WB JEE 2011 | Functions Question 6 | Mathematics

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 2023

MCQ (Single Correct Answer)

-0.5

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

never changes sign.

changes sign only once.

changes sign more than once but finitely many times.

changes sign infinitely many times.

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

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

x < 1

2 < x

1 $$\le$$ x $$\le$$ 2

2 < x < 3

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