PYQ Vault
EbooksTutor

Day 67: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked 3 times: 12 May 2024 S1*, 18 Apr 2026 S2*, 19 Apr 2026 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    79
    If f(x)=∣5x−3∣f(x) = |5x - 3| is defined on interval [0,1][0, 1], then the value of ∫01f(x) dx\int_0^1 f(x)\,dx is...

    Tap an option to check your answer.

  2. Question 2

    Definite Integration. Asked 3 times: 15 Apr 2026 S1*, 16 Apr 2026 S1, 18 Apr 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    82
    The value of the definite integral ∫0log⁡e5exex−1ex+3 dx\int_0^{\log_e 5}\dfrac{e^x\sqrt{e^x - 1}}{e^x + 3}\,dx is equal to...

    Tap an option to check your answer.

  3. Question 3

    Differential Equations. Asked 3 times: 23 Apr 2025 S1*, 13 Apr 2026 S2*, 18 Apr 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    86
    A body cools from 100 ∘C100\ ^\circ\mathrm{C} to 60 ∘C60\ ^\circ\mathrm{C} in 20 minutes, the temperature of the surroundings being 20 ∘C20\ ^\circ\mathrm{C}. The total time taken (in minutes) for the body to cool down to 40 ∘C40\ ^\circ\mathrm{C} is ...

    Tap an option to check your answer.

  4. Question 4

    Applications of Derivative. Asked 3 times: 12 May 2024 S1, 22 Apr 2025 S2, 17 Apr 2026 S1 See all 3 times it was asked

    74
    The derivative of the function f(x)=cos⁡4x+sin⁡4x, 0≤x≤2πf(x) = \cos^4 x + \sin^4 x,\ 0 \le x \le 2\pi is positive for

    Tap an option to check your answer.

  5. Question 5

    Trigonometric Functions. Asked 3 times: 13 May 2024 S2, 25 Apr 2025 S2, 16 Apr 2026 S2 See all 3 times it was asked

    67
    If (tan⁡−1x)2+(cot⁡−1x)2=5π28(\tan^{-1}x)^2 + (\cot^{-1}x)^2 = \dfrac{5\pi^2}{8}, then the value of xx is equal to...

    Tap an option to check your answer.