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Day 582: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 27 Jan 2024

    177
    Let f(x)=∫0xg(t)log⁡e(1−t1+t)dtf(x) =\int_{0}^{x} g(t)\log_{e}\left( \frac{1 - t}{1 + t} \right)dt, where gg is a continuous odd function. If ∫−π/2π/2(f(x)+x2cos⁡x1+ex)dx=(πα)2−α\int_{- \pi/2}^{\pi/2} \left( f(x) +\frac{x^{2}\cos x}{1 +e^{x}} \right)dx =\left( \frac{\pi}{\alpha} \right)^{2}- \alpha, then α\alpha is equal to. ............

  2. Question 2

    Limits and Continuity. Asked once: 2021 Paper 1

    67
    If f:R→Rf:R\rightarrow R is a function defined by f(x)=[x−1]cos⁡(2x−12)πf(x) = \lbrack x- 1\rbrack \cos\left( \frac{2x- 1}{2} \right)\pi, where [.] denotes the greatest integer function, then ff is :

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  3. Question 3

    Matrices. Asked once: 26 Jul 2022

    64
    Let AA be a 2×22 \times 2 matrix with det(A)=−1det(A) = - 1 and det ((A+I)(Adj(A)+I))=4((A + I)(Adj(A) + I)) = 4. Then the sum of the diagonal elements of AA can be:

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  4. Question 4

    Permutations and Combinations. Asked once: 2021 Paper 18

    84
    If 1⋅ 1P1+2⋅ 2P2+3⋅ 3P3+…+15⋅ 15P15= qPr−s, 0≤s≤11\cdot\,^{1}P_{1}+ 2 \cdot\,^{2}P_{2}+ 3 \cdot\,^{3}P_{3}+ \ldots + 15 \cdot\,^{15}P_{15}=\,^{q}P_{r}- s,\ 0 \leq s \leq 1, then q+sCr−s^{q+s}C_{r - s} is equal to

  5. Question 5

    Probability. Asked once: 2021 Paper 16

    48
    The probability that a randomly selected 2-digit number belongs to the set {n∈N:(2n−2)\left\{ n\in N:\left( 2^{n}- 2 \right) \right. is a multiple of 3}\} is equal to

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