Embibe Experts Solutions for Chapter: Determinants and Matrices, Exercise 1: Exercise 1

For any $\Delta ABC$, the value of determinant $\left|\begin{array}{ccc}{\sin }^{2}A& cotA& 1\\ {\sin }^{2}B& cotB& 1\\ {\sin }^{2}C& cotC& 1\end{array}\right|$ is equal to-

If  $a, b, c$ are $pth$, $qth$ and $rth$ terms of a GP, then $\left|\begin{array}{lll}\log a& p& 1\\ \log b& q& 1\\ \log c& r& 1\end{array}\right|$ is equal to

If number of elements in a matrix is $60$ then how many different order of matrix are possible -

If $D_p=\left|\begin{array}{ccc}p& 15& 8\\ p^2& 35& 9\\ p^3& 25& 10\end{array}\right|$,then $D_1+D_2+D_3+D_4+D_5$ is equal to -

$\left|\begin{array}{ccc}{b}^2+c^2& a^2& a^2\\ b^2& c^2+a^2& b^2\\ c^2& c^2& a^2+b^2\end{array}\right|=$

If $\left|\begin{array}{ccc}1+ax& 1+bx& 1+cx\\ 1+a_{1}x& 1+b_{1}x& 1+c_{1}x\\ 1+a_{2}x& 1+b_{2}x& 1+c_{2}x\end{array}\right|=A_0+A_{1}x+A_2{x}^2+A_3{x}^3$ , then $A_0$ is

The greatest value of $x$ satisfying the equation $\left|\begin{array}{ccc}{2}^{11}-x& -2^{12}& 2^{11}\\ -2^{12}& 2^{11}-x& 2^{11}\\ 2^{11}& 2^{11}& -2^{12}-x\end{array}\right|=0$ is

If  $p{x}^4+q{x}^3+r{x}^3+sx+t=\left|\begin{array}{ccc}{x}^2+3x& x-1& x+3\\ x+1& 2-x& x-3\\ x-3& x+4& 3x\end{array}\right|$ then $t$ is equal to -