The question is a little light on introductory explanation. In fact, there isn't any that I can see.
The way I understand it, [ M L T⁻¹ ] means the PHYSICAL DIMENSIONS of (Mass)·(Length)·(1/Time). Then, the choices are expressions of various quantities that you run into in Physics ... like 'mvr' means 'mass·velocity·radius', 'mat' means 'mass·acceleration·time' etc. ... and it wants to know which one of the choices would end up having the dimensions of [ M L T⁻¹ ] ?
I'm not going to go through all of them, but here's one:
Take 'm·v·r' : 'm' is a mass. The 'v' is a velocity, so it's something like (meters)/(sec), which is dimensions of (length) / (time) or [ L·T⁻¹ ]. The 'r' is radius, so it has dimensions of length [ L ].
The whole product of 'm·v·r' has dimensions of [M] · [L·T⁻¹] · [ L ]. Multiply that out, and it's [ M L² T⁻¹ ] . That's NOT the dimensions that the question is asking for [ M L T⁻¹ ] so the answer isn't choice-A 'm v r' .
I believe it's going to turn out to be choice-B . ' m·a·t ' . The 'a' is acceleration. That's like (meters)/(sec²), so the dimensions of acceleration are [ L T⁻² ] . I'm sure you can carry the ball from this point.
