Differential Equations - 13 - Free MCQ Test with solutions for Maths

The function f defined by f(x) - x [1 + 1/3 sin (log x²)], a ≠ 0,/(0) = 0 ([] represents the greatest integer function) is

If f is twice differentiable function such that f ''(x) = - f(x), f '(x) = g(x) and h(x) = [f(x)]² + [g(x)]², also if h(5) = 11, then h(10) is equal to

The solution of the equation 

The solution of 

The solution of the differential equation 

The solution of the differential equation y(2xy + e^x)dx - e^xdy = 0 is

The solution of the differential equation 

The half-life of a radioactive substance is the time required for one-half of that substance to decay. The amount of ¹¹C, an isotope of carbon present at a future time t (in months) is given by A(t) = 100 exp [- 0.0338 t]. The half life of the material in months is

Consider a pair of differential equations 
Eliminating t in the two equations results in 

The rare at which body changes temperature is proportional to the difference between its temperature and ihat of the surrounding medium. This is called Newton's law of cooling. If y = f{t} is the unknown temperature of The body at time t and M(t) denotes the known temperature of the surrounding medium, Newton's law' leads to the differential equation where k is a positive constant.

tan^-1 x + tan^-1 y = c is the general solution of the differential equation

The differential equation  represents

If u = log (x³ + y² + z³ - 3xyz), then 

The solution of the differential equal ion (1 + x²) dy/dx = (1 + y²) is

If a population grows at the rate of 5% per year, it will double (in years) after

The differential equation of all circles passing through the origin and having their centres on the y-axis is

The geometrical interpretation of the graph of the differential equation:  is a family of

The solution curves of the given differential equation: xdx - dy = 0 constitute a family of

If left to grow undisturbed, the fish population in a lake would be 50 per cent more than it was in the previous year. However, for research purposes 100 fishes are added to the population each year. If the initial population of fish in the pond was zero then how many years the slocking program should continue till the population increases to 2000?