Question

Match List-l with List-ll

List I		List II
A.	\(\sqrt{\frac{0.81\times0.484}{0.064\times6.25}}\)	I.	0.024
B.	\(\sqrt{\frac{0.204\times42}{0.07\times3.4}}\)	II.	0.99
C.	\(\sqrt{\frac{0.081\times0.324\times4.624}{1.5625\times0.0289\times72.9\times64}}\)	III.	50
D.	\(\sqrt{\frac{9.5\times0.085}{0.0017\times0.19}}\)	IV.	6

Choose the correct answer from the options given below:

• (A) - (I), (B) - (IV), (C) - (III), (D) - (II)
• (A) - (I), (B) - (III), (C) - (IV), (D) - (II)
• (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
• (A) - (II), (B) (I), (C) - (IV), (D) - (III)

Answer 1

The Correct Option is C

To solve the given problem, we need to match each expression in List I with its corresponding numerical value in List II. We'll do this by calculating each expression one by one.

1. Expression A: \(\sqrt{\frac{0.81\times0.484}{0.064\times6.25}}\)
   • Calculate the numerator: \(0.81 \times 0.484 = 0.39144\).
   • Calculate the denominator: \(0.064 \times 6.25 = 0.4\).
   • Compute the fraction: \(\frac{0.39144}{0.4} = 0.9786\).
   • Finally, compute the square root: \(\sqrt{0.9786} \approx 0.99\).
   • Thus, Expression A corresponds to II (0.99).
2. Expression B: \(\sqrt{\frac{0.204\times42}{0.07\times3.4}}\)
   • Calculate the numerator: \(0.204 \times 42 = 8.568\).
   • Calculate the denominator: \(0.07 \times 3.4 = 0.238\).
   • Compute the fraction: \(\frac{8.568}{0.238} = 36\).
   • Finally, compute the square root: \(\sqrt{36} = 6\).
   • Thus, Expression B corresponds to IV (6).
3. Expression C: \(\sqrt{\frac{0.081\times0.324\times4.624}{1.5625\times0.0289\times72.9\times64}}\)
   • Calculate the numerator: \(0.081 \times 0.324 \times 4.624 = 0.12102912\).
   • Calculate the denominator: \(1.5625 \times 0.0289 \times 72.9 \times 64 = 211.172544\).
   • Compute the fraction: \(\frac{0.12102912}{211.172544} \approx 0.000573\).
   • Finally, compute the square root: \(\sqrt{0.000573} \approx 0.024\).
   • Thus, Expression C corresponds to I (0.024).
4. Expression D: \(\sqrt{\frac{9.5\times0.085}{0.0017\times0.19}}\)
   • Calculate the numerator: \(9.5 \times 0.085 = 0.8075\).
   • Calculate the denominator: \(0.0017 \times 0.19 = 0.000323\).
   • Compute the fraction: \(\frac{0.8075}{0.000323} = 2500\).
   • Finally, compute the square root: \(\sqrt{2500} = 50\).
   • Thus, Expression D corresponds to III (50).

Therefore, the correct matches are:

• (A) - (II),
• (B) - (IV),
• (C) - (I),
• (D) - (III).

Thus, the correct answer is: (A) - (II), (B) - (IV), (C) - (I), (D) - (III).