Mathematical & Quantitative Reasoning

Q1. 2^10?

1. A.1024✓ Correct
2. B.2048
3. C.256
4. D.512

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Q2. 5!?

1. A.25
2. B.720
3. C.60
4. D.120✓ Correct

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Q3. 17 % 5?

1. A.3
2. B.5
3. C.4
4. D.2✓ Correct

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Q4. log2(8)?

1. A.4
2. B.8
3. C.3✓ Correct
4. D.2

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Q5. Sum of first 10 naturals?

1. A.50
2. B.55✓ Correct
3. C.45
4. D.100

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Q6. C(n,2) represents?

1. A.The product n times 2
2. B.Ways to choose 2 from n✓ Correct
3. C.The quotient n divided by 2
4. D.The sum of n plus 2

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Q7. GCD(12,8)?

1. A.6
2. B.2
3. C.4✓ Correct
4. D.8

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Q8. O(n), n from 10 to 100 scales?

1. A.Stays the same
2. B.About 100x slower
3. C.About 10x slower✓ Correct
4. D.About 2x slower

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Q9. What is a prime?

1. A.Any odd number in the range
2. B.Divisible by any number at all
3. C.Only 1 and itself as divisors✓ Correct
4. D.Any even number in the range

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Q10. LCM(4,6)?

1. A.2
2. B.10
3. C.24
4. D.12✓ Correct

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Q11. Euclidean GCD complexity?

1. A.O(a+b)
2. B.O(a*b)
3. C.O(log(min(a,b)))✓ Correct
4. D.O(n^2)

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Q12. Subsets of n elements?

1. A.2^n✓ Correct
2. B.n^2
3. C.n
4. D.n!

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Q13. Pigeonhole Principle?

1. A.n items in m slots (n>m): one has >1✓ Correct
2. B.A specific data structure type
3. C.A search algorithm for arrays
4. D.A sorting algorithm technique

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Q14. Geometric series sum?

1. A.a*n
2. B.a(r^n-1)/(r-1)✓ Correct
3. C.n*r
4. D.a+r*n

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Q15. Permutations of n distinct objects?

1. A.2^n
2. B.n!✓ Correct
3. C.n
4. D.n^2

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Q16. Modular arithmetic useful for?

1. A.Only for division operations needed
2. B.Cyclic ops, hashing, overflow prevention✓ Correct
3. C.Only formatting output display
4. D.It has no practical use in CS

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Q17. P(heads) fair coin?

1. A.0.5✓ Correct
2. B.1
3. C.0
4. D.0.25

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Q18. P(5,3)?

1. A.15
2. B.120
3. C.10
4. D.60✓ Correct

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Q19. C(10,3)?

1. A.120✓ Correct
2. B.1000
3. C.720
4. D.30

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Q20. Base case importance?

1. A.Stops infinite recursion as a condition✓ Correct
2. B.It is used only for display output
3. C.It makes the formula longer overall
4. D.It is optional and unneeded

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Q21. Master Theorem for?

1. A.Finding prime numbers only
2. B.Sorting arrays of elements
3. C.Recurrences T(n)=aT(n/b)+f(n)✓ Correct
4. D.Graph traversal algorithms

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Q22. T(n)=2T(n/2)+n?

1. A.O(n)
2. B.O(log n)
3. C.O(n log n)✓ Correct
4. D.O(n^2)

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Q23. Euler's totient phi(n)?

1. A.Count of numbers coprime with n✓ Correct
2. B.The factorial of the number n
3. C.The largest prime factor of n
4. D.The sum of all divisors of n

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Q24. Catalan numbers count?

1. A.Prime numbers in a range
2. B.Greatest common divisor values
3. C.Parenthesizations and binary trees✓ Correct
4. D.Sorted permutations of arrays

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Q25. Fermat's Little Theorem?

1. A.a^p = a (mod p) for prime p✓ Correct
2. B.All prime numbers are odd values
3. C.a^n = n^a for all values
4. D.Every integer has unique factors

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Q26. Sieve of Eratosthenes complexity?

1. A.O(n log n)
2. B.O(n^2)
3. C.O(n log log n)✓ Correct
4. D.O(n)

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Q27. Chinese Remainder Theorem for?

1. A.Sorting elements in arrays
2. B.Graph coloring and partitioning
3. C.Factorization of large numbers
4. D.Simultaneous modular congruences✓ Correct

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Q28. Stirling's approximation significance?

1. A.Approximates n! for growth analysis✓ Correct
2. B.It sorts elements efficiently
3. C.It finds prime numbers quickly
4. D.It solves algebraic equations

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Q29. Handshaking Lemma?

1. A.All vertices have even degree
2. B.The graph is always fully connected
3. C.Sum of degrees equals 2 times edges✓ Correct
4. D.All edges have equal weight values

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Q30. Matrix exponentiation for?

1. A.Sorting matrix rows and columns
2. B.nth term of linear recurrences fast✓ Correct
3. C.Displaying matrices on screen
4. D.Reading matrix input from files

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