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Day 419: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 2021 Paper 7 (same type asked 13 times) See all 13 of this type

    79
    Which of the following is true for y(x)y(x) that satisfies the differential equation? dydx=xy−1+x−y;y(0)=0\frac{dy}{dx}=xy- 1 +x-y;y(0) = 0 :

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  2. Question 2

    Differential Equations. Asked once: 5 Apr 2024 (same type asked 41 times) See all 41 of this type

    64
    If y=y(x)y = y(x) is the solution of the differential equation dydx+2y=sin⁡(2x),y(0)=34\frac{dy}{dx}+ 2y = \sin(2x),y(0) =\frac{3}{4}, then y(π8)y\left( \frac{\pi}{8} \right) is equal to :

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  3. Question 3

    Three Dimensional Geometry. Asked once: 4 Apr 2024 (same type asked 33 times) See all 33 of this type

    84
    If the shortest distance between the lines x+22=y+33=z−54\frac{x + 2}{2}=\frac{y + 3}{3}=\frac{z - 5}{4} and x−31=y−2−3=z+42\frac{x - 3}{1}=\frac{y - 2}{- 3}=\frac{z + 4}{2} is 3835k\frac{38}{3\sqrt{5}}k and  ∫0k[x2]dx=α−α,\ \int_{0}^{k} \left\lbrack x^{2} \right\rbrack dx = \alpha -\sqrt{\alpha}, where  [x]\ \lbrack x\rbrack denotes the greatest integer function, then 6α36\alpha^{3} is equal to

  4. Question 4

    Determinants. Asked once: 5 Apr 2024 (same type asked 26 times) See all 26 of this type

    164
    The values of m,nm,n, for which the system of equations x+y+z=4x + y + z = 4, 2x+5y+5z=172x + 5y + 5z = 17,
    x+2y+mz=nx + 2y + mz = n
    has infinitely many solutions, satisfy the equation:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 28 Jun 2022 (same type asked 19 times) See all 19 of this type

    171
    Let the image of the point P(1,2,3)P(1,2,3) in the line L:x−63=y−12=z−23L:\frac{x - 6}{3}=\frac{y - 1}{2}=\frac{z - 2}{3} be QQ. let R(α,β,γ)R(\alpha,\beta,\gamma) be a point that divides internally the line segment PQPQ in the ratio 1:31:3. Then the value of 22(α+β+γ)22(\alpha+\beta+\gamma) is equal to