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Day 563: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 1 Feb 2024

    154
    The value of ∫01(2x3−3x2−x+1)13dx\int_{0}^{1} \left( 2x^{3}- 3x^{2}- x + 1 \right)^{\frac{1}{3}}dx is equal to:

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  2. Question 2

    Indefinite Integration. Asked once: 2021 Paper 1

    74
    If ∫cos⁡x−sin⁡x8−sin⁡2xdx=asin⁡−1(sin⁡x+cos⁡xb)+c\int\frac{\cos x- \sin x}{\sqrt{8 - \sin2x}}dx=a\sin^{- 1}\left( \frac{\sin x+ \cos x}{b} \right)+c, where cc is a constant of integration, then the ordered pair (a,b)(a,b) is equal to :

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  3. Question 3

    Limits and Continuity. Asked once: 26 Jun 2022

    66
     lim⁡x→12sin⁡(cos⁡−1x)−x1−tan⁡(cos⁡−1x)\ \lim_{x\rightarrow\frac{1}{\sqrt{2}}} \frac{\sin\left( \cos^{- 1}x \right)-x}{1 - \tan\left( \cos^{- 1}x \right)} is equal to:

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  4. Question 4

    Matrices. Asked once: 29 Jul 2022

    63
    Let AA and BB be two 3×33 \times 3 non-zero real matrices such that ABAB is a zero matrix. Then

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  5. Question 5

    Permutations and Combinations. Asked once: 27 Jun 2022

    84
    The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is