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Day 457: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 6 Apr 2026 S2

    62
    Let x=9x = 9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity is 13\frac{1}{3}. Let P(α,0),α>0P(\alpha,0),\alpha> 0, be a focus of E and AB be a chord passing through P . Then the locus of the mid point of AB is :

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  2. Question 2

    Definite Integration. Asked once: 5 Apr 2026 S1

    70
    The value of the integral ∫π6π3(4−csc⁡2xcos⁡4x)dx\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \left( \frac{4 -\csc^{2}x}{\cos^{4}x} \right)dx is :

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  3. Question 3

    Determinants. Asked once: 9 Apr 2024

    180
    Consider the matrices: A=[2−53 m],B=[20 m]A =\begin{bmatrix} 2 & - 5 \\ 3 & \text{ }m \end{bmatrix},B =\begin{bmatrix} 20 \\ \text{ }m \end{bmatrix} and X=[xy]X=\begin{bmatrix} x \\ y \end{bmatrix}. Let the set of all mm, for which the system of equations AX=BAX = B has a negative solution (i.e., x<0x < 0 and y<0y < 0 ), be the interval (a, b). Then 8∫ab∣ A∣dm8\int_{a}^{b} |\text{ }A|dm is equal to.

  4. Question 4

    Differential Equations. Asked once: 30 Jan 2024

    165
    Let f:R−{0}→Rf:\mathbb{R}\mathbf{- \{ 0\} \rightarrow}\mathbb{R} be a function satisfying f(xy)=f(x)f(y)f\left( \frac{x}{y} \right)=\frac{f(x)}{f(y)} for all x,y,f(y)≠0x,y,f(y) \neq 0. If f′(1)=2024f^{'}(1) = 2024, then

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  5. Question 5

    Differentiation. Asked once: 9 Apr 2024

    73
    Let f(x)=ax3+bx2+cx+41f(x) = ax^{3}+ bx^{2}+ cx + 41 be such that f(1)=40,f′(1)=2f(1) = 40,f^{'}(1) = 2 and f′′(1)=4f^{''}(1) = 4. Then a2+b2+c2a^{2}+b^{2}+c^{2} is equal to:

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