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Day 542: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 12 Apr 2023

    77
    Let CC be the circle in the complex plane with centre z0=12(1+3i)z_{0}=\frac{1}{2}(1 + 3i) and radius r=1r = 1. Let z1=1+z_{1}= 1 + ii and the complex number z2z_{2} be outside the circle C such that ∣z1−z0∣∣z2−z0∣=1\left| z_{1}-z_{0} \right|\left| z_{2}-z_{0} \right|= 1. If z0,z1z_{0},z_{1} and z2z_{2} are collinear, then the smaller value of ∣z2∣2\left| z_{2} \right|^{2} is equal to

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  2. Question 2

    Conic Sections. Asked once: 7 Apr 2025

    128
    Let
    A={(α,β)∈R×R:∣α−1∣≤4 and ∣β−5∣≤6}A\mathbf{= \{(}\alpha,\beta) \in R \times R:|\alpha- 1| \leq 4\text{~and~}|\beta- 5| \leq 6\}
    and
    B={(α,β)∈R×R:16(α−2)2+9(β−6)2≤144}.B=\left\{ (\alpha,\beta) \in R \times R:16(\alpha- 2)^{2}+ 9(\beta- 6)^{2}\leq 144 \right\}.
    Then

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  3. Question 3

    Definite Integration. Asked once: 9 Apr 2024

    165
    The integral ∫1/43/4cos⁡(2cot⁡−11−x1+x)dx\int_{1/4}^{3/4} \cos\left( 2\cot^{- 1}\sqrt{\frac{1 -x}{1 +x}} \right)dx is equal to:

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  4. Question 4

    Determinants. Asked once: 2021 Paper 4

    72
    The following system of linear equations
    3x+3y+2z=93x+2y+2z=9x−y+4z=8\begin{matrix} & 3x + 3y + 2z = 9 \\ & 3x + 2y + 2z = 9 \\ & x - y + 4z = 8 \end{matrix}

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  5. Question 5

    Indefinite Integration. Asked once: 2021 Paper 23

    84
    If ∫sin⁡xsin⁡3x+cos⁡3xdx=\int\frac{\sin x}{\sin^{3}x+\cos^{3}x}dx= αlog⁡e∣1+tan⁡x∣+βlog⁡e∣1−tan⁡x+tan⁡2x∣+γtan⁡−1(2tan⁡x−13)+C\alpha\log_{e}|1 + \tan x| +\beta\log_{e}\left| 1 - \tan x+\tan^{2}x \right|+\gamma\tan^{- 1}\left( \frac{2\tan x- 1}{\sqrt{3}} \right)+C, when CC is constant of integration, then the value of 18(α+β+γ2)18\left( \alpha+\beta+\gamma^{2} \right) is