1
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0

The function $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ defined by $$\mathrm{f}(x)=\mathrm{e}^x+\mathrm{e}^{-x}$$ is :

A
one-one
B
onto
C
bijective
D
not bijective
2
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0

Choose the correct statement :

A
$$x+\sin 2 x$$ is a periodic function
B
$$x+\sin 2 x$$ is not a periodic function
C
$$\cos (\sqrt{x}+1)$$ is a periodic function
D
$$\cos (\sqrt{x}+1)$$ is not a periodic function
3
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0

Let $$f(x) = {x^2} + x\sin x - \cos x$$. Then

A
f(x) = 0 has at least one real root
B
f(x) = 0 has no real root
C
f(x) = 0 has at least one positive root
D
f(x) = 0 has at least one negative root
4
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0

Let p(x) be a polynomial with real co-efficient, p(0) = 1 and p'(x) > 0 for all x $$\in$$ R. Then

A
p(x) has at least two real roots
B
p(x) has only one positive real root
C
p(x) may have negative real root
D
p(x) has infinitely many real roots
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