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Day 467: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 4 Apr 2024

    87
    Let A be a 3×33 \times 3 matrix of non-negative real elements such that A[111]=3[111]A\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}= 3\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}. Then the maximum value of det(A)det(A) is

  2. Question 2

    Differential Equations. Asked once: 6 Apr 2023

    86
    Let y=y(x)y = y(x) be a solution of the differential equation (xcosx)dy+(xysinx+ycosx−1)dx=0(xcosx)dy + (xysinx + ycosx - 1)dx = 0, 0<x<π20 < x <\frac{\pi}{2}. If π3y(π3)=3\frac{\pi}{3}y\left( \frac{\pi}{3} \right)=\sqrt{3}, then ∣π6y′′(π6)+2y′(π6)∣\left| \frac{\pi}{6}y^{''}\left( \frac{\pi}{6} \right)+ 2y^{'}\left( \frac{\pi}{6} \right) \right| is equal to

  3. Question 3

    Differentiation. Asked once: 5 Apr 2024

    169
    If y(θ)=2cos⁡θ+cos⁡2θcos⁡3θ+4cos⁡2θ+5cos⁡θ+2y(\theta) =\frac{2\cos\theta + \cos2\theta}{\cos3\theta + 4\cos2\theta + 5\cos\theta + 2}, then at θ=π2,y′′+y′+y\theta =\frac{\pi}{2},y^{''}+y^{'}+ y is equal to:

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  4. Question 4

    Indefinite Integration. Asked once: 3 Apr 2025

    65
    Let f(x)=∫ x33−x2dxf(x) =\int_{}^{}\ x^{3}\sqrt{3 -x^{2}}dx. If 5f(2)=−45f(\sqrt{2}) = - 4, then f(1)f(1) is equal to.

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  5. Question 5

    Inverse Trigonometric Functions. Asked once: 13 Apr 2023

    162
    The range of f(x)=4sin⁡−1(x2x2+1)f(x) = 4\sin^{- 1}\left( \frac{x^{2}}{x^{2}+ 1} \right) is

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