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Day 161: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 21 Jan 2026 S2 (same type asked 4 times) See all 4 of this type

    57
    Let the line L pass through the point (−3,5,2)( - 3,5,2) and make equal angles with the positive coordinate axes. If the distance of L from the point ( −2,r,1- 2,r,1 ) is 143\sqrt{\frac{14}{3}}, then the sum of all possible values of rr is :

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  2. Question 2

    Trigonometric Equations. Asked once: 27 Jan 2024 (same type asked 4 times) See all 4 of this type

    87
    Let the set of all a∈Ra \in R such that the equation cos⁡2x+asin⁡x=2a−7\cos2x + a\sin x = 2a - 7 has a solution be [p,q]\lbrack p,q\rbrack and r=tan⁡9∘−tan⁡27∘−1cot⁡63∘+tan⁡81∘r = \tan9^{\circ}- \tan27^{\circ}-\frac{1}{\cot63^{\circ}}+ \tan81^{\circ}, then pqr is equal to

  3. Question 3

    Binomial Theorem. Asked once: 25 Jan 2023 (same type asked 4 times) See all 4 of this type

    156
    ∑k=0645+kC3\sum_{k=0}^{6} {}^{45+k}C_{3} is equal to

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  4. Question 4

    Differential Equations. Asked once: 8 Apr 2024 (same type asked 4 times) See all 4 of this type

    79
    Let y=y(x)y=y(x) be the solution of the differential equation (1+y2)etan⁡xdx+cos⁡2x(1+e2tan⁡x)dy=0\left( 1 +y^{2} \right)e^{\tan x}dx+\cos^{2}x\left( 1 +e^{2\tan x} \right)dy= 0, y(0)=1y(0) = 1. Then y(π4)y\left( \frac{\pi}{4} \right) is equal to:

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  5. Question 5

    Differentiation. Asked once: 14 Jun 2022 (same type asked 4 times) See all 4 of this type

    167
    If y=tan⁡−1(sec⁡x3−tan⁡x3), π2<x3<3π2y =\tan^{- 1}\left( \sec x^{3}- \tan x^{3} \right),\ \frac{\pi}{2}<x^{3}<\frac{3\pi}{2}, then

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