The rate at which the population of a city increases varies as the population present. Within the period of $30$ years,the population grew from $20$ lakhs to $40$ lakhs. Then,the population after a further period of $15$ years will be (Take $\sqrt{2} = 1.41$) (in $lakhs$)

The rate of reduction of a person's assets is proportional to the square root of the assets at that moment. If the assets at the beginning are $10000$ and they dwindle down to $5625$ in $2$ years, then in how many years will the person be bankrupt (in $years$)?

The growth of population is proportional to the number present. If the population of a colony doubles in $50$ years,then the population will become triple in . . . . . . years.

The area enclosed by the closed curve $C$ given by the differential equation $\frac{dy}{dx} + \frac{x+a}{y-2} = 0, y(1) = 0$ is $4\pi$. Let $P$ and $Q$ be the points of intersection of the curve $C$ and the $y$-axis. If normals at $P$ and $Q$ on the curve $C$ intersect the $x$-axis at points $R$ and $S$ respectively,then the length of the line segment $RS$ is

$A$ piece of steel is heated to $100^{\circ}C$ and allowed to cool in a room. Which graph correctly represents the cooling process?

Water at $100^{\circ} C$ cools in $15 \text{ minutes}$ to $75^{\circ} C$ in a room temperature of $25^{\circ} C$. Then the temperature of water after $30 \text{ minutes}$ is