Job Roles Questions and Answers

Q:

One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?

A) 110	B) 120
C) 130	D) 140

Answer & Explanation Answer: B) 120

Explanation:

Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m
Area = 15 x 8 =120 sq. m

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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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Q:

Find the ratio of the areas of the incircle and circumcircle of a square.

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

Answer & Explanation Answer: B) 1:2

Explanation:

Let the side of the square be x. Then, its diagonal = $\sqrt{2 x^{2}} = \sqrt{2 x}$

Radius of incircle = $\frac{x}{2}$

Radius of circum circle= $\sqrt{2} \times \frac{x}{2} = \frac{x}{\sqrt{2}}$

Required ratio = $\frac{{πx}^{2}}{4} : \frac{{πx}^{2}}{2} = \frac{1}{4} : \frac{1}{2} = 1 : 2$

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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:

Two concentric circles form a ring. The inner and outer circumferences of ring are $\frac{518}{7}$ m and $\frac{352}{7}$ m respectively. Find the width of the ring.

A) 4	B) 5
C) 6	D) 7

Answer & Explanation Answer: A) 4

Explanation:

Let the inner and outer radii be r and R metres.

Then $2 πR = \frac{352}{7} = > R = \frac{352}{7} * \frac{7}{22} * \frac{1}{2} = 8 m$

$2 πR = \frac{528}{7} = > R = \frac{528}{7} * \frac{7}{22} * \frac{1}{2} = 12 m$

=> Width of the ring = (R - r) = (12 - 8) m = 4 m.

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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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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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