Download App

DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
MCQ
The determinant $\begin{vmatrix}\text{b}^2-\text{ab}&\text{b}-\text{c}&\text{bc}-\text{ac}\\\text{ab}-\text{a}^2&\text{a}-\text{b}&\text{b}^2-\text{ab}\\\text{bc}-\text{ac}&\text{c}-\text{a}&\text{ab}-\text{a}^2\end{vmatrix}$ equals:
  • A
    $abc(b - c)(c - a)(a - b)$
  • B
    $(b - c)(c - a)(a - b)$
  • C
    $(a + b + c)(b - c)(c - a)(a - b)$
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
$\begin{vmatrix}\text{b}^2-\text{ab}&\text{b}-\text{c}&\text{bc}-\text{ac}\\\text{ab}-\text{a}^2&\text{a}-\text{b}&\text{b}^2-\text{ab}\\\text{bc}-\text{ac}&\text{c}-\text{a}&\text{ab}-\text{a}^2\end{vmatrix}$
$=\begin{vmatrix}\text{b}(\text{b}-\text{a})&\text{b}-\text{c}&\text{c}(\text{b}-\text{a})\\\text{a}(\text{b}-\text{a})&\text{a}-\text{b}&\text{b}(\text{b}-\text{a})\\\text{c}(\text{b}-\text{a})&\text{c}-\text{a}&\text{a}(\text{b}-\text{a})\end{vmatrix}$
$=(\text{b}-\text{a})^2\begin{vmatrix}\text{b}&\text{b}-\text{c}&\text{c}\\\text{a}&\text{a}-\text{b}&\text{b}\\\text{c}&\text{c}-\text{a}&\text{a}\end{vmatrix} [$Taking $(b - a)$ common from $C_1$ and $C_3]$
$=(\text{b}-\text{a})^2\begin{vmatrix}0&\text{b}-\text{c}&\text{c}\\0&\text{a}-\text{b}&\text{b}\\0&\text{c}-\text{a}&\text{a}\end{vmatrix} [$Applying $C_1\rightarrow C_1 - C_2 - C_3]$
$=0$
Hence, the correct option is $(d)$

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 DETERMINANTS→DETERMINANTS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The vector$(s)$ which is/are coplanar with vectors $\hat{i}+\hat{j}+2 \hat{k}$ and $\hat{i}+2 \hat{j}+\hat{k}$, and perpendicular to the vector $\hat{i}+\hat{j}+\hat{k}$ is/are

$(A)$ $\hat{j}-\hat{k}$ $(B)$ $-\hat{i}+\hat{j}$ $(C)$ $\hat{i}-\hat{j}$ $(D)$ $-\hat{j}+\hat{k}$

→
The angle between the lines $2x = 3y = - z$ and $6x = - y = - 4z$, is ......... $^o$
→
Let  $a,b,c\; \in R.$ If $f\left( x \right) = a{x^2} + bx + c$ is such that $a + b + c = 3$ and $f\left( {x + y} \right) = f\left( x \right) + f\left( y \right) + xy,$ $\forall x,y \in R,$ then $\mathop \sum \limits_{n = 1}^{10} f\left( n \right)$ is equal to : 
→
If $y =\frac{x}{{a\, +\frac{x}{{b\, +\frac{x}{{a\, + \frac{x}{{b\, +\frac{x}{{a\, + \frac{x}{{b\, }}......+\infty }}\,\,\,}}\,\,\,}}\,\,\, }}\,\,\, }}\,\,\,$ then $\frac{{dy}}{{dx}}$=
→
The least and greatest value of $f(x)=x^3-6 x^2+9 x$ in $[0,6],$ are
→
Value of $\left| {\begin{array}{*{20}{c}}
  {{{(b + c)}^2}}&{{a^2}}&{{a^2}} \\ 
  {{b^2}}&{{{(a + c)}^2}}&{{b^2}} \\ 
  {{c^2}}&{{c^2}}&{{{(a + b)}^2}} 
\end{array}} \right|$ is equal to
→
The angle between the lines whose direction cosines are proportional to $(1, 2, 1)$ and $(2, -3, 6)$ is
→
$\int_{}^{} {\sqrt {\frac{{a - x}}{x}} \;dx = } $
→
For the function $f (x) =$ $\frac{1}{{x + {2^{\frac{1}{{(x - 2)}}}}}}$ , $x \ne 2$ which of the following holds ?
→
Let $f(x)\, = \left\{ \begin{gathered}
  \frac{1}{{\left| x \right|}}, \,\,\,\,\,\,\,\,\,\,\,\,\left| x \right|\, \geqslant \,1\,\, \hfill \\
  a{x^2} + b\,,\,\left| x \right|\, < \,1 \hfill \\ 
\end{gathered}  \right.$ be continuous and differentiable everywhere. Then $a$ and $b$ are
→