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Day 61: JEE Mains Maths

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

  1. Question 1

    Probability. This type asked 3 times: 2021 Paper 21, 14 Jun 2022, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 3 of this type

    57
    If a random variable x has the probability distribution
    xx01234567
    p(x)p(x)02k2kkk3k3k2k22k^{2}2k2kk2+kk^{2}+k7k27k^{2}
    then P(3<x≤6)P(3 < x \leq 6) is equal to

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  2. Question 2

    Application of Derivatives. This type asked 3 times: 10 Apr 2023, 27 Jan 2024, 21 Jan 2026 S2. This one: 21 Jan 2026 S2 See all 3 of this type

    52
    Let f:R→Rf:R \rightarrow R be a twice differentiable function such that f′′(x)>0f^{''}(x) > 0 for all x∈Rx \in R and f′(a−1)=0f^{'}(a - 1) = 0, where a is real number. Let g(x)=f(tan⁡2x−2tan⁡x+a)g(x) = f\left( \tan^{2}x - 2\tan x + a \right), 0<x<π20 < x <\frac{\pi}{2}. Consider the following two statements : (I) g is increasing in (0,π4)\left( 0,\frac{\pi}{4} \right) (II) g is decreasing in (π4,π2)\left( \frac{\pi}{4},\frac{\pi}{2} \right) Then,

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  3. Question 3

    Conic Sections. This type asked 3 times: 22 Jan 2025, 2 Apr 2025, 21 Jan 2026 S2. This one: 21 Jan 2026 S2 See all 3 of this type

    56
    Let one end of a focal chord of the parabola y2=16xy^{2}= 16x be (16, 16). If P(α,β)P(\alpha,\beta) divides this focal chord internally in the ratio 5:25:2, then the minimum value of α+β\alpha + \beta is equal to :

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  4. Question 4

    Inverse Trigonometric Functions. This type asked 3 times: 14 Jun 2022, 22 Jan 2025, 21 Jan 2026 S2. This one: 21 Jan 2026 S2 See all 3 of this type

    73
    Let the maximum value of (sin⁡−1x)2+(cos⁡−1x)2\left( \sin^{- 1}x \right)^{2} + \left( \cos^{- 1}x \right)^{2} for x∈[−32,12]x \in \left\lbrack - \frac{\sqrt{3}}{2},\frac{1}{\sqrt{2}} \right\rbrack be mnπ2\frac{m}{n}\pi^{2}, where gcd(m,n)=1gcd(m,n) = 1. Then m+nm + n is equal to ____\_\_\_\_ .

  5. Question 5

    Relations and Functions. This type asked 3 times: 2021 Paper 20, 25 Jun 2022, 21 Jan 2026 S2. This one: 21 Jan 2026 S2 See all 3 of this type

    63
    Let A={x:∣x2−10∣≤6}A =\left\{ x:\left| x^{2}- 10 \right|\leq 6 \right\} and B={x:∣x−2∣>1}\mathbf{B = \{ x:|x - 2| > 1\}}. Then

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