# 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 NoQuestionsClass
1The 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
2Find the coordinates of points on the ( x ) axis which are at a distance of 17 units
from the point (11,-8)
11
3If ( 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
4If 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
5If three points ( (h, 0),(a, b) ) and ( (0, k) ) lie on a line, show that ( frac{a}{h}+frac{b}{k}=1 )11
6Find the inclination of the line ( ( ) in
degrees ) whose slope is 1
11
7Let ( 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
8Find inclination (in degrees) of a line perpendicular to x-axis.11
9Slope ( =-4 ) and ( y ) -intercept ( =2, ) then
the equation of line is ( m x+y=c . ) Find
( boldsymbol{m}+boldsymbol{c} )
11
10Find 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
11Find 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
12Find 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
13If 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
14Which 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
1513. The incentre of the triangle with vertices (1, 3), (0,0) and
(2,0) is
(2000)
1
11
16If 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
1715. 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
18The 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
20If 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
21The 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
22In 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
23If 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
24Given 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
25The 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
2620. 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
27less 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
(b) a-b+c<o
(d) a+b-c<0
11
2815.
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
29A 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
3023. 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
31Find 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
32IX, 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
33Using 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
34The 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
35Find the distance between each of the
following pairs of points. ( boldsymbol{L}(mathbf{5},-mathbf{8}), boldsymbol{M}(-mathbf{7},-mathbf{3}) )
11
36The ( 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
37Using section formula. show that the points (-3,-1),(1,3) and (-1,1) are collinear.11
38The 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
39The distance between (3,5) and (5,3)
A ( cdot 2 sqrt{2} )
B. ( sqrt{2} )
( c cdot 2 )
D. None
11
40Find the acute angle between the lines ( sqrt{3 x}+y=1 ) and ( x+sqrt{3 y}=1 )11
41The 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
42The 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
43If the inclination of a line is ( 45^{circ}, ) then
the slope of the line is?
A . 0
B. –
( c cdot 1 )
D. 2
11
44Find 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
45LE 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
46Calculate the angles marked with small etters in the following diagram.
(iii) Rhombus
11
47In 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
48The 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
49Find 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
50For 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
51In 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
52For 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
53Find the slope of the line passing
through the points ( A(-2,1) ) and
( boldsymbol{B}(mathbf{0}, boldsymbol{3}) )
11
54Find 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
55The slope of any line which is parallel to the ( x ) -axis is
( mathbf{A} cdot mathbf{0} )
B.
( c cdot-1 )
( D )
11
56The 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
57on 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
58Find 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
59Find the area of the triangle whose
vertices are:
¡) (2,3),(-1,0),(2,-4)
ii) (-5,-1),(3,-5),(5,2)
11
60The 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
61If two vertices of an equilateral triangle ( operatorname{are}(3,0) ) and ( (6,0), ) find the third
vertex.
11
6212.
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
63The 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
64If ( 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
65Find 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
66If 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
67Let ( 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
6828.
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
6961. The x-intercept of the graph of
7x – 3y = 2 is
(4)
11
70Find the value of ( x ) so that the points
( (x,-1),(2,1) ) and (4,5) are collinear.
11
71Determine 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
72Find the slope of the line, which makes
an angle of ( 30^{circ} ) with the positive
direction of ( y ) -axis measured anticlockwise
11
73If ( 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
74The 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
76Find 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
77Identify without plotting, the lines parallel to the ( x ) or ( y ) axis: ( 3-7 y=0 )11
78In what ratio is the line segment joining
(-3,-1) and (-8,-9) is divided at the point ( left(-5, frac{-21}{5}right) ? )
11
79If 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
80Distance 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
81Let ( 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
82Two 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
83The 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
84Gradient 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
85An 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
8623. 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
87If ( 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
88The 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
89The distance from ( (mathbf{9}, mathbf{0}) ) to ( (mathbf{3}, mathbf{4}) )11
90If (-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
91Find 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
92If 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
93The 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
948.
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
95What 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?
B. Square
c. Rectangle
D. Rhombus
11
96The 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
97Coordinates 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
98The 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
99Find the slope of the line passing through the points ( C(3,5) ) and
( boldsymbol{D}(-mathbf{2},-mathbf{3}) )
11
100The 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
101If ( 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
102The distance between the points ( left(frac{1}{2}, frac{3}{2}right) ) and ( left(frac{3}{2}, frac{-1}{2}right) ) is11
103The 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
104How many equilateral triangles of side 2a with one vertex at origin and side along the ( x ) -axis is possible.11
105One 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
106Trapezoid ( 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
107If 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
108Find 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
109The 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
110If 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
111Find 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
(d) (-3,-8)
4
A atrial
11
1130
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
114The 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
115Obtain 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
116Find the distance of the point (-1,1) from the line ( 12(x+6)=5(y-2) )11
117ffigure ( 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
118What 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
119Find the equation of the line
perpendicular to ( boldsymbol{x}-mathbf{7} boldsymbol{y}+mathbf{5}=mathbf{0} ) and
having ( boldsymbol{x} ) -intercept 3
11
120Prove 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
121The 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
122If 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
123n fig. ( 2, ) lines ( l_{1} | l_{2} . ) The value of ( x ) is :
( A cdot 70 )
B. 30
( c cdot 40 )
D. 50
11
124Find the angle between the lines
represented by ( 3 x^{2}+4 x y-3 y^{2}=0 )
11
125The 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
126In 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
127Find 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
128Tow 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
129A 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
130Find that point on y axis which as
equidistant from point (6,5) and (-4,3)
11
131It 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
132Find 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
133There 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
134The 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
135Find the slope of the line joining the
points ( (2 a, 3 b) ) and ( (a,-b) )
11
1361919)
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
137The 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
138Is 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
139The vertices of ( Delta A B C ) are (-2,1),(5,4)
and (2,-3) respectively Find the area of triangle
11
140Find 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
141Find 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
143In figure, write another name for ( angle 1 )11
144The 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
146Area of a triangle whose vertices are
0), (2,3),(5,8) is
A ( .1 / 2 )
B.
( c cdot 2 )
D. 3/2
11
147The 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
D. rhombus
11
148If 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
149If ( 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
150The 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
152A 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
153Equation 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
154What 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
155One 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
156Line 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
157The number of straight lines which are equally inclined to both the axes is ;
A . 4
B.
( c cdot 3 )
( D )
11
158Prove 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
159The 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
160If 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
161Find the distance between the points (0,8) and (6,0)11
162Which 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
163The 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
164A 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
165Which point on y-axis is equidistant from (2,3) and (-4,1)( ? )11
166Find 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
167In 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
168If ( 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
169The 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
170The 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
171Draw 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
172What loci are represented by the equations:
( (x+y)^{2}-c^{2}=0 )
11
173Prove that the straight line ( x+y= ) touches the parabola ( y=x-x^{2} )11
174If 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
175The 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
176The 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
177Find the angles between the lines ( sqrt{3} x+y=1 ) and ( x+sqrt{3} y=1 )11
1789.
The orthocentre of the triangle formed by the lines xy = 0
and x+y=1 is
(1995S)
@ (6) 6 (5) © (,0) (a (24)
11
179If 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
180Find 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
18114.
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
182Find the distance between the following pairs of point. ( boldsymbol{P}(-mathbf{5}, mathbf{7}), boldsymbol{Q}(-mathbf{1}, mathbf{3}) )11
183In 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
184In 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
185A 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
186Points ( 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
187The 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
188In 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
190In 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
191Find 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
192Find 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
193Write the slope of the line whose
inclination is ( 45^{circ} )
11
194Find the inclination of the line ( ( ) in degrees ) whose slope is ( frac{mathbf{1}}{sqrt{mathbf{3}}} )11
195In 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
196Find the distance of the point (6,8) and the origin.11
197Find the slope of the line whose
inclination is
( mathbf{1 0 5}^{circ} )
11
198A 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
199If 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
200Find 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
201The 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
203Show 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
204n 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
20511.
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
206The 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
207The 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
208Given 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
210If 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
211For 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
212Prove 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
213The 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
214What 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
215The 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
216The 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
217In 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
218Find the distance between the following pairs of points:(-5,7),(-1,3)11
219The 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
220The 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
221The 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
222The 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
223If ( 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
224The 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
225The 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
226If 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
228n 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
229The 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
230If vertices of a triangle are (0,4),(4,1) and ( (7,5), ) find its perimeter.11
231The 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
23216. 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
23318. 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
235The 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
236evaluate:
( mathbf{3} boldsymbol{x}-mathbf{5} boldsymbol{y}=mathbf{1 6} ; boldsymbol{x}-mathbf{3} boldsymbol{y}=mathbf{8} )
11
237Find 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
238Find 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
2392.
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
24014.
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
241The 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
242Lines ( 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
243The 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
244Find the areas of the triangles the whose coordinates of the points are respectively. (5,2),(-9,-3) and (-3,-5)11
245The 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
246ff ( 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
248If 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
249The 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
250Find 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
251Vyum
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
252A 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
253The 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
254The 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
25574. 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
256Given 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
258If 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
259f ( 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
260Find the slope of the line perpendicular
to the line joining the points (2,-3) and ( (mathbf{1}, mathbf{4}) )
11
261The 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
262The ( 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
26332. 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
264Prove that the points (-3,0),(1,-3) and (4,1) are the vertices of an isosceles right-angled triangle. Find the area of this triangle11
265f point ( (x, y) ) is equidistant from points
(7,1) and (3,5) show that ( y=x-2 )
11
266Find the slope of the line passing
through the points ( G(-4,5) ) and ( boldsymbol{H}(-mathbf{2}, mathbf{1}) )
11
267The 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
268If (-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
269The 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
270If 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
27116.
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
272Find 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
273The 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
274The 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
275The 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
276Slope 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
277If 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
278The 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
279Find 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
2807.
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
281Find 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
282The 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
283Find the distance between the following
pair of points. (-5,7) and (-1,3)
11
284Find the distances between the
following pair of points. ( \$ \$(4,-7) ) and ( (-1, )
5)( \$ \$ )
11
285Draw 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
286Without using distance formula, show that points (-2,-1),(4,0),(3,3) and (-3,2) are the vertices of a parallelogram11
287The 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
288If ( 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
289A 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
290What 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
291The 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
292What 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
293For 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
294The 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
295The 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
296A 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
297The 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
2981.
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
299The 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
300A 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
30120.
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
302The 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
30324.
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
304A 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
30519. 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
306The 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
307Investigate 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
308Let ( 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
309Find the equation of the line that
passes through the points (-1,0) and
(-2,4)
11
310Find 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
311Prove that the points (-7,-3),(5,10),(15,8) and (3,-5)
taken in order are the corners of a
parallelogram.
11
312Line ( 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
313If 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
314Prove that the points ( (0,0),left(3, frac{pi}{2}right), ) and ( left(3, frac{pi}{6}right) ) form an equilateral triangle.11
315Find 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}} )
11
316If 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
31820. 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
31934. 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
320If 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
321Find 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
322The 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
323f ( 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
324The 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
325Which 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
326Find the slope of the line which make the following angle with the positive direction of ( x- ) axis :
( frac{2 pi}{3} )
11
327In 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
328In 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
32952. 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
330If ( 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
331The 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
332Equation 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
333The 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
334f ( 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
335Find 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
337Let ( 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
338Let ( 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
339Let ( 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
341Three 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
342Find the angle which the straight line ( y=sqrt{3} x-4 ) makes with y-axis.11
343f 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
344n 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
345The 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
346If ( (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
347Find the distance between (8,-8) from
the origin.
11
348The 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
349Find a point on ( boldsymbol{y}-boldsymbol{a} boldsymbol{x} boldsymbol{i} boldsymbol{s} ) which is
equidistant from (-5,-2) and (3,2)
11
350Prove that:
( mathbf{3} boldsymbol{x}-mathbf{5} boldsymbol{y}=mathbf{1 6} ; boldsymbol{x}-mathbf{3} boldsymbol{y}=mathbf{8} )
11
351The 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
352If 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
353The 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
354Find 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
355Find the distance of the line ( 4 x+7 y+ )
( 5=0 ) from the point (1,2) along the
line ( 2 x-y=0 )
11
356The 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
357Find the area of the triangle whose vertices are (-5,7),(4,5) and (-4,-5)11
358What is the distance of points ( boldsymbol{A}(mathbf{5},-mathbf{7}) )
from ( y ) -axis.
11
359The 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
360Find the equation of the straight line
equally inclined to the lines, ( 3 x=4 y+ )
7 and ( 5 y=12 x+6 )
11
361Show 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
36215. 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
363Find the distance between
( (x+3, x-3) ) from the origin.
11
364Slope 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
36552. 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
366Using 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
368A 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
369If 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
370If 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
371Write 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
373The coordinate of vertices of triangles are given. Identify the types of triangles (3,-3)(3,5)(11,-3)11
374If 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
375If 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
376The 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
377Which 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
378In 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
379Let the opposite angular points of a square be (3,4) and ( (1,-1) . ) Find the coordinates of the remaining angular points.11
380A 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
381If 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
382Column II gives the area of triangles whose vertices are given in column I match them correctly.11
383The 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
384In 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
38518.
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
38629.
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
387Prove 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
388If 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
389Show that the following points are collinear.
(3,-2),(-2,8) and (0,4)
11
390The 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
391Find 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
392The 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
393The 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
394If 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
395Find 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
396Find 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
397Find the slope of the line passing through the points ( A(2,3) ) and ( B(4,7) )11
398State 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
399Distance 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
400The 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
401Solve the following question:
Find the slope of the line passing through the points ( A(2,3) ) and ( B(4,7) )
11
402Find the value of ( k, ) if the points
( A(7,-2), B(5,1) ) and ( C(3,2 k) ) are
collinear.
11
403A parallel line is drawn from point ( P(5,3) ) to ( y ) -axis, what is the distance
between the line and ( y ) -axis.
11
404There 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
405In 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
406If 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
408The 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
11
409The 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
410Area 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
41110. 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
412The 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
413Point ( 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
414Find the slope of the line, which makes
an angle of ( 30^{circ} ) with the positive
direction of ( y- ) axis measured
anticlockwise.
11
415Find 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
416Int 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
417The 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
418Triangle 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
419The 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
420Prove 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
421Find 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
422Given 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
423The 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
425Find the slope of line having inclination
( mathbf{6 0}^{circ} )
11
426Find 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
427If 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
428Find the distance of the point (-1,1) from the line ( 12(x+6)=5(y-2) )11
429Which 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
430Srivani walks ( 12 m ) due East and turns
left and walks another 5 m, how far is
she from the place she started?
11
431The 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
432Points ( 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
433Which of the following points is equidistant from (3,2) and (-5,-2)( ? )
в. (0,-2)
D. (2,-2)
11
434Find the centre of the circle passing through (6,-6),(3,-7) and (3,3)11
435If 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
436If
( 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
437Find inclination (in degrees) of a line
parallel to ( y ) -axis.
11
438The points (-2,5) and (3,-5) are plotted in xy planes. Find the slope and ( y ) intercept of the line joining the points.11
439The line joining the points (-6,8) and
(8,-6) is divided into four equal parts;
find the coordinates of the points of
section
11
4406.
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
441Line ( 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
442The distance or origin from the point ( P(3,2) ) is :
A ( cdot sqrt{2} )
B. ( sqrt{15} )
c. ( sqrt{13} )
D. ( sqrt{11} )
11
443Find 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
444Find the distance between ( boldsymbol{x}+boldsymbol{y}+mathbf{1}= )
0 and ( 2 x+2 y+5=0 )
11
445Points 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
446If ( 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
447n 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
450Equation 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
451Plot 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
452Find the distance between the parallel
lines
( 3 x+2 y=7 ) and ( 9 x+6 y=5 )
11
453Find 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
454Let ( 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
455If ( 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
456The 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
457Show that the points ( A(2,-2), B(8,4), C(5,7), D(-1,1) ) are the
vertices of a rectangle.
11
458Let ( 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
459Find 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
460Find 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
462I : 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
463If 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
464Find the equation of a straight line:
with slope 2 and ( y- ) intercept 3
11
465The 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
466The 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
467Determine the ratio in which the point ( P(3,5) ) divides the join of ( A(1,3) & )
( boldsymbol{B}(mathbf{7}, mathbf{9}) )
11
468If 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
469Find the distance between
(2,3,-5) and (1,6,3)
11
470Find 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
471Find the equation of a straight line:
with slope ( -1 / 3 ) and ( y- ) intercept -4
11
4729.
(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
47312. 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
474The 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
475VII
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
476Find the co-ordinate of points on ( x ) -axis
which are at a distance of 5 units form
the point ( (mathbf{6},-mathbf{3}) )
11
477Find the distance between the points
(2,1) and (3,2)
11
478Two rails are algebraically represented by the equations ( 3 x-5 y-20=0 ) and ( 6 x- ) ( 10 y+40=0 )11
479Find 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
480Find 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
481Find 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
482Classify 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
483Find the slope of the line passing the two given points ( (a, 0) ) and ( (0, b) )11
484A 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
485If 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
486Given ( 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
487Write the inclination of a line which is
parallel to x-axis.
11
488Find the distance between the following pair of points. (-2,-3) and (3,2)11
489find the acute angle between ( y=5 x+ )
6 and ( y=x )
11
490Find the area of the triangle whose
vertices are (10,-6),(2,5) and (-1,3)
11
491The 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
492The 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
D. rhombus
11
493Find the point on the curve ( y=x^{3}- )
( 2 x^{2}-x, ) where the tangents are parallel
to ( 3 x-y+1=0 )
11
494Consider 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
495The 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
496Find the value ( k ). for which the point ( (-1, )
3) lies on the graph of the equation ( 2 x- ) ( y+k=0 )
11
497Find the area of the triangle with
vertices at the points:
(0,0),(6,0) and (4,3)
11
498ху
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
499A 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
500The 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
50135.
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
502If 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
503On 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
504The 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
505If 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
506Two 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
508The 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
509Find 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
510The 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
511The 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
512The distance from origin to (5,12) is
A . 13
B. 17
c. 10
D. 7
11
513Find the distance between (8,3) and (3,2)11
514( left(2,30^{circ}right) ) and ( left(4,120^{circ}right) )11
515If 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
516Two 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
517Find the coordinates of the points of trisection of the line segment joining (1,-2) and (-3,4)11
518Find, if possible, the slope of the line through the points (2,5) and (-4,5)11
519In 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
520Consider 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
521Find 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
523If 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
524Three 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
525A 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
526n 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
527The 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
528If 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
529Find 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
530Show 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
533In 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
534Let 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
535The 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
536A 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
538Find 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
539In 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
540Find 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
541Find 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
542In 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
54427.
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
545Show 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
54617. 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
547Find the equation of line equally inclined to coordinate axes and passes
through (-5,1,-2)
11
548Find the area of square whose one pair of the opposite vertices are (3,4) and ( (5, )
6)
11
549The 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
550The 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
551Find 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
552The distance between (-4,-5) and (-4,-10) is
units.
A . 15
B. 10
( c .5 )
D.
11
553If 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
554The 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
555Find the coordinates of the points where
the graph of the equation ( 3 x+4 y=21 )
intersect ( x- ) axis and ( y- ) axis.
11
556Find the angle between the curves given below:
( boldsymbol{y}^{2}=boldsymbol{4} boldsymbol{x}, boldsymbol{x}^{2}+boldsymbol{y}^{2}=mathbf{5} )
11
557Find the slope of the line that passes through the points (2,0) and (2,4)11
558If ( 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
559Find ( 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
560Find the angles of inclination of straight lines whose slopes are ( sqrt{mathbf{3}} )11
561Find 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
562The 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
563A 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
564Find the inclination of the line whose
slope is 0
11
565An 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
566The line through (1,5) parallel to ( x ) -axis
is
A. ( x=1 )
B. ( y=5 )
c. ( y=1 )
D. x = 5
11
567If 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
56828. 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
569Find the distance between the following
pair of points:
( (a, 0) ) and ( (0, b) )
11
570Find 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
571The 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
572Equation 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
573The 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
574The 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
575The lines represented by ( 3 x+4 y=8 ) and ( p x+2 y=7 ) are parallel. Find the value of
( p )
11
576The 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
577The 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
578Find the shortest distance of (3,4) from
origin.
11
579The 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
58064. 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
581The 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
c. rectangle
D. parallelogram
11
582Find the areas of the triangles the
whose coordinates of the points are
respectively. ( (a, b+c),(a, b-c) ) and ( (-a, c) )
11
583Find the slope of a line passing through the following points:
( (3-5) ) and (1,2)
11
584Find the length of the perpendicular
from the point (5,4) on the straight line.
11
585A 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
586The 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
587Show that the triangle whose vertices ( operatorname{are}(8,-4),(9,5) ) and (0,4) is an
isosceles triangle.
11
588Find the slope of the line having its
inclination ( 60^{circ} )
11
589The 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
590Find the slope of line which passes through the point (7,11) and (9,15)11
591Find the angle subtended at the origin
by the line segment whose end points ( operatorname{are}(0,100) ) and (10,0)
11
592The 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
593Find the angle of inclination of straight line whose slope is ( frac{1}{sqrt{3}} )11
594Find 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
596PULP
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
597The 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
598The 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
599Find 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
600For 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
601In 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
603The 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
604Prove that the points (3,0)(6,4) and (-1,3) are the vertices of a right angled isosceles triangle.11
605The 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
606Identify 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
607Find the slope of the line perpendicular to ( A B ) if ( A=(0,-5) ) and ( B=(-2,4) )11
608If 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
609The 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
610Consider 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
611If 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
612If 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
613The 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
614During 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
615A 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
616Find slope if ( theta=150^{circ} )11
617The 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
618Find 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
620Find 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
621A 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
622If 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
623Find 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
624State 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
625If 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
626Find 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
627A 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
628Write 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
629The graph of ( x=5 ) is perpendicular to
A. x-axis
B. y-axis
c. Line ( y=x )
D. Line ( y=-x )
11
630The 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
631Find the distance between the following pair of points:
(-6,7) and (-1,-5)
11
632Perpendicular distance between ( 2 x+ ) ( 2 y-z+1=0 ) and ( 2 x+2 y-x+4= )
0 is
11
633The 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
634If 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
635Choose 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
636A line a passes through (3,-4) and is parallel to y – axis find its equation.11
637What 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
63821. 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
63938.
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
640Find 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
641In what ratio does the point ( left(frac{1}{2}, 6right) ) divide the line segment joining the points (3,5) and (-7,9)( ? )11
642PQRS 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
643Find the value of ( x ) in the
diagram below
11
644The 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
645Find 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
646If 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
64730. 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
648Find 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
649The 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
650Find the equation of a straight line cutting off an intercept -1 from ( y- ) axis and being equally inclined to the axes.11
651If 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
652The 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
653Find 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
654The 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
655In the figure the arrow head segments
are parallel then find the value of ( x ) and
( y )
11
656Find 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
657A 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
658Te
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
659The 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
D. rhombus
11
660Find the coordinate of point which divides ( A(5,6) ) and (5,10) in 2: 311
661Find the distance of the point (36,15) from origin.11
662What is the slope of a line whose inclination with the positive direction of
( x ) axis is ( 120^{circ} ? )
11
663A 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
664Show 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
665Equation(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
666Find 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
667Find 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
668Find 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
669Find the equation of the line intersecting the ( x ) -axis at a distance of
3 units to the left of origin with slope
-2
11
670Find 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
671If ( 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
672Write 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
673Find the distance between (4,5) and (5,6)
A ( cdot sqrt{2} )
B. ( sqrt{3} )
( c cdot sqrt{6} )
D. ( sqrt{7} )
11
6747.
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
675Which 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
676Find 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
677Find 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
67816.
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
679The 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
680Find 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
681For 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
682State 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
683Find the area of triangle formed by the points (8,-5),(-2,-7) and (5,1)11
684If 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
685The 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
686The 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 to11
68714
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
688The 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
689If 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
690The 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
691The 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
692The 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
693The 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
694The 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
695Find the distance between the points (1,5) and (5,8)11
696Find 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
697The 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
698A 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
699the 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
700The 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
701How many points are there on the ( x- ) axis whose distance from the point
(2,3) is less than 3 units?
11
7025.
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
11
703Find the slope of the line with
inclination ( 60^{circ} )
11
704Find if possible, the slope of the line through the points ( (1 / 2,3 / 4) ) and ( (-1 / 3,5 / 4) )11
70518. 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
70619. 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
707Find 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
708Find the slope of the straight line passing through the points (3,-2) and (-1,4)11
709Say true or false. The distance of the point (5,3) from the ( X ) -axis is 5 units.
A . True
B. False
11
710If ( 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
711Find the slope of the line which make the following angle with the positive direction of ( x- ) axis
( -frac{pi}{4} )
11
712For 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
11
713Find the slope of the line passing through the points (3,-2)( &(7,-2) )11
714If 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
715Three 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
716pouvoiy.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
718A 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
719A point ( P(2,-1) ) is equidistant from the points ( (a, 7) ) and ( (-3, a) . ) Find ‘a’11
720If 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
721Find the distance between the origin
and the point (5,12)
11
722Which 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
72427.
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
725Find the angle between ( y-sqrt{3} x=5 & )
( sqrt{mathbf{3}} boldsymbol{y}-boldsymbol{x}+boldsymbol{6}=mathbf{0} )
11
726If 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
727The 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
728Find the distance between two complex
nymbers ( z_{1}=2+3 i ) and ( z_{2}=7-9 i ) on
the complex plane.
11
729Find 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
730If ( 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
731Using 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
732The 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
733Four 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
734If 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
735The 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
736Find the slope and ( y ) -intercept of line
( boldsymbol{y}-mathbf{3} boldsymbol{x}=mathbf{5} )
11
737If 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
738The 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
739The 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
740Say true or false
Points (1,7),(4,2),(-1,-1) and
(-4,4) are the vertices of a square
A. True
B. False
11
741Find the slope of the straight line passing through the points (3,-2) and (7,2)11
742Value 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
744Find the inclination of the line whose
slope is ( frac{mathbf{1}}{sqrt{mathbf{3}}} )
11
745If 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
746The 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
74731. 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]
11
748Find 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
74913. 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
750Find 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 triangle11
751The 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
753The 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
754The 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
755Find 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
756Find 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
757Which 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
75817. 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
7593.
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
760The 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
761The 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
762The 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
763The 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
764f ( boldsymbol{pi} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{2 5}, ) write ( boldsymbol{y} ) in terms of ( boldsymbol{x} )11
765A 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
766Find 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
767The 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
768Find 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
769If 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
770Find the slope of a non-vertical line
( boldsymbol{a} boldsymbol{x}+boldsymbol{b} boldsymbol{y}+boldsymbol{c}=mathbf{0} )
11
771If ( 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
772If (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
773The 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
774For 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
775The 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
776The points (6,2),(2,5) and (9,6) form the vertices of a ( _{–} ) triangle.
A . right
B. equilateral
c. right isosceles
D. scalene
11
777f ( 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
778Find inclination (in degrees) of a line perpendicular to y-axis.11
7793.
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
780If ( 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
781Find 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
782Find 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
783The 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
784If 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
785The 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
786The 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
787There 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
788A point ( A(p, q) ) is 2 units away from ( x- )
axis and 5 units from ( y- ) axis. What
would be its coordinate?
11
789Find the locus of the point equidistant from (-1,2) and (3,0)11
790Solve 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
791A 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
792Find 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
793The 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
794Starting 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
795Find 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
796A 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
797The 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
798Find the equation of straight lines passing through (1,1) and which are at a distance of 3 units from (-2,3)11
799A 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
800In 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
801Locus 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
802The 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
803The 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
804Consider 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
805A 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
806The 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
807Find the slope and ( y ) -intercept of the line given by the equation ( 2 y+3 x=-2 )11
808If 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
809Prove 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
810The 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
811Find 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
812Prove 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
813The 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
814U 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
815Find 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
816If 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
817Find the shortest distance between the
( x^{2}+y^{2}=9 ) and (6,8) is
11
818Prove that
(4,0),(-2,-3),(3,2),(-3,-1)
coordinates are not the vertices of
parallelogram.
11
819If 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
820AP 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
821Which 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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