This document contains a sample paper for class 10th with 31 questions across 4 sections - A, B, C and D. The questions cover topics in mathematics, geometry and probability. The final two questions ask about child labour and steps to abolish it.

1. A.R TUTION CENTRE
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Sample paper for
class 10th
SECTION-A
1) Find the value of k for which the equation 2x2 –(k-
1)x+8=0 will have real and equal roots?
2) The tops of two poles of height 20m and 14m are
connected by wire. If the wire makes an angle of
30°with the horizontal. Then find the length of the
wire?
3) The probability of guessing the correct answer to
certain questions is
𝑃
12
. If the probability of not
guessing the correct answer to same question is
3/4 then find the value of P?

2. 4) How can you show using concept of area that
three points P, Q and R whose co-ordinates given
are collinear?
SECTION-B
5) The angles of a triangle are in A.P. the greater
angle is twice the least. Find all angles of the
triangle?
6) Find the roots of the quadratic equation a2
b2
x2
+b2
x-a2
x-1= 0?
7) Two tangents PA and PB are drawn to a circle with
centre O, such that angle APB =120°.Prove that
OP=2 AP?
8) Draw two tangents from the end points of the
diameter of a circle of radius 3.5 cm. Are these
tangents are parallel?
9) By geometrical construction, it is possible to divide
a line segment in ratio√3:
1
√3
?
10) Find the area of right triangle if radius of its circum
circle is 5cm and altitude draw hypotenuse is 4cm?

3. SECTION-C
11) Show that the sum of an A.P whose first term is a
,the second term is b and the last term is c is equal
to
( 𝑎+𝑐)(𝑏+𝑐−2𝑎)
2(𝑏−𝑎)
?
12) The sum of a number and its positive square root
is
6
25
.Find the number?
13) ABC is a right triangle, right angled at B, such that
BC=6cm and AB=8cm. find the radius of its in
circle?
14) If from a point 100m above the ground, the angles
of depression of two objects due south on the
ground are 60° and 45° then find the distance
between the objects?
15) Three coins are tossed. What is the probability of
getting A) Two heads B) At least two heads
C) At most two heads
16) If P(x ,y) is any point on the line segment joining
the points A (a ,o) the show that
𝑥
𝑎
+
𝑦
𝑏
=1
17) If A (1, 2), B (4, 3), c (6, 6) are the three vertices of
a ІІ gm .ABCD. Find the Co- ordinates of the fourth
vertex D.

4. 18) In cylinder of a base radius 10 cm, liquid is filled to
the height of 9cm.a meal cube of diagonal 8√3 cm
is immersed completely in the liquid. Find the
height by which the water will rise in cylinder.
19) In a triangle ABC of the given figure angle A=58°,
angle B=42°, angle C=80° with A,B and C as centre,
circles of equal radii 7cm are drawn. Find the area
common to the triangle ABC and the three circles.
(𝜋 =
22
7
)
20) Water running in a cylindrical pipe of inner
diameter 7cm, is collected in a container at the
rate of 192.5 liters per minute. Find the rate of
flow of water in the pipe in km/hr.
SECTION-D
21) The taxi fare after each km, when the fare is Rs 15
for the first km and Rs8 for each additional km,
does not from as A.P as the total fare (Rs) after
each km is 15,8,8,8. A) Is he statement true?

5. B) If the taxi owner uses a mileage meter which
shows 10% extra for each km which value is
violated by the taxi owner.
22) Solve the following equation for x:-
9x2
-9 (a+ b) x + (2a2
+5ab+2b2
) = 0
23) If n times the nth
term of an A.P is equal to m times
the mth
term, prove that its (m+ n)th
term is equal
to zero.
24) If all the sides of ll gm touch a circle, show that the
ll gm is a rhombus.
25) Draw ABC such that BC=5cm angle ABC=60°
and angle ACB=30° now construct A`BC`
similar ABC with A`B : AB = 3:2
26) The angle of elevation of a cloud from a print 60m
above a lake is 30° and the angle of depression of
the reflection of a cloud is 60°. Find the height of
the cloud.
27) In a survey it was found that 120 students like to
drink tea, 80 students like to drink coffee and 50
students like to take soft drink. If a student is

6. selected at random among them, find the
probability that the student a) likes to drink tea
b) likes to drink coffee c) likes to drink tea or soft
drink d) does not like to drink soft drink
28) Find the value of k for which points A (-6, 10)
B (-4, k) C (3,-8) are collinear. Also find the ratio
in which B divides AC and the length of AC
29) The height of a cone is 30cm. A small cone is
cut off at the top by a plane parallel to the base. If
its volume be
1
27
th of the volume of the cone, at
what height above the base is the section made?
30) In a triangular park, the three corners are
used to make play areas for children in the form of
sectors of radii 14m each .If the sides of the park
are 52m, 56m and 60m. Find the area of the
remaining portion of the park.
31) A shopkeeper involved children in colouring
lattu (a playing top), which is shaped like a
hemisphere surmounted by a cone. The entire
height of lattu is 7cm and diameter of the lattu is
6cm. find the area they had to paint 20 such lattu.

7. a) How is the child labour an abuse for the
society?
b) What steps do you think must taken to abolish
child labour?