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Day 103: JEE Mains Maths

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

  1. Question 1

    Probability. This type asked 2 times: 2021 Paper 2, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 2 of this type

    74
    Let S be a set of 5 elements and P(S)P(S) denote the power set of S . Let E be an event of choosing an ordered pair (A, B) from the set P(S)×P(S)P(S) \times P(S) such that A∩B=∅A \cap B = \varnothing. If the probability of the event E is 3p2q\frac{3^{p}}{2^{q}}, where p,q∈Np,q \in \mathbb{N}, then p+qp + q is equal to

  2. Question 2

    Sequences and Series. This type asked 2 times: 4 Apr 2025, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 2 of this type

    55
    Let α1,α2,α3,α4\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4} be an A.P. of four terms such that each term of the A.P. and its common difference ll are integers. If α1+α2+α3+α4=48\alpha_{1}+\alpha_{2}+\alpha_{3}+\alpha_{4}= 48 and α1α2α3α4+l4=361\alpha_{1}\alpha_{2}\alpha_{3}\alpha_{4}+l^{4}= 361, then the largest term of the A.P. is equal to

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  3. Question 3

    Straight Lines. This type asked 2 times: 25 Jul 2022, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 2 of this type

    53
    Let the angles made with the positive x -axis by two straight lines drawn from the point P(2,3)P(2,3) and meeting the line x+y=6x + y = 6 at a distance 23\sqrt{\frac{2}{3}} from the point P be θ1\theta_{1} and θ2\theta_{2}. Then the value of (θ1+θ2)\left( \theta_{1}+\theta_{2} \right) is :

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  4. Question 4

    Conic Sections. This type asked 2 times: 29 Jan 2025, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 2 of this type

    57
    Let each of the two ellipses E1:x2a2+y2 b2=1,(a>b)E_{1}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,(a > b) and E2:x2 A2+y2 B2=1,( A<B)E_{2}:\frac{x^{2}}{{\text{ }A}^{2}}+\frac{y^{2}}{{\text{ }B}^{2}}= 1,(\text{ }A < B) have eccentricity 45\frac{4}{5}. Let the lengths of the latus recta of E1E_{1} and E2E_{2} be l1\mathcal{l}_{1} and l2\mathcal{l}_{2}, respectively, such that 2l12=9l22\mathcal{l}_{1}^{2}= 9\mathcal{l}_{2}. If the distance between the foci of E1E_{1} is 8 , then the distance between the foci of E2E_{2} is

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  5. Question 5

    Conic Sections. This type asked 2 times: 24 Jan 2023, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 2 of this type

    69
    An equilateral triangle OAB is inscribed in the parabola y2=4xy^{2}= 4x with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

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