Day 519: MHT-CET Maths

1. A.
   $\frac{\pi}{6}$
2. B.
   $\frac{\pi}{3}$
3. C.
   $\frac{\pi}{2}$
4. D.
   $\frac{2\pi}{3}$

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1. A.
   $\frac{|\bar{b} \times \bar{c}|}{|\bar{c} - \bar{b}|}$
2. B.
   $\frac{|\bar{a} \times \bar{b} + \bar{b} \times \bar{c} + \bar{c} \times \bar{a}|}{|\bar{c} - \bar{b}|}$
3. C.
   $\frac{|\bar{a} \times \bar{b} + \bar{b} \times \bar{c} + \bar{c} \times \bar{a}|}{|\bar{c} \times \bar{b}|}$
4. D.
   $\frac{|\bar{b} \times \bar{c}|}{|\bar{a}|}$

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1. A.
   2 units/sec
2. B.
   $3\sqrt{3}$ units/sec
3. C.
   $\sqrt{3}$ units/sec
4. D.
   $2\sqrt{3}$ units/sec

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1. A.
   $\frac{1}{4}$
2. B.
   $\frac{5}{4}$
3. C.
   $\frac{- 1}{2}$
4. D.
   $\frac{3}{4}$

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1. A.
   $\frac{1}{3}\tan^{- 1}\left( \frac{x}{3} \right) - \frac{3}{x^{2} + 9} + c$, where $c$ is the constant of integration.
2. B.
   $\frac{1}{3}\tan^{- 1}\left( \frac{x}{3} \right) - \frac{1}{x^{2} + 9} + c$, where c is the constant of integration.
3. C.
   $\frac{1}{3}\tan^{- 1}\left( \frac{x}{3} \right) + \frac{3}{x^{2} + 9} + c$, where $c$ is the constant of integration.
4. D.
   $\frac{1}{3}\tan^{- 1}\left( \frac{x}{3} \right) - \frac{1}{x^{2} + 9} + c$, where c is the constant of integration.

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