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Day 470: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 24 Jan 2023

    173
    Let S={θ∈[0,2π):tan⁡(πcos⁡θ)+tan⁡(πsin⁡θ)=0}S = \{\theta \in \lbrack 0,2\pi):\tan(\pi \cos\theta) + \tan(\pi \sin\theta) = 0\}. Then ∑θ∈Ssin⁡2(θ+π4)\sum_{\theta \in S} \sin^{2}\left( \theta +\frac{\pi}{4} \right) is equal to

  2. Question 2

    Trigonometric Identities. Asked once: 21 Jan 2026 S1

    68
    The value of csc⁡10∘−3sec⁡10∘\csc10^{\circ}-\sqrt{3}\sec10^{\circ} is equal to:

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  3. Question 3

    Vector Algebra. Asked once: 4 Apr 2025

    150
    Let the three sides of a triangle ABCABC be given by the vectors 2i^−j^+k^,i^−3j^−5k^2\widehat{i} - \widehat{j} + \widehat{k},\widehat{i} - 3\widehat{j} - 5\widehat{k} and 3i^−4j^−4k^3\widehat{i} - 4\widehat{j} - 4\widehat{k}. Let GG be the centroid of the triangle ABCABC. Then 6(∣AG→∣2+∣BG→∣2+∣CG→∣2)6\left( |\overrightarrow{AG}|^{2} + |\overrightarrow{BG}|^{2} + |\overrightarrow{CG}|^{2} \right) is equal to.

  4. Question 4

    Application of Derivatives. Asked once: 24 Jan 2025

    137
    Let (2,3)(2,3) be the largest open interval in which the function f(x)=2log⁡e(x−2)−x2+ax+1f(x) = 2\log_{e}(x- 2) -x^{2}+ax+ 1 is strictly increasing and (b, c) be the largest open interval, in which the function g(x)=(x−1)3(x+2−a)2g(x) = (x- 1)^{3}(x+ 2 -a)^{2} is strictly decreasing. Then 100(a+b−c)100(a+b-c) is equal to:

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  5. Question 5

    Application of Integrals. Asked once: 23 Jan 2026 S2

    62
    The area of the region enclosed between the circles x2+y2=4x^{2}+y^{2}= 4 and x2+(y−2)2=4x^{2}+ (y - 2)^{2}= 4 is :

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