Day 36: MHT-CET Maths

1. A.
   $\dfrac{2}{9\pi}\ ft/sec$
2. B.
   $\dfrac{4}{9\pi}\ ft/sec$
3. C.
   $\dfrac{8}{9\pi}\ ft/sec$
4. D.
   $\dfrac{10}{9\pi}\ ft/sec$

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1. A.
   $xy = 2$
2. B.
   $y = 2x$
3. C.
   $x^2y = 2$
4. D.
   $x^3y = 2$

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1. A.
   $-45$
2. B.
   $-120$
3. C.
   $-105$
4. D.
   $-129$

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1. A.
   $-\dfrac{e^x}{(1 - e^x)^3}$
2. B.
   $\dfrac{e^x}{(e^x - 1)^3}$
3. C.
   $\dfrac{1}{(1 - e^x)^3}$
4. D.
   $\dfrac{e^x}{(1 - e^x)^3}$

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1. A.
   $\dfrac{1}{\sqrt{13}}\tan^{-1}\left(\dfrac{4\tan x + 1}{\sqrt{13}}\right) + c$
2. B.
   $\dfrac{2}{\sqrt{11}}\tan^{-1}\left(\dfrac{4\tan x + 2}{\sqrt{11}}\right) + c$
3. C.
   $\dfrac{1}{11}\tan^{-1}\left(\dfrac{2\tan x + 1}{11}\right) + c$
4. D.
   $\dfrac{1}{\sqrt{11}}\tan^{-1}\left(\dfrac{4\tan x + 1}{\sqrt{11}}\right) + c$

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