PYQ Vault
EbooksTutor

Day 477: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked once: 1 Feb 2024

    174
    If y=(x+1)(x2−x)xx+x+x+115(3cos⁡2x−5)cos⁡3xy=\frac{(\sqrt{x}+ 1)\left( x^{2}-\sqrt{x} \right)}{x\sqrt{x}+x+\sqrt{x}}+\frac{1}{15}\left( 3\cos^{2}x- 5 \right)\cos^{3}x, then 96y′(π6)96y^{'}\left( \frac{\pi}{6} \right) is equal to :

  2. Question 2

    Indefinite Integration. Asked once: 23 Jan 2025

    129
    Let ∫x3sin⁡x dx=g(x)+C\int x^{3}\sin x\,dx = g(x)+C, where CC is the constant of integration. If 8(g(π2)+g′(π2))=απ3+βπ2+γ, α,β,γ∈Z8\left(g\left(\frac{\pi}{2}\right)+g'\left(\frac{\pi}{2}\right)\right)=\alpha\pi^{3}+\beta\pi^{2}+\gamma,\ \alpha,\beta,\gamma\in Z, then α+β−γ\alpha+\beta-\gamma equals:

    Tap an option to check your answer.

  3. Question 3

    Inverse Trigonometric Functions. Asked once: 13 Apr 2023

    176
    For x∈(−1,1]x \in ( - 1,1\rbrack, the number of solutions of the equation sin⁡−1x=2tan⁡−1x\sin^{- 1}x = 2\tan^{- 1}x is equal to

  4. Question 4

    Limits and Continuity. Asked once: 24 Jan 2025

    53
    Let f:R−{0}→R\mathbf{f:R - \{ 0\} \rightarrow R} be a function such that f(x)−6f(1x)=353x−52f(x) - 6f\left( \frac{1}{x} \right)=\frac{35}{3x}-\frac{5}{2}. If the lim⁡x→0(1αx+f(x))=β\lim_{x \rightarrow 0} \left( \frac{1}{\alpha x}+ f(x) \right)= \beta; α,β∈R\alpha,\beta \in R, then α+2β\alpha + 2\beta is equal to

    Tap an option to check your answer.

  5. Question 5

    Matrices. Asked once: 7 Apr 2025

    74
    The number of singular matrices of order 2 , whose elements are from the set {2,3,6,9}\{ 2,3,6,9\} is.