MCQOPTIONS
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MCQOPTIONS
This section includes 48 Mcqs, each offering curated multiple-choice questions to sharpen your Data Structures and Algorithms knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
According to Gabriel lame, how many steps does Euclid's algorithm require to solve a problem? |
| A. | Less than five times the number of digits |
| B. | More than five times the number of digits |
| C. | Less than two times the number of digits |
| D. | More than two times the number of digits |
| Answer» B. More than five times the number of digits | |
| 2. |
The dictionary ordering of elements is known as? |
| A. | Lexicographical order |
| B. | Colexicographical order |
| C. | Well order |
| D. | Sorting |
| Answer» B. Colexicographical order | |
| 3. |
Who demonstrated the difference in numerical stability? |
| A. | Strassen |
| B. | Bailey |
| C. | Lederman |
| D. | Higham |
| Answer» E. | |
| 4. |
What is the total running time of Euclid's algorithm? |
| A. | O(N) |
| B. | O(N log M) |
| C. | O(N log N) |
| D. | O(log N +1) |
| Answer» B. O(N log M) | |
| 5. |
What is the time complexity of Heap's algorithm? |
| A. | O(n log n) |
| B. | O(n2) |
| C. | O(n*n!) |
| D. | O(n!) |
| Answer» E. | |
| 6. |
Counting intersections can be done using the inclusion-exclusion principle only if it is combined with De Morgan's laws of complementing. |
| A. | true |
| B. | false |
| Answer» B. false | |
| 7. |
Who discussed techniques for reducing the memory requirements for Strassen's algorithm? |
| A. | Strassen |
| B. | Lederman |
| C. | Bailey |
| D. | Higham |
| Answer» D. Higham | |
| 8. |
Compute the product matrix using Strassen's matrix multiplication algorithm.Given a11=1; a12=3;a21=5;a22=7 b11=8;b12=4;b21=6;b22=2 |
| A. | c11=20;c12=12;c21=100;c22=15 |
| B. | c11=22;c12=8;c21=90;c22=32 |
| C. | c11=15;c12=7;c21=80;c22=34 |
| D. | c11=26;c12=10;c21=82;c22=34 |
| Answer» E. | |
| 9. |
Running time of Strassen's algorithm is better than the naïve Theta(n3) method. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 10. |
Euclidean algorithm does not require the calculation of prime factors. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 11. |
What is the GCD of 20 and 12 using Euclid's algorithm? |
| A. | 8 |
| B. | 2 |
| C. | 4 |
| D. | 6 |
| Answer» D. 6 | |
| 12. |
The number of elements in the power set increases when there are duplicates present in the set. |
| A. | True |
| B. | False |
| Answer» C. | |
| 13. |
What is the running time of Strassen's algorithm for matrix multiplication? |
| A. | O(n2.81) |
| B. | O(n3) |
| C. | O(n1.8) |
| D. | O(n2) |
| Answer» B. O(n3) | |
| 14. |
____________ is one of the most useful principles of enumeration in combinationatorics and discrete probability. |
| A. | Inclusion-exclusion principle |
| B. | Quick search algorithm |
| C. | Euclid's algorithm |
| D. | Set theory |
| Answer» B. Quick search algorithm | |
| 15. |
Strassen's matrix multiplication algorithm follows ___________ technique. |
| A. | Greedy technique |
| B. | Dynamic Programming |
| C. | Divide and Conquer |
| D. | Backtracking |
| Answer» D. Backtracking | |
| 16. |
Which of the following statement is incorrect with respect to generalizing the solution using the inclusion-exclusion principle? |
| A. | including cardinalities of sets |
| B. | excluding cardinalities of pairwise intersections |
| C. | excluding cardinalities of triple-wise intersections |
| D. | excluding cardinalities of quadraple-wise intersections |
| Answer» D. excluding cardinalities of quadraple-wise intersections | |
| 17. |
What is the recurrence relation used in Strassen's algorithm? |
| A. | 7T(n/2) + Theta(n2) |
| B. | 8T(n/2) + Theta(n2) |
| C. | 7T(n/2) + O(n2) |
| D. | 8T(n/2) + O(n2) |
| Answer» B. 8T(n/2) + Theta(n2) | |
| 18. |
Who invented the concept of inclusion-exclusion principle? |
| A. | Abraham de Moivre |
| B. | Daniel Silva |
| C. | J.J. Sylvester |
| D. | Sieve |
| Answer» B. Daniel Silva | |
| 19. |
If GCD of two numbers is 1, then the two numbers are said to be ________ |
| A. | Co-prime numbers |
| B. | Prime numbers |
| C. | Composite numbers |
| D. | Rational numbers |
| Answer» B. Prime numbers | |
| 20. |
What is the running time of naïve matrix multiplication algorithm? |
| A. | O(n2.81) |
| B. | O(n4) |
| C. | O(n) |
| D. | O(n3) |
| Answer» E. | |
| 21. |
While generating partitions of integer 3 we consider 2 1 and 1 2 to be different partitions. |
| A. | true |
| B. | false |
| Answer» C. | |
| 22. |
If 4 is the GCD of 16 and 12, What is the GCD of 12 and 4? |
| A. | 12 |
| B. | 6 |
| C. | 4 |
| D. | 2 |
| Answer» D. 2 | |
| 23. |
The number of scalar additions and subtractions used in Strassen's matrix multiplication algorithm is ________ |
| A. | O(n2.81) |
| B. | Theta(n2) |
| C. | Theta(n) |
| D. | O(n3) |
| Answer» C. Theta(n) | |
| 24. |
Which one of the following problem types does inclusion-exclusion principle belong to? |
| A. | Numerical problems |
| B. | Graph problems |
| C. | String processing problems |
| D. | Combinatorial problems |
| Answer» E. | |
| 25. |
The Euclid's algorithm runs efficiently if the remainder of two numbers is divided by the minimum of two numbers until the remainder is zero. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 26. |
Which of the following is not an application of inclusion-exclusion principle? |
| A. | Counting intersections |
| B. | Graph coloring |
| C. | Matching of bipartite graphs |
| D. | Maximum flow problem |
| Answer» E. | |
| 27. |
Euclid's algorithm is used for finding ___________ |
| A. | GCD of two numbers |
| B. | GCD of more than three numbers |
| C. | LCM of two numbers |
| D. | LCM of more than two numbers |
| Answer» B. GCD of more than three numbers | |
| 28. |
Strassen's algorithm is a/an_____________ algorithm. |
| A. | Non- recursive |
| B. | Recursive |
| C. | Approximation |
| D. | Accurate |
| Answer» C. Approximation | |
| 29. |
Which of the following is true according to Ramanujan's congruence? |
| A. | No. of partitions are divisible by 5 for a number 3 more than a multiple of 5 |
| B. | No. of partitions are divisible by 5 for a number 4 more than a multiple of 5 |
| C. | No. of partitions are divisible by 5 for a number 2 more than a multiple of 5 |
| D. | No. of partitions are divisible by 5 for a number 1 more than a multiple of 5 |
| Answer» C. No. of partitions are divisible by 5 for a number 2 more than a multiple of 5 | |
| 30. |
Strassen's algorithm is quite numerically stable as the naïve method. |
| A. | True |
| B. | False |
| Answer» C. | |
| 31. |
Heap's algorithm requires an auxiliary array to create permutations. |
| A. | true |
| B. | false |
| Answer» C. | |
| 32. |
What will be the output of the code that generates permutations and also has the ability to handle duplicates, for the input str[]='AA'? |
| A. | AA |
| B. | AA,AA |
| C. | A,A |
| D. | A |
| Answer» B. AA,AA | |
| 33. |
Which of the following is a correct representation of inclusion-exclusion principle? |
| A. | |A U B|=|A|+|B|-|A,B| |
| B. | |A,B|=|A|+|B|-|A U B| |
| C. | |A U B|=|A|+|B|+|A,B| |
| D. | |A,B|=|A|+|B|+|A U B| |
| Answer» B. |A,B|=|A|+|B|-|A U B| | |
| 34. |
Who invented Euclid's algorithm? |
| A. | Sieve |
| B. | Euclid |
| C. | Euclid-Sieve |
| D. | Gabriel lame |
| Answer» C. Euclid-Sieve | |
| 35. |
____________ is an arithmetic function that calculates the total number of positive integers less than or equal to some number n, that are relatively prime to n. |
| A. | Euler's phi function |
| B. | Euler's omega function |
| C. | Cauchy's totient function |
| D. | Legrange's function |
| Answer» B. Euler's omega function | |
| 36. |
Strassen's Matrix Algorithm was proposed by _____________ |
| A. | Volker Strassen |
| B. | Andrew Strassen |
| C. | Victor Jan |
| D. | Virginia Williams |
| Answer» B. Andrew Strassen | |
| 37. |
How many iterating statements are involved in the naïve method of matrix multiplication? |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 38. |
Which of the following is the correct mathematical application of Euclid's algorithm? |
| A. | Determination of prime numbers |
| B. | Lagrange's four square theorem |
| C. | Cauchy-Euler theorem |
| D. | Residue theorem |
| Answer» C. Cauchy-Euler theorem | |
| 39. |
What is the total running time of the binary GCD algorithm? |
| A. | O(N) |
| B. | O(N2) |
| C. | O(log N) |
| D. | O(N log N) |
| Answer» C. O(log N) | |
| 40. |
Which of the following is not an application of Euclid's algorithm? |
| A. | Simplification of fractions |
| B. | Performing divisions in modular arithmetic |
| C. | Solving quadratic equations |
| D. | Solving diophantine equations |
| Answer» D. Solving diophantine equations | |
| 41. |
What is the formula for Euclidean algorithm? |
| A. | GCD (m,n) = GCD (n, m mod n) |
| B. | LCM(m,n)=LCM(n, m mod n) |
| C. | GCD(m,n,o,p) = GCD (m, m mod n, o, p mod o) |
| D. | LCM (m,n,o,p) = LCM (m, m mod n, o, p mod o) |
| Answer» B. LCM(m,n)=LCM(n, m mod n) | |
| 42. |
How many permutations will be formed from the array arr={1,2,3}? |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 43. |
Number of elements in the power set of set S={1,2,2} will be? |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 44. |
According to inclusion-exclusion principle, a n-tuple wise intersection is included if n is even. |
| A. | True |
| B. | False |
| Answer» C. | |
| 45. |
Using the inclusion-exclusion principle, find the number of integers from a set of 1-100 that are not divisible by 2, 3 and 5. |
| A. | 22 |
| B. | 25 |
| C. | 26 |
| D. | 33 |
| Answer» D. 33 | |
| 46. |
What will be the lexicographical order of permutations formed from the array arr={1,2,3}? |
| A. | {{2,1,3},{3,2,1},{3,1,2},{2,3,1},{1,2,3},{1,3,2}} |
| B. | {{1,2,3},{1,3,2},{2,3,1},{2,1,3},{3,2,1},{3,1,2}} |
| C. | {{1,2,3},{1,3,2},{2,1,3},{2,3,1},{3,1,2},{3,2,1}} |
| D. | {{2,1,3},{3,1,2},{3,2,1},{2,3,1},{1,2,3},{1,3,2}} |
| Answer» D. {{2,1,3},{3,1,2},{3,2,1},{2,3,1},{1,2,3},{1,3,2}} | |
| 47. |
What is the formula to calculate the element present in second row, first column of the product matrix? |
| A. | M1+M7 |
| B. | M1+M3 |
| C. | M2+M4 - M5 + M7 |
| D. | M2+M4 |
| Answer» E. | |
| 48. |
Let A={1,2,3} B={2,3,4} C={1,3,5} D={2,3}. Find the cardinality of sum of all the sets. |
| A. | 6 |
| B. | 5 |
| C. | 4 |
| D. | 7 |
| Answer» C. 4 | |