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.

Constructions Questions

List of constructions Questions

Question NoQuestionsClass
1Choose 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
2In 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
3Draw 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
4Construct 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
5Construct 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
6Draw 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
7In 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
8In 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
9Construct a pair of tangents to a circle
of radius ( 4 mathrm{cm} ) such that the acute
angle between the tangents is ( 45^{circ} )
10
10In 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
11Construct 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
12The point (4,0) lie on the line
A. ( y-x=0 )
В. ( y=0 )
c. ( x=0 )
D. ( y+x=0 )
10
13Construct 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
14Write down the co-ordinates of the points
( A ) to ( J ) marked in the following diagram:
10
15In what ratio does (-4,6) divides the line segment joining the point ( boldsymbol{A}(-mathbf{6}, mathbf{4}) )
and ( B(3,-8) )
10
16nd 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
17If 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
19The lengths of the tangents (in ( c m ) ) measured by a ruler are:
( mathbf{A} cdot mathbf{6} )
B. 7
c. 8
D. 9
10
20n 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
22Point (0,-9) lies
A. on the ( X ) -axis
B. In the II quadrant
c. on the Y-axis
D. In the ( I V ) quadrant
10
23Find the equation for the graph above.
( mathbf{A} cdot x=3 )
( mathbf{B} cdot y=3 )
C. ( y=-5 )
D. ( x=-5 )
10
24Construct 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
25Draw ( angle A B C ) of measure ( 110^{circ} ) and
bisect it.
9
26Using 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
27If 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
28The 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
29Construct 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
30Construct a triangle ( A B C ) whose
perimeter is ( 12.5 mathrm{cm} ) and whose base
angles are ( 60^{circ} ) and ( 75^{circ} )
9
31If ( 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
32The 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
33Find the co-ordinate of a points on ( x )
axis which is equidistant from the
points (-2,5) and (2,-3)
10
34If ( 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
35To 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
36The 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
38Construct 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
39Construct a triangle XYZ in which ( angle Y= )
( 30^{0}, angle Z=90^{0} ) and ( X Y+Y Z+Z X=11 mathrm{cm} )
9
40If 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
41If 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
42Find 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
43From (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
45Construct 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
46Draw 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
47Construct 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
48Draw 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
49In 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
50Construct 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
51Draw ( angle P O Q ) of measure ( 75^{circ} ) and find
its line of symmetry.
9
52Construct 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
53Draw 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
55Measure 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
56Show 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
57What is an angle bisector?9
58In 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
59Construct a triangle ( A B C ) whose perimeter ( 12 mathrm{cm} ) and who base angles
( operatorname{are} 50^{circ} ) and ( 80^{circ} )
9
60Construct 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
61Find 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
62Construct 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
63Any point on the ( x ) -axis is of the form
( mathbf{A} cdot(x, y) )
в. ( (0, y) )
c. ( (x, 0) )
D. ( (x, x) )
10
64Find the length ( E C )
( s )
D
10
65The 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
67Draw a line segment of length ( 6.3 mathrm{cm} ) &
divide it in the ratio ( 3: 4 . ) Measure the
two parts.
10
68Perimeter 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
69The line joining the points (1,-2) and
(-3,4) is trisected; find the
coordinates of the points of trisection.
10
70Write 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
71In 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
72Construct 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
73If ( 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
74What is the equation for the graph
shown above?
( mathbf{A} cdot y=2 )
B. ( y=-4 )
c. ( x=2 )
D. ( x=-4 )
10
75Draw the line joining the following
points. ( P(-4,5) ) and ( Q(3,-4) )
10
76Write the following based on the graph. The ordinate of Lis
( 4 .-7 )
B
( c_{1}-5 )
None of these
10
77What 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
78Construct 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
79Draw ( angle A B C ) of measure ( 115^{circ} ) and
bisect it.
9
80Plot the point (5,0) on a graph paper.10
81If 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
82Divide the line segment ( A B=12 mathrm{cm} ) in
6 equal parts.
10
83Construct 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
84Construct 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
85Construct 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
87To 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
89The 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
90Draw ( 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
91Construct 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
92Draw ( angle L M N=165^{circ} ) and divide in into
four equal parts.
9
93The point (0,6) lies on:
A. X-axis
B. Y-axis
c. origin
D. None
10
94The 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
95Draw 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
96Find 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
97Construct 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
99Plot 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
100The 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
101To 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
102Draw 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
103PQ 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
104Draw 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
105f the sides of a parallelogram touch a
circle. Prove that the parallelogram is a rhombus.
10
106The length of ( D E= )
1
B
( c cdot 13 )
D
10
107Draw 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
108Draw 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
109Draw a line ( P Q=12.5 mathrm{cm} . ) Divide it 7
equal parts.
10
110Draw 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
111Draw 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
112To 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
113The 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
quadrilateral.
10
114To 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
115Draw 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
117Find 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
118Points ( (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
119To 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
120The 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
121Draw an angle of measure ( 147^{circ} ) and
construct its bisector.
9
122The length of ( D C= )
B
( c .30 )
D
10
123The intercepts made by the line ( x+ )
( 5 y=3 ) on the ( X ) -axis is a.Find ( a )
10
124Construct 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
125Construct 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
126In ( 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
127The 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
128On 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
129Construct 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
130In the figure, show that perimeter of ( triangle A B C=2(A P+B Q+C R) )10
131What are the coordinates of ( boldsymbol{S} ) ?
( A cdot(3,2) )
B. (3,-2)
( c cdot(-2,3) )
D. (-3,-2)
10
132Draw a line segment of 6cm and divide it in the ratio 3: 210
133Draw 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
134Draw ( angle A B C ) of measure ( 120^{circ} ) and
bisect it.
9
135Which 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
136Transform ( 2 x-3 y+5=0 ) to the
parallel axes through the point (2,-3)
10
137In 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
138Construct 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
139Which 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
140Which 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
141See 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
142Construct 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
143Triangle ( 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
144Construct a triangle ( A B C ) whose
perimeter ( 12 mathrm{cm} ) and whose base angles
are ( 65^{circ} ) and ( 85^{circ} )
9
1455.
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
146Construct an angle of ( 45^{circ} ) from a
horizontal line and justify the
construction.
9
147Draw 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
148To 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
149A 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
150Find the area of the triangle formed by the line ( y=2 x+4 ) and coordinate
axes
10
151Construct a triangle ( boldsymbol{X} boldsymbol{Y} boldsymbol{Z} ) whose
perimeter ( 15 mathrm{cm} ) and whose base angles
are ( 60^{circ} ) and ( 70^{circ} )
9
152Construct a triangle ( A B C ) whose
perimeter ( 12 mathrm{cm} ) and whose base angles
are ( 50^{circ} ) and ( 80^{circ} )
9
153Find 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
154Rearrange 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
155Construct a bisector of an angle.9
156Construct ( 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
157If 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
158In 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
160Which 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
161Draw the following angles using ruler and compasses. Also label them.
( mathbf{1 8 0}^{circ} )
9
162Construct 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
163If 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
164Construct 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
165Construct 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
167A 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
168Quadrilaterals ABCD and PQRS are
similar.What is the length of PQ?
A . 2.67
B. 3.75
( c )
( D .5 )
10
169To 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
170Draw 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
171Construct ( 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
172The 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
173What 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
174topp
Q туре your question
which of the following construction
is/are possible?
4
10
175The 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
176If 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
177Construct ( 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
179Draw 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
180In the diagram
Write the sum of coordinates of ( boldsymbol{U} )
10
181Coordinates of point ( boldsymbol{R} ) are
( mathbf{A} cdot(1,1) )
B. (-1,-1)
( mathbf{C} cdot(-1,1) )
D. (1,-1)
10
182Construct 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
183A straight line parallel to the ( x ) -axis has equation
A. ( x=a )
B . ( y=a )
( mathbf{c} cdot y=x )
D. ( y=-x )
10
184Draw 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
185Construct 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
187Which 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
188Construct 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
189To 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
191These 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
192In 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
193In abscissa of a point ( P ) is negative and ordiante of ( P ) is positive, then ( P ) lies in :
A. I Quadrant
B. II Quadrant
c. III Quadrant
D. IV Quadrant
10
194Draw 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
195Construct 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
196In 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.
(i) Radhika scored 20 marks.
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
198To 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
199Draw 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
201Construct ( 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
202Construct 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
203Construct ( 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
204To 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
205Construct an equilateral triangle of side
( mathbf{5 . 5} mathrm{cm} )
10
206The 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
207Solve: ( frac{2}{x}+frac{3}{y}=13, frac{5}{x}+frac{7}{y}=31 )10
208Find the coordinates of the point of trisection of the line segment joining (1,-2) and (-3,4)10
209Construct ( 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
210If 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
212State 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
213In 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
214Which 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
216The 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
217The coordinates of ( B ) is ( (3,-2) . ) If true
enter 1 or else.
10
218Draw 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
219Which 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
220The 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
221Construct 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
222Which 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
223In 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
224The 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
225Construct two tangent to a circle of
radius ( 3.5 mathrm{cm} ) from a point ( 4.5 mathrm{cm} ) away from the circle.
10
226Which 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
227Draw a right angle and construct its bisector.9
228Plot 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
229Construct 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
230Triangles ( 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
231Find the ratio in which (2,1) divides the
line segment joining ( (mathbf{1}, mathbf{4}),(mathbf{4},-mathbf{5}) )
10
232Every point is located in one of the four quadrants.10
233Draw 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
234Construct a perpendicular line from
point ( p ) to any line ( A B )
9
235Draw 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
236Construct a bisector of an angle of ( 60^{circ} )9
237The point (0,3) lies on
A. ( + ) ve ( x ) -axis
B. + -ve y-axis
c. – ve ( x ) -axis
D. – ve y-axis
10
238Construct ( 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
239Determine a point which divides a line
segment of length ( 12 mathrm{cm} ) internally in
the ratio ( 2: 3 . ) Also, justify you
construction.
10
240Construct a triangle ( A B C, ) whose
perimeter is ( 12 mathrm{cm} ) and whose sides are
in the ratio 2: 3: 4
9
241The 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
242Which is last step?
4. ( (a) )
3. ( (b) )
( (c) )
2
10
243Draw 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
244Draw the graph of the equation ( 2 x+ )
( mathbf{3} boldsymbol{y}+boldsymbol{6}=mathbf{0} )
10
245Bisecting means dividing into two
parts.
A. Unequal
B. Equal
c. Triangular
D. None of these
9
246If ( 3 cos theta=1, ) find the value of
( frac{6 sin ^{2} theta+tan ^{2} theta}{4 cos theta} )
10
247Find 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
248Take a circle with centre ( C ) and
construct a tangent to a circle from an
external point ( boldsymbol{P} )
10
249Identify 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
251Construct a triangle ( M N P, ) whose
perimeter is ( 15 mathrm{cm} ) and whose sides are
in the ratio 2: 3: 4
9
252If ( 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
253Construct 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
254The 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
255For 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
256The 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
257If 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
258If 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
259Construct 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
260Draw ( 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
261State to which quadrant does the following points belong:
( U(-6.2,4.3) )
10
262n the figure, if ( A B=A C ) prove that ( B Q= )
( mathrm{QC} )
10
263Find 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
264Construct 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
265Draw 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
266Construct 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
267Construct a triangle ( P Q R ), whose
perimeter is ( 14 mathrm{cm} ) and whose sides are
in the ratio 2: 4: 5
9
268Construct 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
269Draw the graph of the equation ( y=3 x )10
270The intercepts made by the line ( x- ) ( 2 y=6 ) on the ( Y ) -axis is b.Find ( b )10
271Draw 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
272The 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
273Draw 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
274If ( 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
275Let ( 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
276Construct 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
277Which shape has the verties (3,2),(0,5),(-3,2) and (0,-1)( ? )
A. Rectangle
B. Square
c. Trapezium
D. Rhombus
10
278Construct 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
279Divide a line segment of length ( 9 mathrm{cm} )
internally in the ratio 4: 3
10
280Construct three tangents ( from a point outside to the circle ( ) ) to the circle of
radius ( 5 mathrm{cm} )
10
281The 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
282Construct 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
283Lay down the positions of the points whose polar coordinates are
( left(-1,-180^{circ}right) )
10

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