If | , * 20 c a_1 & b_1 & c_1 a_2 & b_2 & c_2 a_3 & b_3 & c_3 , |… - Vidyadip

MCQ

If $\left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right| = 5$; then the value of $\left| {\,\begin{array}{*{20}{c}}{{b_2}{c_3} - {b_3}{c_2}}&{{c_2}{a_3} - {c_3}{a_2}}&{{a_2}{b_3} - {a_3}{b_2}}\\{{b_3}{c_1} - {b_1}{c_3}}&{{c_3}{a_1} - {c_1}{a_3}}&{{a_3}{b_1} - {a_1}{b_3}}\\{{b_1}{c_2} - {b_2}{c_1}}&{{c_1}{a_2} - {c_2}{a_1}}&{{a_1}{b_2} - {a_2}{b_1}}\end{array}\,} \right|$is

A
$5$
✓
$25$
C
$125$
D
$0$

✓

Answer

Correct option: B.

$25$

b
(b) Required determinant
$|adj\,A|$=$|A{|^{3 - 1}}$,$\,{\rm{where}}A = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$
$ = {5^2} = 25,$ $(\because \,\,|adj\,A| = |a{|^{n - 1}})$

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

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The number of distinct real roots of the equaiton, $\left|\begin{array}{*{20}{c}}
{\cos \,\,x}&{\sin \,\,x}&{\sin \,\,x}\\
{\sin \,\,x}&{\cos \,\,x}&{\sin \,\,x}\\
{\sin \,\,x}&{\sin \,\,x}&{\cos \,\,x}
\end{array}\right|\,\, = \,\,0$ in the interval $\left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is

Let $f(x)$ be defined in $[-2, 2]$ by

$f(x) = max (4 -x^2, 1 + x^2), -2 < x < 0 $

$= min (4 -x^2, 1 + x^2), 0 < x < 2$.

The $f(x)$

If $\text{y}=\sin^{-1}\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big),$ then $\frac{\text{dy}}{\text{dx}}=$

Choose the correct answer from the given four options.
Let F = 3x - 4y be the objective function.
Minimum value of F is:

Choose the correct answer from the given four options.
The value of $\cos^{-1}\Big(\cos\frac{3\pi}{2}\Big)$ is equal to:

Let $f : R \rightarrow R$ be a function defined by $\text{f(x)}=\frac{\text{e}^{|\text{x}|}-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}.$ Then,

Let $f(x)=2 x^3-3 x^2-12 x+5$ on $[-2,4]$. The relative maximum occurs at $x=$

$\int_{}^{} {\frac{{\cos 2x + x + 1}}{{{x^2} + \sin 2x + 2x}}} \;dx = $

Let $a, b$ and $c$ be distinct positive numbers. If the vectors $a \hat{i}+a \hat{j}+c \hat{k}, \hat{i}+\hat{k}$ and $c \hat{i}+c \hat{j}+b \hat{k}$ are co-planar, then $\mathrm{c}$ is equal to:

The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is: