If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2 + y^2 + 4x - 6y = 12$ externally at the point $(1, -1)$,then the radius of $C$ is

$A$ driver applies the brakes on seeing the red traffic signal $400 ~m$ ahead. At the time of applying the brakes,the vehicle was moving with $15 ~m/s$ and retarding at $0.3 ~m/s^2$. The distance covered by the vehicle from the traffic light $1$ minute after the application of brakes is (in $~m$)

The rate of disintegration of a fixed quantity of a radioactive element can be increased by

On addition of $1 \, mL$ solution of $10\% \, NaCl$ to $10 \, mL$ gold sol in the presence of $0.0250 \, g$ of starch,the coagulation is just prevented. What is the gold number of starch?

Which of the following crops have been brought to India from the New World?

For the reaction $SnO_{2(s)} + 2H_{2(g)} \rightleftharpoons 2H_2O_{(g)} + Sn_{(l)}$,calculate $K_p$ at $900 \ K$ where the equilibrium steam-hydrogen mixture was $45\% \ H_2$ by volume.