JEE MainPhysicsModerateUnit and dimension

A force F is given by: F = at + bt^2, where t represents time.
What are dimensions of a and b?

Show answer and solution

\lbrack F\rbrack = \lbrack at\rbrack;\ \lbrack a\rbrack = \left\lbrack \frac{F}{t} \right\rbrack = \left\lbrack \frac{{MLT}^{- 2}}{T} \right\rbrack = \left\lbrack {MLT}^{- 3} \right\rbrack

\lbrack F\rbrack = \left\lbrack \lbrack b\rbrack = \left\lbrack \frac{F}{t^{2}} \right\rbrack = \left\lbrack \frac{{MLT}^{- 2}}{T^{2}} \right\rbrack = \left\lbrack {MLT}^{- 4} \right\rbrack

Source: Grass-G / P-05 Physics paper 10 October.docx

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