MCQ
If $ \displaystyle \begin{vmatrix}\text{a} &\text{amp; }\text{b} &\text{amp; 0}\\ 0 &\text{amp; a} &\text{amp; b}\\\text{b}&\text{amp; a}&\text{amp; 0}\end{vmatrix}=0,$ then the order is:
  • 3 × 3
  • B
    2 × 3
  • C
    2 × 2
  • D
    None of these

Answer

Correct option: A.
3 × 3
There are 3 rows and 3 columns.Therefore the order of the matrix is 3 × 3.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Let $f: R \rightarrow R$ be given by $f(x)=\left[x^2\right]+[x+1]-3$ where $[x]$ denotes the greatest integer less than or equal to $x$. Then, $f(x)$ is:
If $I_{m, n}=\int_{0}^{1} x^{m-1}(1-x)^{n-1} d x,$ for $m, n \geq 1$ and $\int_{0}^{1} \frac{x^{m-1}+x^{n-1}}{(1+x)^{m+n}} d x=\alpha I_{m, n}, \alpha \in R,$ then $\alpha$ equals .... .
If $a,b,c$ are positive integers, then the determinant $\Delta = \left| {\,\begin{array}{*{20}{c}}{{a^2} + x}&{ab}&{ac}\\{ab}&{{b^2} + x}&{bc}\\{ac}&{bc}&{{c^2} + x}\end{array}\,} \right|$ is divisible by
Let $x \in R$ and let $P =\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 2 & 2 \\ 0 & 0 & 3\end{array}\right], Q =\left[\begin{array}{lll}2 & x & x \\ 0 & 4 & 0 \\ x & x & 6\end{array}\right]$ and $R = PQP ^{-1}$. 

Then which of the following options is/are correct?

$(1)$ For $x =1$, there exists a unit vector $\alpha \hat{ i }+\beta \hat{ j }+\gamma \hat{ k }$ for which $R \left[\begin{array}{l}\alpha \\ \beta \\ \gamma\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$

$(2)$ There exists a real number $x$ such that $P Q=Q P$

$(3)$ $\operatorname{det} R=\operatorname{det}\left[\begin{array}{lll}2 & x & x \\ 0 & 4 & 0 \\ x & x & 5\end{array}\right]+8$, for all $x \in R$

$(4)$ For $x=0$, if $R\left[\begin{array}{l}1 \\ a \\ b\end{array}\right]=6\left[\begin{array}{l}1 \\ a \\ b\end{array}\right]$, then $a+b=5$

If $y = {(x{\cot ^3}x)^{3/2}},$ then ${{dy} \over {dx}} = $
Let $\text{A}=\{\text{x}\in\text{R}:-1\leq\text{x}\leq1\}=\text{B}.$ Then, the mapping $f : A → B$ given by $f(x) = x|x|$ is:
The function $f(x) = {\sin ^4}x + {\cos ^4}x$ increases, if
Let $f(x)=\int_0^x g(t) \log _e\left(\frac{1-t}{1+t}\right) d t$, where $g$ is a continuous odd function. If $\int_{-\pi / 2}^{\pi / 2}\left(f(x)+\frac{x^2 \cos x}{1+e^x}\right) d x=\left(\frac{\pi}{\alpha}\right)^2-\alpha$, then $\alpha$ is equal to..............
If $I=\int\limits_{1}^{2} \frac{d x}{\sqrt{2 x^{3}-9 x^{2}+12 x+4}},$ then
Choose the correct answer from the given four options. For any vector $\vec{\text{a}},$ the value of $(\vec{\text{a}}\times\hat{\text{i}})^2+(\vec{\text{a}}\times\hat{\text{j}})^2+(\vec{\text{a}}\times\hat{\text{k}})^2$ is :