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Day 499: JEE Mains Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: 29 Jan 2024

    157
    The sum of the solutions x∈Rx\in\mathbb{R} of the equation 3cos⁡2x+cos⁡32xcos⁡6x−sin⁡6x=x3−x2+6\frac{3\cos2x+\cos^{3}2x}{\cos^{6}x-\sin^{6}x}=x^{3}-x^{2}+ 6 is

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  2. Question 2

    Vector Algebra. Asked once: 5 Apr 2024

    157
    Consider three vectors a→,b→,c→\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}. Let ∣a→∣=2,∣b→∣=3|\overrightarrow{a}| = 2,|\overrightarrow{b}| = 3 and a→=b→×c→\overrightarrow{a}=\overrightarrow{b}\times\overrightarrow{c}. If α∈[0,π3]\alpha \in\left\lbrack 0,\frac{\pi}{3} \right\rbrack is the angle between the vectors b→\overrightarrow{b} and c→\overrightarrow{c}, then the minimum value of 27∣c→−a→∣227|\overrightarrow{c}-\overrightarrow{a}|^{2} is equal to :

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  3. Question 3

    Application of Derivatives. Asked once: 5 Apr 2024

    178
    Let the maximum and minimum values of (8x−x2−12−4)2+(x−7)2,x∈R\left( \sqrt{8x -x^{2}- 12}- 4 \right)^{2}+ (x - 7)^{2},x \in R be MM and mm respectively. Then M2−m2M^{2}-m^{2} is equal to

  4. Question 4

    Application of Integrals. Asked once: 28 Jan 2025

    134
    The area of the region bounded by the curves x(1+y2)=1x\left( 1 +y^{2} \right)= 1 and y2=2xy^{2}= 2x is :

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  5. Question 5

    Binomial Theorem. Asked once: 30 Jan 2024

    167
    Suppose 2−p,p,2−α,α2 - p,p,2 - \alpha,\alpha are the coefficient of four consecutive terms in the expansion of (1+x)n(1 + x)^{n}. Then the value of p2−α2+6α+2pp^{2}-\alpha^{2}+ 6\alpha + 2p equals

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