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Day 325: MHT-CET Maths

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

  1. Question 1

    Mathematical Logic. Asked once: 26 Apr 2025 S1 (same type asked 14 times) See all 14 of this type

    118
    If the truth value of the expression [(p∨q)∧(q→r)∧(∼r)]→(p∧q)\lbrack(p\vee q) \land (q\rightarrow r) \land ( \sim r)\rbrack \rightarrow (p\land q) is False, then truth values of p,q,rp,q,r are respectively.

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  2. Question 2

    Line and Plane. Asked once: 15 Apr 2026 S2 (same type asked 13 times) See all 13 of this type

    93
    If the lines r⃗=(i^+mj^+3k^)+λ(2i^+3j^+4k^)\vec{r} = (\hat{i} + m\hat{j} + 3\hat{k}) + \lambda(2\hat{i} + 3\hat{j} + 4\hat{k}) and r⃗=(4i^+j^)+μ(5i^+mj^+k^)\vec{r} = (4\hat{i} + \hat{j}) + \mu(5\hat{i} + m\hat{j} + \hat{k}) intersect each other, then m =

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  3. Question 3

    Definite Integration. Asked once: 15 Apr 2026 S2 (same type asked 13 times) See all 13 of this type

    82
    If f(x)f(x) is an even function, then ∫−22(∣x∣+f(x)sin⁡x) dx\displaystyle\int_{-2}^{2}(|x| + f(x)\sin x)\,dx is

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  4. Question 4

    Trigonometric Functions. Asked once: 22 Apr 2025 S2 (same type asked 12 times) See all 12 of this type

    101
    Considering only the principal values of the inverse trigonometric function, the value of tan⁡(cos⁡−1152−sin⁡−1417)\tan\left( \cos^{- 1}\frac{1}{5\sqrt{2}}-\sin^{- 1}\frac{4}{\sqrt{17}} \right) is

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  5. Question 5

    Binomial Distribution. Asked once: 19 Apr 2025 S1 (same type asked 12 times) See all 12 of this type

    119
    If a random variable X follows the Binomial distribution B(33,p)B(33,p) such that 3P(X=0)=P(X=1)3P(X = 0) = P(X = 1), then the variance of X is

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