UGC NET Questions (Paper – 1)

To convert 1023 to base five, we divide repeatedly by 5 and collect the remainders, obtaining digits 1, 3, 0, 4 and 3 which give 13043₅. Expanding 13043₅ as 1×5⁴ + 3×5³ + 0×5² + 4×5¹ + 3×5⁰ gives 625 + 375 + 0 + 20 + 3 = 1023. Thus 13043 is the correct base-five representation of 1023.

Option A:
13034₅ expands to 1×625 + 3×125 + 0×25 + 3×5 + 4 = 625 + 375 + 0 + 15 + 4 = 1019. This is slightly less than 1023 and therefore cannot be the correct representation.

Option B:
12403₅ corresponds to 1×625 + 2×125 + 4×25 + 0×5 + 3 which is 625 + 250 + 100 + 0 + 3 = 978. This value is far smaller than 1023. Hence this option is incorrect.

Option C:
13103₅ stands for 1×625 + 3×125 + 1×25 + 0×5 + 3 = 625 + 375 + 25 + 0 + 3 = 1028. This is greater than 1023 by five, showing that the digit configuration is not correct.

Option D:
13043₅ gives 625 + 375 + 0 + 20 + 3 = 1023, which exactly matches the decimal number. The pattern of digits reflects accurate repeated division by 5 and correct positional weighting.