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Day 481: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 5 Apr 2026 S2

    61
    Let the point P be the vertex of the parabola y=x2−6x+12y=x^{2}- 6x+ 12. If a line passing through the point PP intersects the circle x2+y2−2x−4y+3=0x^{2}+y^{2}- 2x- 4y+ 3 = 0 at the points R and S , then the maximum value of (PR+PS)2(PR + PS)^{2} is:

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  2. Question 2

    Definite Integration. Asked once: 2 Apr 2026 S1

    75
    If α=∫023log⁡2(x2+4)dx+∫242x−4dx\alpha = \int_{0}^{2\sqrt{3}} \log_{2}\left( x^{2} + 4 \right)dx + \int_{2}^{4} \sqrt{2^{x} - 4}dx, then α2\alpha^{2} is equal to ____\_\_\_\_ .

  3. Question 3

    Determinants. Asked once: 15 Apr 2023

    74
    Let the system of linear equations
    −x+2y−9z=7- x + 2y - 9z = 7
    −x+3y+7z=9- x + 3y + 7z = 9
    −2x+y+5z=8- 2x + y + 5z = 8
    −3x+y+13z=λ- 3x + y + 13z = \lambda
    has a unique solution x=α,y=β,z=γx = \alpha,y = \beta,z = \gamma. Then the distance of the point (α,β,γ)(\alpha,\beta,\gamma) from the plane 2x−2y+z=λ2x - 2y + z = \lambda is

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  4. Question 4

    Differential Equations. Asked once: 25 Jul 2022

    70
    The slope of the tangent to a curve C:y=y(x)C:y = y(x) at any point [x,y)\lbrack x,y) on it is 2e2x−6e−x+92+9e−2x\frac{2e^{2x}- 6e^{- x}+ 9}{2 + 9e^{- 2x}}. If CC passes through the points (0,12+π22)\left( 0,\frac{1}{2}+\frac{\pi}{2\sqrt{2}} \right) and (α,12e2α)\left( \alpha,\frac{1}{2}e^{2\alpha} \right) then eαe^{\alpha} is equal to:

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  5. Question 5

    Differentiation. Asked once: 29 Jan 2024

    79
    Suppose
    f(x)=(2x+2−x)tan⁡xtan⁡−1(x2−x+1)(7x2+3x+1)3f(x) =\frac{\left( 2^{x}+2^{- x} \right)\tan x\sqrt{\tan^{- 1}\left( x^{2}- x + 1 \right)}}{\left( 7x^{2}+ 3x + 1 \right)^{3}}
    Then the value of f′(0)f^{'}(0) is equal to

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