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Day 546: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 8 Apr 2024

    166
    Let ∫αlog⁡e4dxex−1=π6\int_{\alpha}^{\log_{e}4} \frac{dx}{\sqrt{e^{x}- 1}}=\frac{\pi}{6}. Then eαe^{\alpha} and e−αe^{-\alpha} are the roots of the equation :

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  2. Question 2

    Indefinite Integration. Asked once: 2021 Paper 20

    85
    If ∫dx(x2+x+1)2=atan⁡−1(2x+13)+b(2x+1x2+x+1)+C\int\frac{dx}{\left( x^{2}+x+ 1 \right)^{2}}=a\tan^{- 1}\left( \frac{2x+ 1}{\sqrt{3}} \right)+b\left( \frac{2x+ 1}{x^{2}+x+ 1} \right)+C, x>0x > 0 where CC is the constant of integration, then the value of 9(3a+b)9(\sqrt{3}a+b) is equal to

  3. Question 3

    Limits and Continuity. Asked once: 25 Jul 2022

    156
    lim⁡x→π482−(cos⁡x+sin⁡x)72−2sin⁡2x\lim_{x \rightarrow\frac{\pi}{4}} \frac{8\sqrt{2}- (\cos x + \sin x)^{7}}{\sqrt{2}-\sqrt{2}\sin2x} is equal to

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  4. Question 4

    Matrices. Asked once: 1 Feb 2023

    158
    If A=12[13−31]A =\frac{1}{2}\begin{bmatrix} 1 & \sqrt{3} \\ -\sqrt{3} & 1 \end{bmatrix}, then:

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  5. Question 5

    Permutations and Combinations. Asked once: 28 Jul 2022

    81
    Let SS be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A,B,C,D,E}\mathbf{\{ A,B,C,D,E\}} or a number from {1,2,3,4,5}\mathbf{\{ 1,2,3,4,5\}} with the repetition of characters allowed. If the number of passwords in SS whose at least one character is a number from {1,2,3,4,5}\mathbf{\{ 1,2,3,4,5\}} is α×56\alpha \times5^{6}, then α\alpha is equal to