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Day 21: JEE Mains Maths

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

  1. Question 1

    Probability. This type asked 6 times: 25 Jul 2022, 26 Jul 2022, 27 Jul 2022, 29 Jul 2022, 1 Feb 2023, 13 Apr 2023. This one: 13 Apr 2023 See all 6 of this type

    164
    The random variable XX follows binomial distribution BB (n,p)(n,p) for which the difference of the mean and the variance is 1 . If 2P(X=2)=3P(X=1)2P(X = 2) = 3P(X = 1), then n2P(X>1)n^{2}P(X > 1) is equal to

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  2. Question 2

    Binomial Theorem. This type asked 6 times: 25 Jul 2022, 27 Jul 2022, 28 Jul 2022, 30 Jan 2023, 1 Feb 2023, 10 Apr 2023. This one: 10 Apr 2023 See all 6 of this type

    169
    Let the number (22)2022+(2022)22(22)^{2022}+ (2022)^{22} leave the remainder α\alpha when divided by 3 and β\beta when divided by 7. Then (α2+β2)\left( \alpha^{2}+\beta^{2} \right) is equal to

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  3. Question 3

    Conic Sections. This type asked 6 times: 2021 Paper 4, 25 Jun 2022, 26 Jun 2022, 28 Jul 2022, 30 Jan 2023, 10 Apr 2023. This one: 10 Apr 2023 See all 6 of this type

    84
    Let a common tangent to the curves y2=4xy^{2}= 4x and (x−4)2+y2=16(x - 4)^{2}+y^{2}= 16 touch the curves at the points PP and QQ. Then (PQ)2(PQ)^{2} is equal to

  4. Question 4

    Limits and Continuity. This type asked 6 times: 2021 Paper 4, 2021 Paper 12, 2021 Paper 18, 2021 Paper 20, 25 Jul 2022, 1 Feb 2023. This one: 1 Feb 2023 See all 6 of this type

    73
    lim⁡n→∞[11+n+12+n+13+n+⋯+12n]\lim_{n \rightarrow \infty} \left\lbrack \frac{1}{1 + n}+\frac{1}{2 + n}+\frac{1}{3 + n}+ \cdots +\frac{1}{2n} \right\rbrack is equal to

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  5. Question 5

    Three Dimensional Geometry. This type asked 6 times: 2021 Paper 23, 2021 Paper 24, 2021 Paper 26, 26 Jul 2022, 24 Jan 2023, 30 Jan 2023. This one: 30 Jan 2023 See all 6 of this type

    171
    Let a line LL pass through the point P(2,3,1)P(2,3,1) and be parallel to the line x+3y−2z−2=0=x−y+x + 3y - 2z - 2 = 0 = x - y + 2z2z. If the distance of LL from the point (5,3,8)(5,3,8) is α\alpha, then 3α23\alpha^{2} is equal to