1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined by $$\mathrm{f}(x)=\frac{\mathrm{e}^{|x|}-\mathrm{e}^{-x}}{\mathrm{e}^x+\mathrm{e}^{-x}}$$, then

A
$$f$$ is both one-one and onto
B
$$f$$ is one-one but not onto
C
$$f$$ is onto but not one-one
D
$$f$$ is neither one-one nor onto
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

For every real number $$x \neq-1$$, let $$\mathrm{f}(x)=\frac{x}{x+1}$$. Write $$\mathrm{f}_1(x)=\mathrm{f}(x)$$ & for $$\mathrm{n} \geq 2, \mathrm{f}_{\mathrm{n}}(x)=\mathrm{f}\left(\mathrm{f}_{\mathrm{n}-1}(x)\right)$$. Then $$\mathrm{f}_1(-2) \cdot \mathrm{f}_2(-2) \ldots . . \mathrm{f}_{\mathrm{n}}(-2)$$ must be

A
$$\frac{2^{\mathrm{n}}}{1.3 .5 \ldots \ldots(2 \mathrm{n}-1)}$$
B
$$1$$
C
$$\frac{1}{2}\binom{2 n}{n}$$
D
$$\binom{2 \mathrm{n}}{\mathrm{n}}$$
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The equation $$2^x+5^x=3^x+4^x$$ has

A
no real solution
B
only one non-zero real solution
C
infinitely many solutions
D
only three non-negative real solutions
4
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

In the interval $$( - 2\pi ,0)$$, the function $$f(x) = \sin \left( {{1 \over {{x^3}}}} \right)$$.

A
never changes sign.
B
changes sign only once.
C
changes sign more than once but finitely many times.
D
changes sign infinitely many times.
WB JEE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12