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Day 482: JEE Mains Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 8 Apr 2024

    72
    Let I(x)=∫6sin⁡2x(1−cot⁡x)2dxI(x) = \int\frac{6}{\sin^{2}x(1 - \cot x)^{2}}dx. If I(0)=3I(0) = 3, then I(π12)I\left( \frac{\pi}{12} \right) is equal to:

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  2. Question 2

    Inverse Trigonometric Functions. Asked once: 1 Feb 2023

    64
    Let SS be the set of all solutions of the equation cos⁡−1(2x)−2cos⁡−1(1−x2)=π,x∈[−12,12]\cos^{- 1}(2x) - 2\cos^{- 1}\left( \sqrt{1 -x^{2}} \right)= \pi,x \in\left\lbrack -\frac{1}{2},\frac{1}{2} \right\rbrack. Then ∑x∈S2sin⁡−1(x2−1)\sum_{x \in S} 2\sin^{- 1}\left( x^{2}- 1 \right) is equal to

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  3. Question 3

    Limits and Continuity. Asked once: 9 Apr 2024

    151
    Limx→0e−(1+2x)12xxLim_{x \rightarrow 0}\frac{e - (1 + 2x)^{\frac{1}{2x}}}{x} is equal to:

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  4. Question 4

    Matrices. Asked once: 4 Apr 2025

    72
    Let A=[cos⁡θ0−sin⁡θ010sin⁡θ0cos⁡θ]A = \begin{bmatrix} \cos\theta & 0 & - \sin\theta \\ 0 & 1 & 0 \\ \sin\theta & 0 & \cos\theta \end{bmatrix}. If for some θ∈(0,π)\theta \in (0,\pi), A2=ATA^{2} = A^{T}, then the sum of the diagonal elements of the matrix (A+I)3+(A−I)3−6 A(A + I)^{3} + (A - I)^{3} - 6\text{ }A is equal to.

  5. Question 5

    Permutations and Combinations. Asked once: 24 Jan 2025

    75
    Let S={p1,p2,…,p10}S=\left\{p_{1},p_{2},\ldots,p_{10}\right\} be the set of first ten prime numbers. Let A=S∪PA=S\cup P, where PP is the set of all possible products of distinct elements of SS. Then the number of all ordered pairs (x,y)(x,y), x∈Sx\in S, y∈Ay\in A, such that xx divides yy, is