1
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
$$\binom{2 \mathrm{n}}{\mathrm{n}}$$
2
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
3
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
4
WB JEE 2022
+1
-0.25

Domain of $$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}}$$ is

A
x < 1
B
2 < x
C
1 $$\le$$ x $$\le$$ 2
D
2 < x < 3
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