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Day 110: JEE Mains Maths

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

  1. Question 1

    Definite Integration. This type asked 2 times: 11 Apr 2023, 9 Apr 2024. This one: 9 Apr 2024 See all 2 of this type

    168
    The value of the integral ∫−12log⁡e(x+x2+1)dx\int_{- 1}^{2} \log_{e}\left( x+\sqrt{x^{2}+ 1} \right)dx is:

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  2. Question 2

    Differentiation. This type asked 2 times: 2021 Paper 20, 9 Apr 2024. This one: 9 Apr 2024 See all 2 of this type

    164
    If log⁡ey=3sin⁡−1x\log_{e}y= 3\sin^{- 1}x, then (1−x2)y′′−xy′(1 -x^{2})y^{''}-xy^{'} at x=12x=\frac{1}{2} is equal to :

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  3. Question 3

    Indefinite Integration. This type asked 2 times: 2021 Paper 21, 9 Apr 2024. This one: 9 Apr 2024 See all 2 of this type

    67
    Let ∫2−tan⁡x3+tan⁡xdx=12(αx+log⁡e∣βsin⁡x+γcos⁡x∣)+C\int\frac{2 - \tan x}{3 + \tan x}dx =\frac{1}{2}\left( \alpha x +\log_{e}|\beta \sin x + \gamma \cos x| \right)+ C , where CC is the constant of integration. Then α+γβ\alpha +\frac{\gamma}{\beta} is equal to:

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  4. Question 4

    Application of Derivatives. This type asked 2 times: 29 Jan 2024, 8 Apr 2024. This one: 8 Apr 2024 See all 2 of this type

    65
    The number of critical points of the function f(x)=(x−2)2/3(2x+1)f(x) = (x- 2)^{2/3}(2x+ 1) is:

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  5. Question 5

    Differential Equations. This type asked 2 times: 11 Apr 2023, 8 Apr 2024. This one: 8 Apr 2024 See all 2 of this type

    179
    Let α∣x∣=∣y∣exy−β,α,β∈N\alpha|x| = |y|e^{xy - \beta},\alpha,\beta \in N be the solution of the differential equation xdy−ydx+xy(xdy+ydx)=0xdy - ydx + xy(xdy + ydx) = 0, y(1)=2y(1) = 2. Then α+β\alpha + \beta is equal to