Question

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.

If E and F are two events such that P(E) = 1/4, P(F) = 1/2 and P(E ∩ F) = 1/8, find (i) P(E or F) (ii) P(not E and not F).

From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.

A balloon, which always remains spherical, has a variable diameter ${\frac{2}{3}}(3x+1)$ . Find the rate of change of its volume with respect to x.

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

Form the differential equation of all circles which is tough the x-axis at the origin.

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