What is the sum of the first 21 terms of the AP?
I. The common difference of the A.P. is 3
II. The $$11^{th}$$ term of the A.P. is 31.

If a is first term and d is common difference of an AP.

Then nth term of that AP is$$=a+(n-1)d.$$

Sum of n terms of an AP is$$=\ \frac{\ n}{2}\left\{2a+\left(n-1\right)d\right\}.$$

So, from statement I wecan not say the value of a and n.

II.

11th term of that AP is 31, 

So, $$a+\left(11-1\right)3=31.$$

or,a=1.

Sum of first 21 terms is $$=\ \frac{\ 21}{2}\left\{2\times1+\left(21-1\right)\times3\right\}.$$

$$\ =\frac{\ 21}{2}\left\{2+60\right\}.$$

$$\ =\ 21\times\ 31=651.$$

So, B is correct choice.