JEE Main 2021 (Online) 25th July Morning Shift | Functions Question 74 | Mathematics | JEE Main - ExamSIDE.com

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1

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

+4

-1

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

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

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

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

Then which of the following statements is true?

A

There exists an onto function f : N $$\to$$ N such that fog = f

B

There exists a one-one function f : N $$\to$$ N such that fog = f

C

gogog = g

D

There exists a function : f : N $$\to$$ N such that gof = f

2

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

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 :

A

$$\left[ {0,{1 \over e}} \right)$$

B

[log_e2, log_e3)

C

[1, e)

D

[0, log_e2)

3

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

The number of solutions of sin⁷x + cos⁷x = 1, x$$\in$$ [0, 4$$\pi$$] is equal to

A

11

B

7

C

5

D

9

4

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

If the domain of the function $$f(x) = {{{{\cos }^{ - 1}}\sqrt {{x^2} - x + 1} } \over {\sqrt {{{\sin }^{ - 1}}\left( {{{2x - 1} \over 2}} \right)} }}$$ is the interval ($$\alpha$$, $$\beta$$], then $$\alpha$$ + $$\beta$$ is equal to :

A

$${3 \over 2}$$

B

2

C

$${1 \over 2}$$

D

1

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