| , * 20 c b^2 + c^2 & a^2 & a^2 b^2 & c^2 + a^2 & b^2 c^2 & c^2 … - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}{{b^2} + {c^2}}&{{a^2}}&{{a^2}}\\{{b^2}}&{{c^2} + {a^2}}&{{b^2}}\\{{c^2}}&{{c^2}}&{{a^2} + {b^2}}\end{array}\,} \right| = $

A
$abc$
B
$4abc$
✓
$4{a^2}{b^2}{c^2}$
D
${a^2}{b^2}{c^2}$

✓

Answer

Correct option: C.

$4{a^2}{b^2}{c^2}$

$\Delta = \left| {\,\begin{array}{*{20}{c}}{{b^2} + {c^2}}&{{a^2}}&{{a^2}}\\{{b^2}}&{{c^2} + {a^2}}&{{b^2}}\\{{c^2}}&{{c^2}}&{{a^2} + {b^2}}\end{array}\,} \right|$
$= - 2\,\left| {\,\begin{array}{*{20}{c}}0&{{c^2}}&{{b^2}}\\{{b^2}}&{{c^2} + {a^2}}&{{b^2}}\\{{c^2}}&{{c^2}}&{{a^2} + {b^2}}\end{array}\,} \right|,$
by ${R_1}→{R_1}-(R_2 + R_3)$
$= - 2\,\left| {\,\begin{array}{*{20}{c}}0&{{c^2}}&{{b^2}}\\{{b^2}}&{{a^2}}&0\\{{c^2}}&0&{{a^2}}\end{array}\,} \right|,$
by $\begin{array}{l}{R_2} \to {R_2} - {R_1}\\{R_3} \to {R_3} - {R_1}\end{array}$
$= - 2\{ - {c^2}({b^2}{a^2}) + {b^2}( - {c^2}{a^2})\} = 4{a^2}{b^2}{c^2}$.
Trick : Put $a=1,b=2,c=3$ so that the option give different values.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Consider three points $\mathrm{P}=(-\sin (\beta-\alpha),-\cos \beta), \mathrm{Q}=(\cos (\beta-\alpha), \sin \beta)$ and $\mathrm{R}=(\cos (\beta-\alpha+\theta), \sin (\beta-\theta))$, where $0<$ $\alpha, \beta, \theta<\frac{\pi}{4}$. Then

A straight line $L$ through the point $(3,-2)$ is inclined at an angle $60^{\circ}$ to the line $\sqrt{3} x+y=1$. If $L$ also intersects the $x$-axis, then the equation of $L$ is

The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is

The number of roots of the equation $\log ( - 2x)$ $ = 2\log (x + 1)$ are

Let $A=\left[\begin{array}{lll}2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1\end{array}\right], B=\left[B_1, B_2, B_3\right],$ where $B_1, \mathrm{B}_2, \mathrm{~B}_3$ are column matrices, and $\mathrm{AB}_1=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], \mathrm{AB}_2=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], \mathrm{AB}_3=\left[\begin{array}{l}3 \\ 2 \\ 1\end{array}\right]$ If $\alpha=|B|$ and $\beta$ is the sum of all the diagonal elements of $B,$ then $\alpha^3+\beta^3$ is equal to

If $A = \left( {\begin{array}{*{20}{c}}2&{ - 1}\\{ - 1}&2\end{array}} \right)$ and $I$ is the unit matrix of order $2$, then ${A^2}$ equals

Let $S$ be a subset of the plane defined by $S=\{(x, y):|x|+2|y|=1\}$. Then, the radius of the smallest circle with centre at the origin and having non-empty intersection with $S$ is

If $\frac{d y}{d x}=\frac{2^{x} y+2^{y} \cdot 2^{x}}{2^{x}+2^{x+y} \log _{e} 2}, y(0)=0$, then for $y=1$ the value of $x$ lies in the interval:

Let $x = x ( y )$ be the solution of the differential equation
$
y=\left(x-y \frac{d x}{d y}\right) \sin \left(\frac{x}{y}\right), y>0 \text { and } x(1)=\frac{\pi}{2} .
$
Then $\cos (x(2))$ is equal to :

Let $A B C$ be an acute scalene triangle, and $O$ and $H$ be its circumcentre and orthocentre respectively. Further, let $N$ be the mid-point of $O$. The value of the vector sum $\overrightarrow{N A}+\overrightarrow{N B}+\overrightarrow{N C}$ is