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Day 301: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 2 Apr 2025 (same type asked 7 times) See all 7 of this type

    57
    If θ∈[−2π,2π]\theta\in \lbrack - 2\pi,2\pi\rbrack, then the number of solutions of 22cos⁡2θ+(2−6)cos⁡θ−3=02\sqrt{2}\cos^{2}\theta+ (2 -\sqrt{6})\cos\theta-\sqrt{3}= 0 is equal to:

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  2. Question 2

    Complex Numbers. Asked once: 13 Apr 2023 (same type asked 7 times) See all 7 of this type

    166
    Let S={Z∈C:zˉ=i(z2+Re(zˉ))}S =\left\{ Z \in C:\bar{z}= i\left( z^{2}+ Re(\bar{z}) \right) \right\}. Then ∑z∈S∣z∣2\sum_{z \in S} |z|^{2} is equal to

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  3. Question 3

    Vector Algebra. Asked once: 13 Apr 2023 (same type asked 7 times) See all 7 of this type

    168
    Let for a triangle ABCABC,
    AB→=−2i^+j^+3k^\overrightarrow{AB}= - 2\widehat{i}+\widehat{j}+ 3\widehat{k}
    CB→=αi^+βj^+γk^\overrightarrow{CB}= \alpha\widehat{i}+ \beta\widehat{j}+ \gamma\widehat{k}
    CA→=4i^+3j^+δk^\overrightarrow{CA}= 4\widehat{i}+ 3\widehat{j}+ \delta\widehat{k}
    If δ>0\delta > 0 and the area of the triangle ABCABC is 565\sqrt{6}, then CB→⋅CA→\overrightarrow{CB}\cdot\overrightarrow{CA} is equal to

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  4. Question 4

    Conic Sections. Asked once: 15 Apr 2023 (same type asked 7 times) See all 7 of this type

    72
    The number of common tangents, to the circles x2+y2−18x−15y+131=0x^{2}+y^{2}- 18x - 15y + 131 = 0 and x2+y2−6x−6y−7=0x^{2}+y^{2}- 6x - 6y - 7 = 0, is :

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  5. Question 5

    Definite Integration. Asked once: 5 Apr 2024 (same type asked 7 times) See all 7 of this type

    79
    The value of ∫−ππ2y(1+sin⁡y)1+cos⁡2ydy\int_{- \pi}^{\pi} \frac{2y(1 + \sin y)}{1 +\cos^{2}y}dy is :

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