At what time between 2 o’clock and 3 o’clock will the hands of a clock be together?

Time between 2 o’clock and 3 o’clock when the hour hand and minute hand coincide

When the hour hand and minute hand coincide, the time is calculated using the formula:

​$$\theta = | 30 H - \frac{11}{2}M|$$

​​when the hour hand and minute hand coincide: $$\theta = 0^o$$, H = 2 ​

​$$0 = | 30 \times2 - \frac{11}{2}M|\\ \ \\ 0 = |60 - \frac{11}{2}M|\\ \ \\ 60 = \frac{11}{2}M\\ \ \\ M = 60\times\frac{2}{11}\\ \ \\ M = 10\frac{10}{11}$$​​

If fractions or detailed calculations are included, the closest approximation to $$\bf10 \frac{10}{11}$$ past 2

Thus, correct answer is (b)