Both the assertion and reason are correct. The presence of a positive zero error means the Vernier scale is shifted, causing an overestimation of measurements. The reason accurately describes a possible cause for such errors.
The Correct answer is: Both (A) and (R) are correct but (R) is not the correct explanation of (A)
Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter $ D $ of a tube. The measured value of $ D $ is:
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: