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Day 334: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 8 Apr 2024 (same type asked 12 times) See all 12 of this type

    165
    There are three bags X,YX,Y and ZZ. Bag XX contains 5 one-rupee coins and 4 five-rupee coins; Bag YY contains 4 one-rupee coins and 5 five-rupee coins and Bag ZZ contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag YY, is:

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  2. Question 2

    Permutations and Combinations. Asked once: 12 Apr 2023 (same type asked 12 times) See all 12 of this type

    61
    The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0,1,3,5,70,1,3,5,7 and 9 without repetition, is equal to

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  3. Question 3

    Definite Integration. Asked once: 1 Feb 2024 (same type asked 11 times) See all 11 of this type

    88
    If ∫−π/2π/282cos⁡xdx(1+esin⁡x)(1+sin⁡4x)=απ+βlog⁡e(3+2\int_{- \pi/2}^{\pi/2} \frac{8\sqrt{2}\cos xdx}{\left( 1 +e^{\sin x} \right)\left( 1 +\sin^{4}x \right)}= \alpha\pi + \beta\log_{e}(3 + 2 2\sqrt{2} ), where α,β\alpha,\beta are integers, then α2+β2\alpha^{2}+\beta^{2} equals

  4. Question 4

    Limits and Continuity. Asked once: 5 Apr 2024 (same type asked 11 times) See all 11 of this type

    68
    If the function f(x)=sin⁡3x+αsin⁡x−βcos⁡3xx3f(x) =\frac{\sin3x + \alpha \sin x - \beta \cos3x}{x^{3}}, x∈Rx \in R, is continuous at x=0x = 0, then f(0)f(0) is equal to :

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  5. Question 5

    Binomial Theorem. Asked once: 25 Jan 2023 (same type asked 11 times) See all 11 of this type

    172
    The remainder when (2023)2023(2023)^{2023} is divided by 35 is