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Day 306: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 20 (same type asked 6 times) See all 6 of this type

    79
    ∫616log⁡ex2log⁡ex2+log⁡e(x2−44x+484)dx\int_{6}^{16} \frac{\log_{e}x^{2}}{\log_{e}x^{2}+\log_{e}\left( x^{2}- 44x+ 484 \right)}dx is equal to:

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  2. Question 2

    Relations and Functions. Asked once: 30 Jan 2024 (same type asked 6 times) See all 6 of this type

    168
    If the domain of the function f(x)=log⁡ef(x) =\log_{e} (2x+34x2+x−3)+cos⁡−1(2x−1x+2)\left( \frac{2x + 3}{4x^{2}+ x - 3} \right)+\cos^{- 1}\left( \frac{2x - 1}{x + 2} \right) is  (α,β]\ (\alpha,\beta\rbrack, then the value of 5β−4α5\beta - 4\alpha is equal to

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  3. Question 3

    Straight Lines. Asked once: 22 Jan 2025 (same type asked 6 times) See all 6 of this type

    53
    Let the triangle PQRPQR be the image of the triangle with vertices (1,3),(3,1)(1,3),(3,1) and (2,4)(2,4) in the line x+2y=2x + 2y = 2. If the centroid of △PQR\bigtriangleup PQR is the point (α,β)(\alpha,\beta), then 15(α−β)15(\alpha - \beta) is equal to :

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  4. Question 4

    Permutations and Combinations. Asked once: 25 Jun 2022 (same type asked 6 times) See all 6 of this type

    82
    The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is

  5. Question 5

    Inverse Trigonometric Functions. Asked once: 29 Jun 2022 (same type asked 6 times) See all 6 of this type

    75
    The domain of the function cos⁡−1(2sin⁡−1(14x2−1)π)\cos^{- 1}\left( \frac{2\sin^{- 1}\left( \frac{1}{4x^{2}- 1} \right)}{\pi} \right) is:

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