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Day 430: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 30 Jan 2023 (same type asked 33 times) See all 33 of this type

    73
    The line l1l_{1} passes through the point (2,6,2)(2,6,2) and is perpendicular to the plane 2x+y−2z=102x + y - 2z = 10. Then the shortest distance between the line l1l_{1} and the line x+12=y+4−3=z2\frac{x + 1}{2}=\frac{y + 4}{- 3}=\frac{z}{2} is:

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  2. Question 2

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

    153
    If the system of equations
    x+y+z=6x + y + z = 6
    2x+5y+αz=β2x + 5y + \alpha z = \beta
    x+2y+3z=14x + 2y + 3z = 14
    has infinitely many solutions, then α+β\alpha + \beta is equal to:

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  3. Question 3

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

    160
    Let y=y(x)y = y(x) be the solution curve of the differential equation dydx+(2x2+11x+13x3+6x2+11x+6)\frac{dy}{dx}+\left( \frac{2x^{2}+ 11x + 13}{x^{3}+ 6x^{2}+ 11x + 6} \right) y=(x+3)x+1,x>−1y =\frac{(x + 3)}{x + 1},x > - 1, which passes through the point (0,1)(0,1). Then y(1)y(1) is equal to:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 29 Jan 2023 (same type asked 33 times) See all 33 of this type

    157
    The shortest distance between the lines x−12=y−21=z−6−3\frac{x - 1}{2}=\frac{y - 2}{1}=\frac{z - 6}{- 3} and x−12=y+8−7=z−45\frac{x - 1}{2}=\frac{y + 8}{- 7}=\frac{z - 4}{5}

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  5. Question 5

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

    63
    If the system of linear equations.
    8x+y+4z=−28x + y + 4z = - 2
    x+y+z=0x + y + z = 0
    λx−3y=μ\lambda x - 3y = \mu
    has infinitely many solutions, then the distance of the point (λ,μ,−12)\left( \lambda,\mu, -\frac{1}{2} \right) from the plane 8x+y+4z+2=08x + y + 4z + 2 = 0 is :

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