If $$\theta $$ and $$\delta $$ be the latitude of a place and declination of a star respectively, the upper culmination of the star will be north of zenith if its zenith distance, is A. $$\delta – \theta $$ B. $$\theta – \delta $$ C. $$\theta + \delta $$ D. $$\frac{{\theta + \delta }}{2}$$

The correct answer is $\boxed{\theta – \delta}$.

The zenith distance of a star is the angle between the star and the zenith, which is the point directly overhead. The declination of a star is its angular distance from the celestial equator. The celestial equator is an imaginary line in the sky that is directly above the Earth’s equator.

If a star is located at a declination of $\delta$, then it will be visible at its upper culmination when the zenith distance is $\theta – \delta$. This is because the zenith distance is equal to the latitude of the observer minus the declination of the star.

For example, if the observer is located at a latitude of $\theta = 45^\circ$ and the star has a declination of $\delta = 30^\circ$, then the zenith distance of the star at its upper culmination will be $\theta – \delta = 15^\circ$.

The other options are incorrect because they do not take into account the latitude of the observer.