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Day 431: JEE Mains Maths

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

  1. Question 1

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

    70
    If y=y(x),x∈(0,π2)y = y(x),x \in\left( 0,\frac{\pi}{2} \right) be the solution curve of the differential equation
    (sin⁡22x)dydx+(8sin⁡22x+2sin⁡4x)y= 2e−4x(2sin⁡2x+cos⁡2x),  with  y(π4)=e−π,\begin{matrix} & \left( \sin^{2}2x \right)\frac{dy}{dx}+\left( 8\sin^{2}2x + 2\sin4x \right)y = \\ & \ 2e^{- 4x}(2\sin2x + \cos2x),\ \text{~with~}\ y\left( \frac{\pi}{4} \right)=e^{- \pi}, \end{matrix}
    then y(π6)y\left( \frac{\pi}{6} \right) is equal to:

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  2. Question 2

    Three Dimensional Geometry. Asked once: 25 Jan 2023 (same type asked 33 times) See all 33 of this type

    170
    The shortest distance between the lines x+1=2y=−12zx + 1 = 2y = - 12z and x=y+2=6z−6x = y + 2 = 6z - 6 is

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  3. Question 3

    Determinants. Asked once: 29 Jun 2022 (same type asked 26 times) See all 26 of this type

    67
    If the system of linear equations
    2x+y−z=72x + y - z = 7
    x−3y+2z=1x - 3y + 2z = 1
    x+4y+δz=kx + 4y + \delta z = k, where δ,k∈R\delta,k \in R has infinitely many solutions, then δ+k\delta + k is equal to:

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  4. Question 4

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

    161
    Let y=y(x)y = y(x) be the solution curve of the differential equation dydx+1x2−1y=(x−1x+1)12\frac{dy}{dx}+\frac{1}{x^{2}- 1}y =\left( \frac{x - 1}{x + 1} \right)^{\frac{1}{2}}, x>1x > 1 passing through the point (2,13)\left( 2,\sqrt{\frac{1}{3}} \right). Then 7y(8)\sqrt{7}y(8) is equal to

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  5. Question 5

    Three Dimensional Geometry. Asked once: 25 Jan 2023 (same type asked 33 times) See all 33 of this type

    176
    If the shortest distance between the line joining the points (1,2,3)(1,2,3) and (2,3,4)(2,3,4), and the line x−12=y+1−1=z−20\frac{x - 1}{2}=\frac{y + 1}{- 1}=\frac{z - 2}{0} is a, then 28a228a^{2} is equal to