Home

Class 10th Board

Class 10th Board 2015

Class 10th Board exam papers

Last 6 years - Previous year question papers

Chapter 1: Class 10th Board 2020

330 questions

Chapter 2: Class 10th Board 2019

171 questions

Chapter 3: Class 10th Board 2018

57 questions

Chapter 4: Class 10th Board 2017

67 questions

Chapter 5: Class 10th Board 2016

67 questions

Chapter 6: Class 10th Board 2015

67 questions

Mathematics Science

Class 10th Board 2015

Topic List

questions: 67

Verified solutions and explanations

Verified

Easy (58)Medium (9)

Question 1

Easy

Find the

2 5^{th}

term of the A.P.

- 5, \frac{- 5}{2}, 0, \frac{5}{2}, \dots

Topic:

Arithmetic Progressions

Exam:

Class 10th Board 2015

View 4 solutions

Question 2

Easy

A pole casts a shadow of length

23 m

on the ground, when the sun's elevation is

6 0^{\circ}

. Find the height of the pole.

Topic:

Some Application of Trigonometry

Exam:

Class 10th Board 2015

View solution

Question 3

Easy

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers

1, 2, 3, 4, 5, 6, 7, 8

and these are equally likely outcomes. Find the probability that the arrow will point at any factor of 8.

Topic:

Probability

Exam:

Class 10th Board 2015

View 3 solutions

Question 4

Easy

Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

Topic:

Circles

Exam:

Class 10th Board 2015

View 6 solutions

Question 5

Easy

In Figure

, O

is the centre of a circle.

PT

and

PQ

are tangents to the circle from an external point

P

. If

∠ TPQ = 7 0^{\circ}

, find

∠ TRQ

Topic:

Circles

Exam:

Class 10th Board 2015

View solution

Question 6

Easy

In Figure ,

PQ

is a chord of length

8 cm

of a circle of radius

5 cm

. The tangents at

P

and

Q

intersect at a point

T

. Find the lengths of

TP

and TQ.

Topic:

Circles

Exam:

Class 10th Board 2015

View 3 solutions

Question 7

Easy

Solve for

x

x^{2} - (3 + 1) x + 3 = 0

Topic:

Quadratic Equations

Exam:

Class 10th Board 2015

View solution

Question 8

Easy

The fourth term of an A.P. is 11 . The sum of the fifth and seventh terms of the A.P. is 34 . Find its common difference.

Topic:

Arithmetic Progressions

Exam:

Class 10th Board 2015

View solution

Question 9

Easy

Show that the points

(a, a), (- a, - a)

and

(- 3 a, 3 a)

are the vertices of an equilateral triangle.

Topic:

Coordinate Geometry

Exam:

Class 10th Board 2015

View 8 solutions

Question 10

Easy

For what values of

k

are the points

(8, 1), (3, - 2 k)

and

(k, - 5)

collinear ?

Topic:

Coordinate Geometry

Exam:

Class 10th Board 2015

View solution

Question 11

Easy

Point A lies on the line segment

PQ

joining

P (6, - 6)

and

Q (- 4, - 1)

in such a way that

\frac{PA}{PQ} = \frac{2}{5}

. If point

P

also lies on the line

3 x + k (y + 1) = 0

, find the value of

k

Topic:

Coordinate Geometry

Exam:

Class 10th Board 2015

View 2 solutions

Question 12

Easy

Solve for

x

x^{2} + 5 x - (a^{2} + a - 6) = 0

Topic:

Quadratic Equations

Exam:

Class 10th Board 2015

View solution

Question 13

Easy

In an A.P., if the 12th term is –13 and the sum of its first four terms is 24, find the sum of its first ten terms.

Topic:

Arithmetic Progressions

Exam:

Class 10th Board 2015

View 2 solutions

Question 14

Easy

A bag contains 18 balls out of which x balls are red.
(i) If one ball is drawn at random from the bag, what is the probability that it is not red ?
(ii) If 2 more red balls are put in the bag, the probability of drawing a red ball will be

\frac{9}{8}

times the probability of drawing a red ball in the first case. Find the value of x.

Topic:

Probability

Exam:

Class 10th Board 2015

View solution

Question 15

Easy

From the top of a tower of height

50 m

, the angles of depression of the top and bottom of a pole are

3 0^{\circ}

and

4 5^{\circ}

respectively. Find
(i) how far the pole is from the bottom of a tower,
(ii) the height of the pole. (Use

3 = 1 \cdot 732

)

Topic:

Some Application of Trigonometry

Exam:

Class 10th Board 2015

View solution

Question 16

Easy

The long and short hands of a clock are

6 cm

and

4 cm

long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use

π = 3 \cdot 14

)

Topic:

Area Related to Circles

Exam:

Class 10th Board 2015

View 2 solutions

Question 17

Easy

Two spheres of same metal weigh

1 kg

and

7 kg

. The radius of the smaller sphere is

3 cm

. The two spheres are melted to form a single big sphere. Find the diameter of the new sphere.

Topic:

Surface Areas and Volumes

Exam:

Class 10th Board 2015

View 2 solutions

Question 18

Easy

A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of

\frac{3}{2}

cm and its depth is

\frac{8}{9}

cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.

Topic:

Surface Areas and Volumes

Exam:

Class 10th Board 2015

View solution

Question 19

Easy

In Figure , ABCD is a trapezium with

A B ∣∣ D C

, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. If arcs of equal radii 7 cm have been drawn, with centres A, B, C and D, then find the area of the shaded region.

Topic:

Surface Areas and Volumes

Exam:

Class 10th Board 2015

View solution

Question 20

Easy

A solid right-circular cone of height 60 cm and radius 30 cm is dropped in a right-circular cylinder full of water of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder, in cubic metres. (Take

π = \frac{22}{7}

)

Topic:

Surface Areas and Volumes

Exam:

Class 10th Board 2015

View solution

1 2 3 4

Get instant study help from an expert tutor 24/7

Download Filo