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Day 342: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 29 Jun 2022 (same type asked 7 times) See all 7 of this type

    84
    The number of elements in the set S=S= {θ∈[−4π,4π]:3cos⁡22θ+6cos⁡2θ−\left\{ \theta\in \lbrack - 4\pi,4\pi\rbrack:3\cos^{2}2\theta+ 6\cos2\theta- \right.  10cos⁡2θ+5=0}\left. \ 10\cos^{2}\theta+ 5 = 0 \right\} is

  2. Question 2

    Complex Numbers. Asked once: 27 Jul 2022 (same type asked 7 times) See all 7 of this type

    90
    Let S={z∈C:z2+zˉ=0}S =\left\{ z\in C:z^{2}+\bar{z}= 0 \right\}. Then ∑z∈S(Re(z)+Im(z))\sum_{z \in S} (Re(z) + Im(z)) is equal to

  3. Question 3

    Vector Algebra. Asked once: 28 Jun 2022 (same type asked 7 times) See all 7 of this type

    164
    Let a→=αi^+2j^−k^\overrightarrow{a}= \alpha\widehat{i}+ 2\widehat{j}-\widehat{k} and b→=−2i^+αj^+k^\overrightarrow{b}= - 2\widehat{i}+ \alpha\widehat{j}+\widehat{k}, where α∈R\alpha \in R. If the area of the parallelogram whose adjacent sides are represented by the vectors a→\overrightarrow{a} and b→\overrightarrow{b} is 15(α2+4)\sqrt{15\left( \alpha^{2}+ 4 \right)}, then the value of 2∣a→∣2+(a→⋅b→)∣b→∣22|\overrightarrow{a}|^{2}+ (\overrightarrow{a}\cdot\overrightarrow{b})|\overrightarrow{b}|^{2} is equal to

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  4. Question 4

    Conic Sections. Asked once: 2021 Paper 9 (same type asked 7 times) See all 7 of this type

    65
    Choose the correct statement about two circles whose equations are given below:
    x2+y2−10x−10y+41=0x^{2}+y^{2}- 10x - 10y + 41 = 0
    x2+y2−22x−10y+137=0x^{2}+y^{2}- 22x - 10y + 137 = 0

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  5. Question 5

    Definite Integration. Asked once: 1 Feb 2024 (same type asked 7 times) See all 7 of this type

    62
    The value of the integral ∫0π4xdxsin⁡4(2x)+cos⁡4(2x)\int_{0}^{\frac{\pi}{4}} \frac{xdx}{\sin^{4}(2x) +\cos^{4}(2x)} equals:

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