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

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

Similar questions

If the set $R=\{(a, b) ; a+5 b=42, a, b \in \mathbb{N}\}$ has $m$ elements and $\sum_{n=1}^m\left(1+i^{n !}\right)=x+i y$, where $I=\sqrt{-1}$, then the value of $m+x+y$ is :

Let $\mathrm{a}$ and $\mathrm{b}$ be real constants such that the function $f$ defined by $f(x)=\left\{\begin{array}{cc}x^2+3 x+a & x \leq 1 \\ b x+2, & x>1\end{array}\right.$ be differentiable on $R$. Then, the value of $\int_{-2}^2 f(x) d x$ equals

Number of real values of $x\in \left( 0,\pi \right)$ for which $\frac{8}{3\sin x-\sin 3x}+3{{\sin }^{2}}x\le 5$, is

If $a, b, c$ are non-zero real numbers and if the system of equations $(a - 1 )x = y + z,$ $(b - 1 )y = z + x ,$ $(c - 1 )z= x + y,$ has a non-trivial solution, then $ab + bc + ca$ equals

Let $[t]$ denote the greatest integer less than or equal to $\mathrm{t}$. Let $\mathrm{f}(\mathrm{x})=\mathrm{x}-[\mathrm{x}], \mathrm{g}(\mathrm{x})=1-\mathrm{x}+[\mathrm{x}]$, and $h(x)=\min \{f(x), g(x)\}, x \in[-2,2]$. Then $h$ is :

Let distinct lines $L_1,L_2$ belong to family of lines $(x -2y -3) + \lambda (x + 3y + 2) = 0$ and $B_1$ is angle bisector of $L_1$ and $L_2$ which passes through point $A(2,3),$ then equation of other bisector of $L_1$ and $L_2$ is ($\lambda$ is a parameter)

The function $f:R \to R$ is defined by $f(x) = {\cos ^2}x + {\sin ^4}x$ for $x \in R$, then $f(R) \in $

Let the shortest distance between the lines $L : \frac{ x -5}{-2}=\frac{ y -\lambda}{0}=\frac{ z +\lambda}{1}, \lambda \geq 0$ and $L _1: x +1= y -$ $1=4-z$ be $2 \sqrt{6}$. If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is $\ce{NOT}$ possible?

If $S$ is a set of $P(x)$ is polynomial of degree $ \le 2$ such that $P(0) = 0,$$P(1) = 1$,$P'(x) > 0{\rm{ }}\forall x \in (0,\,1)$, then

If $19^{th}$ terms of non -zero $A.P.$ is zero, then its ($49^{th}$ term) : ($29^{th}$ term) is