Download App

STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
$\left| {\begin{array}{*{20}{c}}0&a&{ - b}\\{ - a}&0&c\\b&{ - c}&0\end{array}} \right| = $
  • A
    $ - 2abc$
  • B
    $abc$
  • ✓
    $0$
  • D
    ${a^2} + {b^2} + {c^2}$
✓

Answer

Correct option: C.
$0$
c
(c)$\left| {\,\begin{array}{*{20}{c}}0&a&{ - b}\\{ - a}&0&c\\b&{ - c}&0\end{array}\,} \right| = 0$ (Since value of determinant of skew-symmetric matrix of odd orders is $0$).

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The $n^{th}$ term of the series $\frac{2}{{1!}} + \frac{7}{{2\,!}} + \frac{{15}}{{3\,!}} + \frac{{26}}{{4\,!}} + .....$ is
→
If $\operatorname{gcd}( m , n )=1$ and $1^2-2^2+3^2-4^2+\ldots \ldots$ $+(2021)^2-(2022)^2+(2023)^2=1012 m ^2 n$, then $m ^2- n ^2$ is equal to
→
A cone of maximum volume is inscribed in a given sphere, then ratio of the height of the cone to diameter of the sphere is
→
Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $A B C D$ if the diagonal $\overrightarrow{B D}=\hat{i}+2 \hat{j}+3 \hat{k}$ then the area of the parallelogram is equal to
→
The trace of a square matrix is defined to be the sum of its diagonal entries. If $A$ is a $2 \times 2$ matrix such that the trace of $A$ is $3$ and the trace of $A^3$ is -$18$ , then the value of the determinant of $A$ is.$ . . . . $
→
The number of solutions of the equation $\cos 2 \theta \cos \frac{\theta}{2}+\cos \frac{5 \theta}{2}=2 \cos ^{3} \frac{5 \theta}{2}$ in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is :
→
If the domain of the function $f(x)=\cos ^{-1}\left(\frac{2-|x|}{4}\right)+\left(\log _e(3-x)\right)^{-1}$ is $[-\alpha, \beta)-\{y\}$, then $\alpha+\beta+\gamma$ is equal to :
→
If $S$ is the sum to infinity of a $G.P.$, whose first term is $a$, then the sum of the first $n$ terms is
→
Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$. If it passes through the point $(1,6)$, then the length of its latus-rectum is :
→
If the product of the roots of the equation $2{x^2} + 6x + $ ${\alpha ^2} + 1 = 0$ is $ - \alpha $, then the value of $\alpha $ will be
→