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Day 446: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 24 Jan 2026 S2

    75
    The number of elements in the set {x∈[0∘,180∘]:tan⁡(x+100∘)=tan⁡(x+50∘)tan⁡xtan⁡(x−50∘)}\left\{ x \in \left\lbrack 0^{\circ},180^{\circ} \right\rbrack:\tan\left( x + 100^{\circ} \right) = \tan\left( x + 50^{\circ} \right)\tan x\tan\left( x - 50^{\circ} \right) \right\} is ____\_\_\_\_ .

  2. Question 2

    Trigonometric Identities. Asked once: 2 Apr 2026 S2

    63
    Let P={θ∈[0,4π]:tan⁡2θ≠1}P=\left\{ \theta\in \lbrack 0,4\pi\rbrack:\tan^{2}\theta\neq 1 \right\} and S={a∈Z:2(cos⁡8θ−sin⁡8θ)sec⁡2θ=a2,θ∈P}S=\left\{ a\in Z:2\left( \cos^{8}\theta-\sin^{8}\theta \right)\sec2\theta=a^{2},\theta\in P \right\}. Then n(S)n(S) is :

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  3. Question 3

    Vector Algebra. Asked once: 4 Apr 2026 S1

    74
    Let a→k=(tan⁡θk)i^+j^{\overrightarrow{a}}_{k} = \left( \tan\theta_{k} \right)\widehat{i} + \widehat{j} and b→k=i^−(cot⁡θk)j^{\overrightarrow{b}}_{k} = \widehat{i} - \left( \cot\theta_{k} \right)\widehat{j}, where θk=2k−1π2n+1\theta_{k} = \frac{2^{k - 1}\pi}{2^{n} + 1}, for some n∈N,n>5n \in \mathbb{N},n > 5. Then the value of ∑k=1n∣a→k∣2∑k=1n∣b→k∣2\frac{\sum_{k = 1}^{n} \left| {\overrightarrow{a}}_{k} \right|^{2}}{\sum_{k = 1}^{n} \left| {\overrightarrow{b}}_{k} \right|^{2}} is ____\_\_\_\_ .

  4. Question 4

    Application of Derivatives. Asked once: 24 Jan 2026 S2

    65
    Consider the following three statements for the function f:(0,∞)→Rf:(0,\infty) \rightarrow R defined by
    f(x)=∣log⁡ex∣−∣x−1∣:f(x) =\left| \log_{e}x \right|- |x - 1|:
    (I) f is differentiable at all x>0x > 0. (II) f is increasing in ( 0,1 ). (III) f is decreasing in ( 1,∞1,\infty ). Then.

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  5. Question 5

    Application of Integrals. Asked once: 5 Apr 2026 S2

    74
    Let f:R→Rf:R \rightarrow R be a function such that f(x)+3f(π2−x)=sin⁡x,x∈Rf(x) + 3f\left( \frac{\pi}{2} - x \right) = \sin x,x \in R. Let maximum value of ff on RR be α\alpha. If the area of the region bounded by the curves g(x)=x2g(x) = x^{2} and h(x)=βx3h(x) = \beta x^{3}, β>0\beta > 0, is α2\alpha^{2}, then 30β330\beta^{3} is equal to ____\_\_\_\_