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Day 202: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 2021 Paper 2 (same type asked 2 times) See all 2 of this type

    64
    The probability that two randomly selected subsets of the set {1,2,3,4,5}\mathbf{\{ 1,2,3,4,5\}} have exactly two elements in their intersection is

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  2. Question 2

    Sequences and Series. Asked once: 4 Apr 2025 (same type asked 2 times) See all 2 of this type

    140
    Consider two sets AA and BB, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of BB be 36 and q respectively. Let d and D be the common differences of AP's in A and B respectively such that D=d+3, d>0D = d + 3,\text{ }d > 0. If p+qp−q=195\frac{p + q}{p - q}=\frac{19}{5}, then p−qp - q is equal to.

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  3. Question 3

    Straight Lines. Asked once: 25 Jul 2022 (same type asked 2 times) See all 2 of this type

    72
    A line, with the slope greater than one, passes through the point A(4,3)A(4,3) and intersects the line x−y−2=0x - y - 2 = 0 at the point BB. If the length of the line segment ABAB is 293\frac{\sqrt{29}}{3}, then BB also lies on the line:

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  4. Question 4

    Conic Sections. Asked once: 29 Jan 2025 (same type asked 2 times) See all 2 of this type

    62
    Let the ellipse, E1:x2a2+y2 b2=1,a>bE_{1}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,a > b and E2:x2 A2+y2 B2=1, A<BE_{2}:\frac{x^{2}}{{\text{ }A}^{2}}+\frac{y^{2}}{{\text{ }B}^{2}}= 1,\text{ }A < B have same eccentricity 13\frac{1}{\sqrt{3}}. Let the product of their lengths of latus rectums be 323\frac{32}{\sqrt{3}}, and the distance between the foci of E1E_{1} be 4. If E1E_{1} and E2E_{2} meet at A,B,CA,B,C and DD, then the area of the quadrilateral ABCD equals:

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  5. Question 5

    Conic Sections. Asked once: 24 Jan 2023 (same type asked 2 times) See all 2 of this type

    172
    Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ\lambda red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn CC is 0.4 then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola y2=λxy^{2}= \lambda x with one vertex at the vertex of the parabola, is