Amiya Kumar 
🔢 Base Sytem Practice Quiz (5 Questions)
Understand how numbers are formed using different digits in different bases. This is essential for CAT, SSC, Banking, and other competitive exams.
📝 Base System Practice Quiz (5 Questions)
1. What is the decimal value of \( (1021)_3 \)?
\( 1 \times 3^3 + 0 \times 3^2 + 2 \times 3^1 + 1 \times 3^0 = 27 + 0 + 6 + 1 = \boxed{34} \)
2. Which of the following numbers is not valid in base 5?
(a) 431
(b) 502
(c) 134
(d) 210
(a) 431
(b) 502
(c) 134
(d) 210
Option (b) 502 is invalid because 5 is not allowed in base 5.
3. Convert \( (2A)_\text{16} \) to decimal.
\( 2 \times 16^1 + A \times 16^0 = 2 \times 16 + 10 = \boxed{42} \)
4. Find the largest 2-digit number in base 7.
Largest 2-digit number = \( 7^2 - 1 = \boxed{48} \)
5. Which base allows the number \( (238)_x \) to be valid?
The highest digit is 8. So, base must be \( > 8 \). So minimum valid base = \boxed{9}
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