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Day 338: MHT-CET Maths

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

  1. Question 1

    Mathematical Logic. Asked once: 25 Apr 2025 S1 (same type asked 7 times) See all 7 of this type

    124
    If the statements p,qp,q and rr are true, false and true statements respectively, then the truth value of the statement pattern [∼q∧(p∨∼q)∧∼r]∨p\lbrack \sim q\land (p\vee \sim q) \land \sim r\rbrack \vee p and the truth value of its dual statement respectively are

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  2. Question 2

    Trigonometric Functions. Asked once: 13 May 2024 S2 (same type asked 7 times) See all 7 of this type

    115
    The solutions of sin⁡x+sin⁡5x=sin⁡3x\sin x+\sin 5x=\sin 3x in (0,π2)\left(0,\frac{\pi}{2}\right) are

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  3. Question 3

    Differentiation. Asked once: 20 Apr 2025 S2 (same type asked 7 times) See all 7 of this type

    146
    If u=tan⁡−1xtan⁡−1x+1u =\frac{\tan^{- 1}x}{\tan^{- 1}x+ 1} and v=tan⁡−1(tan⁡−1x)v =\tan^{- 1}\left( \tan^{- 1}x \right) then dudv=\frac{du}{dv}=

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  4. Question 4

    Mathematical Logic. Asked once: 26 Apr 2025 S1 (same type asked 7 times) See all 7 of this type

    119
    Consider statements p:S1p:S_{1} is closed; q:S2q:S_{2} is closed; r:S3r:S_{3} is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively.

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  5. Question 5

    Vectors. Asked once: 11 May 2024 S2 (same type asked 7 times) See all 7 of this type

    114
    If a⃗=i^+j^+k^\vec{a} = \hat{i}+\hat{j}+\hat{k}, b⃗=4i^+3j^+4k^\vec{b} = 4\hat{i}+3\hat{j}+4\hat{k} and c⃗=i^+αj^+βk^\vec{c} = \hat{i}+\alpha\hat{j}+\beta\hat{k} are linearly dependent vectors and ∣c⃗∣=3|\vec{c}|=\sqrt{3}, then the value of α\alpha and β\beta are respectively.

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