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Class 10th Board

Class 10th Board 2016

Class 10th Board exam papers

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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

Mathematics Science

Chapter 6: Class 10th Board 2015

67 questions

Class 10th Board 2016

Topic List

questions: 67

Verified solutions and explanations

Verified

Easy (57)Medium (10)

Question 1

Easy

In Fig., AOB is a diameter of a circle with centre

O

and

AC

is a tangent to the circle at

A

. If

∠ BOC = 13 0^{\circ}

, then find

∠ ACO

Topic:

Circles

Exam:

Class 10th Board 2016

View solution

Question 2

Easy

An observer,

1.7 m

tall, is

203 m

away from a tower. The angle of elevation from the eye of observer to the top of tower is

3 0^{\circ}

. Find the height of tower.

Topic:

Some Application of Trigonometry

Exam:

Class 10th Board 2016

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Question 3

Easy

For what value of

k

will the consecutive terms

2 k + 1, 3 k + 3

and

5 k - 1

form an A.P. ?

Topic:

Arithmetic Progressions

Exam:

Class 10th Board 2016

View 3 solutions

Question 4

Easy

20 tickets, on which numbers 1 to 20 are written, are mixed thoroughly and then a ticket is drawn at random out of them. Find the probability that the number on the drawn ticket is a multiple of 3 or 7.

Topic:

Probability

Exam:

Class 10th Board 2016

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Question 5

Easy

A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits. Find the number.

Topic:

Pair of Linear Equations in Two Variables

Exam:

Class 10th Board 2016

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Question 6

Easy

Find the ratio in which the point

(- 3, k)

divides the line-segment joining the points

(- 5, - 4)

and

(- 2, 3)

. Also find the value of

k

Topic:

Coordinate Geometry

Exam:

Class 10th Board 2016

View 3 solutions

Question 7

Easy

In Fig., from a point

P

, two tangents

PT

and

PS

are drawn to a circle with centre

O

such that

∠ SPT = 12 0^{\circ}

, Prove that

OP = 2 PS

Topic:

Circles

Exam:

Class 10th Board 2016

View 2 solutions

Question 8

Easy

Prove that the points

(2, - 2), (- 2, 1)

and

(5, 2)

are the vertices of a right angled triangle. Also find the area of this triangle.

Topic:

Coordinate Geometry

Exam:

Class 10th Board 2016

View 3 solutions

Question 9

Easy

If the ratio of sum of the first

m

and

n

terms of an A.P. is

m^{2} : n^{2}

, show that the ratio of its

m^{th}

and

n^{th}

terms is

(2 m - 1) : (2 n - 1)

Topic:

Arithmetic Progressions

Exam:

Class 10th Board 2016

View 4 solutions

Question 10

Easy

In fig. are two concentric circles of radii

6 cm

and

4 cm

with centre

O

. If AP is a tangent to the larger circle and BP to the smaller circle and length of AP is

8 cm

, find the length of BP.

Topic:

Circles

Exam:

Class 10th Board 2016

View solution

Question 11

Easy

Find the area of shaded region in Fig. , where a circle of radius

6 cm

has been drawn with vertex

O

of an equilateral triangle

OAB

of side

12 cm

. (Use

π = 3.14

and

3 = 1.73)

Topic:

Area Related to Circles

Exam:

Class 10th Board 2016

View 2 solutions

Question 12

Easy

A hemispherical tank, of diameter

3 m

, is full of water. It is being emptied by a pipe at the rate of

3 \frac{4}{7}

litre per second. How much time will it take to make the tank half empty ?

[Use π = \frac{22}{7}]

Topic:

Surface Areas and Volumes

Exam:

Class 10th Board 2016

View 2 solutions

Question 13

Easy

If the point

C (- 1, 2)

divides internally the line-segment joining the points A

(2, 5)

and

B (x, y)

in the ratio

3 : 4

, find the value of

x^{2} + y^{2}

Topic:

Coordinate Geometry

Exam:

Class 10th Board 2016

View 2 solutions

Question 14

Easy

In fig. is a chord

AB

of a circle, with centre

O

and radius

10 cm

, that subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence find the area of major segment ALBQA. (use

π = 3.14

)

Topic:

Area Related to Circles

Exam:

Class 10th Board 2016

View solution

Question 15

Easy

Divide 56 in four parts in A.P. such that the ratio of the product of their extremes

(1^{st}

and

4^{th})

to the product of means

(2^{nd}

and

3^{rd})

5 : 6

Topic:

Arithmetic Progressions

Exam:

Class 10th Board 2016

View solution

Question 16

Easy

Solve the given quadratic equation for

x : 9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 ab + 2 b^{2}) = 0

Topic:

Quadratic Equations

Exam:

Class 10th Board 2016

View solution

Question 17

Easy

A cylindrical tub, whose diameter is

12 cm

and height

15 cm

is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone.

Topic:

Surface Areas and Volumes

Exam:

Class 10th Board 2016

View solution

Question 18

Easy

A metal container, open from the top, is in the shape of a frustum of a cone of height

21 cm

with radii of its lower an upper circular ends as

8 cm

and

20 cm

respectively. Find the cost of milk which can completely fill the container at the rate of ₹ 35 per litre.

[

Use

π = \frac{22}{7}]

Topic:

Surface Areas and Volumes

Exam:

Class 10th Board 2016

View solution

Question 19

Easy

Two men on either side of a

75 m

high building and in line with base of building observe the angles of elevation of the top of the building as

3 0^{\circ}

and

6 0^{\circ}

. Find the distance between the two men. (Use

3 = 1.73

)

Topic:

Some Application of Trigonometry

Exam:

Class 10th Board 2016

View solution

Question 20

Easy

A game consist of tossing a one-rupee coin 3 times and noting the outcome each time.Ramesh will win the game if all the tosses show the same result, (i.e. either all three heads or all three tails) and loses the game otherwise. Find the probability that Ramesh will lose the game

Topic:

Probability

Exam:

Class 10th Board 2016

View solution

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