Arrange the following in increasing order of their values: A. 160.32 × 40.36…
2025
Arrange the following in increasing order of their values:
A. 160.32 × 40.36
B. (1/25)[81/3 + 271/3]-2
C. (1024)-1/5
D. (8/125)-1/3
सही विकल्प चुनें:
- A.
B < D < A < C
- B.
B < C < D < A
- C.
C < D < B < A
- D.
C < B < D < A
Attempted by 16 students.
Show answer & explanation
Correct answer: B
Calculate each expression:
A = 16^0.32 * 4^0.36
= (2^4)^0.32 * (2^2)^0.36
= 2^1.28 * 2^0.72
= 2^2 = 4
B = (1/25)[8^(1/3) + 27^(1/3)]^-2
= (1/25)[2 + 3]^-2
= (1/25) * 5^-2
= 1/625
C = (1024)^(-1/5)
= (2^10)^(-1/5)
= 2^-2 = 1/4
D = (8/125)^(-1/3)
= ((2/5)^3)^(-1/3)
= (2/5)^-1 = 5/2
Thus, in increasing order: 1/625 < 1/4 < 5/2 < 4.
Therefore, B < C < D < A. Hence, Option B is correct.