Download App

3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $\left| {\,\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}\,} \right| = k(a + b + c)({a^2} + {b^2} + {c^2}$ $ - bc - ca - ab)$, then $k =$
  • A
    $1$
  • B
    $2$
  • ✓
    $-1$
  • D
    $-2$
✓

Answer

Correct option: C.
$-1$
c
(c) $\left| {\,\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}\,} \right| = a(bc - {a^2}) - b({b^2} - ca) + c(ab - {c^2})$

= $ - {a^3} - {b^3} - {c^3} + 3abc$ = $ - 1\,[{a^3} + {b^3} + {c^3} - 3abc]$

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

==> $k = - 1$.

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The area of figure bounded by $y = {e^x},\,y = {e^{ - x}}$ and the straight line $x = 1$ is
→
The optimal value of the objective function is attained at the points.
→
If $|\vec{\text{a}}|=\big|\vec{\text{b}}\big|,$ then $\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big)=$
  1. Positive
  2. Negetive
  3. 0
  4. None of these
→
The distance of the point (-1, -5, -10) from the point of intersection of the line $\vec{\text{r}}.=2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}+\lambda(3\hat{\text{i}}+4\hat{\text{j}}+12\hat{\text{k}})$ and the plane $\vec{\text{r}}.=(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}})=5$ is:
  1. 9
  2. 13
  3. 17
  4. None of these
→
If $f(x)=\frac{\left(\tan 1^{\circ}\right) x+\log _{\varepsilon}(123)}{x \log _{\varepsilon}(1234)-\left(\tan 1^{\circ}\right)}, x > 0$, then the least value of $f(f(x))+f\left(f\left(\frac{4}{x}\right)\right)$ is $...........$.
→
A fair coin is tossed 99 times. If X is the number of times head appears, then P(X = r) is maximum when r is:
    →
    Let $A =$ $\left[ {\begin{array}{*{20}{c}}1&{\sin \theta }&1\\{ - \sin \theta }&1&{\sin \theta }\\{ - 1}&{ - \sin \theta }&1\end{array}} \right]$, where $0 \le \theta < 2\pi$ , then
    →
    $\int {\left( {{{\sin }^4}x - {{\cos }^4}x} \right)\,dx = } $
    →
    The function $f(x)=2|x|+|x+2|-|| x+2|-2| x||$ has a local minimum or a local maximum at $x=$

    $(A)$ $-2$ $(B)$ $\frac{-2}{3}$ $(C)$ $2$ $(D)$ $\frac{2}{3}$

    →
    $\int_{ - 3}^3 {\frac{{{x^2}\sin x}}{{1 + {x^6}}}\,dx = } $
    →