Question

One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red.

Find the angle between the vectors ${\vec{a}}={\hat{i}}+{\hat{j}}-{\hat{k}}$ and ${\vec{b}}={\hat{i}}-{\hat{j}}+{\hat{k}}$

If P(A) = 2/5, P(B) = 1/3, P(A ∩ B) = 1/5, then find P(A' / B') .

Find the differential equation of the family of curves y²= 4ax.

The radius r of a right circular cone is decreasing at the rate of 3 cm/minute and the height h is increasing at the rate of 2 cm/minute. When r = 9 cm and h = 6 cm, find the rate of change of its volume.

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

The radius r of the base of a right circular cone is decreasing at the rate of 2 cm/min. and height h is increasing at the rate of 3 cm/min. When r = 3.5 cm and h = 6 cm, find the rate of change of the volume of the cone. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$