In a bank,the principal increases continuously at the rate of $5 \%$ per year. In how many years will Rs $1000$ double itself?

The slope at any point of a curve $y=f(x)$ is given by $\frac{dy}{dx}=3x^2$ and it passes through $(-1,1)$. The equation of the curve is

Let $I$ be the purchase value of an equipment and $V(t)$ be the value after it has been used for $t$ years. The value $V(t)$ depreciates at a rate given by the differential equation $\frac{dV(t)}{dt} = -k(T - t)$,where $k > 0$ is a constant and $T$ is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is:

The rate of decay of mass of a certain substance at time $t$ is proportional to the mass at that instant. The time during which the original mass of $m_{0}$ grams will be reduced to $m_{1}$ grams is (where $k$ is the constant of proportionality):

The differential equation of displacement of all $Simple \ Harmonic \ Motions$ of given period $T = 2\pi / n$ is:

In a bank,the principal increases continuously at the rate of $6 \%$ per year. Then the time required to double $₹ 6000$ is (in years)