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Day 374: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Limits and Continuity. Asked once: 2021 Paper 4 (same type asked 6 times) See all 6 of this type

    70
    lim⁡n→∞[1n+n(n+1)2+n(n+2)2+……+n(2n−1)2]\lim_{n\rightarrow \infty} \left\lbrack \frac{1}{n}+\frac{n}{(n+ 1)^{2}}+\frac{n}{(n+ 2)^{2}}+ \ldots\ldots +\frac{n}{(2n- 1)^{2}} \right\rbrack is equal to:

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  2. Question 2

    Definite Integration. Asked once: 2021 Paper 6 (same type asked 6 times) See all 6 of this type

    65
    Consider the integral
    I=∫010[x]e[x]ex−1dxI=\int_{0}^{10} \frac{\lbrack x\rbrack e^{\lbrack x\rbrack}}{e^{x- 1}}dx
    where [x]\lbrack x\rbrack denotes the greatest integer less than or equal to xx. Then the value of II is equal to:

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  3. Question 3

    Application of Integrals. Asked once: 14 Jun 2022 (same type asked 5 times) See all 5 of this type

    176
    The area (in sq. units) of the region enclosed between the parabola y2=2xy^{2}= 2x and the line x+y=4x+y= 4 is

  4. Question 4

    Complex Numbers. Asked once: 2021 Paper 20 (same type asked 5 times) See all 5 of this type

    67
    If S={z∈C:z−iz+2i∈R}S=\left\{ z\in\mathbb{C}:\frac{z -i}{z + 2i}\in\mathbb{R} \right\}, then:

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  5. Question 5

    Differential Equations. Asked once: 21 Jan 2026 S2 (same type asked 41 times) See all 41 of this type

    66
    Let y=y(x)y = y(x) be the solution of the differential equation secxdydx−2y=2+3sin⁡x,x∈(−π2,π2)secx\frac{dy}{dx}- 2y = 2 + 3\sin x,x \in\left( -\frac{\pi}{2},\frac{\pi}{2} \right), y(0)=−74y(0) = -\frac{7}{4}. Then y(π6)y\left( \frac{\pi}{6} \right) is equal to:

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