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Day 590: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 25 Jul 2022

    62
    If α,β,γ,δ\alpha,\beta,\gamma,\delta are the roots of the equation x4+x3+x2+x+1=0x^{4}+x^{3}+x^{2}+ x + 1 = 0, then α2021+β2021+γ2021+δ2021\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021} is equal to.

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  2. Question 2

    Conic Sections. Asked once: 28 Jan 2025

    75
    Let E1:x29+y24=1E_{1}:\frac{x^{2}}{9}+\frac{y^{2}}{4}=1 be an ellipse. Ellipses are constructed such that their centres and eccentricities are the same as that of E1E_{1}, and the length of the minor axis of EiE_{i} is the length of the major axis of Ei+1 (i≥1)E_{i+1}\ (i\geq 1). If AiA_{i} is the area of the ellipse EiE_{i}, then 5π(∑i=1∞Ai)\frac{5}{\pi}\left(\sum_{i=1}^{\infty} A_{i}\right) is equal to

  3. Question 3

    Definite Integration. Asked once: 13 Apr 2023

    61
    ∫0∞6e3x+6e2x+11ex+6dx\int_{0}^{\infty} \frac{6}{e^{3x}+ 6e^{2x}+ 11e^{x}+ 6}dx

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  4. Question 4

    Matrices. Asked once: 14 Jun 2022

    69
    Let S={n:1≤n≤50\mathbf{S = \{}\sqrt{n}:1 \leq n \leq 50 and nn is odd }\} Let a∈Sa \in S and A=[10a−110−a01]A =\begin{bmatrix} 1 & 0 & a \\ - 1 & 1 & 0 \\ - a & 0 & 1 \end{bmatrix} If ∑a∈Sdet(adjA)=100λ\sum_{a \in S} det(adjA) = 100\lambda, then λ\lambda is equal to

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  5. Question 5

    Permutations and Combinations. Asked once: 2021 Paper 3

    77
    The total number of positive integral solutions (x,y,z)(x,y,z) such that xyz=24xyz= 24 is

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