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Day 585: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 27 Jan 2024

    157
    For 0<a<10 < a < 1, the value of the integral ∫0πdx1−2acosx+a2\int_{0}^{\pi} \frac{dx}{1 - 2acosx +a^{2}} is:

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  2. Question 2

    Matrices. Asked once: 26 Jun 2022

    173
    Let X=[010001000],Y=αI+βX+γX2X=\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix},Y=\alpha I+\beta X+\gamma X^{2} and Z=α2I−αβX+(β2−αγ)X2,α,β,γ∈RZ =\alpha^{2}I -\alpha\beta X +\left( \beta^{2}-\alpha\gamma \right)X^{2},\alpha,\beta,\gamma\in R. If Y−1=Y^{- 1}= [15−2515015−250015]\begin{bmatrix} \frac{1}{5} & \frac{- 2}{5} & \frac{1}{5} \\ 0 & \frac{1}{5} & \frac{- 2}{5} \\ 0 & 0 & \frac{1}{5} \end{bmatrix}, then (α−β+γ)2(\alpha-\beta+\gamma)^{2} is equal to

  3. Question 3

    Permutations and Combinations. Asked once: 2021 Paper 17

    88
    Let nn be a non-negative integer. Then the number of divisors of the form " 4n+14n+ 1 " of the number (10)10⋅(11)11⋅(13)13(10)^{10}\cdot (11)^{11}\cdot (13)^{13} is equal to

  4. Question 4

    Probability. Asked once: 2021 Paper 12

    48
    Let A,BA,B and CC be three events such that the probability that exactly one of AA and BB occurs is (1−k)(1 -k), the probability that exactly one of BB and CC occurs is (1−2k)(1 - 2k), the probability that exactly one of CC and AA occurs is (1−k)(1 - k) and the probability of all A,BA,B and CC occur simultaneously is k2k^{2}, where 0<k<10 < k < 1. Then the probability that at least one of A,BA,B and CC occur is:

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  5. Question 5

    Quadratic Equations. Asked once: 2021 Paper 26

    76
    A natural number has prime factorization given by n=2x3y5zn =2^{x}3^{y}5^{z}, where yy and zz are such that y+z=5y + z = 5 and y−1+z−1=56,y>zy^{- 1}+z^{- 1}=\frac{5}{6},y > z. Then the number of odd divisors of nn, including 1, is:

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