Day 417: MHT-CET Maths

1. A.
   $f(x)$ is not continuous at $x = 0$
2. B.
   $f(x)$ is decreasing in $(-1, \infty)$
3. C.
   $f(x)$ is increasing in $(-1, \infty)$
4. D.
   $f(x)$ has maxima at $x = 1$

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1. A.
   $f'(x)$
2. B.
   $g'(x)$
3. C.
   $3g'(x)$
4. D.
   $3f'(x)$

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1. A.
   $x + c$
2. B.
   $\dfrac{x}{2} + c$
3. C.
   $\dfrac{x^2}{2} + c$
4. D.
   $x^2 + c$

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

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1. A.
   the vector lies along one of the coordinate axes.
2. B.
   the vector $\bar{r}$ is equally inclined to the three coordinate axes.
3. C.
   The vector $\bar{r}$ is perpendicular to the vector $\hat{i} + \hat{j} + \hat{k}$
4. D.
   The vector $\bar{r}$ makes an angle of $\dfrac{\pi}{3}$ with each of the coordinate axes.

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