The population $P=P(t)$ at time $t$ of a certain species follows the differential equation $\frac{dP}{dt}=0.5 P-450$. If $P(0)=850$,then the time at which the population becomes zero is

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is $290 \ K$ and the metal temperature drops from $370 \ K$ to $330 \ K$ in $10 \ \text{minutes}$,then the time required to drop the temperature up to $295 \ K$ is

$A$ 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:

In a bank,the principal increases continuously at a rate of $x \%$ per year. Then the rate,$x$,if ₹$100$ doubles itself in $10$ years,is (Given $\log 2 = 0.6931$) (in $\%$)

The normal to a curve at $P(x, y)$ meets the $x$-axis at $G$. If the distance of $G$ from the origin is twice the abscissa of $P$, then the curve is

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