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

MCQ

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

A
${a^3} + {b^3} + {c^3} - 3abc$
✓
$3abc - {a^3} - {b^3} - {c^3}$
C
${a^3} + {b^3} + {c^3} - {a^2}b - {b^2}c - {c^2}a$
D
$(a+b+c)(a^2+b^2+c^2+ab+bc+ca)$

✓

Answer

Correct option: B.

$3abc - {a^3} - {b^3} - {c^3}$

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

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

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

On expanding,

$ - (a + b + c)\,({a^2} + {b^2} + {c^2} - ab - bc - ca)$

= $ -(a^3 + b^3 + c^3 - 3abc) = 3abc - a^3 -b^3 - c^3$

Trick : Put $a = 1,\,b = 2,\,c = 3$ and check it.

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

Choose the correct answers from the given four options : For the function $\text{f(x)}=\text{x}+\frac{1}{\text{x}},\text{x}\in[1,3],$ the value of $c$ for mean value theorem is :

The circumference of a circle is measured as $28\ cm$ with an error of $0.01\ cm$. The percentage error in the area is :

Derivative of ${x^6} + {6^x}$ with respect to $x $ is

If the function $f:[1,\;\infty ) \to [1,\;\infty )$ is defined by $f(x) = {2^{x(x - 1)}},$ then ${f^{ - 1}} (x)$ is

Can $\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}$ be the direction cosines of any directed line:

$Q^+$ is the set of all positive rational numbers with the binary operation $*$ defined by $\text{a}^*\text{b}=\frac{\text{ab}}2\ \forall\text{ a, b}\in\text{Q}^+$. The inverse of an element $\text{a}\in\text{Q}^+$ is:

Let $f$ be a differentiable function satisfying $f ( x )=\frac{2}{\sqrt{3}} \int_{0}^{\sqrt{3}} f \left(\frac{\lambda^{2} x }{3}\right) d \lambda, x >0$ and $f (1)=\sqrt{3}$. If $y=f(x)$ passes through the point $(\alpha, 6)$, then $\alpha$ is equal to $.........$

If $\text{A}=\begin{bmatrix} \text{a} & 0 & 0 \\ 0 & \text{a} & 0 \\ 0 & 0 &\text{a} \end{bmatrix},$ then the value of $\text{|adj A|}$ is:

$\int_{}^{} {x\sqrt {\frac{{1 - {x^2}}}{{1 + {x^2}}}} } \;dx = $

A function f from the set of natural numbers to integers defined by $\text{f(n)}=\begin{cases}\frac{\text{n}-1}{2},&\text{when n is odd}\\-\frac{\text{n}}{2},&\text{when n is even}\end{cases}$