Mathematics

CBSE Class 10

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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°

4.

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

$\frac{7}{8}$

$\frac{1}{8}$

$\frac{5}{8}$

$\frac{3}{4}$

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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

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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

C.

2

It is given that AB = 5 and BC = 12

Using pythagoras theorem

${\mathrm{AC}}^{2}={\mathrm{AB}}^{2}+{\mathrm{BC}}^{2}\phantom{\rule{0ex}{0ex}}={5}^{2}+{12}^{2}\phantom{\rule{0ex}{0ex}}=169\phantom{\rule{0ex}{0ex}}\mathrm{Thus}\mathrm{AC}=13\phantom{\rule{0ex}{0ex}}$

We know that two tangents drwan to a circlefrom the same point that is exterior to

the circle are of equal iengths.

Thus AM = AQ = a

Similarly MB = BP = b and PC = CQ = c

We know AB = a+b = 5

BC = b+c = 12 and AC = a+c = 13

Solving simultaneously we get a = 3, b =2, c = 10

We also know that the tangent is perpendicular to the radius.

Thus OMBP is a square with side b

Hence the length of the radius of the circle inscribed in the right angled triangle is 2 cm.

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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.

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.

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