PYQ Vault
EbooksTutor

Day 242: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 24 Jan 2023 (same type asked 6 times) See all 6 of this type

    85
    The value of 8π∫0π2(cos⁡x)2023(sin⁡x)2023+(cos⁡x)2023dx\frac{8}{\pi}\int_{0}^{\frac{\pi}{2}} \frac{(\cos x)^{2023}}{(\sin x)^{2023}+ (\cos x)^{2023}}dx is

  2. Question 2

    Relations and Functions. Asked once: 4 Apr 2024 (same type asked 6 times) See all 6 of this type

    78
    If the domain of the function sin⁡−1(3x−222x−19)+log⁡e(3x2−8x+5x2−3x−10)\sin^{- 1}\left( \frac{3x - 22}{2x - 19} \right)+\log_{e}\left( \frac{3x^{2}- 8x + 5}{x^{2}- 3x - 10} \right) is  (α,β]\ (\alpha,\beta\rbrack, then 3α+10β3\alpha + 10\beta is equal to :

    Tap an option to check your answer.

  3. Question 3

    Straight Lines. Asked once: 24 Jan 2025 (same type asked 6 times) See all 6 of this type

    69
    Let the lines 3x−4y−α=0,8x−11y−33=03x - 4y - \alpha = 0,8x - 11y - 33 = 0, and 2x−3y+λ=02x - 3y + \lambda = 0 be concurrent. If the image of the point (1,2)(1,2) in the line 2x−3y+λ=02x - 3y + \lambda = 0 is (5713,−4013)\left( \frac{57}{13},\frac{- 40}{13} \right), then ∣αλ∣|\alpha\lambda| is equal to :

    Tap an option to check your answer.

  4. Question 4

    Determinants. Asked once: 2021 Paper 9 (same type asked 6 times) See all 6 of this type

    64
    The solutions of the equation ∣1+sin⁡2xsin⁡2xsin⁡2xcos⁡2x1+cos⁡2xcos⁡2x4sin⁡2x4sin⁡2x1+4sin⁡2x∣=0,(0<x<π)\left| \begin{matrix} 1 +\sin^{2}x & \sin^{2}x & \sin^{2}x \\ \cos^{2}x & 1 +\cos^{2}x & \cos^{2}x \\ 4\sin2x & 4\sin2x & 1 + 4\sin2x \end{matrix} \right|= 0,(0 <x<\pi), are

    Tap an option to check your answer.

  5. Question 5

    Permutations and Combinations. Asked once: 9 Apr 2024 (same type asked 6 times) See all 6 of this type

    174
    The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is