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 \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to:
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The density of the copper ($^{64}Cu$) nucleus is greater than that of the carbon ($^{12}C$) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to $A^{1/3}$.
In the light of the above statements, choose the most appropriate answer from the options given below: