﻿ CBSE Class 10 Mathematics Solved Question Paper 2013 | Previous Year Papers | Zigya

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# CBSE Class 10 Mathematics Solved Question Paper 2013

#### Short Answer Type

1.

Solve the following quadratic equation for x;

#### Multiple Choice Questions

2.

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime-number less than 23,is

• $\frac{7}{90}$

• $\frac{10}{90}$

• $\frac{4}{45}$

• $\frac{9}{89}$

C.

$\frac{4}{45}$

S = { 1, 2, 3,........90 }

n(s) = 90

The prime number less than 23 are 2, 3, 5, 7, 11, 13, 17 and 19

Let event E be defined as 'getting a prime number less than 23'.

n(E) = 8

3.

The probability of getting an even number, when a die is thrown once, is

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{6}$

• $\frac{5}{6}$

A.

$\frac{1}{2}$

S = { 1, 2, 3, 4, 5, 6 }

let event E be defined as 'getting an even number'.

n(E) = { 2, 4, 6 }

4.

The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30o. The distance of the car from the base of the tower (in m.) is

• $25\sqrt{3}$

• $50\sqrt{3}$

• $75\sqrt{3}$

• 150

C.

$75\sqrt{3}$ Let AB be the tower of height 75 m and C be position of the car.

In

5.

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, $\angle$B = 90o and DS = 5 cm, then the radius of thecircle (in cm) is • 11

• 18

• 6

• 15

A.

11 Given: Ab, BC,CD,and AD tangents to the circle with centre O at

Q,P,S and R respectively.

AB=29 cm, AD=23 cm, DS=5 cm and $\angle$B=900

Construction: Join PQ.

We know that, the lengths of the tangents drawn from an external

point to a circle are equal.

DS=DR=5 cm

$\therefore$AR= AD - DR= 23 cm- 5 cm= 18 cm

AQ=AR= 18 cm

$\therefore$ QB = AB - AQ = 29 cm - 18 cm= 11 cm

QB = BP = 11 cm

In $∆$

6.

In fig., PA and PB are two tangents drawn from an external point P to a circlewith centre C and radius 4 cm. If PA PB, then the length of each tangent is • 3

• 4

• 5

• 6

B.

4

Therefore, APBC is a square having side equal to 4 cm.
Therefore, length of each tangent is 4 cm.

#### Short Answer Type

7.

How many three-digit natural numbers are divisible by 7?

Three digit numbers divisible by 7 are

105, 112, 119, .......994

This is an AP with first term (a) =105 and comman difference (d)= 7

#### Multiple Choice Questions

8.

If the difference between the circumference and the radius of a circle is 37cm, then using  , the circumference (in cm) of the circle is:

• 154

• 44

• 14

• 7

B.

44

Let r be the radius of the circle,

From the given information, we have

9.

The common difference of AP 1 1 6q 1 12q, , 3q 3q 3q
... is:

• q

• -q

• -2

• 2

C.

-2

10.

In fig., the area of triangle ABC (in sq. units) is • 15

• 10

• 7.5

• 2.5

C.

7.5 From the figure, the coordinates of A, B, and C are (1,3), (-1, 0) and (4, 0)

respectively.