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 \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32