EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 2nd April 2017>Q 49

MEDIUM

JEE Main

IMPORTANT

Earn 100

The function $f : R \to [- \frac{1}{2}, \frac{1}{2}]$ defined as $f (x) = \frac{x}{1 + x^{2}},$ is:

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Important Questions on Functions

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 2nd April 2017>Q 50

Let

a, b, c \in R

. If

f (x) = a x^{2} + b x + c

is such that

a + b + c = 3

and

f (x + y) = f (x) + f (y) + x y, \forall x, y \in R

, then

\sum_{n = 1}^{10} f (n)

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 9th April 2017>Q 51

The function

f : N \to I

defined by

f (x) = x - 5 [\frac{x}{5}]

, where

N

is the set of natural numbers and

[x]

denotes the greatest integer less than or equal to

x

, is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 9th April 2016>Q 52

For

x \in R, x \neq 0, x \neq 1,

let

f_{0} (x) = \frac{1}{1 - x}

and

f_{n + 1} (x) = f_{0} (f_{n} (x)), n = 0, 1, 2, \dots . .

Then the value of

f_{100} (3) + f_{1} (\frac{2}{3}) + f_{2} (\frac{3}{2})

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 3rd April 2016>Q 53

If

f (x) + 2 f (\frac{1}{x}) = 3 x, x \neq 0,

and

S = \{x \in R : f (x) = f (- x)\}

, then

S

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 19th April 2014>Q 54

The function $f (x) = |sin 4 x| + |cos 2 x|,$ is a periodic function with a fundamental period

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 19th April 2014>Q 55

Let

f : R \to R

be defined by

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

then

f

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 6th April 2014>Q 56

If

a \in R

and the equation

- 3 (x - [x])^{2} + 2 (x - [x]) + a^{2} = 0

(where

[x]

denotes the greatest integer

\leq

x

) has no integral solution, then all possible values of

a

lie in the interval

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 24 June 2022 Shift 1>Q 57

The domain of

f (x) = \frac{\cos^{- 1} (\frac{x^{2} - 5 x + 6}{x^{2} - 9})}{\log (x^{2} - 3 x + 2)}

is