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

MCQ

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

A
${(a + b + c)^2}$
✓
${(a + b + c)^3}$
C
$(a + b + c)(ab + bc + ca)$
D
None of these

✓

Answer

Correct option: B.

${(a + b + c)^3}$

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

= $\left| {\,\begin{array}{*{20}{c}}{ - \Sigma a}&0&{2a}\\{\Sigma a}&{ - \Sigma a}&{2b}\\0&{\Sigma a}&{c - a - b}\end{array}\,} \right|$ , $\left( \begin{array}{l}{C_1} \to {C_1} - {C_2}\\{C_2} \to {C_2} - {C_3}\end{array} \right)$

= ${(\Sigma a)^2}\,\left| {\,\begin{array}{*{20}{c}}{ - 1}&0&{2a}\\1&{ - 1}&{2b}\\1&1&{c - a - b}\end{array}\,} \right| = {(\Sigma a)^3}$, ( on expansion)

= ${(a + b + c)^3}$.

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

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

$\int_{}^{} {\frac{{{x^3}}}{{\sqrt {1 - {x^8}} }}dx = } $

From a set of 100 cards numbered 1 to 100, one card is drawn at randow. The probability number obtained on the card is divisible by 6 or 8 but not by 24 is

The linear inequalities or equations or restrictions on the variables of a linear programming problem are called:

Let * be a binary operation on R defined by a * b = ab + 1. Then, * is:

If $f(x)$ is a continuous and differentiable function satisfying $f(x).f(f(x)) = x^2 + 1, \, f(1) = 2, \,f'(1) = k$, then the value of $f'(2)$ is

The order and the degree of the differential equation $\left(1+3 \frac{d y}{d x}\right)^2=4 \frac{d^3 y}{d x^3}$ respectively are

A matrix $A=\left[a_{i j}\right]_{3 \times 3}$ is defined by $a_{i j}=\left\{\begin{array}{cc}2 i+3 j & , \quad i<j \\ 5 & , \quad i=j \\ 3 i-2 j & , \quad i>j\end{array}\right.$

The number of elements in A which are more than 5 , is 4 :

Statement $-1 :$ The point $A(1, 0, 7)$ is the mirror image of the point $B( 1, 6, 3)$ in the line: $\frac{x}{1} = \frac{{y - 1}}{2} = \frac{{z - 2}}{3}$

Statement $-2 :$ The line $\frac{x}{1} = \frac{{y - 1}}{2} = \frac{{z - 2}}{3}$ bisects the line joining $A(1, 0, 7)$ and $B( 1, 6, 3)$

The value of $\int\limits^\pi_{-\pi}\sin^3\text{x}\cos^2\text{x}\text{ dx}$ is:

Let $f(x)=\frac{x+1}{x-1}$ for all $x \neq 1$. Let $f^1(x)=f(x), f^2(x)=f(f(x))$ and generally $f^n(x)=f\left(f^{n-1}(x)\right)$ for $n>1$. Let $P=f^1(2) f^2(3) f^3(4) f^4(5)$ Which of the following is a multiple of $P$ ?