PYQ Vault
EbooksTutor

Day 90: MHT-CET Maths

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

  1. Question 1

    Definite Integration. This type asked 3 times: May 2022 S1, 11 May 2024 S1, 17 Apr 2026 S2. This one: 17 Apr 2026 S2 See all 3 of this type

    83
    The value of the definite integral ∫0π15+4cos⁡x dx\int_0^\pi\dfrac{1}{5 + 4\cos x}\,dx is equal to ...

    Tap an option to check your answer.

  2. Question 2

    Differential Equations. This type asked 3 times: 16 May 2023 S2, 17 Apr 2026 S1, 17 Apr 2026 S2. This one: 17 Apr 2026 S2 See all 3 of this type

    81
    The function f(x)=∫0xdt1+cos⁡tf(x) = \int_0^x\dfrac{dt}{1 + \cos t} satisfies which of the following differential equations?

    Tap an option to check your answer.

  3. Question 3

    Sets, Relations and Functions. This type asked 3 times: 4 May 2023 S2, 11 May 2024 S2, 17 Apr 2026 S2. This one: 17 Apr 2026 S2 See all 3 of this type

    67
    If f(x)=1−x1+xf(x) = \dfrac{1 - x}{1 + x}, then f(f(cos⁡x))=f(f(\cos x)) =

    Tap an option to check your answer.

  4. Question 4

    Probability Distribution. This type asked 3 times: 11 May 2024 S1, 20 Apr 2025 S1, 17 Apr 2026 S1. This one: 17 Apr 2026 S1 See all 3 of this type

    100
    A box contains 8 red and N green balls. Two balls are drawn at random from it. If X is the random variable representing the number of green balls drawn and E(X)=1.2E(X) = 1.2, then N=…N = \ldots

    Tap an option to check your answer.

  5. Question 5

    Vectors. This type asked 3 times: 16 May 2023 S2, 21 Apr 2025 S1, 17 Apr 2026 S1. This one: 17 Apr 2026 S1 See all 3 of this type

    91
    Let aˉ=(a1i^+a2j^+a3k^), bˉ=(b1i^+b2j^+b3k^), cˉ=(c1i^+c2j^+c3k^)\bar{a} = (a_1\hat{i} + a_2\hat{j} + a_3\hat{k}),\ \bar{b} = (b_1\hat{i} + b_2\hat{j} + b_3\hat{k}),\ \bar{c} = (c_1\hat{i} + c_2\hat{j} + c_3\hat{k}) be three non-zero vectors such that aˉ\bar{a} is a unit vector perpendicular to both bˉ\bar{b} and cˉ\bar{c}. If the angle between bˉ\bar{b} and cˉ\bar{c} is π3\dfrac{\pi}{3} then ∣a1a2a3b1b2b3c1c2c3∣2=\begin{vmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{vmatrix}^2 =

    Tap an option to check your answer.