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Day 483: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 22 Jan 2025

    56
    A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ\mu and σ2\sigma^{2} denote the mean and variance of XX, then the value of 64(μ+σ2)64\left( \mu +\sigma^{2} \right) is :

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  2. Question 2

    Quadratic Equations. Asked once: 7 Apr 2025

    148
    For t>−1t > - 1, let αt\alpha_{t} and βt\beta_{t} be the roots of the equation
    ((t+2)17−1)x2+((t+2)16−1)x+((t+2)121−1)=0\left( (t + 2)^{\frac{1}{7}} - 1 \right)x^{2} + \left( (t + 2)^{\frac{1}{6}} - 1 \right)x + \left( (t + 2)^{\frac{1}{21}} - 1 \right) = 0
    If lim⁡t→−1+αt=a\lim_{t \rightarrow - 1^{+}} \alpha_{t} = a and lim⁡t→−1+βt=b\lim_{t \rightarrow - 1^{+}} \beta_{t} = b, then 72(a+b)272(a + b)^{2} is equal to

  3. Question 3

    Relations and Functions. Asked once: 24 Jan 2025

    130
    Let
    A={x∈(0,π)−{π2}:log⁡(2/π)∣sin⁡x∣+log⁡(2/π)∣cos⁡x∣=2}A =\left\{ x \in (0,\pi) -\left\{ \frac{\pi}{2} \right\}:\log_{(2/\pi)}|\sin x| +\log_{(2/\pi)}|\cos x| = 2 \right\}
    And B={x≥0:x(x−4)−3∣x−2∣+6=0}\mathbf{B = \{ x \geq 0:}\sqrt{x}(\sqrt{x}- 4) - 3|\sqrt{x}- 2| + 6 = 0\}. Then n(A∪B)n(A \cup B) is equal to:

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  4. Question 4

    Sequences and Series. Asked once: 24 Jan 2026 S1

    54
    Let 729,81,9,1,…729,81,9,1,\ldots. be a sequence and PnP_{n} denote the product of the first nn terms of this sequence. If 2∑n=140(Pn)1n=3α−13β2\sum_{n = 1}^{40} \left( P_{n} \right)^{\frac{1}{n}}=\frac{3^{\alpha}- 1}{3^{\beta}} and gcd(α,β)=1gcd(\alpha,\beta) = 1, then α+β\alpha + \beta is equal to

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  5. Question 5

    Statistics. Asked once: 2021 Paper 10

    71
    Let in a series of 2n2n observations, half of them are equal to a and remaining half are equal to - a. Also by adding a constant bb in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a2+b2a^{2}+b^{2} is equal to:

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