What will be the length (in cm) of mercury column in a barometer tube, when the atmospheric pressure is 75 cm of mercury and the tube is inclined at an angle of 60⁰ to the  vertical?

Let $l$ be length of the mercury column in the barometer tube. As the barometer tube is inclined at an angle of 60^o to the vertical, effective height (vertical) of the mercury column $=l \cos {60}^{\circ }$. Since atmospheric pressure is 75 cm of mercury column, 

$l \cos {60}^{\circ }=75$

$\text{ or, }l=\frac{75}{\cos {60}^{\circ }}=\frac{75}{1/2}=150\mathrm{cm}$