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Day 496: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 27 Jun 2022

    68
    If cos⁡−1(y2)=log⁡e(x5)5,∣y∣<2\cos^{- 1}\left( \frac{y}{2} \right)=\log_{e}\left( \frac{x}{5} \right)^{5},|y| < 2, then :

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  2. Question 2

    Differentiation. Asked once: 8 Apr 2023

    70
    Let f(x)=sin⁡x+cos⁡x−2sin⁡x−cos⁡x,x∈[0,π]−{π4}f(x) =\frac{\sin x + \cos x -\sqrt{2}}{\sin x - \cos x},x \in \lbrack 0,\pi\rbrack -\left\{ \frac{\pi}{4} \right\}. Then f(7π12)f′′(7π12)f\left( \frac{7\pi}{12} \right)f^{''}\left( \frac{7\pi}{12} \right) is equal to

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  3. Question 3

    Indefinite Integration. Asked once: 29 Jan 2024

    70
    For x∈(−π2,π2)x \in\left( -\frac{\pi}{2},\frac{\pi}{2} \right), if y(x)=∫csc⁡x+sin⁡xcsc⁡xsec⁡x+tan⁡xsin⁡2xdxy(x) = \int\frac{\csc x + \sin x}{\csc x\sec x + \tan x\sin^{2}x}dx and lim⁡x→(π2)−y(x)=0\lim_{x \rightarrow\left( \frac{\pi}{2} \right)^{-}} y(x) = 0 then y(π4)y\left( \frac{\pi}{4} \right) is equal to

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  4. Question 4

    Inverse Trigonometric Functions. Asked once: 25 Jul 2022

    180
    Let x=sin⁡(2tan⁡−1α)x = \sin\left( 2\tan^{- 1}\alpha \right) and y=sin⁡(12tan⁡−143)y = \sin\left( \frac{1}{2}\tan^{- 1}\frac{4}{3} \right). If S={α∈R:y2=1−x}S =\left\{ \alpha \in R:y^{2}= 1 - x \right\}, then ∑α∈S16α3\sum_{\alpha \in S} 16\alpha^{3} is equal to

  5. Question 5

    Limits and Continuity. Asked once: 31 Jan 2024

    67
    lim⁡x→0e2∣sin⁡x∣−2∣sin⁡x∣−1x2\lim_{x \rightarrow 0} \frac{e^{2|\sin x|}- 2|\sin x| - 1}{x^{2}}

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