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Q:

If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

A) 55%	B) 65%
C) 75%	D) 85%

Answer & Explanation Answer: C) 75%

Explanation:

Let original radius = R.

New radius = $\frac{50}{100} R$ = $\frac{50}{100} R$

Original area = $\frac{R}{2}$ and new area = ${πR}^{2}$

$\frac{3 {πR}^{2}}{4} * \frac{1}{{πR}^{2}} * 100$

Decrease in area = $π {(\frac{R}{2})}^{2} = \frac{{πR}^{2}}{4}$ = 75%

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Filed Under: Area
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Q:

When six fairs coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads ?

A) 15	B) 42
C) 16	D) 40

Answer & Explanation Answer: B) 42

Explanation:

The question requires you to find number of the outcomes in which at most 3 coins turn up as heads.

i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads or 3 coins turn heads.

The number of outcomes in which 0 coins turn heads is $6 C_{0}$ =1

The number of outcomes in which 1 coin turns head is = $6 C_{1}$ =6

The number of outcomes in which 2 coins turn heads is $6 C_{2}$ =15

The number of outcomes in which 3 coins turn heads is $6 C_{3}$ =20

Therefore, total number of outcomes =1+6+15+20= 42 outcomes

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Q:

A sector of 120, cut out from a circle, has an area of $\frac{66}{7} c m^{2}$ . Find the radius of the circle ?

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: C) 3

Explanation:

Let the radius of the circle be r cm. Then,

$\frac{120}{360} {πr}^{2} = \frac{66}{7}$

$r^{2} = \frac{66}{7} * \frac{7}{22} * 3$

r=3.

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Q:

The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle

A) 44	B) 22
C) 33	D) 84

Answer & Explanation Answer: D) 84

Explanation:

Let inner radius be r metres. Then, 2 $π$ r = 440 ; r = $440 \times \frac{7}{44}$ = 70 m.

Radius of outer circle = (70 + 14) m = 84 m.

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Filed Under: Area
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Q:

A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.

A) 14	B) 13
C) 12	D) 11

Answer & Explanation Answer: A) 14

Explanation:

Distance covered in one revolution = $\frac{88 \times 1000}{1000}$ = 88m.

$2 {πR}^{2} = 88 \Rightarrow 2 \times \frac{22}{7} \times R = 88 \Rightarrow R = 88 \times \frac{7}{44}$

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Q:

The diameter of the driving wheel of a bus is 140 cm. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ?

A) 150	B) 250
C) 350	D) 550

Answer & Explanation Answer: B) 250

Explanation:

Circumference = No.of revolutions * Distance covered

Distance to be covered in 1 min. = (66 X1000)/60 m = 1100 m.
Circumference of the wheel = 2 x (22/7) x 0.70 m = 4.4 m.
Number of revolutions per min. =(1100/4.4) = 250.

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Q:

In how many ways can 4 sit at a round table for a group discussions?

A) 9	B) 3
C) 6	D) 12

Answer & Explanation Answer: C) 6

Explanation:

We get this using the formula of circular permutations i.e., (4 - 1)! = 3! =6

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Filed Under: Permutations and Combinations

Q:

When Dr. Ram arrives in his dispensary, he finds 12 patients waiting to see him. If he can see only one patients at a time,find the number of ways, he can schedule his patients if 3 leave in disgust before Dr. Ram gets around to seeing them.

A) 479001600	B) 79833600
C) 34879012	D) 67800983

Answer & Explanation Answer: B) 79833600

Explanation:

There are 12 - 3 = 9 patients.They can be seen in $12 P_{9}$ = 79833600 ways

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Filed Under: Permutations and Combinations

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