magnetic field

Your argument is completely right, but you are not answering the question that you are asked to answer.

Your equation, v = r(2.pi/T) = (2.pi.r)/T = circumference of circle/time taken for one revolution.

Be aware that this equation is just the general equation [velocity = distance/time] applying to a general circular path. It is universally true as long as the path is a circle with CONSTANT RADIUS r.

The circular path described in the question is produced under a specific condition that a magnetic field is acting a charged particle. You are then asked for the relationship between the period T and the velocity v of the charged particle.

In that case, your equation v = r(2.pi/T) needs to develope further to account for the effect of magnetic force on the charged particle.

Since v = r(2.pi/T), or T = 2.pi(r/v), under the action of the magnetic field, the radius of the circle r, is no longer a constant. In fact, r dpenends on v. The higher the speed of the charged particle, the larger the radius of the cicular path r will be.

It can be shown that r/v = m/qB (where m is the mass of the charged particle carrying charge q under the magnetic field B), which is a constant. Thus,
T = 2.pi.(constant) = constant.

I hope now you could realize that your answer is not correct because you have assumed that r is fixed independent of v. But in fact, this is not the case under the action of magnetic field on a charged particle.