Question

Obtain the differential equation of the family of circles passing through the points (a, 0) and (– a, 0).

Find the general solution of the differential equation. $x y\,{\frac{d y}{d x}}=(x+2)(y+2).$

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’.

Find : $\textstyle\int e^{x}\,{\frac{\sqrt{1+\sin2x}}{1+\cos2\,x}}\,d x$.

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

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

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