UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 72

MEDIUM

UPSC CDS

IMPORTANT

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The perpendicular dropped from a vertex of a right-angled triangle upon the hypotenuse divides it into two segments of lengths $9$ units and $16$ units respectively. What is the length of the perpendicular?

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Important Questions on UPSC CDS (I) Previous Year Paper 2022

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 73

If $43^{x} \times 47^{y} = {(2021)}^{2}, x \neq 0, y \neq 0,$ then what is the value of the following?

$\frac{4 xy + x + y}{2 xy - x - y}$

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 74

Let $a, b, c, d$ be positive integers. If

$\frac{1}{a + \frac{1}{b + \frac{1}{c + \frac{1}{d}}}} = \frac{17}{60}$

then what is the product of $a, b, c, d$ ?

MEDIUM

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 75

If

x^{2} = 17 x + y

and

y^{2} = x + 17 y, x \neq y

, then what is the value of

\sqrt{x^{2} + y^{2} + 1 ?}

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 76

What is the least value of

n

if

194480 + n = m^{4}

, Where

m

and

n

are natural numbers?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 77

If

\frac{x - y}{x \sqrt{y} + y \sqrt{x}} = \frac{1}{x}; (x > 0, y > 0)

then what is the value of

\frac{x}{y}

?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 78

Three congruent circles touches each other (each of radius

4 cm

). What is the area of the portion included between them?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 79

A car travels from

A

to

B

at a speed of

40 km / hr

, travels back from

B

to

A

at a speed of

30 km / hr

and again goes from

A

to

B

at a speed of

60 km / hr

. What is the average speed of the car?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 11 - UPSC CDS (I) Previous Year Paper 2022>Elementary Mathematics>Q 80

What is the smallest natural number from the following which must be subtracted from

9410

to make the remaining number a perfect square?