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Day 412: MHT-CET Maths

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

  1. Question 1

    Differential Equations. Asked once: 3 May 2023 S2 (same type asked 15 times) See all 15 of this type

    128
    The general solution of the differential equation xcos⁡y dy=(xexlog⁡x+ex) dxx\cos y\,dy=(xe^{x}\log x+e^{x})\,dx is given by

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  2. Question 2

    Mathematical Logic. Asked once: 16 May 2023 S2 (same type asked 14 times) See all 14 of this type

    110
    Truth values of p→rp \to r is F and p↔qp \leftrightarrow q is F. Then the truth values of (∼p∨q)→(p∨∼q)(\sim p \vee q) \to (p \vee \sim q) and (p∧∼q)→(∼p∧q)(p \wedge \sim q) \to (\sim p \wedge q) are respectively

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  3. Question 3

    Differential Equations. Asked once: 3 May 2023 S1 (same type asked 14 times) See all 14 of this type

    105
    The differential equation [1+(dydx)2]⋅(d2ydx2)1/2=kx\left[1+\left(\frac{dy}{dx}\right)^2\right]\cdot\left(\frac{d^2y}{dx^2}\right)^{1/2}=kx is of

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  4. Question 4

    Definite Integration. Asked once: 4 May 2023 S1 (same type asked 13 times) See all 13 of this type

    126
    The integral ∫−1/21/2([x]+log⁡e1+x1−x)dx\int_{-1/2}^{1/2}\left([x]+\log_e\frac{1+x}{1-x}\right)dx, where [x][x] represents greatest integer function, equals

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  5. Question 5

    Trigonometric Functions. Asked once: 10 May 2023 S1 (same type asked 12 times) See all 12 of this type

    112
    The numerical value of tan⁡ ⁣(2tan⁡−1 ⁣15+π4)\tan\!\left(2\tan^{-1}\!\frac{1}{5}+\frac{\pi}{4}\right)

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