1
WB JEE 2024
+1
-0.25

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
+1
-0.25

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
+1
-0.25

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
+2
-0.5

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