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Day 58: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. This type asked 3 times: 1 Feb 2024, 22 Jan 2026 S2, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 3 of this type

    60
    If α,β\alpha,\beta, where α<β\alpha<\beta, are the roots of the equation λx2−(λ+3)x+3=0\lambda x^{2}- (\lambda+ 3)x + 3 = 0 such that 1α−1β=13\frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3}, then the sum of all possible values of λ\lambda is :

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  2. Question 2

    Conic Sections. This type asked 3 times: 14 Jun 2022, 28 Jan 2025, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 3 of this type

    56
    Let the image of parabola x2=4yx^{2}= 4y, in the line x−y=1x - y = 1 be (y+α)2=b(x−c),a,b,c∈N(y + \alpha)^{2}= b(x - c),a,b,c \in N. Then a+ba + b +c is equal to

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  3. Question 3

    Differential Equations. This type asked 3 times: 29 Jan 2024, 5 Apr 2024, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 3 of this type

    66
    Let y=y(x)y = y(x) be a differentiable function in the interval (0,∞)(0,\infty) such that y(1)=2y(1) = 2. and lim⁡t→x(t2y(x)−x2y(t)x−t)=3\lim_{t \rightarrow x} \left( \frac{t^{2}y(x) -x^{2}y(t)}{x - t} \right)= 3 for each x>0x > 0. Then 2y(2)2y(2) is equal to

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  4. Question 4

    Definite Integration. This type asked 3 times: 27 Jul 2022, 29 Jan 2025, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 3 of this type

    71
    Let a differentiable function ff satisfy the equation ∫036f(tx36)dt=4αf(x)\int_{0}^{36} f\left( \frac{tx}{36} \right)dt = 4\alpha f(x). If y=f(x)y = f(x) is a standard parabola passing through the points (2,1)(2,1) and (−4,β)( - 4,\beta), Then βα\beta^{\alpha} is equal to ____\_\_\_\_.

  5. Question 5

    Probability. This type asked 3 times: 29 Jul 2022, 29 Jan 2025, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 3 of this type

    61
    Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A . Then a ball is randomly drawn from the bag A . If the probability, that the ball drawn is white, is pq,gcd(p,q)=1\frac{p}{q},gcd(p,q) = 1, then p+qp + q is equal to

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