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Day 501: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked once: 31 Jan 2023

    64
    y=f(x)=sin⁡3(π3(cos⁡(π32(−4x3+5x2+1)32)))y = f(x) =\sin^{3}\left( \frac{\pi}{3}\left( \cos\left( \frac{\pi}{3\sqrt{2}}\left( - 4x^{3}+ 5x^{2}+ 1 \right)^{\frac{3}{2}} \right) \right) \right). Then, at x=1x = 1,

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  2. Question 2

    Indefinite Integration. Asked once: 29 Jan 2024

    160
    If
    ∫ sin⁡32x+cos⁡32xsin⁡3xcos⁡3xsin⁡(x−θ)dx=Acos⁡θtan⁡x−sin⁡θ+Bcos⁡θ−sin⁡θcot⁡x+C\int_{}^{}\ \frac{\sin^{\frac{3}{2}}x + \cos^{\frac{3}{2}}x}{\sqrt{\sin^{3}x\cos^{3}x\sin(x - \theta)}}dx = A\sqrt{\cos\theta \tan x - \sin\theta} + B\sqrt{\cos\theta - \sin\theta \cot x} + C
    where CC is the integration constant, then ABAB is equal to

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  3. Question 3

    Inverse Trigonometric Functions. Asked once: 26 Jun 2022

    169
    If the inverse trigonometric functions take principal values, then cos⁡−1(310cos⁡(tan⁡−1(43))+25sin⁡(tan⁡−1(43)))\cos^{- 1}\left( \frac{3}{10}\cos\left( \tan^{- 1}\left( \frac{4}{3} \right) \right)+\frac{2}{5}\sin\left( \tan^{- 1}\left( \frac{4}{3} \right) \right) \right) is equal to :

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  4. Question 4

    Limits and Continuity. Asked once: 13 Apr 2023

    72
    Among: (S1): lim⁡n→∞1n2(2+4+6+………+2n)=1\lim_{n \rightarrow \infty} \frac{1}{n^{2}}(2 + 4 + 6 + \ldots\ldots\ldots + 2n) = 1 (S2): lim⁡n→∞1n16(115+215+315+………+n15)=116\lim_{n \rightarrow \infty} \frac{1}{n^{16}}\left( 1^{15}+2^{15}+3^{15}+ \ldots\ldots\ldots +n^{15} \right)=\frac{1}{16}

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  5. Question 5

    Matrices. Asked once: 8 Apr 2024

    68
    Let A=[2a013105 b]A =\begin{bmatrix} 2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & \text{ }b \end{bmatrix}. If A3=4 A2−A−21IA^{3}= 4{\text{ }A}^{2}- A - 21I, where I is the identity matrix of order 3×33 \times 3, then 2a+3b2a + 3b is equal to:

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