Day 224: MHT-CET Maths

1. A.
   $\frac{x^2}{2}+3x-\log|x|+c$
2. B.
   $\frac{x^2}{2}+3x+2\log|x|+c$
3. C.
   $\frac{x^2}{2}-3x+2\log|x|+c$
4. D.
   $\frac{x^2}{2}-3x-\log|x|+c$

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1. A.
   $\cot x + \cot^2 x + c$, where c is the constant of integration
2. B.
   $\tan x - \cot x - 3x + c$, where c is the constant of integration
3. C.
   $2\sin^5 x + 2\cos^5 x + c$, where c is the constant of integration
4. D.
   $\sin^3 x + 2\cos^3 x + c$, where c is the constant of integration

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1. A.
   $\bar{r}\cdot\left(-5\hat{i} - 3\hat{j} + 11\hat{k}\right) + \dfrac{135}{2} = 0$
2. B.
   $\bar{r}\cdot\left(\dfrac{3}{2}\hat{i} + \dfrac{7}{2}\hat{j} - \dfrac{9}{2}\hat{k}\right) + \dfrac{135}{2} = 0$
3. C.
   $\bar{r}\cdot\left(4\hat{i} + 5\hat{j} - 10\hat{k}\right) + 4 = 0$
4. D.
   $\bar{r}\cdot\left(-\hat{i} + 2\hat{j} + \hat{k}\right) + 4 = 0$

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1. A.
   $2,\frac{25}{4}$
2. B.
   $\ - 2,\frac{25}{4}$
3. C.
   $2,\frac{- 25}{4}$
4. D.
   $\ - 2,\frac{- 25}{4}$

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1. A.
   $\dfrac{13}{9!}$
2. B.
   $\dfrac{1}{210}$
3. C.
   $\dfrac{1}{35}$
4. D.
   $0$

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