﻿ The incircle of an isosceles triangle ABC, in which AB = AC, touc

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## CBSE Class 10 Mathematics Solved Question Paper 2014

#### Multiple Choice Questions

1.

The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 isa multiple of 4, is

• $\frac{4}{15}$

• $\frac{2}{12}$

• $\frac{1}{5}$

• $\frac{1}{3}$

2.

Two circles touch each other externally at P. AB is a common tangent to the circlestouching them at A and B. The value of ∠APB is

• 30°

• 45°

• 60°

• 90°

3.

If k, 2k- 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is

• 2

• 3

• -3

• 5

4.

In a family of 3 children, the probability of having at least one boy is

• $\frac{7}{8}$

• $\frac{1}{8}$

• $\frac{5}{8}$

• $\frac{3}{4}$

5.

A chord of a circle of radius 10 cm subtends a right angleat its centre. The length of the chord (in cm) is

• 5$\sqrt{2}$

• 10$\sqrt{2}$

• $\frac{5}{\sqrt{2}}$

• 10$\sqrt{3}$

6.

ABCD is a rectangle whose three vertices are B (4, 0), C(4,3) and D(0, 3). The length of one of its diagonals is

• 5

• 4

• 3

• 25

7.

The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower (in metres) is

• $50\sqrt{3}$

• $150\sqrt{3}$

• $150\sqrt{2}$

• 75

8.

In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is

• 4

• 3

• 2

• 1

# 9.The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively. Prove that BD = DC.

Given: $∆\mathrm{ABC}$ is an isosceles triangle with a circle inscribed in the triangle.

To prove: BD=DC

Proof:

AF and AE are tangents drawn to the circle from point A.

Since two tangents drwan to a circle from the same exterior point are equal.

AF=AE=a

Similarly  BF=BD=b  and  CD=CE=c

We also know that $∆\mathrm{ABC}$ is an isosceles triangle

Thus AB=AC

a+b=a+c

Thus b=c

Therefore, BD=DC

Hence proved.

10.

Two different dice are tossed together. Find the probability

(i) That the number on each die is even.

(ii) That the sum of numbers appearing on the two dice is 5.