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Day 436: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2021 Paper 2 (same type asked 33 times) See all 33 of this type

    85
    Let λ\lambda be an integer. If the shortest distance between the lines x−λ=2y−1=−2zx-\lambda= 2y- 1 = - 2z and x=y+2λ=z−λx=y+ 2\lambda=z-\lambda is 722\frac{\sqrt{7}}{2\sqrt{2}}, then the value of ∣λ∣|\lambda| is

  2. Question 2

    Differential Equations. Asked once: 2021 Paper 8 (same type asked 41 times) See all 41 of this type

    70
    If the curve y=y(x)y=y(x) is the solution of the differential equation 2(x2+x5/4)dy−y(x+x1/4)dx=2x9/4dx,x>02\left( x^{2}+x^{5/4} \right)dy-y\left( x+x^{1/4} \right)dx= 2x^{9/4}dx,x> 0 which passes through the point (1,1−43log⁡e2)\left( 1,1 -\frac{4}{3}\log_{e}2 \right), then the value of y(16)y(16) is equal to:

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  3. Question 3

    Differential Equations. Asked once: 2021 Paper 8 (same type asked 41 times) See all 41 of this type

    63
    Let y=y(x)y=y(x) be the solution of the differential equation cos⁡x(3sin⁡x+cos⁡x+3)dy=\cos x(3\sin x + \cos x + 3)dy = (1+ysinx(3sin⁡x+cos⁡x+3))dx(1 +ysinx(3\sin x+ \cos x+ 3))dx, 0≤x≤π2,y(0)=00 \leq x\leq\frac{\pi}{2},y(0) = 0. Then, y(π3)y\left( \frac{\pi}{3} \right) is equal to:

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  4. Question 4

    Differential Equations. Asked once: 2021 Paper 6 (same type asked 41 times) See all 41 of this type

    67
    If y=y(x)y=y(x) is the solution of the differential equation dydx+(tan⁡x)y=sin⁡x,0≤x≤π3\frac{dy}{dx}+ (\tan x)y= \sin x,0 \leq x\leq\frac{\pi}{3}, with y(0)=0y(0) = 0, then y(π4)y\left( \frac{\pi}{4} \right) equal to :

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  5. Question 5

    Differential Equations. Asked once: 2021 Paper 3 (same type asked 41 times) See all 41 of this type

    78
    If a curve passes through the origin and the slope of the tangent to it at any point (x,y)(x,y) is x2−4x+y+8x−2\frac{x^{2}- 4x + y + 8}{x - 2}, then this curve also passes through the point:

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