Alternate representations for 2748 decimal – UGC NET Question

To check which option equals 2748, we convert each representation to decimal using its base. For 41443₅, the expansion is 4×5⁴ + 1×5³ + 4×5² + 4×5¹ + 3×5⁰, which gives 4×625 + 1×125 + 4×25 + 4×5 + 3×1. This evaluates to 2500 + 125 + 100 + 20 + 3 = 2748, so 41443₅ equals 2748. Therefore, option B is the correct representation.

Option A:
Option A is a base-4 number whose expansion using powers of 4 gives a decimal result different from 2748. The pattern of digits and the lower base produce a value slightly smaller than 2748. Hence, it is not an equivalent representation of the given decimal number.

Option B:
Option B, when carefully expanded with the correct powers of 5, matches 2748 exactly, showing that it represents the same quantity in base 5. None of the other options produce this decimal value when converted. Therefore, 41443₅ is uniquely correct among the given alternatives.

Option C:
Option C is in base 8 and, when expanded as a sum of powers of 8, gives a decimal value close to but not equal to 2748. The altered least significant digits cause a mismatch with 2748. Hence, it is an incorrect choice.

Option D:
Option D is in base 9, and its expansion using powers of 9 results in a decimal value slightly greater than 2748. Since its calculation does not match the target decimal number, it cannot represent 2748.