Question

If $\begin{vmatrix}x+1 & x-1 \\ x-3 & x+2\end{vmatrix}$ = $\begin{vmatrix}4 & -1 \\ 1 & 3\end{vmatrix}$ , then write the value of x.

If for any 2 × 2 square matrix A, A(adj A) = $\left(\begin{array}{l l }8 & 0 \\ 0 & 8\end{array}\right)$ , then write the value of |A|.

Let A and B are matrices of order 3 x 2 and 2 x 4 respectively. Write the order of matrix (AB).

Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.

Write the inverse of the matrix $\left(\begin{array}{l l }cosθ & -sinθ \\ sinθ & cosθ\end{array}\right)$ .

Find the slope of tangent to the curve y = 3x² – 6 at the point on it whose x-coordinate is 2.

Write the value of : $\textstyle\int{\frac{x+\cos6.x}{3\,x^{2}\,+\,\sin6.x}}\,d x\,.$