If a body cools from $80^{\circ} C$ to $50^{\circ} C$ in a room at a temperature of $25^{\circ} C$ in $30$ minutes,then the temperature of the body after $1$ hour is: (in $^{\circ} C$)

If the population grows at the rate $5 \%$ per year,then the time taken for the population to become double is $\quad$ (Given $\log 2 = 0.6912$) (in $years$)

The area bounded by a curve,the $x$-axis,and the ordinate of some point $(x, y)$ of the curve is equal to the length of the corresponding arc of the curve from a fixed point. If the curve passes through the point $P(0, 1)$,then the equation of this curve is:

If the tangent at a point $P(x, y)$ of a curve is perpendicular to the line that joins the origin with the point $P$,then the curve is

In a certain culture of bacteria,the rate of increase is proportional to the number present. It is found that the number doubles in $4$ hours. Then the number of times the bacteria are increased in $12$ hours is

The principal increases continuously in a newly opened bank at the rate of $10 \%$ per year. An amount of Rs. $2000$ is deposited with this bank. How much will it become after $5$ years? $(e^{0.5} = 1.648)$