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Day 283: MHT-CET Maths

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

  1. Question 1

    Differential Equations. Asked once: 15 Apr 2026 S2 (same type asked 6 times) See all 6 of this type

    84
    The solution of dydx=sin⁡(x+y)+cos⁡(x+y)\dfrac{dy}{dx} = \sin(x + y) + \cos(x + y) is

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  2. Question 2

    Differentiation. Asked once: 25 Apr 2025 S2 (same type asked 6 times) See all 6 of this type

    143
    If y−y−y−........∞=x+x+x+........∞\sqrt{y-\sqrt{y-\sqrt{y- ........\infty}}}=\sqrt{x+\sqrt{x+\sqrt{x+ ........\infty}}} then dy dx=\frac{dy}{\text{ }dx}=

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  3. Question 3

    Indefinite Integration. Asked once: 10 May 2024 S2 (same type asked 6 times) See all 6 of this type

    125
    ∫ex(1−cot⁡x+cot⁡2x) dx=\displaystyle\int e^x(1-\cot x+\cot^2 x)\,dx =

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  4. Question 4

    Indefinite Integration. Asked once: 26 Apr 2025 S2 (same type asked 6 times) See all 6 of this type

    126
    ∫dxx12+x13=Ax12+Bx13+Cx16+Dlog(x16+1)+k\int\frac{dx}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}= Ax^{\frac{1}{2}}+ Bx^{\frac{1}{3}}+ Cx^{\frac{1}{6}}+ Dlog\left( x^{\frac{1}{6}}+ 1 \right)+ k (where k is the integration constant) then values of A,B,CA,B,C and D are respectively,

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  5. Question 5

    Line and Plane. Asked once: 22 Apr 2025 S2 (same type asked 6 times) See all 6 of this type

    104
    If the angle between the line x=y−12=z−3λx =\frac{y - 1}{2}=\frac{z - 3}{\lambda} and the plane x+2y+3z=4x + 2y + 3z = 4 is cos⁡−1514\cos^{- 1}\sqrt{\frac{5}{14}}, then the value of λ\lambda is

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