Straight Lines Questions

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
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
enter 0

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
A) The distance from ( P ) to ( X- )
1)
axis
B) The distance from P to Y-
2) | ( y_{1} mid ) axis
C) The distance from ( P ) to
3) ( sqrt{x_{1}^{2}+y_{1}^{2}} )
origin is
4) ( left|x_{1}right| )
( mathbf{A} cdot A-4, B-2, C-1 )
( mathbf{B} cdot A-2, B-4, C-3 )
( mathbf{c} cdot A-4, B-2, C-3 )
D. ( A-2, B-4, C-1 )

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
determined

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
of ( boldsymbol{R} ) is
A ( cdot x^{2}+y^{2}+7 x-5 y=0 )
B . ( x^{2}+y^{2}-7 x+5 y=0 )
c. ( 5 x-7 y=35 )
D. None of these

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
( lambda_{1}: lambda_{2} ) and ( Q ) divides ( O A ) externally in
the ratio ( lambda_{1}: lambda_{2} ), then ( O A ) is the
harmonic mean of ( O P ) and ( O Q )
A. True
B. False

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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