MCQOPTIONS
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MCQOPTIONS
This section includes 119 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Calculate the value of ⁸C₅. |
| A. | 79 |
| B. | 43 |
| C. | 120 |
| D. | 56 |
| Answer» E. | |
| 52. |
Find the value of a₄ for the recurrence relation aₙ=2aₙ₋₁+3, with a₀=6. |
| A. | 320 |
| B. | 221 |
| C. | 141 |
| D. | 65 |
| Answer» D. 65 | |
| 53. |
A bag contains 25 balls such as 10 balls are red, 7 are white and 8 are blue. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour? |
| A. | 10 |
| B. | 18 |
| C. | 63 |
| D. | 35 |
| Answer» C. 63 | |
| 54. |
Find the coefficient of x⁸ in the expansion of (x+2)¹¹. |
| A. | 640 |
| B. | 326 |
| C. | 1320 |
| D. | 456 |
| Answer» D. 456 | |
| 55. |
There are 28 identical oranges that are to be distributed among 8 distinct girls. How many ways are there to distribute the oranges? |
| A. | ²²P₇ |
| B. | ³⁴C₆ |
| C. | ³⁵C₇ |
| D. | ²⁸C₈ |
| Answer» D. ²⁸C₈ | |
| 56. |
How many substrings (of all lengths inclusive) can be formed from a character string of length 8? (Assume all characters to be distinct) |
| A. | 14 |
| B. | 21 |
| C. | 54 |
| D. | 37 |
| Answer» E. | |
| 57. |
Determine the solution for the recurrence relation aₙ = 6aₙ₋₁−8aₙ₋₂ provided initial conditions a₀=3 and a₁=5. |
| A. | aₙ = 4 * 2ⁿ – 3ⁿ |
| B. | aₙ = 3 * 7ⁿ – 5*3ⁿ |
| C. | aₙ = 5 * 7ⁿ |
| D. | aₙ = 3! * 5ⁿ |
| Answer» C. aₙ = 5 * 7ⁿ | |
| 58. |
If a, b, c, d and e are five natural numbers, then find the number of ordered sets(a, b, c, d, e) possible such that a+b+c+d+e=75. |
| A. | ⁶⁵C₅ |
| B. | ⁵⁸C₆ |
| C. | ⁷²C₇ |
| D. | ⁷⁴C₄ |
| Answer» E. | |
| 59. |
Find the number of factors of the product 5⁸ * 7⁵ * 2³ which are perfect squares. |
| A. | 47 |
| B. | 30 |
| C. | 65 |
| D. | 19 |
| Answer» C. 65 | |
| 60. |
Computational complexity of derangements is of __________ |
| A. | NP-complete |
| B. | NP-hard |
| C. | NP |
| D. | P |
| Answer» B. NP-hard | |
| 61. |
Every linear equation determines a _______ in n-dimensional space for n variables. |
| A. | shipshape |
| B. | hyperplane |
| C. | cone |
| D. | pyramid |
| Answer» C. cone | |
| 62. |
Farhan has received 9 gifts from 9 different people. In how many ways can Farhan receives the gifts such that no one gives him real gifts? |
| A. | 133496 |
| B. | 326654 |
| C. | 218744 |
| D. | 745331 |
| Answer» B. 326654 | |
| 63. |
Determine the probability when a die is thrown 2 times such that there are no fours and no fives occur? |
| A. | 4/9 |
| B. | 56/89 |
| C. | 13/46 |
| D. | 3/97 |
| Answer» B. 56/89 | |
| 64. |
Find the odd positive integer of the number 4380. |
| A. | 108 |
| B. | 48 |
| C. | 75 |
| D. | 8 |
| Answer» C. 75 | |
| 65. |
Given the factorization of a number n, then the sum of divisors can be computed in _______ |
| A. | linear time |
| B. | polynomial time |
| C. | O(logn) |
| D. | o(n+1) |
| Answer» C. O(logn) | |
| 66. |
There are 7 groups in a picnic who has brought their own lunch box, and then the 7 lunch box are exchanged within those groups. Determine the number of ways that they can exchange the lunch box such that none of them can get their own. |
| A. | 655 |
| B. | 328 |
| C. | 1854 |
| D. | 3765 |
| Answer» D. 3765 | |
| 67. |
In how many ways can 10 boys be seated in a row having 28 seats such that no two friends occupy adjacent seats? |
| A. | ¹³P₅ |
| B. | ⁹P₂₉ |
| C. | ¹⁹P₁₀ |
| D. | ¹⁵P₇ |
| Answer» D. ¹⁵P₇ | |
| 68. |
A woman has 14 identical pens to distribute among a group of 10 distinct students. How many ways are there to distribute the 14 pens such that each student gets at least one pencil? |
| A. | ¹⁵C₁₀ |
| B. | ¹⁰C₅ * 11 |
| C. | ¹⁵C₈ * 4! |
| D. | ¹³C₉ |
| Answer» E. | |
| 69. |
When four coins are tossed simultaneously, in _______ number of the outcomes at most two of the coins will turn up as heads. |
| A. | 17 |
| B. | 28 |
| C. | 11 |
| D. | 43 |
| Answer» D. 43 | |
| 70. |
There are six movie parts numbered from 1 to 6. Find the number of ways in which they be arranged so that part-1 and part-3 are never together. |
| A. | 876 |
| B. | 480 |
| C. | 654 |
| D. | 237 |
| Answer» C. 654 | |
| 71. |
The number of binary strings of 17 zeros and 8 ones in which no two ones are adjacent is ___________ |
| A. | 43758 |
| B. | 24310 |
| C. | 32654 |
| D. | 29803 |
| Answer» B. 24310 | |
| 72. |
Suppose that M is the product of k distinct primes. Find the number of ways to write N as the product of positive integers(>1), where the order of terms does not matter. |
| A. | ᴹCₙ₋ₖ |
| B. | ᴺCₘ |
| C. | N * Bₖ |
| D. | Bᴋ |
| Answer» E. | |
| 73. |
The number of diagonals can be drawn in a hexagon is ______ |
| A. | 9 |
| B. | 32 |
| C. | 16 |
| D. | 21 |
| Answer» B. 32 | |
| 74. |
Suppose, there are 7 of your friends who want to eat pizza (8 distinct people in total). You order a 16-cut pizza (16 identical slices). How many distributions of pizza slices are there if each person gets at least one slice of pizza? |
| A. | 346 |
| B. | 6435 |
| C. | 3214 |
| D. | 765 |
| Answer» C. 3214 | |
| 75. |
What is the coefficient of x⁹ in the expansion of (x+5)¹⁴? |
| A. | 5! * ¹⁴C₆ |
| B. | ¹⁴C₅ |
| C. | 54 * ¹⁴C₅ |
| D. | 34 * ¹¹C₅ |
| Answer» D. 34 * ¹¹C₅ | |
| 76. |
For a gaming competition, 8 girls are planning on splitting up into 3 (non-empty) groups. How many ways can they split up into these groups? |
| A. | 465 |
| B. | 1056 |
| C. | 966 |
| D. | 3215 |
| Answer» D. 3215 | |
| 77. |
What is the sum of all 6 digit numbers which can be formed using the digits 2, 3, 5, 6 and 9 exactly once? |
| A. | 986546600 |
| B. | 25611866 |
| C. | 433338798 |
| D. | 319999680 |
| Answer» E. | |
| 78. |
In how many ways can 8 different dolls be packed in 5 identical gift boxes such that no box is empty if any of the boxes hold all of the toys? |
| A. | 2351 |
| B. | 365 |
| C. | 2740 |
| D. | 1260 |
| Answer» E. | |
| 79. |
How many numbers of three digits can be formed with digits 1, 3, 5, 7 and 9? |
| A. | 983 |
| B. | 120 |
| C. | 345 |
| D. | 5430 |
| Answer» C. 345 | |
| 80. |
Evaluate the expression (y+1)⁴ – (y-1)⁴. |
| A. | 3y² + 2y⁵ |
| B. | 7(y⁴ + y² + y) |
| C. | 8(y³ + y¹) |
| D. | y + y² + y³ |
| Answer» D. y + y² + y³ | |
| 81. |
If Sₙ=4Sₙ₋₁+12n, where S₀=6 and S₁=7, find the solution for the recurrence relation. |
| A. | aₙ=7(2ⁿ)−29/6n6ⁿ |
| B. | aₙ=6(6ⁿ)+6/7n6ⁿ |
| C. | aₙ=6(3ⁿ⁺¹)−5n |
| D. | aₙ=nn−2/6n6ⁿ |
| Answer» C. aₙ=6(3ⁿ⁺¹)−5n | |
| 82. |
Determine all possibilities for the solution set of the system of 2 equations in 3 unknowns that has x₁ = 4, x₂ = −7, x₃ = 0 as a solution. |
| A. | one or finitely many |
| B. | infinite |
| C. | finite |
| D. | zero |
| Answer» C. finite | |
| 83. |
The size of a multiset is 6 which is equal to the number of elements in it with counting repetitions (a multiset is an unordered collection of elements where the elements may repeat any number of times). Determine the number of multisets can be grouped from n distinct elements so that at least one element occurs exactly twice? |
| A. | 326 |
| B. | 28 |
| C. | 45 |
| D. | 62 |
| Answer» D. 62 | |
| 84. |
Find the odd positive integer of the number 6500. |
| A. | 43 |
| B. | 17 |
| C. | 12 |
| D. | 87 |
| Answer» D. 87 | |
| 85. |
There are 15 people in a committee. How many ways are there to group these 15 people into 3, 5, and 4? |
| A. | 846 |
| B. | 2468 |
| C. | 658 |
| D. | 1317 |
| Answer» E. | |
| 86. |
In a group of 267 people how many friends are there who have an identical number of friends in that group? |
| A. | 266 |
| B. | 2 |
| C. | 138 |
| D. | 202 |
| Answer» C. 138 | |
| 87. |
In how many ways can you select 9 cupcakes from a box containing 17 cupcakes? |
| A. | 42769 |
| B. | 45398 |
| C. | 24310 |
| D. | 36214 |
| Answer» D. 36214 | |
| 88. |
The solution to the recurrence relation aₙ=aₙ₋₁+2n, with initial term a₀=2 are _________ |
| A. | 4n+7 |
| B. | 2(1+n) |
| C. | 3n² |
| D. | 5*(n+1)/2 |
| Answer» C. 3n² | |
| 89. |
Find the coefficient of x⁷ in (x+4)⁹. |
| A. | 523001 |
| B. | 428700 |
| C. | 327640 |
| D. | 129024 |
| Answer» E. | |
| 90. |
How many ways can 8 prizes be given away to 7 students, if each student is eligible for all the prizes? |
| A. | 40325 |
| B. | 40320 |
| C. | 40520 |
| D. | 40720 |
| Answer» C. 40520 | |
| 91. |
Calculate the sum of divisors of N = 9600. |
| A. | 23250 |
| B. | 47780 |
| C. | 54298 |
| D. | 31620 |
| Answer» E. | |
| 92. |
In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how many persons were present at the party? |
| A. | 15 |
| B. | 14 |
| C. | 16 |
| D. | 17 |
| Answer» C. 16 | |
| 93. |
A head boy, two deputy head boys, a head girl and 3 deputy head girls must be chosen out of a student council consisting of 14 girls and 16 boys. In how many ways can they are chosen? |
| A. | 98072 |
| B. | 27384 |
| C. | 36428 |
| D. | 44389 |
| Answer» C. 36428 | |
| 94. |
How many ways are there to arrange 7 chocolate biscuits and 12 cheesecake biscuits into a row of 19 biscuits? |
| A. | 52347 |
| B. | 50388 |
| C. | 87658 |
| D. | 24976 |
| Answer» C. 87658 | |
| 95. |
Determine the number of derangements of (2, 4, 6, 1, 3, 5) that end with integer 2, 4 and 6 in some order? |
| A. | 128 |
| B. | 29 |
| C. | 54 |
| D. | 36 |
| Answer» E. | |
| 96. |
The number of even positive integers of 3200 is _______ |
| A. | 24 |
| B. | 32 |
| C. | 164 |
| D. | 209 |
| Answer» B. 32 | |
| 97. |
How many even positive integers are there in the number 7362? |
| A. | 16 |
| B. | 58 |
| C. | 35 |
| D. | 165 |
| Answer» B. 58 | |
| 98. |
How many words that can be formed with the letters of the word ‘SWIMMING’ such that the vowels do not come together? Assume that words are of with or without meaning. |
| A. | 430 |
| B. | 623 |
| C. | 729 |
| D. | 1239 |
| Answer» D. 1239 | |
| 99. |
14 different letters of alphabet are given, words with 6 letters are formed from these given letters. How many number of words are there which have at least one letter repeated? |
| A. | 892742 |
| B. | 999988 |
| C. | 213216 |
| D. | 786730 |
| Answer» C. 213216 | |
| 100. |
Let M be a sequence of 9 distinct integers sorted in ascending order. How many distinct pairs of sequences, N and O are there such that i) each are sorted in ascending order, ii) N has 5 and O has 4 elements, and iii) the result of merging N and O gives that sequence? |
| A. | 84 |
| B. | 35 |
| C. | 194 |
| D. | 138 |
| Answer» B. 35 | |