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Number System: Factorial Video Lecture | Quantitative Aptitude (Quant) - CAT
FAQs on Number System: Factorial Video Lecture - Quantitative Aptitude (Quant) - CAT
| 1. What is a factorial and how is it calculated ? |  |
Ans.A factorial, denoted as n!, is the product of all positive integers from 1 to n. It is calculated by multiplying n by (n-1), (n-2), and so on, down to 1. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
| 2. What are some practical applications of factorials ? | |
Ans.Factorials are used in various fields such as mathematics, statistics, and computer science. They are commonly applied in permutations and combinations, calculating probabilities, and solving problems related to arrangements and selections.
| 3. How does the factorial function behave for negative numbers and zero ? | |
Ans.The factorial is defined only for non-negative integers. By convention, 0! is equal to 1. However, factorials for negative integers are undefined.
| 4. Can factorials be calculated for large numbers, and what are the challenges involved ? | |
Ans.Factorials can be calculated for large numbers, but they grow extremely fast, leading to very large results. The challenge lies in computational limits and the potential for overflow in programming languages that cannot handle large integers.
| 5. Are there any approximations for calculating factorials of large numbers ? | |
Ans.Yes, Stirling's approximation is commonly used to estimate the factorial of large numbers. It states that n! is approximately √(2πn) * (n/e)ⁿ, which simplifies calculations for large n without computing the exact factorial.
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