MCQ
If $A$=$\left[ {\begin{array}{*{20}{c}}2&0&0\\0&2&0\\0&0&2\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}1&2&3\\0&1&3\\0&0&2\end{array}} \right],$ then $|AB|$ is equal to
- A$4$
- B$8$
- ✓$16$
- D$32$
$\therefore $ $AB = 2IB = 2B = \left[ {\begin{array}{*{20}{c}}2&4&6\\0&2&6\\0&0&4\end{array}} \right]$
Therefore $|AB| = \left| {\,\begin{array}{*{20}{c}}2&4&6\\0&2&6\\0&0&4\end{array}\,} \right| = 2(8) = 16$
Aliter : $|A| = 2 \times 2 \times 2 = 8$, $|B| = 1 \times 1 \times 2 = 2$
$\therefore $ $|AB| = \,|A|\,|B| = 2 \times 8 = 16$.
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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 $y$ |
$(q)$ $\frac{\pi}{4}$ |
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$(C)$ 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 $\vec{a}+\vec{b}+\sqrt{3} \vec{c}=\overrightarrow{0}$ |
$(s)$ $\frac{\pi}{2}$ |
| $(t)$ $\pi$ |