Question

Find the inverse of the matrix $\left(\begin{array}{l l }-3 & 2 \\ 5 & -3\end{array}\right)$ Hence, find the matrix P satisfying the matrix equation P$\left(\begin{array}{l l }-3 & 2 \\ 5 & -3\end{array}\right)$ = $\left(\begin{array}{l l }1 & 2 \\ 2 & -1\end{array}\right)$ .

Show that the function f(x) = x³ – 3x² + 6x – 100 is increasing on R.

If P(A) = 0.4, P(B) = p, P(A U B) = 0.6 and A and B are given to the independent events, find the value of ‘p’.

A die is rolled. If E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}, find (a) P(E U F)/G] (b)P [(E ∩ F)/G].

If A = $\left(\begin{array}{l l }3 & 1 \\ -1 & 2\end{array}\right)$ and I = $\left(\begin{array}{l l }1 & 0 \\ 0 & 1\end{array}\right)$ find k so that A² = 5A + kI.

Find : $\textstyle\int$$\sqrt{2x-x^{2}\ d x}$

Show that the solution of differential equation : $y=2(x^{2}-1)+c e^{-x^{2}}\,\mathrm{is}\,\frac{d y}{d x}+2x y-4x^{3}=0$