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Day 358: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 4 Apr 2025 (same type asked 33 times) See all 33 of this type

    56
    Let the shortest distance between the lines x−33=y−α−1=z−31\frac{x- 3}{3}=\frac{y-\alpha}{- 1}=\frac{z- 3}{1} and x+3−3=y+72=z−β4\frac{x+ 3}{- 3}=\frac{y+ 7}{2}=\frac{z-\beta}{4} be 3303\sqrt{30}. Then the positive value of 5α+β5\alpha+\beta is.

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  2. Question 2

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

    67
    Let the system of equations: 2x+3y+5z=97x+3y−2z=812x+3y−(4+λ)z=16−μ\begin{matrix} & 2x+ 3y+ 5z= 9 \\ & 7x+ 3y- 2z= 8 \\ & 12x+ 3y- (4 +\lambda)z= 16 -\mu \end{matrix} have infinitely many solutions. Then the radius of the circle centred at ( λ,μ\lambda,\mu ) and touching the line 4x=3y4x = 3y is.

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  3. Question 3

    Three Dimensional Geometry. Asked once: 28 Jan 2025 (same type asked 19 times) See all 19 of this type

    62
    If the image of the point (4,4,3)(4,4,3) in the line x−12=y−21=z−13\frac{x - 1}{2}=\frac{y - 2}{1}=\frac{z - 1}{3} is (α,β,γ)(\alpha,\beta,\gamma), then α+β+γ\alpha + \beta + \gamma is equal to

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  4. Question 4

    Differential Equations. Asked once: 31 Jan 2023 (same type asked 19 times) See all 19 of this type

    155
    Let y=y(x)y = y(x) be the solution of the differential equation (3y2−5x2)y dx+2x(x2−y2)dy=0\left( 3y^{2}- 5x^{2} \right)y\text{ }dx + 2x\left( x^{2}-y^{2} \right)dy = 0 such that y(1)=1y(1) = 1. Then ∣(y(2))3−12y(2)∣\left| (y(2))^{3}- 12y(2) \right| is equal to:

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  5. Question 5

    Determinants. Asked once: 6 Apr 2024 (same type asked 19 times) See all 19 of this type

    170
    If A is a square matrix of order 3 such that det(A)=3det(A) = 3 and
    det(adj(−4adj(−3adj(3adj((2 A)−1)))))=2m3ndet\left( adj\left( - 4adj\left( - 3adj\left( 3adj\left( (2\text{ }A)^{- 1} \right) \right) \right) \right) \right)=2^{m}3^{n}
    then m+2nm + 2n is equal to:

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