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Day 428: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 11 Apr 2023 (same type asked 41 times) See all 41 of this type

    155
    Let y=y(x)y = y(x) be the solution of the differential equations dydx+5x(x5+1)y=(x5+1)2x7,x>0\frac{dy}{dx}+\frac{5}{x\left( x^{5}+ 1 \right)}y =\frac{\left( x^{5}+ 1 \right)^{2}}{x^{7}},x > 0. If y(1)=2y(1) = 2, then y(2)y(2) is equal to

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  2. Question 2

    Three Dimensional Geometry. Asked once: 6 Apr 2023 (same type asked 33 times) See all 33 of this type

    78
    One vertex of a rectangular parallelopiped is at the origin OO and the lengths of its edges along x,yx,y and zz axes are 3, 4 and 5 units respectively. Let PP be the vertex (3,4,5)(3,4,5). Then the shortest distance between the diagonal OP and an edge parallel to zz axis, not passing through OO or PP is:

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  3. Question 3

    Determinants. Asked once: 6 Apr 2023 (same type asked 26 times) See all 26 of this type

    76
    If the system of equations
    x+y+az=bx + y + az = b
    2x+5y+2z=62x + 5y + 2z = 6
    x+2y+3z=3x + 2y + 3z = 3
    has infinitely many solutions, then 2a+3b2a + 3b is equal to

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  4. Question 4

    Differential Equations. Asked once: 8 Apr 2023 (same type asked 41 times) See all 41 of this type

    88
    If the solution curve of the differential equation (y−2log⁡ex)dx+(xlog⁡ex2)dy=0,x>1\left( y - 2\log_{e}x \right)dx +\left( x\log_{e}x^{2} \right)dy = 0,x > 1 passes through the points (e,43)\left( e,\frac{4}{3} \right) and (e4,α)\left( e^{4},\alpha \right), then α\alpha is equal to-

  5. Question 5

    Three Dimensional Geometry. Asked once: 1 Feb 2023 (same type asked 33 times) See all 33 of this type

    72
    The shortest distance between the lines x−51=y−22=z−4−3\frac{x - 5}{1}=\frac{y - 2}{2}=\frac{z - 4}{- 3} and x+31=y+54=z−1−5\frac{x + 3}{1}=\frac{y + 5}{4}=\frac{z - 1}{- 5} is

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