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Day 4: JEE Mains Maths

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

  1. Question 1

    Probability. This type asked 12 times: 2021 Paper 4, 14 Jun 2022, 25 Jan 2023, 8 Apr 2023, 30 Jan 2024, 4 Apr 2024, 6 Apr 2024, 8 Apr 2024, 28 Jan 2025, 2 Apr 2025, 5 Apr 2026 S1, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 12 of this type

    56
    A candidate has to go to the examination center to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are 25,15\frac{2}{5},\frac{1}{5} and 25\frac{2}{5}. The probabilities that the candidate reaches late at the examination center are 15,13\frac{1}{5},\frac{1}{3} and 14\frac{1}{4} if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is :

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  2. Question 2

    Permutations and Combinations. This type asked 12 times: 2021 Paper 3, 14 Jun 2022, 28 Jun 2022, 26 Jul 2022, 29 Jul 2022, 30 Jan 2023, 1 Feb 2023, 12 Apr 2023, 13 Apr 2023, 15 Apr 2023, 8 Apr 2024, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 12 of this type

    73
    The number of numbers greater than 5000 , less than 9000 and divisible by 3 , that can be formed using the digits 0,1,2,5,90,1,2,5,9, if the repetition of the digits is allowed, is ____\_\_\_\_

  3. Question 3

    Definite Integration. This type asked 11 times: 2021 Paper 16, 2021 Paper 19, 2021 Paper 25, 14 Jun 2022, 27 Jun 2022, 29 Jan 2024, 1 Feb 2024, 4 Apr 2024, 28 Jan 2025, 2 Apr 2025, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 11 of this type

    68
    The value of the integral ∫−π4π4(32cos⁡4x1+esin⁡x)dx\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \left( \frac{32\cos^{4}x}{1 +e^{\sin x}} \right)dx is :

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  4. Question 4

    Limits and Continuity. This type asked 11 times: 2021 Paper 4, 2021 Paper 5, 26 Jul 2022, 29 Jul 2022, 13 Apr 2023, 27 Jan 2024, 31 Jan 2024, 5 Apr 2024, 2 Apr 2025, 4 Apr 2025, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 11 of this type

    55
    If lim⁡x→0e(a−1)x+2cos⁡bx+(c−2)e−xxcos⁡x−log⁡e(1+x)=2\lim_{x \rightarrow 0} \frac{e^{(a - 1)x}+ 2\cos bx + (c - 2)e^{- x}}{x\cos x -\log_{e}(1 + x)}= 2, then a2+b2+c2a^{2}+b^{2}+c^{2} is equal to :

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  5. Question 5

    Binomial Theorem. This type asked 11 times: 2021 Paper 4, 2021 Paper 7, 14 Jun 2022, 26 Jun 2022, 25 Jan 2023, 31 Jan 2023, 13 Apr 2023, 29 Jan 2024, 9 Apr 2024, 29 Jan 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 11 of this type

    54
    The remainder when ((64)(64))(64)\left( (64)^{(64)} \right)^{(64)} is divided by 7 is equal to.

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