If a b + c = b c + a = c a + b , then which one of the following statements is correct?

Each fraction is equal to 1 2 only.

Each fraction is equal to 1 or - 1

Each fraction is equal to 1 2 or 1

Each fraction is equal to 1 2 or - 1

E M B I B E

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 56

EASY

UPSC CDS

IMPORTANT

Earn 100

There are two parallel streets each directed North to South. A person in the first street travelling from South to North wishes to take the second street which is on his right side. At some place, he makes a $150 °$ turn to the right, and he travels for $15 minutes$ at the speed of $20 km / hr$ . After that he takes a left turn of $60 °$ and travels for $20 minutes$ at the speed of $30 km / hr$ in order to meet the second street. What is the distance between the two streets?

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Important Questions on UPSC CDS (I) Previous Year Paper 2019

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 57

If

3 \tan θ = c o t θ

, where

0 \leq θ \leq \frac{π}{2}

, then what is the value of

θ

?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 58

What is the value of

\sin^{2} 25 ° + \sin^{2} 65 °

?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 59

What is the value of

\sin^{6} θ + \cos^{6} θ + 3 \sin^{2} θ \cos^{2} θ - 1

?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 60

Consider the following for real number $α, β, γ$ and $δ$ :

$1 . \sec α = \frac{1}{4}$

$2 . \tan β = 20$

$3 . cosec γ = \frac{1}{2}$

$4 . \cos δ = 2$

How many of the above statements are not possible?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 61

Consider the following grouped frequency distribution:

$X$	$F$
$0 - 10$	$8$
$10 - 20$	$12$
$20 - 30$	$10$
$30 - 40$	$P$
$40 - 50$	$9$

If the mean of the above data is $25.2$ , then what is the value of $P$ ?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 62

Consider the following frequency distribution:

$x$	$f$
$8$	$6$
$5$	$4$
$6$	$5$
$10$	$8$
$9$	$9$
$4$	$6$
$7$	$4$

What is the median of the distribution?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 63

The average of

50

consecutive natural numbers is

x

. What will be the new average when the next four numbers are also included?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 5 - UPSC CDS (I) Previous Year Paper 2019>Elementary Mathematics>Q 64

Consider two-digit numbers which remain the same when the digits interchange their position. What is the average of such at two-digit number?

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