Xavier Aptitude Test 2021 Paper

The difference between the hour and minute hand of a clock is given by $\left|30\mathrm{H}-5.5\mathit{m}\right|$ Here $\mathrm{H}$ is the current hour and m represents the number of completed minutes in the current hour.
In the given time frame of 2: 30 to 3: 00 pm.
At 2 : 30 pm the angle =$\left|30.2-5.5.30\right|=105\mathrm{degrees}$
At 3: 00 pm the angle $\left|30.3-5.5.0\right|=90\mathrm{degrees}$
The function of $30.\mathrm{H}-5.5.\mathit{m}|=$ constantly increases as the value of $\mathit{m}$ increases from $31,32................59$
Because of the modulus function, the net value of the function remains positive
Between 2: 30 to 2: 59 the angle is constantly increasing. The minimum value is 2: 30 which is equal to $105\mathrm{degrees}$ which is greaterthan the $90\mathrm{degrees}$ when the time is 3: 00.
Hence $90\mathrm{degrees}$ is the minimum angle.