| 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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