91Ó°ÊÓ

A person places Rs. 20000 in a saving account which pays 5 percent interest per annum, compounded continuously. Find (a) the amount in the account after three years, and \((\mathrm{b})\) the time required for the account to double in value, presuming no withdrawals and no additional deposits. \((\ln 2=0.693)\)

A yeast grows at a rate proportional to its present size. If the original amount doubles in two hours, in how many hours will it triple?

A depositor places Rs. 10,000 in a certificate of deposit which pay 6 percent interest per annum, compounded continuously. How much will be in the account at the end of seven years assuming no additional deposits or withdrawal?

Prove that a curve possessing the property that all its normals pass through a fixed point is a circle.

A cup of tea is prepared in a preheated cup with hot water so that the temperature of both the cup and the brewing tea is initially \(190^{\circ} \mathrm{F}\). The cup is then left to cool in a room kept at a constant \(72^{\circ} \mathrm{F}\). Two minutes later, the temperature of the tea is \(150^{\circ} \mathrm{F}\). Determine (a) the temperature of the tea after 5 minutes. (b) the time required for the tea to reach \(100^{\circ} \mathrm{F}\).

Find a differential equation of circles passing through the points of intersection of unit circle with centre at origin and the line bisecting the first quadrant.

Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hourse for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely?

Form a differential equation of family of parabolas with focus origin and axis of symmetry along the \(\mathrm{x}\)-axis.

Solve \(y^{\prime} \sqrt{1+x+y}=x+y-1\)

A series circuit contains an inductor, resistor and capacitor. Determine the differential equation for the charge \(\mathrm{q}(\mathrm{t})\).