MCQ
$\int_{}^{} {\frac{{{x^2} + x - 6}}{{(x - 2)(x - 1)}}dx = } $
- A$x + 2\log (x - 1) + c$
- B$2x + 2\log (x - 1) + c$
- C$x + 4\log (1 - x) + c$
- ✓$x + 4\log (x - 1) + c$
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If the volume of the parallelopiped, whose adjacent sides are represented by the vectors $\overrightarrow{ u }, \overrightarrow{ v }$ and $\overrightarrow{ w }$ , is $\sqrt{2}$, then the value of $|3 \vec{u}+5 \vec{v}|$ is. . . . .
$f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right) \text {, where } x \in\left[0, \frac{\pi}{2}\right] \text {, }$
consider the following two statements :
($I$) $\mathrm{f}$ is increasing in $\left(0, \frac{\pi}{2}\right)$.
($II$) $\mathrm{f}^{\prime}$ is decreasing in $\left(0, \frac{\pi}{2}\right)$.
Between the above two statements,
$\left| {\begin{array}{*{20}{c}}
{\left[ \pi \right]}&{amp(1 + i\sqrt 3 )}&1 \\
1&0&2 \\
{\operatorname{sgn} ({{\cot }^{ - 1}}x)}&1&{\{ \pi \} }
\end{array}} \right|$ is-