EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 24 January 2023 Shift 1>Q 75

HARD

JEE Main

IMPORTANT

Earn 100

The equation $x^{2} - 4 x + [x] + 3 = x [x]$ , where $[x]$ denotes the greatest integer function, has:

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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 - 24 January 2023 Shift 2>Q 76

Let

f (x)

be a function such that

f (x + y) = f (x) \cdot f (y)

for all

x, y \in N

, If

f (1) = 3

and

\sum_{k = 1}^{n} f (k) = 3279

, then the value of

n

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 24 January 2023 Shift 2>Q 77

If

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

,

x \in R

, then

f (\frac{1}{2023}) + f (\frac{2}{2023}) + f (\frac{3}{2023}) . . . . . . . . . f (\frac{2022}{2023})

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 January 2023 Shift 1>Q 78

For some

a, b, c \in ℕ

, let

f (x) = a x - 3

and

g (x) = x^{b} + c, x \in ℝ

. If

{(f o g)}^{- 1} (x) = {(\frac{x - 7}{2})}^{\frac{1}{3}}

, then

(f \circ g) (a c) + (g \circ f) (b)

is equal to _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 January 2023 Shift 2>Q 79

Let

f (x) = 2 x^{n} + λ, λ \in ℝ, n \in ℕ

, and

f (4) = 133

,

f (5) = 255

. Then the sum of all the positive integer divisors of

(f (3) - f (2))

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 January 2023 Shift 2>Q 80

The number of functions

f : {1, 2, 3, 4} \to {a \in ℤ : | a | \leq 8}

satisfying

f (n) + \frac{1}{n} f (n + 1) = 1, \forall n \in {1, 2, 3}

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 January 2023 Shift 2>Q 81

Let

f : ℝ \to ℝ

be a function defined by

f (x) = \log_{\sqrt{m}} \{\sqrt{2} (\sin x - \cos x) + m - 2\}

, for some

m

, such that the range of

f

is

[0, 2]

. Then the value of

m

is _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 29 January 2023 Shift 1>Q 82

The domain of

f (x) = \frac{\log_{(x + 1)} (x - 2)}{e^{2 \log_{e} x} - (2 x + 3)}, x \in R

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 29 January 2023 Shift 1>Q 83

Let

f : R \to R

be a function such that

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

. Then