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Day 531: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 29 Jan 2025

    146
    If 24∫0π4(sin⁡∣4x−π12∣+[2sin⁡x])dx=2π+α24\int_{0}^{\frac{\pi}{4}} \left( \sin\left| 4x-\frac{\pi}{12} \right|+ \lbrack 2\sin x\rbrack \right)dx= 2\pi+\alpha, where [.] denotes the greatest integer function, then α\alpha is equal to  _____\ \_\_\_\_\_ .

  2. Question 2

    Determinants. Asked once: 2021 Paper 8

    81
    If 1,log⁡10(4x−2)1,\log_{10}\left( 4^{x}- 2 \right) and log⁡10(4x+185)\log_{10}\left( 4^{x}+\frac{18}{5} \right) are in arithmetic progression for a real number xx, then the value of the determinant ∣2(x−12)x−1x210xx10∣\left| \begin{matrix} 2\left( x -\frac{1}{2} \right) & x - 1 & x^{2} \\ 1 & 0 & x \\ x & 1 & 0 \end{matrix} \right| is equal to:

  3. Question 3

    Differentiation. Asked once: 2021 Paper 6

    76
    Let f:S→Sf:S \rightarrow S where S=(0,∞)S = (0,\infty) be a twice differentiable function such that f(x+1)=xf(x)f(x + 1) = xf(x). If g:S→Rg:S \rightarrow R be defined as g(x)=log⁡ef(x)g(x) =\log_{e}f(x), then the value of ∣g′′(5)−g′′(1)∣\left| g^{''}(5) -g^{''}(1) \right| is equal to:

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  4. Question 4

    Indefinite Integration. Asked once: 29 Jul 2022

    158
    For I(x)=∫sec⁡2x−2022sin⁡2022xdxI(x) = \int\frac{\sec^{2}x- 2022}{\sin^{2022}x}dx, if I(π4)=21011I\left( \frac{\pi}{4} \right)=2^{1011}, then

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  5. Question 5

    Limits and Continuity. Asked once: 25 Jan 2023

    68
    The value of lim⁡n→∞1+2−3+4+5−6+⋯…+(3n−2)+(3n−1)−3n2n4+4n+3−n4+5n+4\lim_{n \rightarrow \infty} \frac{1 + 2 - 3 + 4 + 5 - 6 + \cdots\ldots + (3n - 2) + (3n - 1) - 3n}{\sqrt{2n^{4}+ 4n + 3}-\sqrt{n^{4}+ 5n + 4}} is :

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