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Day 411: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 24 Jan 2025 (same type asked 41 times) See all 41 of this type

    59
    Let y=y(x)y = y(x) be the solution of the differential equation (xy−5x21+x2)dx+(1+x2)dy=0\left( xy - 5x^{2}\sqrt{1 +x^{2}} \right)dx +\left( 1 +x^{2} \right)dy = 0, y(0)=0y(0) = 0. Then y(3)y(\sqrt{3}) is equal to

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  2. Question 2

    Three Dimensional Geometry. Asked once: 8 Apr 2024 (same type asked 33 times) See all 33 of this type

    158
    If the shortest distance between the lines x−λ2=y−43=z−34\frac{x - \lambda}{2}=\frac{y - 4}{3}=\frac{z - 3}{4} and x−24=y−46=z−78\frac{x - 2}{4}=\frac{y - 4}{6}=\frac{z - 7}{8} is 1329\frac{13}{\sqrt{29}}, then a value of λ\lambda is :

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  3. Question 3

    Determinants. Asked once: 9 Apr 2024 (same type asked 26 times) See all 26 of this type

    65
    Let λ,μ∈R\lambda,\mu \in R. If the system of equations
    3x+5y+λz=33x + 5y + \lambda z = 3
    7x+11y−9z=27x + 11y - 9z = 2
    97x+155y−189z=μ97x + 155y - 189z = \mu
    has infinitely many solutions, then μ+2λ\mu + 2\lambda is equal to:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 31 Jan 2024 (same type asked 19 times) See all 19 of this type

    156
    Let (α,β,γ)(\alpha,\beta,\gamma) be mirror image of the point (2,3,5)(2,3,5) in the line x−12=y−23=z−34\frac{x - 1}{2}=\frac{y - 2}{3}=\frac{z - 3}{4}. Then 2α+3β+4γ2\alpha + 3\beta + 4\gamma is equal to

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  5. Question 5

    Differential Equations. Asked once: 25 Jun 2022 (same type asked 19 times) See all 19 of this type

    78
    If the solution curve y=y(x)y = y(x) of the differential equation y2dx+(x2−xy+y2)dy=0y^{2}dx +\left( x^{2}- xy +y^{2} \right)dy = 0, which passes through the point (1,1)(1,1) and intersects the line y=3xy =\sqrt{3}x at the point (α,3α)(\alpha,\sqrt{3}\alpha), then value of log⁡e(3α)\log_{e}(\sqrt{3}\alpha) is equal to

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