Day 32: MHT-CET Maths

1. A.
   Linear differential equation $\dfrac{dy}{dx} - y = 2x$, Integrating factor $= e^{-x}$
2. B.
   Linear differential equation $\dfrac{dy}{dx} + y = e^x$, Integrating factor $= e^x$
3. C.
   Linear differential equation $\dfrac{dy}{dx} = x + xy$, Integrating factor $= e^{\frac{x^2}{2}}$
4. D.
   Linear differential equation $x\dfrac{dy}{dx} + 2y = x^2\log x$, Integrating factor $= x^2$

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1. A.
   $y = x\log x - x + c$
2. B.
   $y = x\log x + c$
3. C.
   $y = 1/x + c$
4. D.
   $y = x.\log x + x + c$

Tap an option to check your answer.

1. A.
   $\dfrac{\pi}{2}$
2. B.
   $\pi$
3. C.
   $\dfrac{3\pi}{2}$
4. D.
   $2\pi$

Tap an option to check your answer.

1. A.
   $\dfrac{2\sqrt{30}}{5}$
2. B.
   $\dfrac{2}{3}$
3. C.
   $\dfrac{\sqrt{13}}{5}$
4. D.
   $1$

Tap an option to check your answer.

1. A.
   $\sin^{-1}\left(\dfrac{\sqrt{7}}{3}\right)$
2. B.
   $\sin^{-1}\left(\dfrac{\sqrt{14}}{\sqrt{26}}\right)$
3. C.
   $\sin^{-1}\left(\dfrac{\sqrt{21}}{14}\right)$
4. D.
   $\sin^{-1}\left(\dfrac{\sqrt{28}}{21}\right)$

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