Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 28

EASY

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IMPORTANT

Earn 100

Let $[x]$ denote the greatest integer function. What are the number of solutions of the equation $x^{2} - 4 x + [x] = 0$ in the interval $[0, 2]$ ?

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Important Questions on Solved Paper 2018 (I)

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 29

A survey of

850

students in a University yields that

680

students like music and

215

like dance. What is the least number of students who like both music and dance?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 30

What is the sum of all two-digit numbers, which when divided by

3

leave

2

as the remainder?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 31

If

0 < a < 1,

the value of

\log_{10} a

is negative. This is justified by

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 32

The third term of a

GP

is

3 .

What is the product of the first five terms?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 33

If

x, \frac{3}{2}, z

are in

AP; x, 3, z

are in

GP;

then which one of the following will be in

HP ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 34

What is the value of the sum

\sum_{n = 2}^{11} (i^{n} + i^{n + 1}),

where

i = \sqrt{- 1} ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 35

If

\sin x = \frac{1}{\sqrt{5}}

,

\sin y = \frac{1}{\sqrt{10}}

, where

0 < x < \frac{π}{2}, 0 < y < \frac{π}{2}

. Then what is

(x + y)

equal to?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 2 - Solved Paper 2018 (I)>PAPER I : Mathematics>Q 36

What is

\frac{\sin 5 x - \sin 3 x}{\cos 5 x + \cos 3 x}

equal to ?