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Day 505: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 22 Jan 2026 S1

    65
    The value of ∫−π2π2(1[x]+4)dx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( \frac{1}{\lbrack x\rbrack + 4} \right)dx, where [•] denotes the greatest integer function, is

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  2. Question 2

    Determinants. Asked once: 14 Jun 2022

    153
    Let the system of linear equations
    x+y+αz=2x + y + \alpha z = 2
    3x+y+z=43x + y + z = 4
    x+2z=1x + 2z = 1
    have a unique solution (x∗,y∗,z∗)\left( x^{*},y^{*},z^{*} \right). If (α,x∗),(y∗,α)\left( \alpha,x^{*} \right),\left( y^{*},\alpha \right) and (x∗,−y∗)\left( x^{*}, -y^{*} \right) are collinear points, then the sum of absolute values of all possible values of α\alpha is :

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  3. Question 3

    Differential Equations. Asked once: 14 Jun 2022

    169
    The slope of normal at any point (x,y),x>0,y>0(x,y),x> 0,y> 0 on the curve y=y(x)y=y(x) is given by x2xy−x2y2−1\frac{x^{2}}{xy-x^{2}y^{2}- 1}. If the curve passes through the point (1,1)(1,1), then e.y(e) is equal to

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  4. Question 4

    Differentiation. Asked once: 28 Jul 2022

    158
    Let x(t)=22cos⁡tsin⁡2tx(t) = 2\sqrt{2}\cos t\sqrt{\sin2t} and y(t)=22sin⁡tsin⁡2t,t∈(0,π2)y(t) = 2\sqrt{2}\sin t\sqrt{\sin2t},t \in\left( 0,\frac{\pi}{2} \right). Then 1+(dydx)2d2ydx2\frac{1 +\left( \frac{dy}{dx} \right)^{2}}{\frac{d^{2}y}{dx^{2}}} at t=π4t =\frac{\pi}{4} is equal to

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  5. Question 5

    Indefinite Integration. Asked once: 15 Apr 2023

    90
    Let f(x)=∫dx(3+4x2)4−3x2,∣x∣<23f(x) = \int\frac{dx}{\left( 3 + 4x^{2} \right)\sqrt{4 - 3x^{2}}},|x| <\frac{2}{\sqrt{3}}. If f(0)=0f(0) = 0 and f(1)=1αβtan⁡−1(αβ),α,β>0f(1) =\frac{1}{\alpha\beta}\tan^{- 1}\left( \frac{\alpha}{\beta} \right),\alpha,\beta > 0, then α2+β2\alpha^{2}+\beta^{2} is equal to