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Day 474: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 28 Jan 2026 S1

    71
    In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R−(a,b)\mathbb{R} - (a,b), then a2+b2a^{2} + b^{2} is equal to ____\_\_\_\_ .

  2. Question 2

    Statistics. Asked once: 29 Jun 2022

    167
    The number of values of a∈Na \in N such that the variance of 3,7,12,a,43−a3,7,12,a,43 - a is a natural number is:

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  3. Question 3

    Straight Lines. Asked once: 7 Apr 2025

    58
    If for θ∈[−π3,0]\theta\in\left\lbrack -\frac{\pi}{3},0 \right\rbrack, the points (x,y)=(3tan⁡(θ+π3),2tan⁡(θ+π6))(x,y) =\left( 3\tan\left( \theta+\frac{\pi}{3} \right),2\tan\left( \theta+\frac{\pi}{6} \right) \right) lie on xy+αx+βy+γ=0xy +\alpha x +\beta y +\gamma= 0, then α2+β2+γ2\alpha^{2}+\beta^{2}+\gamma^{2} is equal to :

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  4. Question 4

    Three Dimensional Geometry. Asked once: 8 Apr 2024

    64
    Let P(x,y,z)P(x,y,z) be a point in the first octant, whose projection in the xy−xy- plane is the point QQ. Let OP=γOP =\gamma; the angle between OQ and the positive xx-axis be θ\theta; and the angle between OP and the positive zz-axis be ϕ\phi, where OO is the origin. Then the distance of PP from the xx-axis is :

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  5. Question 5

    Trigonometric Equations. Asked once: 29 Jul 2022

    81
    Let S={θ∈(0,2π):7cos⁡2θ−3sin⁡2θ−2S =\left\{ \theta \in (0,2\pi):7\cos^{2}\theta - 3\sin^{2}\theta - 2 \right.  cos⁡22θ=2}\left. \ \cos^{2}2\theta = 2 \right\}. Then, the sum of roots of all the equations x2−2(tan⁡2θ+cot⁡2θ)x+6sin⁡2θ=0x^{2}- 2\left( \tan^{2}\theta +\cot^{2}\theta \right)x + 6\sin^{2}\theta = 0 θ∈S\theta \in S, is