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Day 494: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 14 Jun 2022

    79
    Let S={θ∈[−π,π]−{±π2}:sin⁡θtan⁡θ+tan⁡θ=sin⁡2θ}S =\left\{ \theta \in \lbrack - \pi,\pi\rbrack -\left\{ \pm\frac{\pi}{2} \right\}:\sin\theta \tan\theta + \tan\theta = \sin2\theta \right\}. If T=∑θ∈Scos⁡2θT =\sum_{\theta \in S} \cos2\theta, then T+n(S)T + n(S) is equal to

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  2. Question 2

    Trigonometric Identities. Asked once: 30 Jan 2024

    152
    For α,β∈(0,π2)\alpha,\beta \in\left( 0,\frac{\pi}{2} \right), let 3sin⁡(α+β)=2sin⁡(α−β)3\sin(\alpha + \beta) = 2\sin(\alpha - \beta) and a real number kk be such that tan⁡α=ktan⁡β\tan\alpha = k\tan\beta. Then the value of kk is equal to:

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  3. Question 3

    Vector Algebra. Asked once: 9 Apr 2024

    159
    Between the following two statements: Statement-I: Let a→=i^+2j^−3k^\overrightarrow{a}=\widehat{i}+ 2\widehat{j}- 3\widehat{k} and b→=2i^+j^−k^\overrightarrow{b}= 2\widehat{i}+\widehat{j}-\widehat{k}. Then the vector r→\overrightarrow{r} satisfying a→×r→=a→×b→\overrightarrow{a}\times\overrightarrow{r}=\overrightarrow{a}\times\overrightarrow{b} and a→⋅r→=0\overrightarrow{a}\cdot\overrightarrow{r}= 0 is of magnitude 10\sqrt{10}. Statement-II: In a triangle ABC,cos⁡2 A+cos⁡2 BABC,\cos2\text{ }A + \cos2\text{ }B +cos⁡2C≥−32+ \cos2C \geq -\frac{3}{2}.

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  4. Question 4

    Application of Derivatives. Asked once: 5 Apr 2024

    62
    Let a rectangle ABCDABCD of sides 2 and 4 be inscribed in another rectangle PQRSPQRS such that the vertices of the rectangle ABCDABCD lie on the sides of the rectangle PQRSPQRS. Let aa and bb be the sides of the rectangle PQRSPQRS when its area is maximum. Then (a+b)2(a + b)^{2} is equal to:

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  5. Question 5

    Application of Integrals. Asked once: 29 Jan 2025

    57
    Let the area of the region {(x,y):2y≤x2+3\left\{ (x,y):2y\leq x^{2}+ 3 \right., y+∣x∣≤3,y≥∣x−1∣}y+ |x| \leq 3,y\geq |x- 1|\} be AA. Then 6A6A is equal to:

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