WB JEE 2022 | Functions Question 21 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

Let $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ for all $$n \in N$$. Then

$$f(n) > g(n)$$

$$f(n) < g(n)$$

f(n) and g(n) are not comparable.

$$f(n) > g(n)$$ if n be even and $$f(n) < g(n)$$ if n be odd.

WB JEE 2022

MCQ (Single Correct Answer)

-0.5

The maximum value of $$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ is

$$2\sqrt e $$

$$2{e^{{1 \over {\sqrt 2 }}}}$$

$$2{e^{ - {1 \over {\sqrt 2 }}}}$$

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.

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