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Day 73: JEE Mains Maths

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

  1. Question 1

    Conic Sections. This type asked 3 times: 25 Jul 2022, 28 Jul 2022, 8 Apr 2023. This one: 8 Apr 2023 See all 3 of this type

    176
    The ordinates of the points PP and QQ on the parabola with focus (3,0)(3,0) and directrix x=−3x=-3 are in the ratio 3:13:1. If the tangents to the parabola at PP and QQ meet at the point (α,β)(\alpha,\beta), then β2α\frac{\beta^{2}}{\alpha} is equal to

  2. Question 2

    Vector Algebra. This type asked 3 times: 2021 Paper 26, 29 Jun 2022, 8 Apr 2023. This one: 8 Apr 2023 See all 3 of this type

    71
    If the points with vectors αi^+10j^+13k^\alpha\widehat{i}+ 10\widehat{j}+ 13\widehat{k}, 6i^+11j^+11k^,92i^+βj^−8k^6\widehat{i}+ 11\widehat{j}+ 11\widehat{k},\frac{9}{2}\widehat{i}+ \beta\widehat{j}- 8\widehat{k} are collinear, then (19α−6β)2(19\alpha - 6\beta)^{2} is equal to

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  3. Question 3

    Application of Integrals. This type asked 3 times: 2021 Paper 25, 28 Jun 2022, 6 Apr 2023. This one: 6 Apr 2023 See all 3 of this type

    159
    The area bounded by the curves y=∣x−1∣+∣x−2∣y = |x - 1| + |x - 2| and y=3y = 3 is equal to

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  4. Question 4

    Differentiation. This type asked 3 times: 2021 Paper 18, 27 Jul 2022, 6 Apr 2023. This one: 6 Apr 2023 See all 3 of this type

    77
    If 2xy+3yx=202x^{y}+ 3y^{x}= 20, then dydx\frac{dy}{dx} at (2,2)(2,2) is equal to

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  5. Question 5

    Binomial Theorem. This type asked 3 times: 2021 Paper 7, 2021 Paper 17, 1 Feb 2023. This one: 1 Feb 2023 See all 3 of this type

    174
    Let the sixth term in the binomial expansion of (log⁡2(10−33)+2xlog⁡235)m\left( \sqrt{\log_{2}\left( 10 -3^{3} \right)}+\sqrt[5]{2^{x\log_{2}3}} \right)^{m}, in the increasing powers of 2(x−2)log⁡232^{(x - 2)\log_{2}3}, be 21 . If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of A.P., then the sum of the squares of all possible values of xx is