The inverse of the matrix \(\begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}\) is 

If P = \(\begin{pmatrix} 1 & 0 & -1 \\ 3 & 4 & 5 \\ -1 & 0 & 1 \end{pmatrix}\), then |P| is 

Find the values of x where the curve y = x\(^3\) + 2x\(^2\) - 5x - 6 crosses the x - axis.

Find x and y, respectively, in the subtraction above carried out in base 5.

In a class of 40 students, each student offers at least one of physics and chemistry. If the number of students that offer physics is three times the number that offer both subjects, and the number that offer chemistry is twice the number that offer physics, find the number of students that offer physics only.