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Day 411: MHT-CET Maths

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

  1. Question 1

    Limits. Asked once: 9 May 2023 S1 (same type asked 10 times) See all 10 of this type

    150
    Let k be a non-zero real number. If f(x)={(ex−1)2sin⁡(xk)log⁡(1+x4),x≠012,x=0f(x)=\begin{cases}\dfrac{(e^x-1)^2}{\sin\left(\frac{x}{k}\right)\log\left(1+\frac{x}{4}\right)}, & x\neq0 \\ 12, & x=0\end{cases} is a continuous function, then the value of k is

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  2. Question 2

    Probability Distribution. Asked once: May 2021 S1 (same type asked 9 times) See all 9 of this type

    147
    A random variable XX has the probability distribution: X:1,2,3,4,5X: 1, 2, 3, 4, 5; P(X=x):K,2K,3K,2K,KP(X=x): K, 2K, 3K, 2K, K. Its variance is

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  3. Question 3

    Mathematical Logic. Asked once: 3 May 2023 S1 (same type asked 9 times) See all 9 of this type

    107
    If pp and qq are statements, then which of the following is a contingency.

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  4. Question 4

    Definite Integration. Asked once: May 2022 S1 (same type asked 8 times) See all 8 of this type

    141
    ∫02[x] dx+∫02∣x−1∣ dx=\int_0^2 [x]\,dx + \int_0^2 |x-1|\,dx = (where [x][x] denotes the greatest integer function.)

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  5. Question 5

    Mathematical Logic. Asked once: 11 May 2024 S1 (same type asked 19 times) See all 19 of this type

    144
    The statement pattern p→∼(p∧∼q)p \to \sim(p \wedge \sim q) is equivalent to

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