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

The rate of decay of a certain substance is directly proportional to the amount present at that instant. Initially,there are $27 \text{ gms}$ of the substance and $3 \text{ hours}$ later it is found that $8 \text{ gms}$ are left. The amount left after one more hour is:

$A$ radioactive substance,with initial mass $m_0$,has a half-life of $h$ days. Then its initial decay rate is given by

The rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of air. The temperature of air is $290 \ K$ and the substance cools from $370 \ K$ to $330 \ K$ in $10 \ minutes$. Then the time to cool the substance up to $295 \ K$ is: (in $min$)

$A$ tangent is drawn at any point $P(x, y)$ on a curve,which passes through $(1, 1)$. The tangent cuts the $X$-axis and $Y$-axis at $A$ and $B$ respectively. If $AP:BP = 3:1$,then:

If the population grows at the rate of $8 \%$ per year,then the time taken for the population to be doubled,is (Given $\log 2 = 0 \cdot 6912$)