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Day 308: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 30 Jan 2023 (same type asked 6 times) See all 6 of this type

    90
    lim⁡x→048x4∫0xt3t6+1dt\lim_{x \rightarrow 0} \frac{48}{x^{4}}\int_{0}^{x} \frac{t^{3}}{t^{6}+ 1}dt is equal to

  2. Question 2

    Application of Derivatives. Asked once: 2021 Paper 6 (same type asked 6 times) See all 6 of this type

    75
    Let ff be a real valued function, defined on R−{−1,1}\mathbf{R - \{ - 1,1\}} and given by f(x)=3log⁡e∣x−1x+1∣−2x−1f(x) = 3\log_{e}\left| \frac{x - 1}{x + 1} \right|-\frac{2}{x - 1}. Then in which of the following intervals, function f(x)f(x) is increasing?

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  3. Question 3

    Vector Algebra. Asked once: 29 Jan 2023 (same type asked 6 times) See all 6 of this type

    88
    Let a→,b→\overrightarrow{a},\overrightarrow{b} and c→\overrightarrow{c} be three non-zero non-coplanar vectors. Let the position vectors of four points A,B,CA,B,C and DD be a→−b→+c→,λa→−3b→+4c→,−a→+2b→−3c→\overrightarrow{a}-\overrightarrow{b}+\overrightarrow{c},\lambda\overrightarrow{a}- 3\overrightarrow{b}+ 4\overrightarrow{c}, -\overrightarrow{a}+ 2\overrightarrow{b}- 3\overrightarrow{c} and 2a→−4b→+6c→2\overrightarrow{a}- 4\overrightarrow{b}+ 6\overrightarrow{c} respectively. If AB→,AC→\overrightarrow{AB},\overrightarrow{AC} and AD→\overrightarrow{AD} are coplanar, then λ\lambda is equal to

  4. Question 4

    Probability. Asked once: 27 Jul 2022 (same type asked 6 times) See all 6 of this type

    166
    Let XX have a binomial distribution B(n,p)B(n,p) such that the sum and the product of the mean and variance of XX are 24 and 128 respectively. If P(X>n−3)=k2nP(X > n - 3) =\frac{k}{2^{n}}, then kk is equal to

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  5. Question 5

    Binomial Theorem. Asked once: 28 Jul 2022 (same type asked 6 times) See all 6 of this type

    73
    The remainder when 72022+320227^{2022}+3^{2022} is divided by 5 is:

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