EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 9th January 2019 Shift 2>Q 40

EASY

JEE Main

IMPORTANT

Earn 100

Let $A =$ { $x \in R : x$ is not a positive integer} $.$ Define a function $f : A \to R$ as $f (x) = \frac{2 x}{x - 1}$ , then $f$ is:

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Important Questions on Functions

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 8th April 2019 Shift 1>Q 41

If

f (x) = \log_{e} (\frac{1 - x}{1 + x}), |x| < 1,

then

f (\frac{2 x}{1 + x^{2}})

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 8th April 2019 Shift 2>Q 42

Let

f (x) = a^{x} (a > 0)

be written as

f (x) = f_{1} (x) + f_{2} (x),

where

f_{1} (x)

is an even function and

f_{2} (x)

is an odd function. Then

f_{1} (x + y) + f_{1} (x - y)

equals:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 10th April 2019 Shift 1>Q 43

Let

f (x) = x^{2}, x \in R

. For any

A \subseteq R,

define

g (A) = {x \in R : f (x) \in A}

. If

S = [0, 4]

, then which one of the following statements is not true?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 10th January 2019 Shift 1>Q 44

Let,

f : R \to R

be a function such that

f (x) = x^{3} + x^{2} f^{'} (1) + x f^{"} (2) + f^{'''} (3), \forall x \in R .

Then

f (2)

equals

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 10th January 2019 Shift 2>Q 45

Let

N

be the set of natural numbers and two functions

f

and

g

be defined as

f, g : N \to N

such that

f (n) = \{\begin{matrix} \frac{n + 1}{2}, i f n i s o d d \\ \frac{n}{2}, i f n i s e v e n \end{matrix}

and

g (n) = n - {(- 1)}^{n} .

Then

f o g

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 12th April 2019 Shift 1>Q 46

For

x \in R,

Let

[x]

denotes the greatest integer

\leq x,

then the sum of the series

[- \frac{1}{3}] + [- \frac{1}{3} - \frac{1}{100}] + [- \frac{1}{3} - \frac{2}{100}] + . . . . . + [- \frac{1}{3} - \frac{99}{100}]

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 12th April 2019 Shift 1>Q 47

For

x ϵ (0, \frac{3}{2}),

let

f (x) = \sqrt{x}, g (x) = t a n x

and

h (x) = \frac{1 - x^{2}}{1 + x^{2}}

. If

ϕ (x) = (h o f) o g) (x),

then

ϕ (\frac{π}{3})

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 12th April 2019 Shift 2>Q 48

If

[x]

denotes the greatest integer

\leq x,

then the system of linear equations

[s i n θ] x + [- c o s θ] y = 0

,

[c o t θ] x + y = 0