mathbf{4} ) A. ( x=3, y=2 ) в. ( x=-3, y=2 ) c. ( x=3, y=-2 ) D. None of these | 10 |

361 | Plot the graph of line ( x=5 ) | 10 |

362 | Equations of the two straight lines passing through the point (3,2) and making an angle of ( 45^{circ} ) with the line ( x-2 y=3, ) are A. ( 3 x+y-7=0 ) and ( x+3 y+9=0 ) B. ( 3 x-y-7=0 ) and ( x+3 y-9=0 ) C ( . x+3 y-7=0 ) and ( x+3 y-9=0 ) D. none of these | 10 |

363 | Five years later, the father’s age will be three times the age of his son. Five years ago, father was seven times as old as his son. Find their present ages. | 10 |

364 | Give the graphical representation of the following equation (a) On the number line and (b) On the Cartesian plane ( 2 x-9=0 ) | 10 |

365 | 51. r *+1-and i+ya Ex-Y then the value of 1 + xay is (1) 2ab 2-62 (2 a2_62 2ab 2ab ab | 10 |

366 | 8 times a 2 digit number is equal to 3 times the number obtained by reversing the order of the digit. If the difference between digit is 5 then find the number. | 10 |

367 | Solve the following pair of linear equations: ( frac{10}{x+y}+frac{2}{x-y}=4 ; frac{15}{x+y}-frac{5}{x-y}= ) -2 | 10 |

368 | If the perimeter of rectangle is ( 24 mathrm{m} ) represent this in the form of equation. | 10 |

369 | Solve the following pair of equations by reducing them to a pair of linear equations: ( frac{1}{2 x}+frac{1}{3 y}=2, frac{1}{3 x}+frac{1}{2 y}=frac{13}{6} ) A ( cdot x=frac{1}{4} ) and ( y=frac{1}{7} ) B. ( x=frac{2}{5} ) and ( y=frac{1}{3} ) c. ( _{x}=frac{3}{7} ) and ( y=frac{1}{7} ) D. ( x=frac{1}{2} ) and ( y=frac{1}{3} ) | 10 |

370 | Solve the following equations by the substitution method ( 11 x-8 y=27,3 x+5 y=-7 ) A. ( x=0, y=1 ) в. ( x=0, y=-5 ) c. ( x=2, y=3 ) D. ( x=1, y=-2 ) | 10 |

371 | ( f frac{x}{a}+frac{y}{b}=1 ) and ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=frac{a b}{a+b} ) then prove that ( frac{boldsymbol{x}^{boldsymbol{n}+mathbf{1}}}{boldsymbol{a}}+frac{boldsymbol{y}^{boldsymbol{n}+mathbf{1}}}{boldsymbol{b}}= ) ( left(frac{a b}{a+b}right)^{n} ) | 10 |

372 | Solve equations using substitution method: ( 5 x-2 y=10 ) and ( 4 x-6 y=3 ) A ( cdot frac{-27}{11} ) and ( frac{25}{22} ) B. ( frac{27}{11} ) and ( frac{-25}{22} ) c. ( frac{27}{11} ) and ( frac{25}{22} ) D. ( frac{-27}{11} ) and ( frac{-25}{22} ) | 10 |

373 | Solve the following pair of equations by reducing them to a pair of linear equations ( frac{5}{x-1}+frac{1}{y-2}=2 ) and ( frac{6}{x-1}- ) ( frac{3}{y-2}=1 ) | 10 |

374 | Solve the following systems of equations by the method of crossmultiplication: ( boldsymbol{x}+mathbf{2} boldsymbol{y}+mathbf{1}=mathbf{0} ) ( 2 x-3 y-12=0 ) | 10 |

375 | Solve the following pair of linear equations by cross miltiplication method ( 0.3 x+0.4 y=2.5 ) and ( 0.5 x-0.3 y= ) ( mathbf{0 . 3} ) A. ( x=-3 ) and ( y=4 ) в. ( x=3 ) and ( y=4 ) c. ( x=4 ) and ( y=-4 ) D. None of these | 10 |

376 | Based on equations reducible to linear equations, solve for ( x ) and ( y ) ( frac{boldsymbol{x}-boldsymbol{y}}{boldsymbol{x} boldsymbol{y}}=mathbf{9} ; frac{boldsymbol{x}+boldsymbol{y}}{boldsymbol{x} boldsymbol{y}}=mathbf{5} ) A ( cdot x=-frac{1}{2}, y=frac{1}{7} ) B. ( _{x}=-frac{1}{5}, y=frac{1}{2} ) c. ( _{x=-frac{1}{5}, y}=frac{1}{7} ) D. None of these | 10 |

377 | Check if (2,3) will lie on the graph of ( (y-2 x)=-3, ) without drawing the graph. | 10 |

378 | Solve ( : frac{9}{x}-frac{4}{y}=8 ) and ( frac{13}{x}+frac{7}{y}= ) ( mathbf{1 0 1} ) A ( cdot x=frac{1}{7} y=frac{1}{6} ) В. ( x=frac{3}{4} y=frac{1}{6} ) c. ( x=frac{1}{4} y=frac{1}{7} ) D. ( x=frac{2}{7} y=frac{1}{7} ) | 10 |

379 | The line passes through ( left(-1, frac{pi}{2}right) ) and perpendicular to the line ( sqrt{3} sin theta+ ) ( 2 cos theta=frac{4}{r} ) is: A ( .2=sqrt{3} r cos theta-2 r sin theta ) в. ( 5=2 sqrt{3} r sin theta+4 r cos theta ) c. ( 2=sqrt{3} r cos theta+2 r sin theta ) D. ( 8=2 sqrt{3} r sin theta-4 r cos theta ) | 10 |

380 | The difference between a two digit number and the number obtained by the interchanging the digits is ( 27 . ) What is the difference between the two digits of the number? ( A cdot 9 ) B. 6 c. 12 D. 3 | 10 |

381 | Reduce the equation ( x+2 y-5=0 ) to slope-intercept form and find its slope and ( boldsymbol{y}- ) intercept. | 10 |

382 | Draw the graph of the following linear equation ( -boldsymbol{x}+boldsymbol{y}=boldsymbol{6} ) | 10 |

383 | Solve: ( a x+b y-c=0 ) ( b x+a y=1+c ) | 10 |

384 | Solve the following systems of linear equations by using the method of elimination by equating the coefficients: (i) ( 3 x+2 y=11 ) (ii)2 ( boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{4} ) | 10 |

385 | Solve the following pair of an equation by elimination the coefficient method: ( x+2 y=11 ) ( 2 x-y=2 ) | 10 |

386 | Find the common solution: ( boldsymbol{y}=mathbf{3} boldsymbol{x}+mathbf{1} ) ( boldsymbol{x}+boldsymbol{y}=mathbf{9} ) | 10 |

387 | The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are respectively, A. 4 and 24 B. 5 and 30 c. 6 and 36 D. 3 and 24 | 10 |

388 | In the system of equations ( frac{12}{x+y}+ ) ( frac{8}{x-y}=8 ) and ( frac{27}{x+y}-frac{12}{x-y}=3, ) the values of ( x ) and ( y ) will be A ( cdot frac{5}{3} ) and ( frac{1}{3} ) B. ( frac{5}{2} ) and ( frac{1}{2} ) c. 2 and ( frac{1}{3} ) D. ( frac{5}{4} ) and ( frac{1}{4} ) | 10 |

389 | Solve by cross multiplication method: ( 6 x+7 y-11=0 ) ( 5 x+2 y=13 ) | 10 |

390 | For the following system of equation determine the value of ( k ) for which the given system of the equation has a unique solution. ( boldsymbol{x}-boldsymbol{k} boldsymbol{y}=mathbf{2} ) ( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y}=-mathbf{5} ) | 10 |

391 | Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: The sum of the digits of a two-dlgit number is ( 9 . ) Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number A. Number is 18 B. Number is 36 c. Number is 81 D. None of these | 10 |

392 | Solve graphically, the following pairs of equations: ( 2 x+y=23 ) ( 4 x-y=19 ) A. ( x=1, y=4 ) B. ( x=9, y=2 ) c. ( x=5, y=0 ) D. ( x=7, y=9 ) | 10 |

393 | Find the equation of the line passing through the point (-4,-3) and perpendicular to the straight line joining (1,3) and (2,7) | 10 |

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