EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 26 August 2021 Shift 2>Q 1

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JEE Main

IMPORTANT

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The domain of the function ${cosec}^{- 1} (\frac{1 + x}{x})$ 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 - 20 July 2021 Shift 1>Q 2

Let

[x]

denote the greatest integer

\leq x

, where

x \in R

. If the domain of the real valued function

f (x) = \sqrt{\frac{|[x]| - 2}{|[x]| - 3}}

is

(- \infty, a) \cup [b, c) \cup [4, \infty), a < b < c

, then the value of

a + b + c

is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 20 July 2021 Shift 2>Q 3

Let

f : R - \{\frac{α}{6}\} \to R

be defined by

f (x) = (\frac{5 x + 3}{6 x - α})

. Then the value of

α

for which

(f o f) (x) = x

, for all

x \in R - \{\frac{α}{6}\},

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 22 July 2021 Shift 1>Q 4

Let

[x]

denote the greatest integer less than or equal to

x .

Then, the values of

x \in R

satisfying the equation

{[e^{x}]}^{2} + [e^{x} + 1] - 3 = 0

lie in the interval:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 22 July 2021 Shift 1>Q 5

If the domain of the function

f (x) = \frac{\cos^{- 1} \sqrt{x^{2} - x + 1}}{\sqrt{\sin^{- 1} (\frac{2 x - 1}{2})}}

is the interval

(α, β],

then

α + β

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 July 2021 Shift 1>Q 6

Let $g : N \to N$ be defined as

$g (3 n + 1) = 3 n + 2$

$g (3 n + 2) = 3 n + 3$

$g (3 n + 3) = 3 n + 1$ , for all $n \geq 0$

Then which of the following statements is true ?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 July 2021 Shift 2>Q 7

Consider function

f : A \to B

and

g : B \to C (A, B, C \subseteq R)

such that

{(g o f)}^{- 1}

exists, then:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 27 July 2021 Shift 1>Q 8

Let

S = \{1, 2, 3, 4, 5, 6, 7\} .

Then the number of possible functions

f : S \to S

such that

f (m \cdot n) = f (m) \cdot f (n)

for every

m, n \in S

and

m \cdot n \in S

, is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 27 July 2021 Shift 2>Q 9

Let

f : R \to R

be defined as

f (x + y) + f (x - y) = 2 f (x) f (y), f (\frac{1}{2}) = - 1 .

Then the value of

\sum_{k = 1}^{20} \frac{1}{\sin (k) \sin (k + f (k))}

is equal to :