The temperature of a body on the Kelvin scale is found to be $x \ K$. When it is measured by a Fahrenheit thermometer,it is found to be $x \ ^\circ F$. The value of $x$ is:

The image of the point $(3, 8)$ in the line $x + 3y = 7$ is

$A$ bar magnet of length $3 \, cm$ has points $A$ and $B$ along its axis at distances of $24 \, cm$ and $48 \, cm$ from the center on opposite sides. The ratio of the magnetic fields at these points is:

The concentration of hydrogen ion in a sample of soft drink is $3.8 \times 10^{-3} \, M$. What is its $pH$ (in $.42$)?

$A$ lead bullet at $27\,^{\circ}C$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat produced is absorbed by the obstacle,the velocity of the bullet at the time of striking is ........ $m/s$. (Melting point of lead $= 327\,^{\circ}C$,specific heat of lead $= 0.03\,cal/g\,^{\circ}C$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)

If $\int \frac{e^x-1}{e^x+1} d x=f(x)+c$,then $f(x)$ is equal to