QUESTION BANK
1 MARK QUESTIONS
CHAPTER : 1 - SIMILARITY
1. For ABC ~ PQR, state all the corresponding congruent angles.
AB
2. ABC ~ PQR. State which ratio of sides are equal to .
PQ
A (ABC) 1 BC
3. ABC ~ APQ, if A (APQ) = , find .
4 PQ
4. In PQR, m P = 90º. S is the midpoint of side QR. If QR = 10 cm, what is the length
of PS ?
5. A (PQR) = 24 cm2, the height QS is 8 cm. What is the length of side PR ?
6. In the adjoining figure, A D
ABCD is a trapezium. 10 15
seg AD || seg PQ || seg BC P Q
AP = 10, PB = 12, DQ = 15. 12 ?
Find the value of QC.
B C
PR 2
7. If PQR ~ XYZ, = and PQ = 12, then find XY.
XZ 3
CHAPTER : 2 - CIRCLE
B
1. O is the centre of the circle.
If m ABC = 80º, the find
m (arc AC) and m (arc ABC).
O
C
A
D
2. What is the relation between ABE A
and ADC for cyclic ABCD ?
•
E
B
C
P
3. If m (arc PNQ) = 140º,
find m PQR. N
R
Q
.. 2 ..
4. In the adjoining figure, A C
chords AB and CD intersect at E.
If DE = 6, BE = 3 and CE = 4, then E
find AE.
D B
CHAPTER : 4 - TRIGONOMETRY
Find where the angle lies if the terminal arm passes through :
1. (5, 7)
2. (– 8, 1)
3. (– 3, – 3)
4. (0, 2)
CHAPTER : 5 - CO-ORDINATE GEOMETRY
1. If m = 5 and c = – 3, then write the equation of the line.
2. What is the x-intercept of line 3x – 4y = 12 ?
3. Write the x-intercept and the y-intercept of the line represented by the equation
x y
+ = 1.
2 3
4. If the slope of a line is 2 and its y-intercept is 5, write its equation.
CHAPTER : 6 - MENSURATION
1. Using Euler’s formula, find F, if V = 6 and E = 12.
2. The radius of the base of a cone is 7 cm and its height is 24 cm. What is its slant
height ?
3. Using Euler’s formula, write the value of V, if E = 30 and F = 12.
4. The radius of the base of a cone is 7 cm and its height is 24 cm. What is its slant
height ?
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QUESTION BANK
2 MARK QUESTIONS
CHAPTER : 1 - SIMILARITY
1. Find the side of square whose diagonal is 16 2 cm .
2. In triangle STR, line l is parallel side TR. S
From the information given in the figure, l x 1.3
find the value of x. P Q
4.5
3.9
T
R
X
3. Ray YM is the angle bisector
of XYZ, where XY = YZ.
M
Find the relation between XM and MZ.
•
•
Y Z
4. In ABC, AB = 3 cm, BC = 5 cm and AC = 4 cm. State the vertex of the triangle which
contains the right angle.
CHAPTER : 2 - CIRCLE
1. In the adjoining figure, M
Q is the centre of circle and PM
and PN are tangent segments to P
40º Q
the circle. If MPN = 40º circle,
find MQN.
N
2. In the adjoining figure, D
seg AB and seg AD are chords
of the circle. C be a point on Q
tangent to the circle at point A. B
If m (arc APB) = 80º and BAD = 30º,
P
then find (i) BAC (ii) m (arc BQD). A C
3. In the adjoining figure,
AB and AC are tangents drawn
from A, and BA CA. Prove that O C
BACO is a square.
B A
4. Point M, in the interior of the circle, is the point of intersection of two chords AB
and CD of the same circle. Show that CM × BD = BM × AC.
.. 4 ..
CHAPTER : 3 - GEOMETRIC CONSTRUCTIONS
1. Construct LMN, such that LM = 6.2 cm, MN = 4.9 cm, LN = 5.6 cm.
2. Draw a circle of radius 3.6 cm, take a point M on it. Draw a tangent to the circle at
M without using centre of the circle.
3. Draw a tangent to a circle of a radius 3.1 cm and centre O at any point ‘R’ on the
circle.
4. Draw a tangent at any point R on the circle of radius 3.4 cm and centre ‘P’.
CHAPTER : 4 - TRIGONOMETRY
1. Find the trigonometric ratios in standard position whose terminal arm passes through
the point :
(i) (4, 3).
(ii) (– 24, – 7).
(iii) (1,-1).
(iv) (– 2,– 3).
CHAPTER : 5 - CO-ORDINATE GEOMETRY
1. Write the following equations in double intercept form and write the x intercept and
y intercept :
(i) 2x – y = 11
(ii) 2x + 3y – 7 = 0
(iii) 2x – y = 3
(iv) 4x – y – 7 = 0
2. Find the slope of the line passing through the points
(i) (–1,3) and (3,5)
(ii) (– 4, 5) and (2, 3)
(iii) (7,8) and (3,4)
(iv) (3, 6) and (– 6, – 7)
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QUESTION BANK
3 MARK QUESTIONS
CHAPTER : 1 - SIMILARITY
1. Prove : In a triangle, the angle bisector divides the side opposite to the angle in the
ratio of the remaining sides.
2. Prove : In a right angled triangle, the square of the hypotenuse is equal to the sum
of the squares of the remaining two sides.
3. Prove : If a line parallel to a side of a triangle intersects other sides in two distinct
points, then the line divides those sides in proportion.
CHAPTER : 2 - CIRCLE
1. Suppose ABC is a triangle inscribed in a circle, the bisector of ABC intersects
the circle again in D, the tangent at D intersects the line BA and line BC in E
and F respectively. Prove that EDA FDC.
2. Secants containing chords RS
and PQ of a circle intersects each
other in point A in the exterior of S
a circle, as shown in figure. R
If m (arc PCR) = 26º and A C •D
m (arc QDS) = 48º then find
P
(a) AQR (b) SPQ (c) RAQ.
Q
3. In the adjoining figure, A
ABC is isosceles triangle with
perimeter 44 cm. The base BC
is of length 12 cm. Sides AB and
AC are congruent. A circle touches P Q
the three sides as shown. Find the
length of a tangent segment from
B C
A to the circle. R
A B
4. In the adjoining figure,
18
line AB is tangent to both the
29
circles touching at A and B. P
O 61
OA = 29, BP = 18, OP = 61
then find AB.
.. 6 ..
CHAPTER : 3 - GEOMETRIC CONSTRUCTIONS
1. Construct LEM such that, LE = 6cm, LM = 7.5 cm, LEM = 90º and draw its
circumcircle.
2. Construct a right angled triangle PQR where PR = 6 cm, QPR = 40º, PRQ = 90º.
Draw circumcircle of PQR.
3. Draw the circumcircle of PMT such that, PM = 5.4 cm, P = 60º, M = 70º.
4. Construct the circumcircle of KLM in which KM = 7 cm, K = 60º, M = 55º.
CHAPTER : 4 - TRIGONOMETRY
Prove :
1 – cos A
1. 1 cos A = cosec A – cot A.
2. sec 2 cos ec 2 = tan + cot .
3. sec6 x – tan6 x = 1 + 3 sec2 x.tan2 x.
1 1 1
4. 1 + 2 1 + = .
tan A cot A sin A – sin4 A
2 2
CHAPTER : 5 - CO-ORDINATE GEOMETRY
2 1 1 4
1. If the points , , , k and , 0 are collinear then find the value of k.
5 3 2 5
2. The vertices of a triangle are A (3, – 4), B (5, 7) and C (– 4, 5). Find the slope of each
side of the triangle ABC.
3. Find the value of k if (– 3, 11), (6, 2) and (k, 4) are collinear points.
–3
4. Find x if the slope of line joining (x, – 2) and (8, – 11) is .
4
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QUESTION BANK
4 MARK QUESTIONS
CHAPTER : 2 - CIRCLE
1. Prove : The opposite angles of a cyclic quadrilateral are supplementary.
2. Prove : The lengths of the two tangent segments to a circle drawn from an external
point are equal.
CHAPTER : 4 - TRIGONOMETRY
1. A pilot in an aeroplane observes that Vashi bridge is on one side of the plane and
Worli sea-link is just on the opposite side. The angle of depression of Vashi bridge and
Worli sea-link are 60º and 30º respectively. If the aeroplane is at a height of 5500 3 m
at that time, what is the distance between Vashi bridge and Worli sea-link ?
2. A tree is broken by the wind. The top struck the ground at an angle of 30º and at a
distance of 30 m from the foot. Find the whole height of the tree. ( 3 = 1.73)
3. A person standing on the bank of a river observes that the angle of elevation of the
top of a tree standing on the opposite bank is 60º. When he moves 40 m away from
the bank, he finds the angle of elevation to be 30º. Find the height of the tree and the
width of the river. ( 3 = 1.73)
4. A tree 12m high, is broken by the wind in such a way that its top touches the
ground and makes an angle 60º with the ground. At what height from the bottom,
the tree is broken by the wind ? ( 3 = 1.73)
CHAPTER : 6 - MENSURATION
1. A piece of cheese is cut in the
shape of the sector of a circle of 6 cm
radius 6 cm. The thickness of the 60º
cheese is 7 cm. Find
7 cm
(a) The curved surface area of the cheese.
(b) The volume of the cheese piece.
.. 8 ..
2. A cylindrical hole of diameter 30 cm is
bored through a cuboid wooden block
with side 1 meter. Find the volume of
the object so formed ( = 3.14).
3. A test tube has diameter 20 mm and
height is 15 cm. The lower portion is a
hemisphere in the adjoining figure.
Find the capacity of the test tube. ( = 3.14). 15 cm
4. The diameter of the base of metallic cone is 2 cm and height is 10 cm. 900
such cones are molten to form 1 right circular cylinder whose radius is 10 cm.
Find total surface area of the right circular cylinder so formed. (Given = 3.14)
.. 9 ..
QUESTION BANK
5 MARK QUESTIONS
CHAPTER : 1 - SIMILARITY
1. Two poles of height ‘a’ meters and S
R
‘b’ meters are ‘p’ meters apart.
Prove that the height ‘h’ drawn from b N
a
of the point of intersection N of the
lines joining the top of each pole to h
the foot of the opposite pole is A B
x T y
ab p
a + b meters.
2. ABC is a triangle where C = 90º. Let BC = a, CA = b, AB = c and let ‘p’ be the
1 1 1
length of the perpendicular from C on AB. Prove that (a) cp = ab, (b) p2 = a 2 + b2
A
3. Let X be any point on side BC of ABC,
XM and XN are drawn parallel to BA M
and CA. MN meets produced CB in T.
N
Prove that TX2 = TB . TC.
T
B X C
4. G is the centroid of ABC. A
GE and GF are drawn parallel
to AB and AC respectively.
Find A (GEF) : A (ABC).
G
B E F C
CHAPTER : 3 - GEOMETRIC CONSTRUCTIONS
HP 4
1. RHP ~ NED, In NED, NE = 7 cm, D = 30º, N = 20º and = ; constructRHP.
ED 5
LR 5
2. LTR ~ HYD, In HYD, HY = 7.2 cm, YD = 6 cm, Y = 40º and = ’ construct
HD 6
LTR.
LM 4
3. LMN ~ XYZ, In LMN, LM = 6 cm, MN = 6.8 cm, LN = 7.6 cm and = ;
XY 3
construct XYZ.
.. 10 ..
CHAPTER : 6 - MENSURATION
1. There are 3 stair-steps as shown in
the figure. Each stair-step has width
25 cm, height 12 cm and length 50 cm.
How many bricks have been used in it if
each brick is 12.5 cm × 6.25 cm × 4 cm.
2. A cylinder of radius 12 cm contains water upto depth of 20 cm. A spherical
iron ball is dropped into the cylinder and thus water level is raised by 6.75 cm.
what is the radius of the ball ?
3.
10 cm 10 cm
10 cm
60 cm
A toy is a combination of a cylinder, hemisphere and a cone, each with radius
10cm. Height of the conical part is 10 cm and total height is 60cm. Find the
total surface area of the toy. ( = 3.14, 2 = 1.41).
4. A 10 m deep well of diameter 1.4 m us dug up in a field and the earth from
digging is spread evenly on the adjoining cuboid field. The length and breadth
of that filled are 55m and 14 m respectively. Find the thickness of the earth
layer spread.
