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Day 209: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 11 Apr 2023 (same type asked 2 times) See all 2 of this type

    61
    The value of the integral ∫−log⁡e2log⁡e2ex(log⁡e(ex+1+e2x))dx\int_{-\log_{e}2}^{\log_{e}2} e^{x}\left( \log_{e}\left( e^{x}+\sqrt{1 +e^{2x}} \right) \right)dx is equal to

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  2. Question 2

    Differentiation. Asked once: 2021 Paper 20 (same type asked 2 times) See all 2 of this type

    90
    If y1/4+y−1/4=2xy^{1/4}+y^{- 1/4}= 2x, and (x2−1)d2ydx2+αxdydx+βy=0\left( x^{2}- 1 \right)\frac{d^{2}y}{dx^{2}}+\alpha x\frac{dy}{dx}+\beta y= 0, then ∣α−β∣|\alpha-\beta| is equal to

  3. Question 3

    Indefinite Integration. Asked once: 2021 Paper 21 (same type asked 2 times) See all 2 of this type

    90
    If ∫2ex+3e−x4ex+7e−xdx=114(ux+vlog⁡e(4ex+7e−x))+C\int\frac{2e^{x}+ 3e^{-x}}{4e^{x}+ 7e^{-x}}dx=\frac{1}{14}\left( ux+v\log_{e}\left( 4e^{x}+ 7e^{-x} \right) \right)+C, where CC is a constant of integration, then u+vu+v is equal to

  4. Question 4

    Application of Derivatives. Asked once: 29 Jan 2024 (same type asked 2 times) See all 2 of this type

    155
    The function f(x)=2x+3(x)23,x∈Rf(x) = 2x + 3(x)^{\frac{2}{3}},x \in R, has

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  5. Question 5

    Differential Equations. Asked once: 11 Apr 2023 (same type asked 2 times) See all 2 of this type

    75
    Let y=y(x)y = y(x) be a solution curve of the differential equation, (1−x2y2)dx=ydx+xdy\left( 1 -x^{2}y^{2} \right)dx = ydx + xdy. If the line x=1x = 1 intersects the curve y=y(x)y = y(x) at y=2y = 2 and the line x=2x = 2 intersects the curve y=y(x)y = y(x) at y=αy = \alpha, then a value of α\alpha is

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