MCQ
The nth derivative of $x{e^x}$ vanishes when
- A$x = 0$
- B$x = - 1$
- ✓$x = - n$
- D$x = n$
Now, ${f^n}(x) = 0$
==> $n{e^x} + x{e^x} = 0$ ==>$x = - n$.
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| Column $I$ | Column $II$ |
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$(A)$ Root$(s)$ of the equation $2 \sin ^2 \theta+\sin ^2 2 \theta=2$ |
$(p)$ $\frac{\pi}{6}$ |
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$(B)$ Points of discontinuity of the function $f(x)=\left[\frac{6 x}{\pi}\right] \cos \left[\frac{3 x}{\pi}\right],$ where $[y]$ denotes the largest integer less than or equal to $y$ |
$(q)$ $\frac{\pi}{4}$ |
|
$(C)$ Volume of the parallelopiped with its edges represented by the vectors $\hat{i}+\hat{j}, \quad \hat{i}+2 \hat{j} \text { and } \hat{i}+\hat{j}+\pi \hat{k}$ |
$(r)$ $\frac{\pi}{3}$ |
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$(D)$ Angle between vectors $\vec{a}$ and $\vec{b}$ where $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors satisfying $\vec{a}+\vec{b}+\sqrt{3} \vec{c}=\overrightarrow{0}$ |
$(s)$ $\frac{\pi}{2}$ |
| $(t)$ $\pi$ |