20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 61

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IMPORTANT

Earn 100

The area of a circle is proportional to the square of its radius. A small circle of radius $3$ $cm$ is drawn within a larger circle of radius $5$ $cm$ . Find the ratio of the area of the annual zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).

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20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 62

The average age of Ram and his two children is

17

years and the average age of Ram's wife and the same children is

16

years. If the age of Ram is

33

years, the age of his wife is:

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20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 63

A person bought

76

cows and sold

20

cows at

15 %

profit,

40

cows at

19 %

profit and remaining

16

cows at

25 %

profit and get a profit of

₹ 6, 750

as a whole. The cost price of each cow is:

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IMPORTANT

20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 64

\frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}}

is -----

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IMPORTANT

20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 65

Two circles with centres $P$ and $Q$ intersect at $B$ and $C$ . $A, D$ are points on the circles with centres $P$ and $Q$ respectively. Such that $A, C, D$ are collinear. Exterior angle $∠ A P B = 130 °$ . If interior angle $∠ B Q D = x$ , then the value of $x$ is:

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20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 66

I

and

O

are respectively the in-centre and circum center of a

△ A B C

. The line

A I

produced intersect the circumcircle of

△ A B C

at the point

D

. If

∠ A B C = x °

,

∠ B I D = y^{°}

and

∠ B O D = z °

, then

\frac{z + x}{y}

is equal to:

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20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 67

A B C D

is a parallelogram

B C

is produced to

Q

such that

B C = C Q

. Then find out the right option.

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IMPORTANT

20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 68

If

\tan θ + \cot θ = 2

, then the value of

(\tan^{n} θ + \cot^{n} θ), θ (0 ° < θ < 90 °), n

is integer is ------

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20 Practice Sets ESIC Upper Division Clerk Preliminary Exam>Chapter 1 - Practice Set>Quantitative Aptitude>Q 69

If

\frac{\sin θ}{x} = \frac{\cos θ}{y}

, then

\sin θ - \cos θ

is equal to ----