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Day 429: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 30 Jan 2023 (same type asked 26 times) See all 26 of this type

    158
    For α,β∈R\alpha,\beta \in R, suppose the system of linear equations
    x−y+z=5x - y + z = 5
    2x+2y+αz=82x + 2y + \alpha z = 8
    3x−y+4z=β3x - y + 4z = \beta
    has infinitely many solutions. Then α\alpha and β\beta are the roots of

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  2. Question 2

    Differential Equations. Asked once: 1 Feb 2023 (same type asked 41 times) See all 41 of this type

    61
    If y=y(x)y = y(x) is the solution curve of the differential equation dydx+ytanx=xsecx,0≤x≤π3,y(0)=1\frac{dy}{dx}+ ytanx = xsecx,0 \leq x \leq\frac{\pi}{3},y(0) = 1, then y(π6)y\left( \frac{\pi}{6} \right) is equal to

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  3. Question 3

    Three Dimensional Geometry. Asked once: 31 Jan 2023 (same type asked 33 times) See all 33 of this type

    71
    Let the shortest distance between the lines L:x−5−2=y−λ0=z+λ1,λ≥0L:\frac{x - 5}{- 2}=\frac{y - \lambda}{0}=\frac{z + \lambda}{1},\lambda \geq 0 and L1:x+1=y−1=4−zL_{1}:x + 1 = y - 1 = 4 - z be 262\sqrt{6}. If (α,β,γ)(\alpha,\beta,\gamma) lies on LL, then which of the following is NOT possible?

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  4. Question 4

    Determinants. Asked once: 24 Jan 2023 (same type asked 26 times) See all 26 of this type

    152
    If the system of equations
    x+2y+3z=34x+3y−4z=48x+4y−λz=9+μ\begin{matrix} & x + 2y + 3z = 3 \\ & 4x + 3y - 4z = 4 \\ & 8x + 4y - \lambda z = 9 + \mu \end{matrix}
    has infinitely many solutions, then the ordered pair (λ,μ)(\lambda,\mu) is equal to :

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  5. Question 5

    Differential Equations. Asked once: 30 Jan 2023 (same type asked 41 times) See all 41 of this type

    78
    Let the solution curve y=y(x)y = y(x) of the differential equation dydx−3x5tan⁡−1(x3)(1+x6)32y=2xexp{x3−tan⁡−1x3(1+x6)}\frac{dy}{dx}-\frac{3x^{5}\tan^{- 1}\left( x^{3} \right)}{\left( 1 +x^{6} \right)^{\frac{3}{2}}}y = 2xexp\left\{ \frac{x^{3}-\tan^{- 1}x^{3}}{\sqrt{\left( 1 +x^{6} \right)}} \right\} pass through the origin. Then y(1)y(1) is equal to:

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