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Day 435: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 2021 Paper 20 (same type asked 41 times) See all 41 of this type

    68
    Let y=y(x)y=y(x) be the solution of the differential equation dydx=2(y+2sin⁡x−5)x−2cos⁡x\frac{dy}{dx}= 2(y+ 2\sin x- 5)x- 2\cos x such that y(0)=7y(0) = 7. Then y(π)y(\pi) is equal to:

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  2. Question 2

    Three Dimensional Geometry. Asked once: 14 Jun 2022 (same type asked 33 times) See all 33 of this type

    90
    If the shortest distance between the line r→=(−i^+3k)+λ(i^−aj^)\overrightarrow{r}= ( -\widehat{i}+ 3k) +\lambda(\widehat{i}-a\widehat{j}) and r→=(−j^+2k)+μ(i^−j^+k)\overrightarrow{r}= ( -\widehat{j}+ 2k) +\mu(\widehat{i}-\widehat{j}+k) is 23\sqrt{\frac{2}{3}}, then the integral value of a is equal to

  3. Question 3

    Differential Equations. Asked once: 2021 Paper 17 (same type asked 41 times) See all 41 of this type

    70
    Let y=y(x)y=y(x) be the solution of the differential equation (x−x3)dy=(y+yx2−3x4)dx, x>2\left(x-x^{3}\right)dy=\left(y+yx^{2}-3x^{4}\right)dx,\ x>2. If y(3)=3y(3)=3, then y(4)y(4) is equal to:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 6 (same type asked 33 times) See all 33 of this type

    78
    If the foot of the perpendicular from point (4,3,8)(4,3,8) on the line L1:x−al=y−23=z−b4L_{1}:\frac{x - a}{l}=\frac{y - 2}{3}=\frac{z - b}{4}, l≠0l\neq 0 is (3,5,7)(3,5,7), then the shortest distance between the line L1L_{1} and line L2:x−23=y−44=z−55L_{2}:\frac{x - 2}{3}=\frac{y - 4}{4}=\frac{z - 5}{5} is equal to:

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  5. Question 5

    Differential Equations. Asked once: 2021 Paper 12 (same type asked 41 times) See all 41 of this type

    51
    Let y=y(x)y=y(x) satisfies the equation dydx−∣A∣=0\frac{dy}{dx}- |A| = 0, for all x>0x> 0, where A=[ysin⁡x10−11201x]A=\begin{bmatrix} y & \sin x & 1 \\ 0 & - 1 & 1 \\ 2 & 0 & \frac{1}{x} \end{bmatrix}. If y(π)=π+2y(\pi) =\pi+ 2, then the value of y(π2)y\left( \frac{\pi}{2} \right) is:

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