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Day 228: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 2 Apr 2025 (same type asked 12 times) See all 12 of this type

    135
    Given three identical bags each containing 10 balls, whose colours are as follows :
    BagRedBlueGreen
    Bag I325
    Bag II433
    Bag III514
    A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is q , then the value of (1p+1q)\left( \frac{1}{p}+\frac{1}{q} \right) is :

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  2. Question 2

    Permutations and Combinations. Asked once: 15 Apr 2023 (same type asked 12 times) See all 12 of this type

    61
    The total number of three-digit numbers, divisible by 3 , which can be formed using the digits 1,3,51,3,5, 8 , if repetition of digits is allowed, is:

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  3. Question 3

    Definite Integration. Asked once: 28 Jan 2025 (same type asked 11 times) See all 11 of this type

    63
    If ∫−π2π296x2cos⁡2x(1+ex)dx=π(απ2+β),α,β∈Z\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^{2}\cos^{2}x}{\left( 1 +e^{x} \right)}dx = \pi\left( \alpha\pi^{2}+ \beta \right),\alpha,\beta \in Z, then (α+β)2(\alpha + \beta)^{2} equals :

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  4. Question 4

    Limits and Continuity. Asked once: 2 Apr 2025 (same type asked 11 times) See all 11 of this type

    139
    If lim⁡x→0cos⁡(2x)+acos(4x)−bx4\lim_{x\rightarrow 0} \frac{\cos(2x) +acos(4x) -b}{x^{4}} is finite, then (a+b)(a+b) is equal to:

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  5. Question 5

    Binomial Theorem. Asked once: 13 Apr 2023 (same type asked 11 times) See all 11 of this type

    75
    Fractional part of the number 4202215\frac{4^{2022}}{15} is equal to

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