| , * 20 c 1/a & a^2 & bc 1/b & b^2 & ca 1/c & c^2 & ab , | = - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}{1/a}&{{a^2}}&{bc}\\{1/b}&{{b^2}}&{ca}\\{1/c}&{{c^2}}&{ab}\end{array}\,} \right| = $

A
$abc$
B
$1/abc$
C
$ab + bc + ca$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d)$\left| {\,\begin{array}{*{20}{c}}{1/a}&{{a^2}}&{bc}\\{1/b}&{{b^2}}&{ca}\\{1/c}&{{c^2}}&{ab}\end{array}\,} \right|$$ = \frac{1}{{abc}}\,\left| {\,\begin{array}{*{20}{c}}1&{{a^3}}&{abc}\\1&{{b^3}}&{abc}\\1&{{c^3}}&{abc}\end{array}\,} \right| = \frac{{abc}}{{abc}}\left| {\,\begin{array}{*{20}{c}}1&{{a^3}}&1\\1&{{b^3}}&1\\1&{{c^3}}&1\end{array}\,} \right| = 0$

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

If $\text{A}=\begin{vmatrix} 1 &\text{amp; 2} \\ 2 &\text{amp; 1} \end{vmatrix}$ and $\text{f}\text{(x)}=\frac{1+\text{x}}{1-\text{x}},$ then $\text{f}(|\text{A}|)$ is:

Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $\text{aRb}$ if a is congruent to $b \forall a, b \in T.$ Then $R$ is:

If $f(x) = \left\{ \begin{array}{l}\,\,\,\,{x^2},\,{\rm{when}}\,\,x \le 1\\x + 5,{\rm{when\,\, }}x > {\rm{1}}\end{array} \right.$, then

Given that $\int\limits^{\infty}_0\frac{\text{x}^2}{(\text{x}^2+\text{a}^2)(\text{x}^2+\text{b}^2)(\text{x}^2+\text{c}^2)}\text{ dx}=\frac{\pi}{2(\text{a}+\text{b})(\text{b}+\text{c})(\text{c}+\text{a})},$ the value of $\int\limits^\infty_0\frac{1}{(\text{x}^2+4)(\text{x}^2+9)},$ is:

The matrix $A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$ is a

A point on the parabola ${y^2} = 18x$ at which the ordinate increases at twice the rate of the abscissa is

If the binary operation $^*$ on $Z$ is defined by $a^* b = a^2 − b^2 + ab + 4,$ then value of $(2^* 3)^*4$ is:

What is the value of $x$ and $y,$ if $2i + 3j = xi + yj:$

If $\int_{-2}^5 f(x) d x=4, \int_0^5(1+f(x)) d x=7$, then the value of the integral $\int_{-2}^0 f(x) dx$ is equal to

$\int_{}^{} {\frac{{dx}}{{(x - {x^2})}} = } $