UGC NET Questions (Paper – 1)

Dividing 2024 repeatedly by 8 yields remainders that form the octal digits 3, 7, 5 and 0, leading to 3750₈. Expanding 3750₈ as 3×8³ + 7×8² + 5×8¹ + 0×8⁰ equals 1536 + 448 + 40 + 0 = 2024. Hence 3750 is the correct octal representation of 2024.

Option A:
3750₈ corresponds exactly to 3×512 + 7×64 + 5×8 + 0 = 2024. This confirms it as the correct octal form of the given decimal number. Its digits reflect the sequence of remainders from the division process.

Option B:
3740₈ represents 3×512 + 7×64 + 4×8 + 0 = 1536 + 448 + 32 = 2016. Since 2016 is less than 2024, this option is not correct.

Option C:
3570₈ equals 3×512 + 5×64 + 7×8 + 0 = 1536 + 320 + 56 = 1912. This decimal value is far from 2024, so the digit pattern is not appropriate.

Option D:
3650₈ gives 3×512 + 6×64 + 5×8 + 0 = 1536 + 384 + 40 = 1960. As 1960 is below 2024, this cannot be the correct conversion.