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Day 433: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 24 Jan 2023 (same type asked 33 times) See all 33 of this type

    171
    If the shortest distance between the lines x+62=y−63=z−64\frac{x +\sqrt{6}}{2}=\frac{y -\sqrt{6}}{3}=\frac{z -\sqrt{6}}{4} and x−λ3=y−264=z+265\frac{x - \lambda}{3}=\frac{y - 2\sqrt{6}}{4}=\frac{z + 2\sqrt{6}}{5} is 6 , then the square of sum of all possible values of λ\lambda is

  2. Question 2

    Determinants. Asked once: 2021 Paper 20 (same type asked 26 times) See all 26 of this type

    86
    If the system of linear equations
    2x+y−z=32x + y - z = 3
    x−y−z=αx - y - z =\alpha
    3x+3y+βz=33x+ 3y+\beta z= 3
    has infinitely many solution, then α+β−αβ\alpha+\beta-\alpha\beta is equal to

  3. Question 3

    Differential Equations. Asked once: 29 Jun 2022 (same type asked 41 times) See all 41 of this type

    82
    Let y=y(x)y=y(x) be the solution of the differential equation
    dydx+2y2cos⁡4x−cos⁡2x=xetan⁡−1(2cot⁡2x),0<x<\frac{dy}{dx}+\frac{\sqrt{2}y}{2\cos^{4}x- \cos2x}=xe^{\tan^{- 1}(\sqrt{2}\cot2x)},0 <x<
    π/2\pi/2 with y(π4)=π232y\left( \frac{\pi}{4} \right)=\frac{\pi^{2}}{32}. If y(π3)=π218e−tan⁡−1(α)y\left( \frac{\pi}{3} \right)=\frac{\pi^{2}}{18}e^{-\tan^{- 1}(\alpha)}, then the value of 3α23\alpha^{2} is equal to

  4. Question 4

    Three Dimensional Geometry. Asked once: 25 Jul 2022 (same type asked 33 times) See all 33 of this type

    166
    The shortest distance between the lines x+7−6=y−67=z\frac{x + 7}{- 6}=\frac{y - 6}{7}= z and 7−x2=y−2=z−6\frac{7 - x}{2}= y - 2 = z - 6 is

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  5. Question 5

    Differential Equations. Asked once: 28 Jun 2022 (same type asked 41 times) See all 41 of this type

    71
    Let y=y(x)y = y(x) be the solution of the differential equation x(1−x2)dydx+(3x2y−y−4x3)=0,x>1x\left( 1 -x^{2} \right)\frac{dy}{dx}+\left( 3x^{2}y - y - 4x^{3} \right)= 0,x > 1, with y(2)=−2y(2) = - 2. Then y(3)y(3) is equal to

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