If a body cools from $135^{\circ} C$ to $80^{\circ} C$ at a room temperature of $25^{\circ} C$ in $60 \text{ minutes}$,then the temperature of the body after $2 \text{ hours}$ is: (in $^{\circ} C$)

If the length of the sub-tangent at any point $P$ on a curve is proportional to the abscissa of the point $P$,then the equation of that curve is ($C$ is an arbitrary constant).

The microorganisms double themselves in $3$ hours. Assuming that the quantity increases at a rate proportional to itself,then the number of times it multiplies itself in $18$ hours is:

The rate at which the population of a city increases varies as the population. In a period of $20$ years,the population increased from $4$ lakhs to $6$ lakhs. In another $20$ years,the population will be (in $lakhs$)

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 $m_{0} \text{ gm}$ will be reduced to $m_{1} \text{ gm}$ is (where $K$ is the constant of proportionality).

If $\frac{d^{2} y}{d x^{2}}=\sin x+e^{x}$,$y(0)=3$,and $\frac{d y}{d x}$ at $x=0$ is $4$,then find the equation of the curve.