List - I(Number) | List - II(Significant figure) |
(A) 1001 | (I) 3 |
(B) 010.1 | (II) 4 |
(C) 100.100 | (III) 5 |
(D) 0.0010010 | (IV) 6 |
To determine the number of significant figures in each number, we apply the following rules:
Matching the Numbers with Their Significant Figures
(A) 1001: All four digits are non-zero, so there are 4 significant figures.
(B) 010.1: The leading zero is not significant, so there are 3 significant figures.
(C) 100.100: All digits are significant, including the trailing zeros after the decimal. Thus, there are 6 significant figures.
(D) 0.0010010: The leading zeros are not significant, but all other digits, including the trailing zero, are significant. This gives 5 significant figures.
Matching
Conclusion: The correct matching is (A)-(II), (B)-(I), (C)-(IV), (D)-(III).
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: