​At what time between 2:00 and 3:00 will the hands of the clock be exactly opposite to each other?

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Correct option is C

To solve the problem, we need to determine the time when the angle between the hour and minute hands is 180° (opposite to each other).

Step 1: Formula Used

The position of the hour hand and the minute hand can be calculated using the following formulas:
- Position of the hour hand = 30H + $$\frac{M}{2}$$​ , where H is the hour and M is the minute.
- Position of the minute hand = 6M , where M is the minute.
To find the time when they are opposite, the absolute difference between these positions should be 180°:

$$| (30H + \frac{M}{2}) - 6M | = 180$$​​

Step 2: Plugging in H = 2 (for the hour 2:00 to 3:00)

The equation becomes:

$$| (30 \times 2 + \frac{M}{2}) - 6M | = 180$$​​


$$| (60 + \frac{M}{2}) - 6M | = 180$$​​

Simplify:

| 60 - 5.5M | = 180

Step 3: Solve for M

Case 1: 60 - 5.5M = 180

$$5.5M = -120 \quad \text{(Not possible, as M cannot be negative.)}$$​​


Case 2: 60 - 5.5M = -180

5.5M = 240


M = $$\frac{240}{5.5} = 43.63636 \quad \text{(approximately).}$$​​

So the time is approximately 2:43:38 .

Step 4: Approximation and Answer

The closest rounded time is 2:45 .

Answer: (c) 2:45