## CBSE CLASS 12 MATHS IMPORTANT QUESTIONS - PROPERTIES OF DETERMINANTS

Here we are providing Important Practice Questions based on Properties of Determinants prepared by Experts for 2019-20 Board Examinations.

### Properties Of Determinants - Extra Practice  Questions

$\begin{array}{l}21.|\begin{array}{ccc}b+c& c+a& a+b\\ q+r& r+p& p+q\\ y+z& z+x& x+y\end{array}|=2|\begin{array}{ccc}a& b& c\\ p& q& r\\ x& y& z\end{array}|.\\ 22.|\begin{array}{ccc}1+a& 1& 1\\ 1& 1+b& 1\\ 1& 1& 1+c\end{array}|=abc+bc+ca+ab\\ 23.|\begin{array}{ccc}a+x& y& z\\ x& a+y& z\\ x& y& a+z\end{array}|={a}^{2}\left(a+x+y+z\right).\\ 24.|\begin{array}{ccc}x+\mathrm{Î»}& 2x& 2x\\ 2x& x+\mathrm{Î»}& 2x\\ 2x& 2x& x+\mathrm{Î»}\end{array}|=\left(5x+\mathrm{Î»}\right){\left(\mathrm{Î»}-x\right)}^{2}.\\ 25.|\begin{array}{ccc}{a}^{2}& bc& ac+{c}^{2}\\ {a}^{2}+ab& {b}^{2}& ac\\ ab& {b}^{2}+bc& {c}^{2}\end{array}|=4{a}^{2}{b}^{2}{c}^{2}\\ 26.|\begin{array}{ccc}1& x& {x}^{2}\\ {x}^{2}& 1& x\\ x& {x}^{2}& 1\end{array}|={\left(1-{x}^{3}\right)}^{2}.\\ 27.|\begin{array}{ccc}x& x+y& x+2y\\ x+2y& x& x+y\\ x+y& x+2y& x\end{array}|=9{y}^{2}\left(x+y\right).\\ 28.|\begin{array}{ccc}3x& -x+y& -x+z\\ x-y& 3y& z-y\\ x-z& y-z& 3z\end{array}|=3\left(x+y+z\right)\left(xy+yz+zx\right).\\ 29.|\begin{array}{ccc}{a}^{2}+1& ab& ac\\ ab& {b}^{2}+1& bc\\ ca& cb& {c}^{2}+1\end{array}|=1+{a}^{2}+{b}^{2}+{c}^{2}.\\ 30.|\begin{array}{ccc}1+{a}^{2}-{b}^{2}& 2ab& -2b\\ 2ab& 1-{a}^{2}+{b}^{2}& 2a\\ 2b& -2a& 1-{a}^{2}-{b}^{2}\end{array}|={\left(1+{a}^{2}+{b}^{2}\right)}^{3}\\ 31.|\begin{array}{ccc}b+c& q+r& y+z\\ c+a& r+p& z+x\\ a+b& p+q& x+y\end{array}|=2|\begin{array}{ccc}a& p& x\\ b& q& y\\ c& r& z\end{array}|\end{array}$

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