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Day 450: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 6 Apr 2026 S1

    74
    For the functions f(θ)=αtan⁡2θ+βcot⁡2θf(\theta) = \alpha\tan^{2}\theta + \beta\cot^{2}\theta, and g(θ)=αsin⁡2θ+βcos⁡2θ,α>β>0g(\theta) = \alpha\sin^{2}\theta + \beta\cos^{2}\theta,\alpha > \beta > 0, let min⁡0<θ<π2f(θ)=max⁡0<θ<πg(θ)\min_{0 < \theta < \frac{\pi}{2}} f(\theta) = \max_{0 < \theta < \pi} g(\theta). If the first term of a G.P. is (α2β)\left( \frac{\alpha}{2\beta} \right), its common ratio is (2βα)\left( \frac{2\beta}{\alpha} \right) and the sum of its first 10 terms is mn,gcd(m,n)=1\frac{m}{n},gcd(m,n) = 1, then m+nm + n is equal to ____\_\_\_\_ .

  2. Question 2

    Statistics. Asked once: 5 Apr 2024

    171
    Let the mean and the standard deviation of the probability distribution
    XXα\alpha10−3-3
    P(X)P(X)13\frac{1}{3}KK16\frac{1}{6}14\frac{1}{4}
    be μ\mu and σ\sigma, respectively. If σ−μ=2\sigma - \mu = 2, then σ+μ\sigma + \mu is equal to

  3. Question 3

    Straight Lines. Asked once: 4 Apr 2026 S2

    60
    Let P(3cos⁡α,2sin⁡α),α≠0P(3\cos\alpha,2\sin\alpha),\alpha\neq 0, be a point on the ellipse x29+y24=1,Q\frac{x^{2}}{9}+\frac{y^{2}}{4}= 1,Q be a point on the circle x2+y2−14x−14y+82=0x^{2}+y^{2}- 14x- 14y+ 82 = 0 and RR be a point on the line x+y=5x+y= 5 such that the centroid of the triangle PQR is (2+cos⁡α,3+23sin⁡α)\left( 2 + \cos\alpha,3 +\frac{2}{3}\sin\alpha \right). Then the sum of the ordinates of all possible points R is:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 3 Apr 2025

    127
    Each of the angles β\beta and γ\gamma that a given line makes with the positive y−y- and zz-axes, respectively, is half of the angle that this line makes with the positive xx-axes. Then the sum of all possible values of the angle β\beta is.

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  5. Question 5

    Trigonometric Equations. Asked once: 9 Apr 2024

    69
    Let
    ∣cos⁡θcos⁡(60∘−θ)cos⁡(60∘+θ)∣≤18,θ∈[0,2π]|\cos\theta \cos(60^{\circ} - \theta)\cos(60^{\circ} + \theta)| \leq\frac{1}{8},\theta \in \lbrack 0,2\pi\rbrack
    Then, the sum of all θ∈[0,2π]\theta \in \lbrack 0,2\pi\rbrack, where cos⁡3θ\cos3\theta attains its maximum value, is:

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