Practice Questions
Concept Explanation
Number formation uses digits with rules on repetition, leading zeros, and divisibility. Count valid digit arrangements carefully.
Key Strategies
- No leading zero: first digit from 1–9, rest from 0–9
- Without repetition: use nPr on digit positions
- With repetition: use nr when allowed
Example
2-digit numbers from {1,2,3,4,5} without repetition: 5 × 4 = 20.
Common Trap
Exclude numbers with leading zero when forming multi-digit numbers.
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Q1 Easy
2-digit numbers from {1,2,3,4,5} without repetition:
Explanation5 × 4 = 20. -
Q2 Medium
3-digit numbers from {0,1,2,3,4} without repetition (no leading 0):
ExplanationFirst digit 4 choices; remaining 4P2 = 12. Total = 48. -
Q3 Medium
2-digit even numbers from {1,2,3,4,5} without repetition:
ExplanationUnits even (2,4): 2 choices. Tens: 4 remaining. Total = 8. -
Q4 Easy
3-digit numbers using digits 1–9 with repetition allowed:
Explanation9^3 = 729. -
Q5 Medium
4-digit numbers from {1,2,3,4,5,6} without repetition:
Explanation6P4 = 6 × 5 × 4 × 3 = 360. -
Q6 Medium
2-digit numbers from {0,1,2,3} without repetition (no leading 0):
ExplanationFirst digit 3 choices (1,2,3); second 3 remaining = 9. -
Q7 Easy
3-digit numbers from {1,2,3,4,5} with repetition allowed:
Explanation5^3 = 125.
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Q8 Easy
5-digit numbers from {1,2,3,4,5} without repetition:
Explanation5! = 120. -
Q9 Medium
3-digit numbers divisible by 5 from {1,2,3,4,5} without repetition:
ExplanationUnits 5 only. Hundreds 4 choices, tens 3 = 12. -
Q10 Medium
2-digit numbers from {1,2,3,4,5,6} without repetition greater than 40:
ExplanationTens 4,5,6 (3). Units 5 remaining each = 15. Wait: 4x = 4*5=20 for tens=4, 5*5=25 for tens=5, 6*5=30 for tens=6 = 20 total. Answer B. -
Q11 Hard
3-digit numbers from {0,1,2,3,4,5} without repetition (no leading 0):
ExplanationFirst digit 5 choices; remaining 5P2 = 20. Total = 100. -
Q12 Easy
1-digit and 2-digit numbers using {1,2,3} without repeating digits within each number:
Explanation1-digit: 3. 2-digit: 3 × 2 = 6. Total = 9. -
Q13 Hard
4-digit even numbers from {1,2,3,4,5} without repetition:
ExplanationUnits 2 or 4 (2 choices). Remaining 4P3 = 24. Total = 48. -
Q14 Medium
3-digit numbers from {1,2,3,4} without repetition and greater than 300:
ExplanationFirst digit 4 only. Remaining 3P2 = 6. Total = 6.
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DS1 Easy
How many 2-digit numbers can be formed without repetition from {1,2,3,4,5}?
Statement IDigits cannot repeat.
Statement IILeading zero is not possible with this set.
ExplanationStatement I alone: 5 × 4 = 20. -
DS2 Medium
How many 3-digit numbers without leading zero?
Statement IDigits are from {0,1,2,3,4}.
Statement IINo digit repeats.
ExplanationNeed both: 4 × 4 × 3 = 48.
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DS3 Easy
How many 3-digit numbers with repetition from 1–9?
Statement IDigits 1 through 9 may repeat.
Statement IIEach number has exactly 3 digits.
ExplanationStatement I alone: 9^3 = 729. -
DS4 Medium
How many 4-digit numbers without repetition from six digits?
Statement IDigits are {1,2,3,4,5,6}.
Statement IINo digit repeats.
ExplanationNeed both: 6P4 = 360.