WB JEE 2022 | Functions Question 23 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-0.5

$$f:X \to R,X = \{ x|0 < x < 1\} $$ is defined as $$f(x) = {{2x - 1} \over {1 - |2x - 1|}}$$. Then

f is only injective

f is only surjective

f is bijective

f is neither injective nor surjective

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Let f : R $$\to$$ R be given by f(x) = | x² $$-$$ 1 |, x$$\in$$R. Then,

f has a local minimum at x = $$\pm$$ 1 but no local maximum.

f has a local minimum at x = 0 but no local minimum.

f has a local minima at x = $$\pm$$ 1 and a local maxima at x = 0.

f has neither a local maxima nor a local minima at any point.

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

f(x) is real valued function such that 2f(x) + 3f($$-$$x) = 15 $$-$$ 4x for all x$$\in$$R. Then f(2) =

$$-$$15

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Consider the functions f₁(x) = x, f₂(x) = 2 + log_e x, x > 0. The graphs of the functions intersect

once in (0, 1) but never in (1, $$\infty$$)

once in (0, 1) and once in (e², $$\infty$$)

once in (0, 1) and once in (e, e²)

more than twice in (0, $$\infty$$)

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