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Day 579: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 30 Jan 2024

    162
    Let f:R→Rf:R \rightarrow R be defined f(x)=ae2x+bex+cxf(x) = ae^{2x}+ be^{x}+ cx. If f(0)=−1,f′(log⁡e2)=21f(0) = - 1,f^{'}\left( \log_{e}2 \right)= 21 and ∫0log⁡e4(f(x)−cx)dx=392\int_{0}^{\log_{e}4} (f(x) - cx)dx =\frac{39}{2}, then the value of ∣a+b+c∣|a + b + c| equals :

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  2. Question 2

    Limits and Continuity. Asked once: 2021 Paper 9

    69
    If lim⁡x→0sin⁡−1x−tan⁡−1x3x3\lim_{x\rightarrow 0} \frac{\sin^{- 1}x-\tan^{- 1}x}{3x^{3}} is equal to LL, then the value of (6L+1)(6L+ 1) is

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  3. Question 3

    Matrices. Asked once: 26 Jul 2022

    153
    Let A=[111]A =\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} and B=[92−102112122132−142−152162172]B =\begin{bmatrix} 9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2} \end{bmatrix}, then the value of A′BAA^{'}BA is:

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  4. Question 4

    Permutations and Combinations. Asked once: 2021 Paper 18

    89
    The number of three-digit even numbers, formed by the digits 0,1,3,4,6,70,1,3,4,6,7 if the repetition of digits is not allowed, is

  5. Question 5

    Probability. Asked once: 2021 Paper 18

    65
    Let AA and BB be independent events such that P(A)=p,P(B)=2pP(A) = p,P(B) = 2p. The largest value of pp, for which PP (exactly one of A,BA,B occurs) =59=\frac{5}{9}, is:

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