If | * 20 c a - b - c & 2a & 2a 2b & b - c - a & 2b 2c & 2c & c -… - Vidyadip

MCQ

If $\left| {\begin{array}{*{20}{c}}
{a - b - c}&{2a}&{2a}\\
{2b}&{b - c - a}&{2b}\\
{2c}&{2c}&{c - a - b}
\end{array}} \right|$ $ = \left( {a + b + c} \right)\,{\left( {x + a + b + c} \right)^2}$ , $x \ne 0$ and $a + b + c \ne 0$, then $x$ is equal to

A
$abc$
✓
$ - 2 \left( {a + b + c} \right)$
C
$ 2 \left( {a + b + c} \right)$
D
$ - \left( {a + b + c} \right)$

✓

Answer

Correct option: B.

$ - 2 \left( {a + b + c} \right)$

b
${R_1} \to {R_1} + {R_2} + {R_3}$

$\left( {a + b + c} \right)\left| {\begin{array}{*{20}{c}}
1&1&1\\
{2b}&{b - a - c}&{2b}\\
{2c}&{2c}&{c - a - b}
\end{array}} \right|$

${c_3} \to {c_3} - {c_1},{c_2} \to {c_2} - {c_1}$

$ = \left( {a + b + c} \right)\left| {\begin{array}{*{20}{c}}
1&0&0\\
{2b}&{ - \left( {a + b + c} \right)}&0\\
{2c}&0&{ - \left( {a + b + c} \right)}
\end{array}} \right|$

$ = {\left( {a + b + c} \right)^3}$

$ = \left( {a + b + c} \right){\left( {x + a + b + c} \right)^2}$

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The corner points of the bounded feasible region are $(60,0),(120,0),(60,40),(40,20)$ and $(20,30)$. For the objective function $z=5 x+10 y \ldots$

$(i)$ Maximum value of $z$.

$(ii)$ Minimum value of $z$.

$(iii)$ Maximum value of $z$ has at

$(iv)$ Minimum value of $z$ has at

If a line has direction ratios 2, -1, -2, determine its direction cosines:

$\frac{1}{3}, \frac{2}{3},\frac{-1}{3}$
$\frac{2}{3}, \frac{-1}{3},\frac{-2}{3}$
$\frac{-2}{3}, \frac{1}{3}, \frac{2}{3}$
None of the above

Let $y=y(x)$ be the solution of the differential equations $\frac{d y}{d x}+\frac{5}{x\left(x^5+1\right)} y=\frac{\left(x^5+1\right)^2}{x^7}, x > 0$. If $y(1)=2$, then $y(2)$ is equal to

The function $\mathrm{f}(\mathrm{x})$, that satisfies the condition $\mathrm{f}(\mathrm{x})=\mathrm{x}+\int_{0}^{\pi / 2} \sin \mathrm{x} \cdot \cos y \mathrm{f}(\mathrm{y}) \mathrm{dy}$, is :

The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$, is equal tọ

Order and degree of differential equation $\frac{{{d^2}y}}{{d{x^2}}} = {\left\{ {y + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} \right\}^{1/4}}$are

If $f(x) = $$\left\{ \begin{array}{l}\frac{{1 - (x)}}{{1 + x}},\,\,\,\,\,x \ne - 1\\\,\,1\,\,\,\,\,\,\,\,\,,\,\,\,\,\,x = - 1\end{array} \right.$, then the value of $f(|2k|)$ will be (where $[. ] $ shows the greatest integer function)

${n^{th}}$ derivative of ${x^{n + 1}}$ is

The system of equations $\lambda x + y + z = 0,$ $ - x + \lambda y + z = 0,$ $ - x - y + \lambda z = 0$, will have a non zero solution if real values of $\lambda $ are given by

The value of the integral $\int_0^{\infty} \frac{ dx }{\left(1+ x ^2\right)(1+ x )^2}$ is