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Day 519: JEE Mains Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 8 Apr 2023

    61
    Let I(x)=∫(x+1)x(1+xex)2 dx, x>0I(x) = \int\frac{(x+1)}{x(1+xe^{x})^{2}}\,dx,\ x>0. If lim⁡x→∞I(x)=0\lim_{x\to\infty}I(x)=0, then I(1)I(1) is equal to

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  2. Question 2

    Inverse Trigonometric Functions. Asked once: 2021 Paper 7

    72
    The sum of possible values of xx for tan⁡−1(x+1)+cot⁡−1(1x−1)=tan⁡−1(831)\tan^{- 1}(x+ 1) +\cot^{- 1}\left( \frac{1}{x- 1} \right)=\tan^{- 1}\left( \frac{8}{31} \right) is :

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  3. Question 3

    Limits and Continuity. Asked once: 31 Jan 2023

    156
    lim⁡x→∞(3x+1+3x−1)6+(3x+1−3x−1)6(x+x2−1)6+(x−x2−1)6x3\lim_{x \rightarrow \infty} \frac{(\sqrt{3x + 1}+\sqrt{3x - 1})^{6}+ (\sqrt{3x + 1}-\sqrt{3x - 1})^{6}}{\left( x +\sqrt{x^{2}- 1} \right)^{6}+\left( x -\sqrt{x^{2}- 1} \right)^{6}}x^{3}

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  4. Question 4

    Matrices. Asked once: 30 Jan 2024

    170
    Let R=(x000y000z)R =\begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix} be a non-zero 3×33 \times 3 matrix, where xsinθ=ysin(θ+2π3)=zsin(θ+4π3)xsin\theta = ysin\left( \theta +\frac{2\pi}{3} \right)= zsin\left( \theta +\frac{4\pi}{3} \right) ≠0,θ∈(0,2π)\neq 0,\theta \in (0,2\pi). For a square matrix MM, let trace (M) denote the sum of all the diagonal entries of M. Then, among the statements: (I) Trace(R)=0Trace(R) = 0 (II) If trace (adj(adj(R))=0(adj(adj(R)) = 0, then RR has exactly one non-zero entry.

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  5. Question 5

    Permutations and Combinations. Asked once: 15 Apr 2023

    82
    A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is