Identify the correct statement: A. If 2^x = \frac{256}{\sqrt{2}}, then x =…
2025
Identify the correct statement:
A. If 2^x = \frac{256}{\sqrt{2}}, then x = \frac{15}{2}
B. \frac{1}{3} of 50% of 150 is greater than \sqrt{576}
C. In the merit list of an examination result, the rank of a student is 5th from the top among 20 students. His rank from the bottom of the list is at 15th position
D. In a class of 30 students, the average weight of 20 students is 45 kg and the rest have an average weight of 40 kg. The average weight of the class is 42.5 kg
- A.
A, B and C Only
- B.
B, C and D Only
- C.
A, B and D Only
- D.
A and B Only
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Statement A: 256 = 2^8 and sqrt(2) = 2^(1/2). So, 256/sqrt(2) = 2^8 / 2^(1/2) = 2^(7.5). Thus, x = 7.5 = 15/2. This statement is correct.
Statement B: 50% of 150 is 75. One-third of 75 is 25. sqrt(576) is 24. Since 25 > 24, this statement is correct.
Statement C: Rank from bottom = Total - Rank from top + 1. Here, 20 - 5 + 1 = 16. The statement claims 15, so it is incorrect.
Statement D: Total weight = (20 * 45) + (10 * 40) = 900 + 400 = 1300. Average weight = 1300 / 30 ≈ 43.33 kg. The statement claims 42.5 kg, so it is incorrect.
Since statements A and B are correct, the correct option is 3.