The correct answer for the number of links in a planar mechanism with revolute joints having 10 instantaneous centers is option 'C', which is 5.

Explanation:
A planar mechanism consists of a series of links connected by joints. In a revolute joint, the two connected links can rotate relative to each other about a common axis. The instantaneous center is the point where the two links would appear to rotate about if they were connected by a pin.

To determine the number of links in a planar mechanism with 10 instantaneous centers, we can use the following formula:

Number of links = Number of instantaneous centers + 1

In this case, the number of instantaneous centers is given as 10. Therefore, the number of links is:

Number of links = 10 + 1 = 11

However, this formula assumes that the mechanism is fully connected and there are no open or floating links. In a planar mechanism, each link must be connected to at least two other links to form a closed loop.

Since the mechanism is planar, it lies in a single plane and cannot have any floating links. Therefore, the correct number of links in this case is the minimum number of links required to form a closed loop, which is 5.

This can be visualized by considering a simple example. Imagine a planar mechanism with a single link connected to 10 instantaneous centers. The link can rotate about each of these centers, but it cannot form a closed loop. To form a closed loop, at least 4 additional links are required, resulting in a total of 5 links.

Hence, the correct answer is option 'C', which is 5.