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Day 409: MHT-CET Maths

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

  1. Question 1

    Mathematical Logic. Asked once: 14 May 2024 S2 (same type asked 14 times) See all 14 of this type

    125
    If the statement p↔(q→p)p \leftrightarrow (q \to p) is false, then true statement/statement pattern is

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  2. Question 2

    Differential Equations. Asked once: 3 May 2023 S2 (same type asked 14 times) See all 14 of this type

    139
    If order and degree of the differential equation (d2ydx2)5+4(d2ydx2)5⋅d3ydx3+d3ydx3=sin⁡x\left(\frac{d^{2}y}{dx^{2}}\right)^{5}+4\left(\frac{d^{2}y}{dx^{2}}\right)^{5}\cdot\frac{d^{3}y}{dx^{3}}+\frac{d^{3}y}{dx^{3}}=\sin x, are mm and nn respectively, then the value of m2+n2m^{2}+n^{2} is equal to

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  3. Question 3

    Mathematical Logic. Asked once: 2 May 2023 S1 (same type asked 14 times) See all 14 of this type

    129
    If the statement p∨∼(q∧r)p \vee \sim(q \wedge r) is false, then the truth values of pp, qq and rr are respectively

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  4. Question 4

    Definite Integration. Asked once: 15 May 2023 S1 (same type asked 13 times) See all 13 of this type

    132
    The value of integral ∫−20[x3+3x2+3x+5+(x+1)cos⁡(x+1)]dx\int_{-2}^{0}\left[x^{3}+3x^{2}+3x+5+(x+1)\cos(x+1)\right]dx is equal to

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  5. Question 5

    Trigonometric Functions. Asked once: 10 May 2023 S2 (same type asked 12 times) See all 12 of this type

    115
    tan⁡(cos⁡−112+tan⁡−112)=\tan\left(\cos^{-1}\frac{1}{\sqrt{2}}+\tan^{-1}\frac{1}{2}\right)=

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