1. |
## Recursion is similar to which of the following? |

A. | switch case |

B. | loop |

C. | if-else |

D. | if elif else |

Answer» B. loop | |

Explanation: recursion is similar to a loop. |

2. |
## Recursion is a method in which the solution of a problem depends on |

A. | larger instances of different problems |

B. | larger instances of the same problem |

C. | smaller instances of the same problem |

D. | smaller instances of different problems |

Answer» C. smaller instances of the same problem | |

Explanation: in recursion, the solution of a problem depends on the solution of smaller instances of the same problem. |

3. |
## Which of the following problems can’t be solved using recursion? |

A. | factorial of a number |

B. | nth fibonacci number |

C. | length of a string |

D. | problems without base case |

Answer» D. problems without base case | |

Explanation: problems without base case leads to infinite recursion call. in general, we will assume a base case to avoid infinite recursion call. problems like finding factorial of a number, nth fibonacci number and |

4. |
## In general, which of the following methods isn’t used to find the factorial of a number? |

A. | recursion |

B. | iteration |

Answer» A. recursion | |

Explanation: the function counts the number of vowels in a string. in this case the number is vowels is 6. |

5. |
## Which of the following recursive formula can be used to find the factorial of a number? |

A. | fact(n) = n * fact(n) |

B. | fact(n) = n * fact(n+1) |

C. | fact(n) = n * fact(n-1) |

D. | fact(n) = n * fact(1) |

Answer» C. fact(n) = n * fact(n-1) | |

Explanation: fact(n) = n * fact(n – 1) can be used to find the factorial of a number. |

6. |
## Suppose the first fibonnaci number is 0 and the second is 1. What is the sixth fibonnaci number? |

A. | 5 |

B. | 6 |

C. | 7 |

D. | 8 |

Answer» A. 5 | |

Explanation: the sixth fibonnaci number is |

7. |
## Which of the following is not a fibonnaci number? |

A. | 8 |

B. | 21 |

C. | 55 |

D. | 14 |

Answer» D. 14 | |

Explanation: 14 is not a fibonnaci number. |

8. |
## Which of the following option is wrong? |

A. | fibonacci number can be calculated by using dynamic programming |

B. | fibonacci number can be calculated by using recursion method |

C. | fibonacci number can be calculated by using iteration method |

D. | no method is defined to calculate fibonacci number |

Answer» D. no method is defined to calculate fibonacci number | |

Explanation: fibonacci number can be calculated by using dynamic programming, recursion method, iteration method. |

9. |
## Which of the following recurrence relations can be used to find the nth fibonacci number? |

A. | f(n) = f(n) + f(n – 1) |

B. | f(n) = f(n) + f(n + 1) |

C. | f(n) = f(n – 1) |

D. | f(n) = f(n – 1) + f(n – 2) |

Answer» D. f(n) = f(n – 1) + f(n – 2) | |

Explanation: the relation f(n) = f(n – 1) + f(n – 2) can be used to find the nth fibonacci number. |

10. |
## Which of the following gives the sum of the first n natural numbers? |

A. | nc2 |

B. | (n-1)c2 |

C. | (n+1)c2 |

D. | (n+2)c2 |

Answer» C. (n+1)c2 | |

Explanation: the sum of first n natural numbers is given by n*(n+1)/2, which is equal to (n+1)c2. |

11. |
## If GCD of two number is 8 and LCM is 144, then what is the second number if first number is 72? |

A. | 24 |

B. | 2 |

C. | 3 |

D. | 16 |

Answer» D. 16 | |

Explanation: as a * b = gcd (a, b) * lcm (a, b). so b = (144 * 8)/72 = 16. |

12. |
## Which of the following is also known as GCD? |

A. | highest common divisor |

B. | highest common multiple |

C. | highest common measure |

D. | lowest common multiple |

Answer» A. highest common divisor | |

Explanation: gcm (greatest common measure), gcf (greatest common factor), hcf (highest common factor) and hcf (highest common divisor) are also known as gcd. |

13. |
## Which of the following is coprime number? |

A. | 54 and 24 |

B. | 4 and 8 |

C. | 6 and 12 |

D. | 9 and 28 |

Answer» D. 9 and 28 | |

Explanation: coprime numbers have gcd 1. so 9 and 28 are coprime numbers. while 54 |

14. |
## In terms of Venn Diagram, which of the following expression gives GCD (Given A ꓵ B ≠ Ø)? |

A. | multiplication of a u b terms |

B. | multiplication of a ꓵ b terms |

C. | multiplication of a*b terms |

D. | multiplication of a-b terms |

Answer» B. multiplication of a ꓵ b terms | |

Explanation: in terms of venn diagram, the gcd is given by the intersection of two sets. so a ꓵ b gives the gcd. while a u b gives the lcm. |

15. |
## What is the GCD according to the given Venn Diagram? |

A. | 2 |

B. | 3 |

C. | 5 |

D. | 6 |

Answer» C. 5 | |

Explanation: in terms of venn diagram, the gcd is given by the intersection of two sets. so a ꓵ b gives the gcd. while a u b gives the lcm. so here a ꓵ b is 5. |

16. |
## What is the GCD of a and b? |

A. | a + b |

B. | gcd (a-b, b) if a>b |

C. | gcd (a+b, a-b) |

D. | a – b |

Answer» B. gcd (a-b, b) if a>b | |

Explanation: as per euclid’s algorithm, gcd (a, b) = gcd (a-b, b) if a > b or gcd (a, b) = gcd (a, b-a) if b > a. |

17. |
## What is the GCD of 48, 18, 0? |

A. | 24 |

B. | 2 |

C. | 3 |

D. | 6 |

Answer» D. 6 | |

Explanation: gcd is largest positive integer that divides each of the integer. so the gcd of 48, 18, 0 is 6. |

18. |
## Is 9 and 28 coprime number? |

A. | true |

B. | false |

Answer» A. true | |

Explanation: coprime numbers have gcd 1. so 9 and 28 are coprime numbers. |

19. |
## If gcd (a, b) is defined by the expression, d=a*p + b*q where d, p, q are positive integers and a, b is both not zero, then what is the expression called? |

A. | bezout’s identity |

B. | multiplicative identity |

C. | sum of product |

D. | product of sum |

Answer» A. bezout’s identity | |

Explanation: if gcd (a, b) is defined by the expression, d=a*p + b*q where d, p, q are positive integers and a, b is both not zero, then the expression is called bezout’s identity and p, q can be calculated by extended form of euclidean algorithm. |

20. |
## Is gcd an associative function. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: the gcd function is an associative function as gcd (a, gcd (b, c)) = gcd (gcd (a, b), c). |

21. |
## Who gave the expression for the probability and expected value of gcd? |

A. | james e. nymann |

B. | riemann |

C. | thomae |

D. | euler |

Answer» A. james e. nymann | |

Explanation: in the year 1972, james e. nymann showed some result to show the probability and expected value of gcd. |

22. |
## What is the computational complexity of Binary GCD algorithm where a and b are integers? |

A. | o (log a + log b)2) |

B. | o (log (a + b)) |

C. | o (log ab) |

D. | o (log a-b) |

Answer» A. o (log a + log b)2) | |

Explanation: from the binary gcd algorithm, it is found that the computational complexity is o (log a + log b)2) as the total number of steps in the execution is at most the total sum of number of bits of a and b. |

23. |
## LCM is also called as |

A. | gcd |

B. | scm |

C. | gcf |

D. | hcf |

Answer» B. scm | |

Explanation: gcd (greatest common divisor), gcf (greatest common factor), hcf (highest common factor) is not an alias for lcm. lcm is also called as smallest common multiple(scm). |

24. |
## What is the LCM of 8 and 13? |

A. | 8 |

B. | 12 |

C. | 20 |

D. | 104 |

Answer» D. 104 | |

Explanation: 104 is the smallest positive integer that is divisible by both 8 and 12. |

25. |
## Which is the smallest number of 3 digits that is divisible by 2, 4, 8? |

A. | 100 |

B. | 102 |

C. | 116 |

D. | 104 |

Answer» D. 104 | |

Explanation: lcm of 2, 4, 8 is 8. so check for the number that is divisible by 8. so 104 is the smallest number that is divisible by 2, 4, 8. |

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