JEE Main 2021 (Online) 25th July Evening Shift | Functions Question 72 | Mathematics | JEE Main - ExamSIDE.com

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1

JEE Main 2021 (Online) 25th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

If [x] be the greatest integer less than or equal to x,

then $$\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over 2}} \right]} $$ is equal to :

A

0

B

4

C

$$-$$2

D

2

2

JEE Main 2021 (Online) 25th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

Consider function f : A $$\to$$ B and g : B $$\to$$ C (A, B, C $$ \subseteq $$ R) such that (gof)^$$-$$1 exists, then :

A

f and g both are one-one

B

f and g both are onto

C

f is one-one and g is onto

D

f is onto and g is one-one

3

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

4

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)

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