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Day 331: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 28 Jan 2026 S2 (same type asked 41 times) See all 41 of this type

    64
    Let y=y(x)y=y(x) be the solution of the differential equation xdydx−y=x2cot⁡x,x∈(0,π)x\frac{dy}{dx}-y=x^{2}\cot x,x\in (0,\pi). If y(π2)=π2y\left( \frac{\pi}{2} \right)=\frac{\pi}{2}, then 6y(π6)−8y(π4)6y\left( \frac{\pi}{6} \right)- 8y\left( \frac{\pi}{4} \right) is equal to :

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  2. Question 2

    Three Dimensional Geometry. Asked once: 7 Apr 2025 (same type asked 33 times) See all 33 of this type

    52
    If the shortest distance between the lines x−12=y−23=z−34\frac{x- 1}{2}=\frac{y- 2}{3}=\frac{z- 3}{4} and x1=yα=z−51\frac{x}{1}=\frac{y}{\alpha}=\frac{z- 5}{1} is 56\frac{5}{\sqrt{6}}, then the sum of all possible values of α\alpha is.

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  3. Question 3

    Determinants. Asked once: 7 Apr 2025 (same type asked 26 times) See all 26 of this type

    144
    Let the system of equations
    x+5y−z=14x+3y−3z=724x+y+λz=μ\begin{matrix} & x+ 5y-z= 1 \\ & 4x+ 3y- 3z= 7 \\ & 24x+y+\lambda z=\mu \end{matrix}
    λ,μ∈R\lambda,\mu\in R, have infinitely many solutions. Then the number of the solutions of this system, If x,y,zx,y,z are integers and satisfy 7≤x+y+z≤777 \leq x + y + z \leq 77, is

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2 Apr 2025 (same type asked 19 times) See all 19 of this type

    126
    If the image of the point P(1,0,3)P(1,0,3) in the line joining the points A(4,7,1)A(4,7,1) and B(3,5,3)B(3,5,3) is Q(α,β,γ)Q(\alpha,\beta,\gamma), then α+β+γ\alpha+\beta+\gamma is equal to.

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  5. Question 5

    Differential Equations. Asked once: 10 Apr 2023 (same type asked 19 times) See all 19 of this type

    70
    The slope of tangent at any point (x,y)(x,y) on a curve y=y(x)y = y(x) is x2+y22xy,x>0\frac{x^{2}+y^{2}}{2xy},x > 0. If y(2)=0y(2) = 0, then a value of y(8)y(8) is

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