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Day 566: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 29 Jan 2023

    174
    Let α1,α2,….,α7\alpha_{1},\alpha_{2},\ldots.,\alpha_{7} be the roots of the equation x7+3x5−13x3−15x=0x^{7}+ 3x^{5}- 13x^{3}- 15x = 0 and ∣α1∣≥∣α2∣≥⋯≥\left| \alpha_{1} \right|\geq\left| \alpha_{2} \right|\geq \cdots \geq ∣α7∣\left| \alpha_{7} \right|. Then α1α2−α3α4+α5α6\alpha_{1}\alpha_{2}-\alpha_{3}\alpha_{4}+\alpha_{5}\alpha_{6} is equal to

  2. Question 2

    Conic Sections. Asked once: 3 Apr 2025

    142
    Let C be the circle of minimum area enclosing the ellipse E:x2a2+y2b2=1E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 with eccentricity 12\frac{1}{2} and foci (±2,0)( \pm 2,0). Let PQR be a variable triangle, whose vertex PP is on the circle CC and the side QRQR of length 2a2a is parallel to the major axis of E and contains the point of intersection of E with the negative yy-axis. Then the maximum area of the triangle PQR is

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  3. Question 3

    Definite Integration. Asked once: 1 Feb 2024

    161
    If ∫0π3cos⁡4xdx=aπ+b3\int_{0}^{\frac{\pi}{3}} \cos^{4}xdx = a\pi + b\sqrt{3}, where aa and bb are rational numbers, then 9a+8 b9a + 8\text{ }b is equal to :

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  4. Question 4

    Limits and Continuity. Asked once: 25 Jun 2022

    69
    Let f(x)f(x) be a polynomial function such that f(x)+f′(x)+f′′(x)=x5+64f(x) +f^{'}(x) +f^{''}(x) =x^{5}+ 64. Then, the value of lim⁡x→1f(x)x−1\lim_{x \rightarrow 1} \frac{f(x)}{x - 1}

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  5. Question 5

    Matrices. Asked once: 29 Jul 2022

    173
    Let x=[111]x =\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} and A=[−12301600−1]A =\begin{bmatrix} - 1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & - 1 \end{bmatrix}. For k∈Nk \in\mathbb{N}, if X′AkX=33X^{'}A^{k}X = 33, then kk is equal to: