WB JEE 2011 | Functions Question 11 | Mathematics

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WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The even function of the following is

$$f(x) = {{{a^x} + {a^{ - x}}} \over {{a^x} - {a^{ - x}}}}$$

$$f(x) = {{{a^x} + 1} \over {{a^x} - 1}}$$

$$f(x) = x.\,{{{a^x} - 1} \over {{a^x} + 1}}$$

$$f(x) = {\log _2}(x + \sqrt {{x^2} + 1} )$$

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

If f(x + 2y, x $$-$$ 2y) = xy, then f(x, y) is equal to

$${1 \over 4}xy$$

$${1 \over 4}({x^2} - {y^2})$$

$${1 \over 8}({x^2} - {y^2})$$

$${1 \over 2}({x^2} + {y^2})$$

WB JEE 2024

MCQ (Single Correct Answer)

-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

$$f$$ is both one-one and onto

$$f$$ is one-one but not onto

$$f$$ is onto but not one-one

$$f$$ is neither one-one nor onto

WB JEE 2024

MCQ (Single Correct Answer)

-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

$$\frac{2^{\mathrm{n}}}{1.3 .5 \ldots \ldots(2 \mathrm{n}-1)}$$

$$1$$

$$\frac{1}{2}\binom{2 n}{n}$$

$$\binom{2 \mathrm{n}}{\mathrm{n}}$$

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