# Determinants

Subject matter experts of JagranJosh have developed chapter wise practice questions of Class 12th as per the relevancy of the chapter in the CBSE board exam. This practice set contains 10 questions with detailed explanations on “Chapter: Determinants” of Mathematics.

• Q1.Using properties of determinants, calculate the value of: $|\begin{array}{ccc}\text{1}& x& {x}^{2}\\ {x}^{2}& \text{1}& x\\ x& {x}^{2}& \text{1}\end{array}|$

• Q2.Using properties of determinants, calculate the value of: $|\begin{array}{ccc}x& y& z\\ {x}^{2}& {y}^{2}& {z}^{2}\\ {x}^{3}& {y}^{3}& {z}^{3}\end{array}|$

• Q3.Using properties of determinants, calculate the value of: $|\begin{array}{ccc}y+k& y& y\\ y& y+k& y\\ y& y& y+k\end{array}|$

• Q4.Using properties of determinants, calculate the value of:
$|\begin{array}{ccc}b+c& a& a\\ b& c+a& b\\ c& c& a+b\end{array}|$

• Q5.Calculate the area between the given points: $\text{A}\text{\hspace{0.17em}}\left(a,b+c\right),\text{B}\text{\hspace{0.17em}}\left(b,c+a\right),\text{C}\text{\hspace{0.17em}}\left(c,a+b\right)$

• Q6.$|\begin{array}{cc}x& x\\ 1& x\end{array}|=|\begin{array}{cc}\text{3}& \text{4}\\ \text{1}& \text{2}\end{array}|,$ write the positive value of x.