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Day 432: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 28 Jun 2022 (same type asked 26 times) See all 26 of this type

    176
    If the system of linear equations 2x−3y=γ+52x - 3y = \gamma + 5, αx+5y=β+1\alpha x + 5y = \beta + 1, where α,β,γ∈R\alpha,\beta,\gamma \in R has infinitely many solutions, then the value of ∣9α+3β+5γ∣|9\alpha + 3\beta + 5\gamma| is equal to

  2. Question 2

    Differential Equations. Asked once: 27 Jul 2022 (same type asked 41 times) See all 41 of this type

    85
    Let y=y(x)y=y(x) be the solution curve of the differential equation sin⁡(2x2)log⁡e(tan⁡x2)dy+(4xy−42xsin(x2−π4))dx=0\sin\left( 2x^{2} \right)\log_{e}\left( \tan x^{2} \right)dy+\left( 4xy- 4\sqrt{2}xsin\left( x^{2}-\frac{\pi}{4} \right) \right)dx= 0, 0<x<π20 <x<\sqrt{\frac{\pi}{2}}, which passes through the point (π6,1)\left( \sqrt{\frac{\pi}{6}},1 \right). Then ∣y(π3)∣\left| y\left( \sqrt{\frac{\pi}{3}} \right) \right| is equal to

  3. Question 3

    Three Dimensional Geometry. Asked once: 24 Jan 2023 (same type asked 33 times) See all 33 of this type

    83
    The shortest distance between the lines x−23=y+12=z−62\frac{x- 2}{3}=\frac{y+ 1}{2}=\frac{z- 6}{2} and x−63=1−y2=z+80\frac{x- 6}{3}=\frac{1 -y}{2}=\frac{z+ 8}{0} is equal to

  4. Question 4

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

    152
    If the system of equations αx+y+z=5,x+2y+3z=4,x+3y+5z=β\alpha x + y + z = 5,x + 2y + 3z = 4,x + 3y + 5z = \beta, has infinitely many solutions, then the ordered pair (α,β)(\alpha,\beta) is equal to:

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  5. Question 5

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

    172
    Let y=y(x),x>1y=y(x),x> 1, be the solution of the differential equation (x−1)dydx+2xy=1x−1(x- 1)\frac{dy}{dx}+ 2xy=\frac{1}{x- 1}, with y(2)=1+e42e4y(2) =\frac{1 +e^{4}}{2e^{4}}. If y(3)=eα+1βeαy(3) =\frac{e^{\alpha}+ 1}{\beta e^{\alpha}}. then the value of α+β\alpha+\beta is equal to