MCQ
$\int {\frac{{{e^{{{\tan }^{ - 1}}\sqrt x }}}}{{\sqrt x + x\sqrt x }}dx = } $
- A${e^{{{\tan }^{ - 1}}\sqrt x }} + c$
- B$\frac{1}{2}{e^{{{\tan }^{ - 1}}\sqrt x }} + c$
- C$\log {\tan ^{ - 1}}\sqrt x + c$
- ✓$2{e^{{{\tan }^{ - 1}}\sqrt x }} + c$
$\frac{1}{1+x} \times \frac{1}{2 \sqrt{x}} d x=d t$
$\frac{d x}{\sqrt{x}+x \sqrt{x}}=2 d t$
$\int \mathrm{e}^{\mathrm{t}} 2 \mathrm{dt}=2 \mathrm{e}^{\mathrm{t}}+\mathrm{c}$
$=2 \mathrm{e}^{\tan ^{-1} \sqrt{\mathrm{x}}}+\mathrm{c}$
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$E=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 3 & 4 \\ 8 & 13 & 18\end{array}\right], P=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]$ and $F=\left[\begin{array}{ccc}1 & 3 & 2 \\ 8 & 18 & 13 \\ 2 & 4 & 3\end{array}\right]$
If $Q$ is a nonsingular matrix of order $3 \times 3$, then which of the following statements is (are) $TRUE$?
$(A)$F $=P E P$ and $P^2=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
$(B)$ $\left| EQ + PFQ ^{-1}\right|=| EQ |+\left| PFQ ^{-1}\right|$
$(C)$ $\left|( EF )^3\right|>| EF |^2$
$(D)$ Sum of the diagonal entries of $P ^{-1} EP + F$ is equal to the sum of diagonal entries of $E + P ^{-1} FP$