Integrals

JEE Main · Mathematics · 16 past questions

These are the board's own papers. 330 more board questions reprinted in the books we use in class are for signed-in students: sign in.

7 of 16 · show all

1. Q2 2026 2 Apr Shift 1

   If $\alpha=\int_0^{2\sqrt3}\log_2(x^2+4)\,dx+\int_2^4\sqrt{2^x-4}\,dx$, then $\alpha^2$ is equal to…

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2. Q5 2026 4 Apr Shift 1

   Let $f$ be a real polynomial of degree $n$ such that $f(x)=f'(x)f''(x)$, for all $x\in\mathbb{R}$. If…

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3. Q7 2026 4 Apr Shift 2

   The integral $\int_0^1 \cot^{-1}\left(1+x+x^2\right)dx$ is equal to…

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4. Q10 2026 5 Apr Shift 1

   The value of the integral $\int_{\pi/6}^{\pi/3}\left(\frac{4-\operatorname{cosec}^{2}x}{\cos^{4}x}\right)dx$…

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5. Q11 2026 5 Apr Shift 2

   Let $(2^{1-a} + 2^{1+a})$, $f(a)$, $(3^a + 3^{-a})$ be in A.P. and $\alpha$ be the minimum value of $f(a)$.…

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6. Q14 2026 8 Apr Shift 2

   The value of the integral $\int_0^2 \frac{\sqrt{x(x^2+x+1)}}{(\sqrt{x+1})(\sqrt{x^4+x^2+1})}\,dx$ is equal to…

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7. Q16 2026 8 Apr Shift 2

   If…

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