WB JEE 2024 | Functions Question 17 | Mathematics

WB JEE 2024

MCQ (More than One Correct Answer)

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Choose the correct statement :

$$x+\sin 2 x$$ is a periodic function

$$x+\sin 2 x$$ is not a periodic function

$$\cos (\sqrt{x}+1)$$ is a periodic function

$$\cos (\sqrt{x}+1)$$ is not a periodic function

WB JEE 2022

MCQ (More than One Correct Answer)

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

f(x) = 0 has at least one real root

f(x) = 0 has no real root

f(x) = 0 has at least one positive root

f(x) = 0 has at least one negative root

WB JEE 2022

MCQ (More than One Correct Answer)

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

p(x) has at least two real roots

p(x) has only one positive real root

p(x) may have negative real root

p(x) has infinitely many real roots

WB JEE 2021

MCQ (More than One Correct Answer)

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Let f and g be periodic functions with the periods T₁ and T₂ respectively. Then f + g is

periodic with period T₁ + T₂

non periodic

periodic with the period T₁

periodic when T₁ = T₂

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