MCQ
$\left| {\,\begin{array}{*{20}{c}}{1 + i}&{1 - i}&i\\{1 - i}&i&{1 + i}\\i&{1 + i}&{1 - i}\end{array}\,} \right| = $
- A$ - 4 - 7i$
- ✓$4 + 7i$
- C$3 + 7i$
- D$7 + 4i$
=$(2 + i)$$\left| {\,\begin{array}{*{20}{c}}0&{ - 2i}&{ - 1}\\0&{ - 1 + 2i}&{2i}\\1&2&{1 - i}\end{array}\,} \right|$ by $\begin{array}{l}{R_1} \to {R_1} - {R_2}\\{R_2} \to {R_2} - {R_3}\end{array}$
= $(2 + i)\,\,\{ - 4{i^2} + ( - 1 + 2i)\} = (2 + i)\,(4 - 1 + 2i)$
= $(2 + i)\,(3 + 2i) = 4 + 7i$.
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| Column $I$ | Column $II$ |
| $(A)$ The set $\left\{\operatorname{Re}\left(\frac{2 i z}{1-z^2}\right): z\right.$ is a complex number, $\left.|z|=1, z \neq \pm 1\right\}$ is | $(p)$ $(-\infty,-1) \cup(1, \infty)$ |
| $(B)$ The domain of the function $f(x)=\sin ^{-1}\left(\frac{8(3)^{x-2}}{1-3^{2(x-1)}}\right)$ is is | $(q)$ $(-\infty, 0) \cup(0, \infty)$ |
| $(C)$ If $f(\theta)=\left|\begin{array}{ccc}1 & \tan \theta & 1 \\ -\tan \theta & 1 & \tan \theta \\ -1 & -\tan \theta & 1\end{array}\right|$, then the set $\left\{f(\theta): 0 \leq \theta<\frac{\pi}{2}\right\}$ is | $(r)$ $[2, \infty)$ |
| $(D)$ If $f(x)=x^{3 / 2}(3 x-10), x \geq 0$, then $f(x)$ is increasing in | $(s)$ $(-\infty,-1] \cup[1, \infty)$ |
| $(t)$ $(-\infty, 0] \cup[2, \infty)$ |