# Constructions Questions

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

#### List of constructions Questions

Question No Questions Class
1 Choose the correct statement:
A. Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.
B. The difference of two sides of a triangle is equal to the third side.
C. The sum of the three sides of a triangle is less than the sum of its three medians.
D. If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.
9
2 In the fig. ( A P ) and ( B P ) are the tangents draw from an external point P. Prove
that ( angle A O B ) and ( angle A P B ) are
supplementary
10
3 Draw a square of ( 4 mathrm{cm} . ) Constuct angle bisectors of 4 angles.Let all meet at 0 measure ( A O ) and ( 0 C . ) Then ( A O^{2}+O C^{2}= )
( mathbf{A} cdot mathbf{8} )
B. 4
c. 16
D. 32
9
4 Construct a triangle ( A B C ) in which
( B C=8 c m, angle B=45^{circ} ) and ( A B )
( boldsymbol{A C}=mathbf{3 . 5} boldsymbol{c m} )
9
5 Construct a tangent to a circle of radius
( 4 c m ) from a point on the concentric
circle of radius ( 6 mathrm{cm} ) and measure its
length. Also verify the measurement by actual calculation.
10
6 Draw a circle of radius ( 5 mathrm{cm} . ) From a
point ( 8 mathrm{cm} ) away from the centre,
construct two tangents to the circle.
Measure them.
(Write the steps of construction).
10
7 In the figure, PQ and PR are the tangents to a circle with centre 0. If ( angle P=frac{4}{5} angle O . ) Find ( angle O ) and ( angle P ) 10
8 In a circle, let ( A B ) be diameter. Let ( P ) is
point on circle. Then measure of angle APB is
A ( .30^{circ} )
B . ( 40^{circ} )
( c .90^{circ} )
D. ( 60^{circ} )
9
9 Construct a pair of tangents to a circle
of radius ( 4 mathrm{cm} ) such that the acute
angle between the tangents is ( 45^{circ} )
10
10 In an equilateral triangle ( Delta A B C ) with
sides ( 5 mathrm{cm} . ) Angle bisectors of ( angle A, angle B, angle C ) meet at point ( 0 . ) Measures of OA approximately is
A . 2.5
B. 4
( c .3 .2 )
D. 2.8
9
11 Construct tangents to a circle of radius
( 4 mathrm{cm} ) at ( Q ) and ( R, ) from a point ( P ) on the
concentric circle of radius ( 6 mathrm{cm} )
10
12 The point (4,0) lie on the line
A. ( y-x=0 )
В. ( y=0 )
c. ( x=0 )
D. ( y+x=0 )
10
13 Construct a triangle with sides ( 5 mathrm{cm}, 6 mathrm{cm} ) and ( 7 mathrm{cm} ) and then another triangle whose sides are ( frac{7}{5} ) times of the corresponding sides of the first triangle. Write down the steps of construction. 10
14 Write down the co-ordinates of the points
( A ) to ( J ) marked in the following diagram:
10
15 In what ratio does (-4,6) divides the line segment joining the point ( boldsymbol{A}(-mathbf{6}, mathbf{4}) )
and ( B(3,-8) )
10
16 nd D are any two points on the same side of a line L.
now how to find a point P on the line L such that PC and
PD are equally inclined to the line L. Justify your steps.
(1980)
9
17 If the point ( P(2,2) ) is equidistant from the points ( A(-2, k) ) and ( B(-2 k,-3) ) find ( k ) 10
18 ( mathbf{A} triangle boldsymbol{A} boldsymbol{B} boldsymbol{C} ) in which ( boldsymbol{A} boldsymbol{B}= )
( mathbf{5 . 4} mathbf{c m}, angle boldsymbol{C} boldsymbol{A} boldsymbol{B}=mathbf{4 5}^{circ} ) and ( boldsymbol{A} boldsymbol{C}+boldsymbol{B} boldsymbol{C}= )
( mathbf{9} mathrm{cm} . ) Then, perimeter of ( Delta boldsymbol{A B C} ) is
A. ( 14.4 mathrm{cm} )
B. ( 11.4 mathrm{cm} )
( c .12 .4 mathrm{cm} )
D. ( 15.4 mathrm{cm} )
9
19 The lengths of the tangents (in ( c m ) ) measured by a ruler are:
( mathbf{A} cdot mathbf{6} )
B. 7
c. 8
D. 9
10
20 n the figure, ( C ) is the centre of the
circle. ( X ) and ( Y ) axes are tangents to the
circle at the points ( A ) and ( B )
respectively. If the coordinates of ( A ) are
( (4,0), ) find the coordinates of ( B ) and ( C )
10
21 ( Delta A M T sim Delta A H E cdot ln Delta A M T, M A= )
( 6.3 c m, angle M A T=120^{circ}, A T=4.9 mathrm{cm} )
( frac{M A}{H A}=frac{7}{5} ) Construct ( Delta A H E )
10
22 Point (0,-9) lies
A. on the ( X ) -axis
c. on the Y-axis
D. In the ( I V ) quadrant
10
23 Find the equation for the graph above.
( mathbf{A} cdot x=3 )
( mathbf{B} cdot y=3 )
C. ( y=-5 )
D. ( x=-5 )
10
24 Construct a triangle similar to a given triangle ( A B C ) with its side equal to ( frac{5}{3} ) of
corresponding side of triangle ( boldsymbol{A B C} ) (i.e., of scale factor ( frac{5}{3} ) ).
10
25 Draw ( angle A B C ) of measure ( 110^{circ} ) and
bisect it.
9
26 Using a ruler and compass only.
(i) Construct a ( triangle A B C ) with the
following data. ( A B=3.5 mathrm{cm}, B C=6 mathrm{cm} ) and
( angle A B C=120^{circ} )
(ii) In the same diagram, draw a circle
with ( B C ) as diameter. Find a point ( P ) on the circumference of the circle which is
equidistant from ( A B ) and ( B C )
(iii) Measure ( angle B C P )
9
27 If tangents are drawn from the end
points of 2 radii that are inclined at an
angle ( 125^{circ}, ) what is the angle between
the tangents?
A . 55
B. ( 110^{circ} )
c. ( 125^{circ} )
D. ( 90^{circ} )
10
28 The areas of two similar triangles are
45 sq. ( mathrm{cm} ) and 80 sq.cm. The sum of their perimeters is ( 35 mathrm{cm} . ) Find the perimeter of each triangle in cm.
( mathbf{A} cdot 15,20 )
B. 13,22
c. 17,18
D. None of these
10
29 Construct a ( triangle A B C ) in which ( A B= )
( mathbf{5} c boldsymbol{m} cdot angle boldsymbol{B}=mathbf{6 0}^{circ} ) altitude ( boldsymbol{C} boldsymbol{D}=mathbf{3} boldsymbol{c m} )
Construct a ( triangle A Q R ) similar to ( triangle A B C )
such that side of ( triangle A Q R ) is 1.5 times
that of the corresponding sides of
( triangle boldsymbol{A} boldsymbol{C} boldsymbol{B} )
10
30 Construct a triangle ( A B C ) whose
perimeter is ( 12.5 mathrm{cm} ) and whose base
angles are ( 60^{circ} ) and ( 75^{circ} )
9
31 If ( P(x, y) ) is any point on the line joining the points ( (a, 0) ) and ( (0, b) ) then the value of ( frac{x}{a}+frac{y}{b} )
( A )
B. 2
( c cdot 3 )
D.
10
32 The construction of a ( Delta A B C ) in which
( B C=6 mathrm{cm} ) and ( angle B=50^{circ}, ) is not
possible when ( (A B-A C) ) is equal to:
A ( .5 .6 mathrm{cm} )
в. ( 5 mathrm{cm} )
( c cdot 6 c m )
D. ( 4.8 mathrm{cm} )
9
33 Find the co-ordinate of a points on ( x )
axis which is equidistant from the
points (-2,5) and (2,-3)
10
34 If ( 2^{2 x-y}=32 ) and ( 2^{x+y}=16 ) then ( x^{2}+ )
( y^{2} ) is equal to
A . 9
B. 10
( c cdot 11 )
D. 13
10
35 To find a point ( boldsymbol{P} ) on the line segment
( A B=6 mathrm{cm}, ) such that ( A P: A B=2: 5 )
in which ratio does the line segment
( A B ) is divided by ( P ? )
10
36 The co-ordinates of the point of trisection of the line segment joining the points (-4,3) and (2,-1) are
A ( .(2,1) )
в. (3,1)
( ^{mathbf{c}} cdotleft(-2, frac{5}{3}right) )
D. None of these
10
37 ( A B C ) is a triangle. ( D ) is a point on ( A B ) such that ( A D=frac{1}{4} A B ) and ( E ) is a point
on ( A C ) such that ( A E=frac{1}{4} A C . ) Prove that ( D E=frac{1}{4} B C )
9
38 Construct a triangle ( P Q R ) in which
( angle Q=30^{circ}, angle R=90^{circ} ) and ( P Q+Q R+ )
( boldsymbol{P R}=11 mathrm{cm} )
9
39 Construct a triangle XYZ in which ( angle Y= )
( 30^{0}, angle Z=90^{0} ) and ( X Y+Y Z+Z X=11 mathrm{cm} )
9
40 If tangents are drawn from the endpoints of two radii that are inclined
at an angle of ( 165^{circ}, ) what is the angle between the tangents?
A ( cdot 5^{circ} )
B. 35
( c cdot 15^{circ} )
D. None of these
10
41 If the mid-point of the line segment joining the points ( A(6, x-2) ) and ( B(-2,4) ) is (2,-3) find the value of ( x ) 10
42 Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2,-1) (1,0),(4,3) and (1,2) meet.
A . (5,1)
в. (1,1)
c. (1,5)
(年. (1,5)
D. ( (1,1-) )
10
43 From (1,4) you travel ( 5 sqrt{2} ) units by making ( 135^{0} ) angles with positive ( x ) axis (anticlockwise) and then 4 units by
making ( 120^{0} ) angle with positive ( x ) -axis (clockwise) to reach Q. Find co-
ordinates of point ( Q )
A ( cdot(+6,9-2 sqrt{3}) )
в. ( (-6,9-2 sqrt{3}) )
c. ( (-6,9+2 sqrt{3}) )
D. ( (+6,9+2 sqrt{3}) )
10
44 ( 1 D= ) 10
45 Construct a triangle ( A B C ) in which
( B C=7 c m, angle B=75^{circ} ) and ( A B+ )
( A D=13 mathrm{cm} )
9
46 Draw a circle of radius ( 3 mathrm{cm} ) and
construct two tangents to it from an
external point ( 8 c m ) away from its
centre
10
47 Construct a rectangle ( A B C D ) of lengh 6 ( mathrm{cm} ) and breadth ( 4 mathrm{cm} . ) Construct angle bisectors of ( angle A ) and ( angle B . ) Let them meet
at 0.The distance of 0 from length ( A B ) is:
A . 3
B. 10
c. 2
D. 8
9
48 Draw a circle with centre 0 and radius 3.5
( mathrm{cm} . ) Take point ( mathrm{P} ) at a distance ( 5.7 mathrm{cm} ) from
the centre. Draw tangents to the circle from point ( P )
10
49 In triangle ( A B C ; ) angle ( A=90^{circ}, ) side
( A B=x c m, A C=(x+5) c m ) and
area ( =150 mathrm{cm}^{2} ). Find the sides of the
triangle.
9
50 Construct a ( triangle P Q R, ) such that ( angle Q=70^{circ} )
( angle R=70^{circ} ) and ( P Q+Q R+R P=10 )
( mathrm{cm} )
9
51 Draw ( angle P O Q ) of measure ( 75^{circ} ) and find
its line of symmetry.
9
52 Construct a scalene triangle ( boldsymbol{A B C} )
given base ( A B=3 c m, ) base angle ( = )
( 90^{circ} ) and sum of the lengths ( B C+ )
( boldsymbol{A C}=mathbf{9} boldsymbol{c m} )
9
53 Draw the tangents to the circle from the
point ( L ) with radius ( 2.9 mathrm{cm} . ) Point ( ^{prime} L^{prime} ) is
at a distance ( 7.5 mathrm{cm} ) from the centre
( boldsymbol{M}^{prime} )
10
54 ( triangle L T R sim triangle H Y D, triangle H Y D ) is such
that ( boldsymbol{H} boldsymbol{Y}=mathbf{7 . 2} boldsymbol{c m}, boldsymbol{Y} boldsymbol{D}=boldsymbol{6} boldsymbol{c m}, angle boldsymbol{Y}= )
( 40^{circ} ) and ( frac{L R}{H D}=frac{5}{6} ) and construct
( triangle boldsymbol{L} boldsymbol{T} boldsymbol{R} )
10
55 Measure the length of ( A B ) with a ruler.
Then ( A B=? )
A ( .7 .5 mathrm{cm} )
B. ( 9.6 mathrm{cm} )
( c .10 mathrm{cm} )
D. ( 8.4 mathrm{cm} )
10
56 Show that the mid-point of the line segment joining the points (5,7) and (3,9) is also the mid-point of the line segment joining the points (8,6) and (0,10) 10
57 What is an angle bisector? 9
58 In Figure ( 1, ) the ratio of ( A B ) to ( B C ) is 7:
5. If ( A C=1, ) calculate the distance
from ( A ) to the midpoint of ( B C )
A ( cdot frac{5}{8} )
B. ( frac{2}{3} )
c. ( frac{19}{24} )
D. ( frac{3}{4} )
10
59 Construct a triangle ( A B C ) whose perimeter ( 12 mathrm{cm} ) and who base angles
( operatorname{are} 50^{circ} ) and ( 80^{circ} )
9
60 Construct a triangle ( A B C ) in which
( B C=5.6 mathrm{cm}, angle B=45^{circ} ) and ( A B+ )
( boldsymbol{A C}=boldsymbol{8} boldsymbol{c m} )
9
61 Find the ratio in which the line joining
( A(1,-5) ) and ( B(-4,5) ) is divided by
the ( x-a x ) is. Also find the co-ordinates
of the point of division.
10
62 Construct a triangle ( A B C ) in which
( B C=7 c m, angle B=75^{circ} ) and ( A B+ )
( boldsymbol{A C}=mathbf{1 3} boldsymbol{c m} )
9
63 Any point on the ( x ) -axis is of the form
( mathbf{A} cdot(x, y) )
в. ( (0, y) )
c. ( (x, 0) )
D. ( (x, x) )
10
64 Find the length ( E C )
( s )
D
10
65 The construction of ( triangle A B C ) in which
( A B=6 mathrm{cm}, angle A=30^{circ}, ) is not possible
when ( boldsymbol{A C}+boldsymbol{B C}= )
( mathbf{A} cdot 6.3 mathrm{cm} )
B. ( 7.2 mathrm{cm} )
( c .5 .6 mathrm{cm} )
D. ( 6.9 mathrm{cm} )
9
66 ( triangle R H P sim triangle N E D ) in ( triangle N E D, N E= )
( 7 mathrm{cm}, angle E=30^{circ}, angle N=20^{circ} ) and ( frac{H P}{E D}=frac{4}{5} )
Construct ( triangle R H P )
10
67 Draw a line segment of length ( 6.3 mathrm{cm} ) &
divide it in the ratio ( 3: 4 . ) Measure the
two parts.
10
68 Perimeter of ( triangle A B C ) is ( 14 mathrm{cm}, mathrm{AB}=4.5 mathrm{cm} )
and ( angle A=80^{circ} . ) Construct ( triangle A B C )
9
69 The line joining the points (1,-2) and
(-3,4) is trisected; find the
coordinates of the points of trisection.
10
70 Write the steps to construct ( triangle A B C, ) in which ( B C=5.2 c m, angle A C B=45^{circ} ) and
perimeter of ( triangle boldsymbol{A B C} ) is ( 10 mathrm{cm} )
9
71 In the figure 0 is the centre of the circle. The tangents at ( mathrm{B} ) and ( mathrm{D} ) intersect each other at point P. If AB is parallel to CD and ( angle A B C=55^{circ} ) Find (i) ( angle B O D ) (ii)
( angle B P D )
10
72 Construct a ( triangle A B C ) in which ( A B= ) ( 4 mathrm{cm}, B C=5 mathrm{cm} ) and ( A C=6 mathrm{cm} )
Now, construct a triangle similar to
( triangle A B C ) such that each of its sides is
two-third of the corresponding sides of ( triangle A B C . ) Also, prove your assertion.
10
73 If ( 4 x+3 y=120, ) find how many non-
negative integer solutions are possible?
( mathbf{A} cdot mathbf{1} )
B. 11
c. Infinite
D. None of these
10
74 What is the equation for the graph
shown above?
( mathbf{A} cdot y=2 )
B. ( y=-4 )
c. ( x=2 )
D. ( x=-4 )
10
75 Draw the line joining the following
points. ( P(-4,5) ) and ( Q(3,-4) )
10
76 Write the following based on the graph. The ordinate of Lis
( 4 .-7 )
B
( c_{1}-5 )
None of these
10
77 What should be the angle between corresponding radii such that the tangents don’t intersect?
A . ( 0^{circ} )
B. ( 90^{circ} )
( c cdot 180^{circ} )
D. ( 45^{circ} )
10
78 Construct a pair of tangents to a cricle of radius ( 3.5 mathrm{cm} ) from a point ( 3.5 mathrm{cm} )
away from the circle.
10
79 Draw ( angle A B C ) of measure ( 115^{circ} ) and
bisect it.
9
80 Plot the point (5,0) on a graph paper. 10
81 If the roots of the equation ( x^{3}-11 x^{2}+ )
( 36 x-36=0 ) are in ( H . P . ) then the
middle root is
A. an even number
B. a perfect square of an integer
c. a prime number
D. a composite number
9
82 Divide the line segment ( A B=12 mathrm{cm} ) in
6 equal parts.
10
83 Construct a triangle of sides ( 5 mathrm{cm}, 6 mathrm{cm} )
and ( 7 mathrm{cm}, ) then construct a triangle
similar to it, whose sides are ( frac{2}{3} ) of
corresponding sides of the first triangle.
10
84 Construct triangle ( boldsymbol{A B C} ) in which
( B C=3.4 c m, A B-A C=1.5 c m ) and
( angle B=45^{circ} )
9
85 Construct a ( triangle A B C ) in which ( A B= )
( 4 mathrm{cm}, angle B=60^{circ} ) and altitude ( C L= )
( 3 mathrm{cm} . ) Construct a ( triangle A D E ) similar to
( triangle A B C ) such that each side of ( triangle A D E )
is ( frac{3}{2} ) times that of the corresponding
side of ( triangle A B C )
10
86 ( triangle L M N sim triangle X Y Z . ln triangle L M N, L M= )
( 6 mathrm{cm}, M N=6.8 mathrm{cm}, L N=7.6 mathrm{cm} ) and
( frac{L M}{X Y}=frac{4}{5} ; ) Construct ( triangle X Y Z )
10
87 To draw a pair of tangents to a circle which are at right angles to each other it is required to draw tangents at end points of two radii which are inclined at an angle of
( mathbf{A} cdot 60^{circ} )
B. ( 90^{circ} )
( c cdot 120^{circ} )
D. ( 45^{circ} )
10
88 ( Delta A B C sim Delta L M N cdot ln Delta A B C, A B= )
( 5.1 mathrm{cm}, angle B=55^{circ}, angle C=65^{circ} ) and
( frac{A C}{L N}=frac{3}{5}, ) then construct ( Delta L M N )
10
89 The coordinates of a point, which lies on ( y ) -axis and is at a distance of 4 units
above ( x ) -axis is
A ( .(0,4) )
в. (4,4)
c. (4,0)
D. (0,-4)
10
90 Draw ( triangle A B C, ) where ( m angle A B C= )
( 90^{circ} ; B C=4 c m ) and ( A C=5 c m ) and
then construct ( triangle B X Y ) with ( 4 / 3 ) scale
factor. Write points of construction
10
91 Construct a ( triangle A B C ) in which ( A B= )
( 6 mathrm{cm}, angle A=30^{circ} ) and ( angle B=60^{circ} )
Construct another ( triangle A B^{prime} C^{prime} ) similar to
( triangle A B C ) with base ( A B^{prime}=8 mathrm{cm} )
10
92 Draw ( angle L M N=165^{circ} ) and divide in into
four equal parts.
9
93 The point (0,6) lies on:
A. X-axis
B. Y-axis
c. origin
D. None
10
94 The line ( A B ) divides the line segment
OP in the ratio
A . 1: 1
B. 3: 4
c. 1: 2
( mathbf{D} cdot 9: 16 )
10
95 Draw an equilateral triangle. Draw angle
bisector of angle A .Let it meet the side
( B C ) at ( D )

Measure the Length BD and CD. Then:
( mathbf{A} cdot B D>C D )
в. ( B D<C D )
c. ( B D=C D )
D. None

9
96 Find the ratio in which the ( y ) -axis
divides the line segment joining the points ( boldsymbol{A}(boldsymbol{3}, boldsymbol{4}) ) and ( boldsymbol{B}(-boldsymbol{2}, mathbf{1}) . ) Also, find
the point of intersection.
A ( cdot 3: 2,left(0, frac{11}{5}right) )
в. ( _{1: 2,left(0, frac{13}{5}right)} )
c. ( _{1: 2,left(0, frac{3}{5}right)} )
D. ( 3: 4,left(0, frac{13}{5}right) )
10
97 Construct a right angled triangle whose
perimeter is equal to ( 10 mathrm{cm} ) and one
acute angle equal to ( 60^{circ} )
9
98 ( mathbf{P} ) is the midpoint of the part of the line ( 3 x+y-2=0 ) intercepted between the
axes. Then the image of ( mathbf{P} ) in origin is
( mathbf{A} cdotleft(-1,-frac{1}{3}right) )
B ( cdotleft(-frac{1}{3},-4right) )
( ^{c} cdotleft(-frac{1}{3},-1right) )
D. (-2,-3)
10
99 Plot the given points on a graph paper and join them with straight lines. Give a special name to the figure obtained:
(3,2),(3,-4),(-2,2) and (-2,-4)
10
100 The perimeters of two similar triangles is in the ratio ( 3: 4 . ) The sum of their
areas is 75 sq. cm. Find the area of each triangle in sq. cm.
A . 30,45
B. 27,48
c. 25,50
D. None of these
10
101 To construct a triangle similar to given ( Delta A B C ) with its sides ( frac{4}{5} ) of that of
( Delta A B C . ) Locate points ( X_{1}, X_{2}, X_{3}, dots )
on ray ( B X ) at equal distances such that
( angle A B X ) is acute. The minimum number
of points to be located on ( B X ) is:
A . 14
B. 5
( c .9 )
D . 20
10
102 Draw a circle of radius ( 3 mathrm{cm} ). Take a
point outside the circle at a distance of
( 6 mathrm{cm} ) from the centre of the circle.
Construct tangents from this point to the circle. Measure the angle between
the tangents and select the correct value from below.
( mathbf{A} cdot 60 )
B. 30
( c cdot 45 )
D. ( 90^{circ} )
10
103 PQ and PR are the tangents to a circle with centre ( O . ) If ( angle P=frac{4}{5} angle O . ) Find
( angle Q P R )
A ( cdot 100^{circ} )
B. ( 180^{circ} )
( c .80^{circ} )
D. None of these
10
104 Draw a ( triangle A B C ) with side ( B C=7 mathrm{cm} )
( angle B=45^{circ}, angle A=105^{circ} . ) Then, construct
a triangle whose sides are ( frac{4}{3} ) times the
corresponding sides of ( triangle boldsymbol{A B C} )
10
105 f the sides of a parallelogram touch a
circle. Prove that the parallelogram is a rhombus.
10
106 The length of ( D E= )
1
B
( c cdot 13 )
D
10
107 Draw a right triangle which the sides (other than hypotenuse) are of lengths
( 4 mathrm{cm} ) and ( 3 mathrm{cm} . ) Then construct another
( mathbf{5} )
triangle whose sides are ( frac{-operatorname{times}}{3} ) the corresponding sides of the given triangle.
10
108 Draw a circle with center ( boldsymbol{O} ) and radius
( 6 mathrm{cm} . ) Take a point ( P ) outside the circle
at a distance of ( 10 mathrm{cm} ) from ( O . ) Draw
tangents to the circle from point ( P . ) Let
the tangents intersect the circle in points ( A ) and ( B . ) Find the approximate
value of ( angle O P B )
A ( .37^{circ} )
B. ( 53^{circ} )
( c cdot 45^{circ} )
D. None of these
10
109 Draw a line ( P Q=12.5 mathrm{cm} . ) Divide it 7
equal parts.
10
110 Draw a circle. Let AB be diameter. Let P
is point on circle. Construct angle bisector of ( angle P . ) The bisector
A. cuts diameter between B and centre
B. cuts diameter between A and centre
c. cuts diameter A and B at centre
D. none
9
111 Draw a circle with centre ( C ) and radius
( 3 mathrm{cm} . ) Take a point ( boldsymbol{P} ) outside the circle
such that ( C P=6 mathrm{cm} . ) Construct
tangents ( boldsymbol{P} boldsymbol{A} ) and ( boldsymbol{P} boldsymbol{B} ) from this point to
the circle, where ( A ) and ( B ) are the
intersection points of the tangents. Then ( boldsymbol{m} angle boldsymbol{A} boldsymbol{C B}=? )
( mathbf{A} cdot 60 )
B. ( 120^{circ} )
( c cdot 30^{circ} )
D. ( 90^{circ} )
10
112 To construct a triangle similar to a given ABC with its sides ( frac{3}{7} ) of the
corresponding sides of ( Delta A B C, ) first draw a ray BX such that ( angle C B X ) is an
acute angle and ( X ) lies on the opposite side of A with respect to BC. Then locate
points ( B_{1}, B_{2}, B_{3}, dots ) on BX at equal distances and next step is to join
A. ( B_{10} ) to ( c )
B. ( B_{3} ) to ( c )
( c cdot B_{7} operatorname{toc} )
D. ( B_{4} ) to ( c )
10
113 The co-ordinates of the vertices of
ロPQRS are
( P(-1,2), Q(-4,-2), R(-4,-3) ) and
( boldsymbol{S}(-1,-mathbf{5}) ) respectively. Draw ( square boldsymbol{P} Q boldsymbol{R} boldsymbol{S} )
and state it is which type of
10
114 To construct a triangle similar to a
( operatorname{given} A B C ) with its sides ( frac{7}{3} ) of the corresponding sides of ( Delta A B C, ) draw a
ray ( B X ) making acute angle with ( B C )
and ( X ) lies on the opposite side of ( A )
with respect to ( B C . ) The points
( B_{1}, B_{2}, dots, B_{7} ) are located at equal
distances on ( B X, B_{3} ) is joined to ( C )
A. True
B. False
10
115 Draw a circle with centre ( O ) and radius
( 6 mathrm{cm} . ) Take a point ( P ) outside the circle
at a distance of ( 10 mathrm{cm} ) from ( 0 . ) Draw
tangents to the circle from point ( P . ) Let
the tangents intersect the circle in points ( A ) and ( B . ) Find ( B P )
A ( .6 mathrm{cm} )
B. ( 8 mathrm{cm} )
c. ( 8.5 mathrm{cm} )
D. None of these
10
116 ( A(-a, 0) ; B(a, 0) ) are fixed points. ( C ) is a point which divides internally ( A B ) in a constantly ration ( tan alpha . ) If ( A C & C B )
subtend equal angles at ( P, ) that the
equation of the locus of ( boldsymbol{P} ) is ( boldsymbol{x}^{2}+boldsymbol{y}^{2}+ )
( 2 a x sec 2 alpha+a^{2}=0 )
10
117 Find the ratio in which the straight line segment joining (-2,-3) and (5,6) is divided by (i) x-axis (ii) y-axis. Also, find the coordinates of the point of division in each case. 10
118 Points ( (mathbf{6}, mathbf{8}),(mathbf{3}, mathbf{7}),(-mathbf{2},-mathbf{2}) ) and
(1,-1) are joined to form a quadrilateral. What will be the structure of the quadrilateral?
A. Rhombus
B. Parallelogram
c. square
D. Rectangle
10
119 To construct a triangle similar to given ( Delta A B C ) with its sides ( frac{3}{5} ) of that of ( Delta A B C, ) a ray ( B X ) is drawn at acute
angle with ( B C ). How many minimum no
of points should be marked on ( B X ? )
( A cdot 2 )
B. 3
( c cdot 4 )
D. 5
10
120 The area of ( square O A P B ) is:
A ( .24 mathrm{cm}^{2} )
B. ( 36 mathrm{cm}^{2} )
c. ( 48 mathrm{cm}^{2} )
D. ( 60 mathrm{cm}^{2} )
10
121 Draw an angle of measure ( 147^{circ} ) and
construct its bisector.
9
122 The length of ( D C= )
B
( c .30 )
D
10
123 The intercepts made by the line ( x+ )
( 5 y=3 ) on the ( X ) -axis is a.Find ( a )
10
124 Construct a ( triangle A B C, ) when ( A B= )
( mathbf{5} . mathbf{2} mathbf{c m}, angle mathbf{A}=mathbf{3 0}^{circ} ) and ( angle mathbf{B}=mathbf{7 5}^{circ} )
9
125 Construct a tangent to a circle of radius
( 4 mathrm{cm} ) from a point on the concentric
circle of radius ( 6 mathrm{cm} ) and measure its
length. Also verify the measurement by actual calculation.
10
126 In ( Delta A B C, A B=5, B C=6, A C=7 )
( Delta P Q R-Delta A B C . ) Perimeter of ( Delta P Q R )
is ( 360 . ) Find ( mathrm{PQ}, ) QR and PR.
10
127 The coordinates of a point whose abscissa is 5 and which lies on the ( x )
axis is
A . (5,0)
B. (0,5)
D. (5,5)
10
128 On the Cartesian plane, ( Q ) is the
midpoint of the straight line ( boldsymbol{P} boldsymbol{R} )
Find the values of ( x ) and ( y )
A ( . x=3, y=2 )
B. ( x=4, y=2 )
c. ( x=4, y=3 frac{1}{2} )
D. ( x=8, y=3 )
10
129 Construct a triangle of sides ( 4 mathrm{cm}, 5 mathrm{cm} )
and ( 6 mathrm{cm} ) and then a triangle similar to it whose sides are ( frac{2}{3} ) of the
corresponding sides of the first
triangle. The length of side ( A^{prime} C^{prime} ) (in ( c m )
is:
10
130 In the figure, show that perimeter of ( triangle A B C=2(A P+B Q+C R) ) 10
131 What are the coordinates of ( boldsymbol{S} ) ?
( A cdot(3,2) )
B. (3,-2)
( c cdot(-2,3) )
D. (-3,-2)
10
132 Draw a line segment of 6cm and divide it in the ratio 3: 2 10
133 Draw a circle with the help of a bangle.
Take a point ( boldsymbol{P} ) outside the circle.

Construct the pair of tangents from this point ( boldsymbol{P} ) to the circle.

10
134 Draw ( angle A B C ) of measure ( 120^{circ} ) and
bisect it.
9
135 Which equation represents the line that
passes through the point (-1,4) and is parallel to the ( y ) -axis?
A. ( y=-1 )
B . ( x=-1 )
c. ( x=4 )
D. ( y=4 )
10
136 Transform ( 2 x-3 y+5=0 ) to the
parallel axes through the point (2,-3)
10
137 In which quadrant or on which axis each of the following points lies. Write abscissa and ordinate each of the
following:
(i) (3,-4)
(ii) (-3,5)
(iii) (-10,0)
(iv) (-2,-7)
10
138 Construct a triangle of sides ( 4 mathrm{cm}, 5 mathrm{cm} )
and ( 6 mathrm{cm} ) and then a triangle similar to it whose sides are ( frac{2}{3} ) of the corresponding sides of the first triangle.
10
139 Which equation represents the line that
passes through the point (-5,-4) and is parallel to the ( y ) -axis?
A . ( x=-5 )
B . ( x=-4 )
c. ( y=-5 )
D. ( y=-4 )
10
140 Which equation represents the line that
passes through the point (2,3) and is parallel to the ( y ) -axis?
( mathbf{A} cdot x=2 )
B. ( y=3 )
c. ( x=3 )
D. ( y=2 )
10
141 See figure and complete the following
statements.

The ( x ) -coordinate and ( y ) -coordinate of the
point ( boldsymbol{L} ) are and
respectively. Hence the coordinate of ( L )
are
A ( .-5,-4,(-5,-4) )
B. -5,-3,(-5,-4)
c. -5,4,(-5,-4)
D. 5,-4,(-5,-4)

10
142 Construct a triangle ( A B C ) in which
( A B=5.8 c m, B C+C A=8.4 mathrm{cm} ) and
( angle B=60^{circ} )
9
143 Triangle ( A B C ) is inscribed in the
parabola described by the equation ( y^{2}-6 x-4 y+10=0 ) so that ( A ) is the
vertex of the parabola and ( B ) and ( C ) are
the end points of the latus rectum of the
parabola. The area of triangle ( A B C ) is
A . 18
B. 9
( c .4 .5 )
D. 2.25
10
144 Construct a triangle ( A B C ) whose
perimeter ( 12 mathrm{cm} ) and whose base angles
are ( 65^{circ} ) and ( 85^{circ} )
9
145 5.
e diameter PQ of a semicircle is 6 cm. Construct a square
BCD with points A, B on the circumference, and the side
on the diameter PQ. Describe briefly the method of
construction.
(1980)
side of a line L.
10
146 Construct an angle of ( 45^{circ} ) from a
horizontal line and justify the
construction.
9
147 Draw a circle with centre ( O ) and radius
( 4 mathrm{cm} . ) Take point ( boldsymbol{A} ) such that ( boldsymbol{d}(boldsymbol{O}, boldsymbol{A})= )
( 9 mathrm{cm} . ) Draw tangents from point ( boldsymbol{A} )
10
148 To construct a triangle similar to given ( Delta A B C ) with its sides ( frac{3}{5} ) of that of ( Delta A B C, ) a ray ( B X ) is drawn at acute
angle with ( B C . ) If we mark points
( B_{1}, B_{2}, B_{3}, dots . ) at equal distances from
( B ) along ( B X, ) then point to be joined in
next step is?
A. ( B_{3} )
в. ( B_{4} )
( c cdot B_{5} )
D. ( B_{6} )
10
149 A triangle ( A B C ) can be constructed in
which ( angle B=60^{circ}, angle C=45^{circ} ) and ( A B+B C )
( +A C=11 mathrm{cm} . ) Is this Statement true?
A . True
B. False
9
150 Find the area of the triangle formed by the line ( y=2 x+4 ) and coordinate
axes
10
151 Construct a triangle ( boldsymbol{X} boldsymbol{Y} boldsymbol{Z} ) whose
perimeter ( 15 mathrm{cm} ) and whose base angles
are ( 60^{circ} ) and ( 70^{circ} )
9
152 Construct a triangle ( A B C ) whose
perimeter ( 12 mathrm{cm} ) and whose base angles
are ( 50^{circ} ) and ( 80^{circ} )
9
153 Find the sum of ‘x’ co-ordinates of the
vertices of a triangle if the mid-points of
its sides be the points (6,-1),(-1,-2) and (1,-4)
10
154 Rearrange the following steps of constructing a triangle when the base angle say ( angle B ) and ( angle C ) and its
perimeter ( boldsymbol{B C}+boldsymbol{C A}+boldsymbol{A B} ) is given:
1. Draw perpendicular bisectors ( boldsymbol{P Q} ) of
( A X ) and ( R S ) of ( A Y )
2. Draw a line segment, say ( X Y ) equal to ( B C+C A+A B )
3. Let ( P Q ) intersect ( X Y ) at ( B ) and ( R S )
intersect ( X Y ) at ( C . ) Join ( A-B ) and
( A-C )
4. Make ( angle L X Y ) equal to ( angle B ) and
( angle M Y X ) equal to ( angle C )
5. Bisect ( angle L X Y ) and ( angle M Y X ). Let these
bisectors intersect at a point ( boldsymbol{A} )
( mathbf{A} cdot 1 rightarrow 3 rightarrow 5 rightarrow 4 rightarrow 2 )
В. ( 2 rightarrow 4 rightarrow 5 rightarrow 1 rightarrow 3 )
c. ( 5 rightarrow 4 rightarrow 3 rightarrow 2 rightarrow 1 )
D. ( 2 rightarrow 3 rightarrow 5 rightarrow 4 rightarrow 1 )
9
155 Construct a bisector of an angle. 9
156 Construct ( triangle L M N ) in which base
( M N=7 mathrm{cm}, angle L M N=75^{circ} ) and
( boldsymbol{L} boldsymbol{M}+boldsymbol{L} boldsymbol{N}=mathbf{9} boldsymbol{c m} )
9
157 If two tangents are drawn at the end points of two radii that are inclined at
an angle of ( 110^{circ} . ) Find the angle between
the tangents.
( mathbf{A} cdot 110^{circ} )
B. 55
( c cdot 70^{circ} )
D. ( 20^{circ} )
10
158 In a triangle ( E D C ), what is the angle ( C ) ?
3.19
( c cdot 7 )
D
10
159 ( triangle A B C sim triangle D E F . triangle A B C ) is such that
( A B=5.2 mathrm{cm}, B C=4.6 mathrm{cm}, angle B=45^{circ} ) and
( frac{B C}{E F}=frac{2}{3} ; ) Construct ( triangle D E F )
10
160 Which equation represents the line that
passes through the point (5,-3) and is parallel to the ( y ) -axis?
A. ( x=-3 )
В. ( y=-3 )
c. ( x=5 )
D. ( y=5 )
10
161 Draw the following angles using ruler and compasses. Also label them.
( mathbf{1 8 0}^{circ} )
9
162 Construct a ( triangle A B C ) in which ( A C= )
( mathbf{5} c m, ) and ( angle B A C=60^{circ} ) and ( A B- )
( B C=1.2 mathrm{cm} )
9
163 If the axes are transformed from origin to the point ( (-2,1), ) then new coordinates of (4,-5) are
A. (2,6)
(年) (2,6)
в. (6,4)
c. (6,-6)
D. (2,-4)
10
164 Construct a ( triangle A B C ) in which ( B C= )
( mathbf{5 . 6} c boldsymbol{m}, angle boldsymbol{B}=mathbf{3 0}^{circ} ) and the difference
between the other sides is ( 3 mathrm{cm} ).
9
165 Construct the bisector of an angle ( 75^{circ} ) 9
166 ( 4 x-3=0 ) is a line parallel to
A . ( y ) axis
B. ( x ) axis
( mathbf{c} cdot y=x )
D. ( y=2 x )
10
167 A pair of perpendicular tangents are
drawn to a circle from an external point. Prove that length of each tangent is equal to the radius of the circle.
10
168 Quadrilaterals ABCD and PQRS are
similar.What is the length of PQ?
A . 2.67
B. 3.75
( c )
( D .5 )
10
169 To construct a triangle similar to given ( Delta A B C ) with sides equal to ( frac{7}{5} ) of the
sides of ( Delta A B C, ) a ray ( B X ) is drawn
such that ( angle C B X ) is acute angle and
( B_{1}, B_{2}, B_{3}, dots ) are marked at equal
distances on ( B X ). The points to be
joined in the next step are:
в. ( B_{5}, C )
( mathbf{c} cdot B_{7}, C )
D. ( B_{2}, C )
10
170 Draw the graph for the linear equation ( 3 y+5=0 ) and select the correct
option:
A. The line is parallel to the ( x ) -axis and passes through ( left(0,-frac{5}{3}right) )
B. The line is parallel to the ( y ) -axis and passes through ( left(0,-frac{5}{3}right) )
c. The line is parallel to the ( x ) -axis and passes through ( left(0, frac{5}{3}right) )
D. The line is parallel to the ( y ) -axis and passes through ( left(0, frac{5}{3}right) )
10
171 Construct ( triangle M N O ) where base ( N O= )
( 6.7 mathrm{cm}, angle M N O=45^{circ} ) and ( M O )
( M N=2.8 mathrm{cm} )
9
172 The angles is to be bisected to obtain an
angle of ( 90^{0} ) is
A ( cdot 60^{0} ) and ( 45^{0} )
B. ( 60^{0} ) and ( 120^{circ} )
( mathrm{c} cdot 120^{0} ) and ( 180^{circ} )
D. ( 30^{circ} ) and ( 60^{circ} )
9
173 What will be the absolute value of ( a ), for which point ( Pleft(frac{a}{2}, 2right) ) is the mid-point of the line segment joining the point
( Q(-5,4) ) and ( R(-1,0) )
10
174 topp
which of the following construction
is/are possible?
4
10
175 The distance between ( Pleft(x_{1}, y_{1}right) ) and
( Qleft(x_{2}, y_{2}right) ) is ( P Q=left|x_{2}-x_{1}right|, ) when PQ is
parallel to the ( x ) -axis. If True enter 1 else 0
10
176 If tangents are drawn from the endpoints of two radii that are inclined
at an angle ( 105^{circ}, ) what is the angle
between the tangents?
A ( cdot 5^{circ} )
B. 35
( c cdot 75 )
D. None of these
10
177 Construct ( Delta A B C, ) such that ( B C= )
( 6 c m, angle A B C=100^{0} ) and ( A C-A B= )
( 2.5 c m )
9
178 ( Delta mathrm{ABC} sim Delta mathrm{LBN}, ln Delta mathrm{ABC}, mathrm{AB}=6.1 mathrm{cm} angle mathrm{B} )
( =45^{circ}, mathrm{BC}=5.4 mathrm{cm} ; frac{A C}{L N}=frac{4}{7} . ) Construct
( Delta A B C ) and ( Delta L B N )
10
179 Draw the tangents to the circle from the
point ( L ) with radius 3 cm. Point ( L ) is at a
distance of ( 8 mathrm{cm} ) from the centre ( M )
10
180 In the diagram
Write the sum of coordinates of ( boldsymbol{U} )
10
181 Coordinates of point ( boldsymbol{R} ) are
( mathbf{A} cdot(1,1) )
B. (-1,-1)
( mathbf{C} cdot(-1,1) )
D. (1,-1)
10
182 Construct a triangle ( A B C ) in which
( A B=5.6 c m, B C=5.4 c m ) and ( angle B= )
( 40^{circ} )
9
183 A straight line parallel to the ( x ) -axis has equation
A. ( x=a )
B . ( y=a )
( mathbf{c} cdot y=x )
D. ( y=-x )
10
184 Draw a right triangle ( A B C ) in which ( B C=12 mathrm{cm}, A B=5 mathrm{cm} ) and ( angle B= )
( 90^{0} . ) Construct a triangle similar to it and of scale factor ( frac{2}{3} . ) Is the new triangle also a right triangle?
A. Yes
B. No
c. can’t say
D. Data insufficient
10
185 Construct a triangle ( A B C, ) given: ( B C=7 )
( mathrm{cm}, mathrm{AB}-mathrm{AC}=1 mathrm{cm} ) and ( angle A B C=45^{circ} )
Measure the lengths of ( A B ) and ( A C ).
( A cdot A B=8.6 mathrm{cm}: A C=7.6 mathrm{cm} )
B. AB = 2.7 cm: AC = 1.7 cm
( mathrm{C} cdot mathrm{AB}=6.1 mathrm{cm}: mathrm{AC}=5.1 mathrm{cm} )
D. Data insufficient
9
186 ( Delta S H R sim Delta S V U . ln Delta S H R, S H= )
( 4.5 mathrm{cm}, H R=5.2 mathrm{cm}, S R=5.8 mathrm{cm} )
and ( frac{S H}{S V}=frac{3}{5} ) Construct ( Delta S V U )
10
187 Which of the following points lie above X-axis
( boldsymbol{a}) boldsymbol{A}(-boldsymbol{3}, boldsymbol{5}) )
( boldsymbol{b}) boldsymbol{B}(boldsymbol{5},-1) )
( c) C(0,2) )
( boldsymbol{d}) boldsymbol{D}(boldsymbol{0}, boldsymbol{2}) )
( e) E(5,1) )
( boldsymbol{f}) boldsymbol{F}(boldsymbol{3}, mathbf{1}) )
10
188 Construct a triangle ( A B C ) in which
( B C=8 c m, angle B=45^{circ} ) and ( A B- )
( A D=3.5 mathrm{cm} )
9
189 To divide a line segment in the ratio ( p ) ( boldsymbol{q}(boldsymbol{p}, boldsymbol{q} text { are integers }) ) a ray ( boldsymbol{A} boldsymbol{X} ) is drawn
so that ( angle B A X ) is an acute angle and
then mark points on ray ( A X ) at equal distances such that the minimum
number of points is:
( mathbf{A} cdot p q )
В. ( p+q-1 )
c. ( p+q )
D. Greater of ( p ) and ( q )
10
190 (5,0) is a point that lies on
A. ( y ) -axis
B. ( x ) -axis
( mathbf{c} cdot y=x )
D. ( y=5 x )
10
191 These two quadrilaterals are similar
What is the value of ( x ) (the length of B’C’)
A ( cdot 2 frac{2}{3} )
B. 5
( c cdot 6 )
D. ( 6 frac{2}{3} )
10
192 In the given quadrilateral ( A B C D, B C=38 ) ( mathrm{cm}, mathrm{QB}=27 mathrm{cm}, mathrm{DC}=25 mathrm{cm} ) and ( mathrm{AD} perp )
DC find the radius of the circle.
10
193 In abscissa of a point ( P ) is negative and ordiante of ( P ) is positive, then ( P ) lies in :
10
194 Draw a triangle ( P Q R ), right angled at ( Q )
such that ( P Q=3 mathrm{cm}, Q R=4 mathrm{cm} . ) Now
construct ( triangle A Q B ) similar to ( triangle P Q R ) each of whose sides is ( frac{7}{5} ) times the
corresponding side of ( triangle boldsymbol{P} Q boldsymbol{R} )
10
195 Construct the triangle with the following measurements and locate the
centroid:
( triangle boldsymbol{X} boldsymbol{Y} boldsymbol{Z} ) with ( boldsymbol{X} boldsymbol{Y}=mathbf{6 . 5 c m}, boldsymbol{Y} boldsymbol{Z}= )
( 5.6 c m ) and ( X Z=7.2 c m )
10
196 In a class test (+3) marks are given for
every correct answer and (-2) marks are given for every incorrect answer and
no marks for not attempting any
question.
If she has got 12 correct answers, how
many questions has she attempted incorrectly?
(ii) Mohini scores (-5) marks in this test, though she has got 7
correct answers How many questions has she attempted incorrectly.
10
197 ( A B ) is divided into maximum
equal parts
4
3
( c )
D. 10
10
198 To construct a triangle similar to given ( Delta A B C ) with its sides ( frac{4}{5} ) of that of
( Delta A B C, ) locate points ( X_{1}, X_{2}, X_{3}, dots . . )
on ray ( B X ) at equal distances such that
( angle A B X ) is acute. The points to be joined
in the next step are:
A. ( X_{4}, C )
в. ( X_{5}, C )
c. ( x_{4}, A )
D. ( X_{5}, A )
10
199 Draw a circle with center ( boldsymbol{O} ) and radius
6cm. Take a point ( boldsymbol{P} ) outside the circle
at a distance of ( 10 mathrm{cm} ) from ( O . ) Draw
tangents to the circle from point ( P . ) Let
the tangents intersect the circle in points ( A ) and ( B . ) Find the approximate
value of ( angle B O P ) in degrees.
A ( .37^{circ} )
B. ( 53^{circ} )
( c cdot 45^{circ} )
D. None of these
10
200 ( odot(P, 4 c m) ) is given. Draw a pair of
tangents through ( A ), which is in the
exterior is ( 60^{circ} . ) Write the construction
steps.
10
201 Construct ( triangle boldsymbol{X} boldsymbol{Y} boldsymbol{Z} ) in which ( angle boldsymbol{Y}= )
( mathbf{3 0}^{o}, angle Z=mathbf{6 0}^{circ} ) and ( boldsymbol{X} boldsymbol{Y}+boldsymbol{Y} boldsymbol{Z}+boldsymbol{Z} boldsymbol{X}= )
( mathbf{1 0} c boldsymbol{m} )
9
202 Construct an equilateral triangle. ( Delta A B C . ) Construct an angle bisector of
( angle A )
Let it meet side ( B C ) at ( D ). Find measures
of ( A B, A C, B D, D C )
Find the relation between ( frac{A B}{A C} ) and ( frac{B D}{D C} )
( mathbf{A} cdot frac{A B}{A C}frac{B D}{D C} )
C ( cdot frac{A B}{A C}=frac{B D}{D C} )
D. None
9
203 Construct ( Delta P Q R, ) such that ( Q R= )
( 6.5 c m, angle P Q R=60^{0} ) and ( P Q-P R= )
( 2.5 c m )
9
204 To construct a triangle similar to given ( triangle A B C ) with its sides ( frac{2}{3} ) of that of
( Delta A B C, ) locate points on ray ( B X ) at
equal distances as ( B_{1}, B_{2}, B_{3}, ldots ) such
that ( angle C B X ) is acute. The points to be
joined in the next step are:
A. ( B_{4}, C )
в. ( B_{3}, C )
c. ( B_{1}, C )
D. ( B_{2}, C )
10
205 Construct an equilateral triangle of side
( mathbf{5 . 5} mathrm{cm} )
10
206 The construction of ( Delta E F G ) when
( F G=3 c m ) and ( m angle G=60^{circ} ) is possible
when difference of ( E F ) and ( E G ) is equal
to:
A . ( 3.2 mathrm{cm} )
B. ( 3.1 mathrm{cm} )
( mathrm{c} .3 mathrm{cm} )
D. 2.8 ( c m )
9
207 Solve: ( frac{2}{x}+frac{3}{y}=13, frac{5}{x}+frac{7}{y}=31 ) 10
208 Find the coordinates of the point of trisection of the line segment joining (1,-2) and (-3,4) 10
209 Construct ( triangle boldsymbol{A B C} ) with ( boldsymbol{B C}=mathbf{6 . 5} mathrm{cm} )
( boldsymbol{A C}=mathbf{5} mathrm{cm} ) and ( angle boldsymbol{C}=mathbf{6 0}^{circ} . )
10
210 If the perpendicular distance of a point
( P ) from the ( X ) -axis is 5 units and the
foot of the perpendicular lies on the
negative direction of ( X ) -axis, then the
point ( boldsymbol{P} ) has
A. ( X ) -coordinate ( =-5 )
B. Y-coordinate = – 5
c. ( Y ) -coordinate ( =-5 ) only
D. ( Y ) -coordinate ( =5 ) or -5
10
211 ( ln ) a ( triangle A B C ) in which ( A C=5 mathrm{cm} ) and
( angle B A C=60^{circ} ) and ( B C-A B=1.2 mathrm{cm} )
The, ( A B ) is
A . 3.18
в. 4.32
( c .5 .12 )
D. None of these
9
212 State which quadrants or on which axis do the following points line?
1. ( boldsymbol{A}(-mathbf{3}, mathbf{2}) )
2. ( B(5,3) )
3. ( C(0,4) )
4. ( boldsymbol{D}(-mathbf{3}, mathbf{0}) )
10
213 In the figure, a circle is inscribed in a
quadrilateral ABCD in which ( angle B=90^{circ} )
If ( A D=23 c m, A B=29 c m ) and ( D S= )
( 5 c m ) find the radius of the circle
10
214 Which is ( 2^{n d} ) step?
( a )
( (b) )
( e cdot(c) )
).
10
215 ( A(-3,2) ) and ( B(5,4) ) are the end points of a line segment, find the sum of coordinates of the mid points of the
line segment.
10
216 The construction of ( Delta L M N ) when
( M N=6 mathrm{cm} ) and ( m angle M=45^{circ} ) is not
possible when difference between ( L M )
and ( L N ) is equal to:
( mathbf{A} cdot 6.9 mathrm{cm} )
B. ( 5.2 mathrm{cm} )
( c .5 mathrm{cm} )
D. 4 ст
9
217 The coordinates of ( B ) is ( (3,-2) . ) If true
enter 1 or else.
10
218 Draw a circle with centre 0 and radius
( 3.5 mathrm{cm} . ) Draw two tangents PA and PB from an external point ( P ) such that ( < )
( A P B=45^{0} . ) What is the value of ( < )
( boldsymbol{A O B}+<boldsymbol{A P B} )
10
219 Which of the following points lie on the negative side of ( x- ) axis ? This question has multiple correct options
A. (-4,0)
в. (-3,2)
c. (0,-4)
D. (5,-7)
10
220 The construction of ( Delta P Q R ) given that
( Q R=5.2 mathrm{cm} ) angle ( Q=50 . ) Is it
possible when the difference of ( P Q ) and
PR is ( 3.5 mathrm{cm} ) ? justify.
9
221 Construct a triangle similar to a given ( triangle A B C ) such that each of its sides is
( (3 / 4)^{t h} ) of the corresponding sides of ( triangle A B C . ) It is given that ( B C= )
( 6 c m, angle B=50^{circ} ) and ( angle C=60^{circ} )
10
222 Which equation represents the line that
passes through the point (1,3) and is parallel to the ( x ) -axis?
( mathbf{A} cdot y=3 )
B. ( y=1 )
( mathbf{c} cdot x=1 )
D. ( x=3 )
10
223 In the figure ( P Q, P R ) and ( B C ) are the
tangents to the circle. BC touches the
circle at ( X . ) If ( P Q=7 mathrm{cm}, ) find the
perimeter of ( triangle boldsymbol{P B C} )
10
224 The graph of ( x=8 ) represents:
A. line parallel to ( y ) -axis and at a distance of 8 units
B. line parallel to ( x ) -axis and at a distance of 8 units
c. line parallel to ( y ) -axis and at a distance of 0 units
D. None of these
10
225 Construct two tangent to a circle of
radius ( 3.5 mathrm{cm} ) from a point ( 4.5 mathrm{cm} ) away from the circle.
10
226 Which of the following could be the value of ( A C-B C ) in the construction
of a triangle ( A B C ) in which base ( A B= )
( mathbf{5} c m, angle A=30^{circ} ? )
A . 5.5
B. 5
c. 2.5
D. None of these
9
227 Draw a right angle and construct its bisector. 9
228 Plot the following points on a graph paper and find out in which quadrant do
they lie?
(i) ( A(3,5) )
(ii) B (-2, 7)
(iii) ( C(-3,-5) ) ( D(2,-7)(v) 0(0,0) )
10
229 Construct a triangle of sides
( 4.2 c m, 5.1 c m ) and ( 6 c m . ) Then construct
a triangle similar to it, whose sides are
( frac{2}{3} ) of corresponding sides of the first triangle.
10
230 Triangles ( A B C ) and ( P Q R ) are similar
What is the length of PQ?
( A )
B. 10.5
( c cdot 13 )
D. 15
10
231 Find the ratio in which (2,1) divides the
line segment joining ( (mathbf{1}, mathbf{4}),(mathbf{4},-mathbf{5}) )
10
232 Every point is located in one of the four quadrants. 10
233 Draw a circle with centre ( O ) and radius
( 6 mathrm{cm} . ) Take a point ( P ) outside the circle
at a distance of ( 10 mathrm{cm} ) from ( 0 . ) Draw
tangents to the circle from point ( P . ) Let the tangents intersect the circle in
points ( A ) and ( B ). Find the area of triangle
OBPin sq.cm.
A .24
B . 26
c. 25
D. None of these
10
234 Construct a perpendicular line from
point ( p ) to any line ( A B )
9
235 Draw a parallelogram ( A B C D ) in which ( B C=5 mathrm{cm}, A B=3 mathrm{cm} ) and ( angle A B C= )
( 60^{0} . ) divide it into triangles ( B C D ) and
( A B D ) by the diagonal ( B D . ) Construct
the triangle ( B D^{prime} C^{prime} ) similar to ( B D C ) with scale factor ( frac{4}{3} . ) Draw the line
( operatorname{segment} D^{prime} A^{prime} ) parallel to ( D A, ) where ( A^{prime} )
lies on extended side ( B A ). Is ( A^{prime} B C^{prime} D^{prime} ) a
parallelogram?
A. Yes
B. No
c. Data insufficient
D. Ambiguous
10
236 Construct a bisector of an angle of ( 60^{circ} ) 9
237 The point (0,3) lies on
A. ( + ) ve ( x ) -axis
B. + -ve y-axis
c. – ve ( x ) -axis
D. – ve y-axis
10
238 Construct ( triangle M N O ) such that ( N O= )
( mathbf{6 . 2} mathrm{cm}, angle boldsymbol{N}=mathbf{5 0}^{circ} ) and ( boldsymbol{M} boldsymbol{O}-boldsymbol{M} boldsymbol{N}= )
( 2.4 mathrm{cm} )
9
239 Determine a point which divides a line
segment of length ( 12 mathrm{cm} ) internally in
the ratio ( 2: 3 . ) Also, justify you
construction.
10
240 Construct a triangle ( A B C, ) whose
perimeter is ( 12 mathrm{cm} ) and whose sides are
in the ratio 2: 3: 4
9
241 The angle subtended at the point (1,2,3) by the points ( P(2,4,5) ) and ( Q(3,3,1) ) is
A ( cdot 90^{circ} )
B. ( 60^{circ} )
( c cdot 30^{circ} )
D. ( 0^{circ} )
( E cdot 45^{circ} )
10
242 Which is last step?
4. ( (a) )
3. ( (b) )
( (c) )
2
10
243 Draw a ( triangle A B C, ) right – angled at ( B ) such that ( A B=3 c m, B C=4 ) cm. Now
construct a ( triangle P B Q ) similar to ( Delta A B C ) each of whose side is ( frac{7}{5} ) times the
corresponding side of ( Delta A B C )
10
244 Draw the graph of the equation ( 2 x+ )
( mathbf{3} boldsymbol{y}+boldsymbol{6}=mathbf{0} )
10
245 Bisecting means dividing into two
parts.
A. Unequal
B. Equal
c. Triangular
D. None of these
9
246 If ( 3 cos theta=1, ) find the value of
( frac{6 sin ^{2} theta+tan ^{2} theta}{4 cos theta} )
10
247 Find the midpoint between the coordinates ( (mathbf{9}, mathbf{3}) ) and ( (mathbf{1}, mathbf{1}) )
( mathbf{A} cdot(5,2) )
B ( cdot(3,2) )
( mathbf{c} cdot(5,1) )
D ( cdot(3,1) )
10
248 Take a circle with centre ( C ) and
construct a tangent to a circle from an
external point ( boldsymbol{P} )
10
249 Identify the true statement.
A. The ( X ) -axis is a vertical line
B. The ( Y ) -axis is a horizontal line
C. The scale on both the axes must be the same in a
Cartesian plane
D. The point of intersection between the ( X ) -axis and ( Y ) axis is called the origin
10
250 ( Delta A M T sim Delta A H E . ln Delta A M T, A M= )
( 6.3 mathrm{cm}, angle M A T=120^{circ}, A T=4.9 mathrm{cm} )
and ( frac{M A}{H A}=frac{7}{5} . ) Construct both the
triangles.
10
251 Construct a triangle ( M N P, ) whose
perimeter is ( 15 mathrm{cm} ) and whose sides are
in the ratio 2: 3: 4
9
252 If ( boldsymbol{A}left(boldsymbol{a}^{2}, boldsymbol{2} boldsymbol{a}right) boldsymbol{B}=left(frac{mathbf{1}}{boldsymbol{a}^{2}}, frac{boldsymbol{-} boldsymbol{2}}{boldsymbol{a}}right), boldsymbol{P}=(boldsymbol{1}, boldsymbol{0}) )
then ( frac{boldsymbol{1}}{boldsymbol{P} boldsymbol{A}}+frac{boldsymbol{1}}{boldsymbol{P} boldsymbol{B}}= )
10
253 Construct a triangle with sides ( 4 mathrm{cm}, 5 ) ( mathrm{cm} ) and ( 7 mathrm{cm} ) and then another triangle whose sides are ( frac{3}{4} ) of the corresponding sides of the first triangle. 10
254 The graph of the equation ( y=a ) is a
straight line parallel to
A . ( x ) -axis
B. ( y ) -axis
c. cannot be determined
D. Not Paralle
10
255 For constructing a triangle whose perimeter and both base angles are given, the first step is to:
A. Draw a base of any length
B. Draw the base of length = perimeter
c. Draw the base angles from a random line.
D. Draw a base of length ( =frac{1}{3} times ) perimeter.
9
256 The graph of ( y=6 ) is a line:
A. parallel to ( x ) -axis & at a distance of 6 units from the
( x- ) axis
B. parallel to ( y ) -axis at a distance of 6 units from the origin
c. making an intercept 6 on the ( x ) -axis
D. making an intercept 6 on both the axes.
10
257 If the midpoints of the line segment joining the points ( P(6, b-2) ) and (-2,4) is ( (2,-3), ) find the value of ( b ) 10
258 If the mid point of the line joining the points ( P(6, b-2) ) and ( Q(-2,4) ) is (2,-3) Find the value of ‘b’ 10
259 Construct a ( Delta A B C ) in which ( A B=5 c m . )
( mathrm{B}=60^{circ} ) altitude ( mathrm{CD}=3 mathrm{cm} . ) Construct
( Delta mathrm{AQR} ) similar to ( Delta mathrm{ABC} ) such that side
of ( Delta A Q R ) is 1.5 times that of the corresponding sides of ( Delta A C B )
10
260 Draw ( overline{P Q}, ) where ( P Q=10 c m . ) Draw
( operatorname{circle} odot(P, 4) ) and ( odot(Q, 3) . ) Draw
tangents to each circle from the centre
of the other circle. Write points of construction.
10
261 State to which quadrant does the following points belong:
( U(-6.2,4.3) )
10
262 n the figure, if ( A B=A C ) prove that ( B Q= )
( mathrm{QC} )
10
263 Find the ratio in which the point
( P(5,4,-6) ) divides the line segment
joining the points ( A(3,2,-4) ) and ( B(9,8,-10) . ) Also, find the harmonic conjugate of ( boldsymbol{P} )
10
264 Construct a triangle with sides ( 5 mathrm{cm}, 6 mathrm{cm} ) and ( 7 mathrm{cm} ) and then another
triangle whose sides are ( frac{7}{5} ) of the
corresponding sides of the first triangle.
10
265 Draw a circle of radius ( 6 mathrm{cm} ) and
construct tangents to it from an external point ( 10 mathrm{cm} ) away from the
centre. Measure and verify the length of
the tangents.
10
266 Construct a triangle ( A B C ) in which
base ( A B=5 c m, angle A=30^{circ} ) and ( A C- )
( B C=2.5 mathrm{cm} )
9
267 Construct a triangle ( P Q R ), whose
perimeter is ( 14 mathrm{cm} ) and whose sides are
in the ratio 2: 4: 5
9
268 Construct a triangle of sides ( 4 mathrm{cm}, 5 mathrm{cm} ) and ( 6 mathrm{cm} ) and then a triangle similar to it whose sides are ( frac{3}{5} ) time of the
corresponding sides of the given triangle.
10
269 Draw the graph of the equation ( y=3 x ) 10
270 The intercepts made by the line ( x- ) ( 2 y=6 ) on the ( Y ) -axis is b.Find ( b ) 10
271 Draw a circle of radius ( 3.2 mathrm{cm} . ) At a point on it, draw a tangent to the circle using the tangent-chord theorem. 10
272 The construction of ( Delta L M N ) when
( M N=7 mathrm{cm} ) and ( m angle M=45^{circ} ) is not
possible when difference of ( L M ) and
( boldsymbol{L} boldsymbol{N} ) is equal to:
A . 4.5
B. 5.5
( c .6 .5 )
D. 7.5
9
273 Draw a triangle ( A B C ) with side ( B C= )
( mathbf{6} c boldsymbol{m}, boldsymbol{A} boldsymbol{B}=mathbf{5} boldsymbol{c m} ) and ( angle boldsymbol{A} boldsymbol{B} boldsymbol{C}=mathbf{6 0}^{boldsymbol{o}} )
Then construct a triangle whose sides
( operatorname{are} frac{3}{4} ) of the corresponding sides of the triangle ( boldsymbol{A B C} )
10
274 If ( y ) -coordinate of a point is zero then
the point will always lie
A . in ( I ) quadrant
B. in ( I I ) quadrant
c. on ( X ) -axis
D. on ( Y ) -axis
10
275 Let ( A B C ) be a right triangle in which
( A B=3 c m, B C=4 c m ) and ( angle B= )
( 90^{circ} . B D ) is the perpendicular from ( B ) on
( A C . ) The circle through ( B, C, D ) is drawn. Construct the tangents from ( boldsymbol{A} ) to this circle.
10
276 Construct a triangle ( A B C ) in which
( A B+A C=5.6 c m, B C=4.5 c m ) and
( angle B=45^{circ} )
9
277 Which shape has the verties (3,2),(0,5),(-3,2) and (0,-1)( ? )
A. Rectangle
B. Square
c. Trapezium
D. Rhombus
10
278 Construct triangle ( boldsymbol{A B C} ) in which
( B C=6 c m, A B-A C=3.1 c m ) and
( angle B=30^{circ} )
9
279 Divide a line segment of length ( 9 mathrm{cm} )
internally in the ratio 4: 3
10
280 Construct three tangents ( from a point outside to the circle ( ) ) to the circle of
10
281 The point which lies in the perpendicular bisector of the line segment joining the points ( A(-2,-5) ) and ( B(2,5) ) is
( A cdot(0,0) )
B. (0, 2)
c. (2, 0)
( D cdot(-2,0) )
10
282 Construct an isosceles triangle whose
base is ( 8 mathrm{cm} ) and altitude ( 4 mathrm{cm} ) and then
another triangle whose sides are ( 1 frac{1}{2} ) times the corresponding sides of the isosceles triangle.
10
283 Lay down the positions of the points whose polar coordinates are
( left(-1,-180^{circ}right) )
10

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