MCQ
${d \over {dx}}({x^2}{e^x}\sin x) = $
- ✓$x\,{e^x}(2\sin x + x\sin x + x\cos x)$
- B$x\,{e^x}(2\sin x + x\sin x - \cos x)$
- C$x\,{e^x}(2\sin x + x\sin x + \cos x)$
- DNone of these
$= x{e^x}(2\sin x + x\sin x + x\cos x)$.
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$\text{Let}\ \vec{\text{a}}\ \text{and}\ \vec{\text{b}}$ be two unit vectors and $\theta$ is the angle between them. Then $\vec{\text{a}}+\vec{\text{b}}$ is a unit vector if,
$\theta=\frac{\pi}{4}$
$\theta=\frac{\pi}{3}$
$\theta=\frac{\pi}{2}$
$\theta=\frac{2\pi}{3}$
Statement $-1 :$ ${\rm{tr}}\left( A \right) = 0$
Statement $-2 :$ $\det \left( A \right) = 1$
$\frac{\text{a}+\text{b}}{2}\int\limits^\text{b}_\text{a}\text{f}(\text{b}-\text{x})\text{dx}$
$\frac{\text{a}+\text{b}}{2}\int\limits^\text{b}_\text{a}\text{f}(\text{b}+\text{x})\text{dx}$
$\frac{\text{b}-\text{a}}{2}\int\limits^\text{b}_\text{a}\text{f}(\text{x})\text{dx}$
$\frac{\text{a}+\text{b}}{2}\int\limits^\text{b}_\text{a}\text{f}(\text{x})\text{dx}$