Question

Which of the following are valid hexadecimal numbers?
• [(i)] 1A3F
• [(ii)] 29GF
• [(iii)] FF12
• [(iv)] 7BHE

• A. (i), (ii) and (iv)
• B. (i), (ii) and (iii)
• C. (i) and (iii)
• D. (i), (iii) and (iv)

Hint:

A hexadecimal number can contain only: \[ 0-9 \quad \text{and} \quad A-F \] If you find letters such as G, H, I, J, etc., the number is immediately invalid.

Answer 1

The Correct Option is C

Concept: The hexadecimal number system is a base-16 number system. Since sixteen distinct symbols are required, hexadecimal uses: \[ 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F \] where \[ A=10,\quad B=11,\quad C=12,\quad D=13,\quad E=14,\quad F=15 \] Any character beyond the letter F is not permitted in a hexadecimal number.

Step 1: Checking number (i): 1A3F The characters present are: \[ 1,\ A,\ 3,\ F \] All of these belong to the valid hexadecimal set. Therefore, \[ 1A3F \] is a valid hexadecimal number.

Step 2: Checking number (ii): 29GF The characters present are: \[ 2,\ 9,\ G,\ F \] The letter G does not belong to the hexadecimal digit set. Therefore, \[ 29GF \] is not a valid hexadecimal number.

Step 3: Checking number (iii): FF12 The characters present are: \[ F,\ F,\ 1,\ 2 \] All characters belong to the hexadecimal digit set. Therefore, \[ FF12 \] is a valid hexadecimal number.

Step 4: Checking number (iv): 7BHE The characters present are: \[ 7,\ B,\ H,\ E \] The letter H is not allowed in hexadecimal notation. Therefore, \[ 7BHE \] is not a valid hexadecimal number.

Step 5: Writing the final result. Valid hexadecimal numbers are: \[ (i)\quad \text{and}\quad (iii) \] Hence, the correct option is: \[ \boxed{(C)\ (i)\ \text{and}\ (iii)} \]