Day 487: MHT-CET Maths

1. A.
   $\ 2\log\left( \frac{2e}{3} \right)$
2. B.
   $\ 2\log\left( \frac{4e}{9} \right)$
3. C.
   $\ \log\left( \frac{2e}{3} \right)$
4. D.
   $\ \log\left( \frac{4e}{9} \right)$

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1. A.
   $f'(0) = 1$
2. B.
   $f'(x)$ is an even function
3. C.
   $f(0) = 0$
4. D.
   $f'(x)$ is an odd function

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1. A.
   $f(x)$ is strictly decreasing on $R$.
2. B.
   $f(x)$ is strictly increasing on $R^+$ and strictly decreasing on $R^-$.
3. C.
   $f(x)$ is strictly increasing on $R$.
4. D.
   $f(x)$ is strictly decreasing on $R^+$ and strictly increasing on $R^-$.

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1. A.
   1 and $-\frac{5}{2}$
2. B.
   $-1$ and $-\frac{1}{2}$
3. C.
   $2$ and $-\frac{7}{2}$
4. D.
   $3$ and $-\frac{9}{2}$

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1. A.
   $\bar{r} = (-\hat{i} + 2\hat{j}) + \lambda(3\hat{i} - \hat{k}) + \mu(\hat{i} + \hat{j} - \hat{k})$
2. B.
   $\bar{r} = (-\hat{i} + 2\hat{j}) + \lambda(3\hat{i} - \hat{k}) + \mu(\hat{i} + 2\hat{j} - \hat{k})$
3. C.
   $\bar{r} = (\hat{i} - 2\hat{j}) + \lambda(3\hat{i} + \hat{k}) + \mu(\hat{i} + \hat{j} - \hat{k})$
4. D.
   $\bar{r} = (-\hat{i} + 2\hat{j}) + \lambda(3\hat{i} - \hat{k}) + \mu(\hat{i} - \hat{j} + \hat{k})$

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