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Day 417: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 6 Apr 2024 (same type asked 41 times) See all 41 of this type

    77
    Let y=y(x)y = y(x) be the solution of the differential equation (1+x2)dydx+y=etan⁡−1x,y(1)=0\left( 1 +x^{2} \right)\frac{dy}{dx}+ y =e^{\tan^{- 1}x},y(1) = 0. Then y(0)y(0) is

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  2. Question 2

    Three Dimensional Geometry. Asked once: 6 Apr 2024 (same type asked 33 times) See all 33 of this type

    69
    The shortest distance between the lines x−32=y+15−7=z−95\frac{x - 3}{2}=\frac{y + 15}{- 7}=\frac{z - 9}{5} and x+12=y−11=z−9−3\frac{x + 1}{2}=\frac{y - 1}{1}=\frac{z - 9}{- 3} is

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  3. Question 3

    Determinants. Asked once: 6 Apr 2024 (same type asked 26 times) See all 26 of this type

    179
    If the system of equations
    2x+7y+λz=32x + 7y + \lambda z = 3
    3x+2y+5z=43x + 2y + 5z = 4
    x+μy+32z=−1x + \mu y + 32z = - 1
    has infinitely many solutions, then (λ−μ)(\lambda - \mu) is equal to

  4. Question 4

    Three Dimensional Geometry. Asked once: 27 Jul 2022 (same type asked 19 times) See all 19 of this type

    164
    If the length of the perpendicular drawn from the point P(a,4,2),a>0P(a,4,2),a > 0 on the line x+12=y−33=z−1−1\frac{x + 1}{2}=\frac{y - 3}{3}=\frac{z - 1}{- 1} is  26\ 2\sqrt{6} units and Q(α1,α2,α3)Q\left( \alpha_{1},\alpha_{2},\alpha_{3} \right) is the image of the point PP in this line, then a+∑i=13αia+\sum_{i= 1}^{3} \alpha_{i} is equal to:

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  5. Question 5

    Differential Equations. Asked once: 2021 Paper 10 (same type asked 19 times) See all 19 of this type

    90
    Let y=y(x)y=y(x) be the solution of the differential equation x dy−y dx=x2−y2 dx, x≥1x\,dy-y\,dx=\sqrt{x^{2}-y^{2}}\,dx,\ x\geq 1, with y(1)=0y(1) = 0. If the area bounded by the lines x=1, x=eπ, y=0x = 1,\ x = e^{\pi},\ y = 0 and the curve y=y(x)y = y(x) is αe2π+β\alpha e^{2\pi}+\beta, then the value of 10(α+β)10(\alpha+\beta) is equal to