UGC NET Questions (Paper – 1)

The system that employs symbols 0–9 and A–F contains sixteen distinct digit symbols. A number system with sixteen symbols is called a hexadecimal system. It is widely used in computing to represent binary data compactly. Therefore hexadecimal is the correct name for this base-16 system.

Option A:
Option A is correct because hex means six and deci means ten, together implying sixteen. The symbol set 0–9 and A–F fits exactly with this description. This terminology is standard in computer science.

Option B:
Option B refers to the binary system, which uses only the digits 0 and 1. It has base 2 and not base 16, so it cannot match a system using sixteen symbols.

Option C:
Option C denotes the octal system, which uses digits 0–7 and therefore has base 8. Octal does not use letters A–F as part of its symbol set. Hence it does not fit the description.

Option D:
Option D is the decimal system, which is limited to digits 0–9 and has base 10. It lacks the letter symbols A–F that extend the value range to fifteen.

Hexadecimal is a positional number system that uses sixteen distinct symbols, namely 0–9 and A–F. Since the base of a number system equals the count of unique digits used, the base for hexadecimal must be 16. This larger base allows compact representation of binary data in groups of four bits. Therefore, 16 is the only correct base for the hexadecimal system.

Option A:
Option A suggests a base of 8, which corresponds to the octal system, not hexadecimal. Octal uses digits 0–7 and so it cannot represent sixteen distinct values with a single digit. Thus, it does not match the properties of hexadecimal.

Option B:
Option B is correct because hexadecimal uses exactly sixteen distinct symbols and therefore has base 16. Each hex digit represents a value from 0 to 15, aligning with the base-16 structure. This is why hexadecimal is very convenient for grouping four binary bits into one hex digit.

Option C:
Option C shows base 10, which is associated with the decimal system using digits 0–9. Decimal cannot directly represent values 10–15 with a single symbol, so it does not match the hexadecimal definition. Hence 10 is not the correct base here.

Option D:
Option D gives base 2, which is used for the binary system that has only two digits 0 and 1. Hexadecimal requires sixteen distinct symbols, so a base of 2 would be entirely inconsistent with its digit set.

In hexadecimal notation, digits 0–9 represent their usual decimal values 0 to 9. After 9, the letters A, B, C, D, E and F represent decimal values 10 to 15. Specifically, A stands for decimal 10. Therefore, the correct mapping for 'A' in hex is 10.

Option A:
Option A gives 9, which is already represented in hexadecimal by the digit '9'. There is no need to reuse this value for 'A'. Hence 9 cannot be the value of 'A'.

Option B:
Option B assigns the value 11, which in hexadecimal is actually represented by the letter 'B'. Thus 11 corresponds to 'B' and not to 'A'. Choosing 11 would misalign the standard hex digit sequence.

Option C:
Option C is correct because in hexadecimal the sequence after 9 goes A=10, B=11, C=12, D=13, E=14 and F=15. This convention is internationally accepted and used in computing. Therefore 'A' must correspond to 10.

Option D:
Option D corresponds to 12, which is represented in hexadecimal by the letter 'C'. Confusing 'A' with this value would break the standard mapping and cause errors in conversions.

In hexadecimal, the sequence of symbols extends beyond 9 by using letters. After the digit '9', the next symbol is 'A', followed by 'B', 'C', 'D', 'E' and 'F'. This allows representation of values 10 to 15. Therefore, the digit that comes immediately after '9' is 'A'.

Option A:
Option A shows "10", which is interpreted as a two-character string rather than a single hex digit. In hexadecimal, 10 usually represents sixteen in decimal, not the next digit after 9. Hence it is not correct as a single digit successor.

Option B:
Option B gives 'B', which is indeed a hexadecimal digit but it follows 'A' in the sequence. The order goes 9, then A, then B. So 'B' is not immediately after '9'.

Option C:
Option C repeats '9', which is the current digit and not the next one. It does not move forward in the hexadecimal ordering. Thus it cannot answer the question that asks for the immediate successor.

Option D:
Option D is correct because in the hexadecimal digit order, 'A' is the symbol that comes right after '9'. It starts the series of letter-based digits representing values from 10 onwards.

In hexadecimal notation, digits 0 through 9 map directly to decimal 0 to 9. After that, letters A, B, C, D, E and F represent decimal 10, 11, 12, 13, 14 and 15 respectively. Thus, decimal 12 is represented by hex digit C.

Option A:
Option A, A, corresponds to decimal 10 in hexadecimal notation. It is two less than 12 and therefore cannot represent decimal 12.

Option B:
Option B, B, stands for decimal 11, which is one less than 12. It is close but still not the correct mapping for 12.

Option C:
Option C, D, represents decimal 13 in hexadecimal. This is greater than 12 and therefore also not suitable.

Option D:
Option D is correct because the standard sequence assigns 12 to C. This mapping is used consistently in computer memory dumps, color codes and other hexadecimal contexts.