Question

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’.

If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.

Find the integrating factor of the differential equation ${\frac{d y}{d x}}+y\ =\ {\frac{1+y}{x}}$

Find the particular solution of the differential equation ${\frac{d y}{d x}}={\frac{1+y^{2}}{1+x^{2}}}$ given that y(0) = ${\sqrt{3}}.$

If E and F are independent events, then show that (i) E and F' are independent events. (ii) E' and F are also independent events.

Find : $\textstyle\int{\frac{d x}{x^{2}+4x+8}}$

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.