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 2026

MCQ (Single Correct Answer)

-0.25

Let $A=[a, \infty)$ denotes the domain, then $f:(a, \infty) \rightarrow B$, which is defined by $f(x)=2 x^3-3 x^2+6$ will have an inverse for the smallest real value of ' $a$ ' if

$\mathrm{a}=0, \mathrm{~B}=[6, \infty)$

$\mathrm{a}=2, \mathrm{~B}=[10, \infty)$

$\mathrm{a}=1, \mathrm{~B}=[5, \infty)$

$\mathrm{a}=-1, \mathrm{~B}=[5, \infty)$

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

Number of elements in the range set of $f(x)=\left[\frac{x}{15}\right]\left[-\frac{15}{x}\right]$, for all $x \in(0,90$ ); (where [.] denotes the greatest integer function) is

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