Question

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

Find : $\textstyle\int$$\textstyle\left\{{\frac{\left(x+\sin^{2}x\right)\sec^{2}x}{1+x^{2}}}\right\}d x~.$

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

The volume of a sphere is increasing at the rate of 8 cm³/sec. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.

Find the sum of the order and the degree of the following differential equations : ${\frac{d^{2}y}{d x^{2}}}+{3{\sqrt\frac{{d y}}{d x}}}+(1+x)=0$

If x changes from 4 to 4·01, then find the approximate change in log x.

The radius r of a right circular cylinder is increasing uniformly at the rate of 0.3 cm/s and its height h is decreasing at the rate of 0.4 cm/s. When r = 3.5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$