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Day 475: JEE Mains Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: 29 Jan 2025

    127
    If sin⁡x+sin⁡2x=1,x∈(0,π2)\sin x +\sin^{2}x = 1,x \in\left( 0,\frac{\pi}{2} \right), then (cos⁡12x+tan⁡12x)+3(cos⁡10x+tan⁡10x+cos⁡8x+tan⁡8x)\left( \cos^{12}x +\tan^{12}x \right)+ 3\left( \cos^{10}x +\tan^{10}x +\cos^{8}x +\tan^{8}x \right) +(cos⁡6x+tan⁡6x)+\left( \cos^{6}x +\tan^{6}x \right) is equal to

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  2. Question 2

    Vector Algebra. Asked once: 2 Apr 2025

    61
    If a→\overrightarrow{a} is nonzero vector such that its projections on the vectors 2i^−j^+2k^,i^+2j^−2k^2\widehat{i}-\widehat{j}+ 2\widehat{k},\widehat{i}+ 2\widehat{j}- 2\widehat{k} and k^\widehat{k} are equal, then a unit vector along a→\overrightarrow{a} is:

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  3. Question 3

    Application of Derivatives. Asked once: 23 Jan 2025

    74
    If the set of all values of a, for which the equation 5x3−15x−a=05x^{3}- 15x - a = 0 has three distinct real roots, is the interval (α,β)(\alpha,\beta), then β−2α\beta - 2\alpha is equal to ____\_\_\_\_

  4. Question 4

    Application of Integrals. Asked once: 22 Jan 2026 S2

    62
    The area of the region A={(x,y):4x2+y2≤8A =\left\{ (x,y):4x^{2}+y^{2}\leq 8 \right. and  y2≤4x}\left. \ y^{2}\leq 4x \right\} is :

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  5. Question 5

    Binomial Theorem. Asked once: 22 Jan 2025

    149
    If ∑r=130r2( 30Cr)2 30Cr−1=α×229\sum_{r = 1}^{30} \frac{r^{2}\left( \ ^{30}C_{r} \right)^{2}}{\ ^{30}C_{r - 1}} = \alpha \times 2^{29}, then α\alpha is equal to