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.
| 1. |
In a game, a fair coin is tossed 6 times. Each time the coin comes up tails, A will pay Rs. 15 but if each time heads come up, A will pay nothing. Determine the probability that A will win Rs. 45 by playing the game? |
| A. | 5/16 |
| B. | 4/31 |
| C. | 3/7 |
| D. | 12/65 |
| Answer» B. 4/31 | |
| 2. |
How many 4-digit numbers can be formed by using 2, 4, 6, 8, 10, 12 without repetition of digits? |
| A. | 15 |
| B. | 42 |
| C. | 70 |
| D. | 127 |
| Answer» B. 42 | |
| 3. |
Determine the solution of the recurrence relation Fₙ=20Fₙ₋₁ − 25Fₙ₋₂ where F₀=4 and F₁=14. |
| A. | aₙ = 14*5ⁿ⁻¹ |
| B. | aₙ = 7/2*2ⁿ−1/2*6ⁿ |
| C. | aₙ = 7/2*2ⁿ−3/4*6ⁿ⁺¹ |
| D. | aₙ = 3*2ⁿ−1/2*3ⁿ |
| Answer» C. aₙ = 7/2*2ⁿ−3/4*6ⁿ⁺¹ | |
| 4. |
What is the recurrence relation for 1, 7, 31, 127, 499? |
| A. | bₙ₊₁=5bₙ₊₁+3 |
| B. | bₙ=4bₙ+7! |
| C. | bₙ=4bₙ₋₁+3 |
| D. | bₙ=bₙ₋₁+1 |
| Answer» D. bₙ=bₙ₋₁+1 | |
| 5. |
A fair coin is tossed 15 times. Determine the probability in which no heads turned up. |
| A. | 2.549 * 10⁻³ |
| B. | 0.976 |
| C. | 3.051 * 10⁻⁵ |
| D. | 5.471 |
| Answer» D. 5.471 | |
| 6. |
What is the middle term in the expansion of (x/2 + 6y)⁸? |
| A. | 45360x⁴ |
| B. | 34210x³ |
| C. | 1207x⁴ |
| D. | 3250x⁵ |
| Answer» B. 34210x³ | |
| 7. |
By the expression \(\left(\frac{x}{3} + \frac{1}{x}\right)^5\), evaluate the middle term in the expression. |
| A. | 10*(x⁵) |
| B. | \(\frac{1}{5}*(\frac{x}{4})\) |
| C. | 10*(\(\frac{x}{3}\)) |
| D. | 6*(x³) |
| Answer» D. 6*(x³) | |
| 8. |
When a programmer compiles her code there is a 95% chance of finding a bug every time. It takes three hours to rewrite her code when she finds out a bug. Determine the probability such that she will finish her coding by the end of her workday. (Assume, a workday is 7 hours) |
| A. | 0.065 |
| B. | 0.344 |
| C. | 0.2 |
| D. | 3.13 |
| Answer» D. 3.13 | |
| 9. |
Determine the number of ways In a single competition a singing couple from 5 boys and 5 girls can be formed so that no girl can sing a song with their respective boy? |
| A. | 123 |
| B. | 44 |
| C. | 320 |
| D. | 21 |
| Answer» C. 320 | |
| 10. |
A postman can put 12 letters into their respective envelopes such that exactly 5 will go into the right envelope. Find the number of ways of doing this work. |
| A. | 2984300 |
| B. | 1610496 |
| C. | 5322167 |
| D. | 3768650 |
| Answer» C. 5322167 | |
| 11. |
A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks? |
| A. | 18 |
| B. | 35 |
| C. | 28 |
| D. | 14 |
| Answer» E. | |
| 12. |
Determine all possibilities for the solution set of a homogeneous system of 4 equations in 4 unknowns. |
| A. | only one |
| B. | finitely many or zero |
| C. | zero |
| D. | one or infinitely many |
| Answer» C. zero | |
| 13. |
Determine all possibilities for the number of solutions of the system of 7 equations in 5 unknowns and it has x₁ = 0, x₂ = −6, and x₃ = 4 as a solution. |
| A. | unique or infinitely many |
| B. | unique |
| C. | finitely many |
| D. | zero |
| Answer» B. unique | |
| 14. |
How many ways are there to divide 4 Indian countries and 4 China countries into 4 groups of 2 each such that at least one group must have only Indian countries? |
| A. | 6 |
| B. | 45 |
| C. | 12 |
| D. | 76 |
| Answer» B. 45 | |
| 15. |
From a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done? |
| A. | 686 |
| B. | 438 |
| C. | 732 |
| D. | 549 |
| Answer» B. 438 | |
| 16. |
There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices? |
| A. | 7! * 6 |
| B. | ⁷C₅ |
| C. | 7! |
| D. | same area |
| Answer» E. | |
| 17. |
There are 2 twin sisters among a group of 15 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two sisters? |
| A. | 15 *12! * 2! |
| B. | 15! * 2! |
| C. | ¹⁴C₂ |
| D. | 16 * 15! |
| Answer» B. 15! * 2! | |
| 18. |
How many words can be formed with the letters of the word ‘CASTLE’ when ‘O’ and ‘A’ occupying end places. |
| A. | 217 |
| B. | 48 |
| C. | 75 |
| D. | 186 |
| Answer» C. 75 | |
| 19. |
Find the number of ways in which 4 people E, F, G, H, A, C can be seated at a round table, such that E and F must always sit together. |
| A. | 32 |
| B. | 290 |
| C. | 124 |
| D. | 48 |
| Answer» E. | |
| 20. |
Determine the number of ways such that 5 men and 5 women be seated at a round table if no two women are seated together. |
| A. | 654870 |
| B. | 144521 |
| C. | 362160 |
| D. | 5634 |
| Answer» D. 5634 | |
| 21. |
What is the sum of divisors of the number 1872? |
| A. | 12493 |
| B. | 5438 |
| C. | 45862 |
| D. | 654 |
| Answer» B. 5438 | |
| 22. |
How many ways can one choose 20 cookies from 45 different types (assuming there are at least 20 of each type)? |
| A. | ⁶⁴C₂₁ * 15 |
| B. | ⁶⁴C₂₀ |
| C. | ⁴⁴C₂₀ * 2! |
| D. | ⁶⁵C₂₂ |
| Answer» C. ⁴⁴C₂₀ * 2! | |
| 23. |
In a picnic with 20 persons where 6 chocolates will be given to the top 8 children(the chocolates are distinct: first, second). How many ways can this be done? |
| A. | ¹⁸C₆ |
| B. | ²⁰P₆ |
| C. | ²⁵C₄ * 6! |
| D. | ¹⁹P5 |
| Answer» C. ²⁵C₄ * 6! | |
| 24. |
Calculate sum of divisors of n = 8620. |
| A. | 7549 |
| B. | 54201 |
| C. | 18102 |
| D. | 654 |
| Answer» D. 654 | |
| 25. |
Find the number of odd positive integers of the number 456. |
| A. | 54 |
| B. | 27 |
| C. | 16 |
| D. | 8 |
| Answer» E. | |
| 26. |
The least number of computers required to connect 10 computers to 5 routers to guarantee 5 computers can directly access 5 routers is ______ |
| A. | 74 |
| B. | 104 |
| C. | 30 |
| D. | 67 |
| Answer» D. 67 | |
| 27. |
How many different choices can be made from 5 roses, 4 marigold and 8 sunflowers if at least one flower is to be chosen for making of garland? |
| A. | 269 |
| B. | 270 |
| C. | 281 |
| D. | 320 |
| Answer» B. 270 | |
| 28. |
Determine all possibilities for the solution set of a homogeneous system of 6 equations in 5 unknowns. |
| A. | only one |
| B. | zero |
| C. | one or infinitely many |
| D. | finitely many |
| Answer» D. finitely many | |
| 29. |
Determine the number of ways of selecting one or more letters from the letters BBBBBB? |
| A. | 6 |
| B. | 73 |
| C. | 23 |
| D. | 56 |
| Answer» B. 73 | |
| 30. |
Determine the independent term of x⁷ in the expansion of (3x² + 4)¹². |
| A. | 220 * 4⁶ |
| B. | 230 |
| C. | 548* 3! |
| D. | 220 * 3⁶ * 4⁶ |
| Answer» E. | |
| 31. |
Determine the average of all four digit numbers that can be made using all the digits 2, 3, 5, 7 and 11 exactly once? |
| A. | 3993 |
| B. | 1555 |
| C. | 5486 |
| D. | 1347 |
| Answer» C. 5486 | |
| 32. |
Determine the number of ways of choosing a cricket team (consists of 11 players) out of 18 players if a particular player is never chosen. |
| A. | 12798 |
| B. | 22800 |
| C. | 31824 |
| D. | 43290 |
| Answer» D. 43290 | |
| 33. |
The number of words of 4 consonants and 3 vowels can be made from 15 consonants and 5 vowels, if all the letters are different is ________ |
| A. | 3! * ¹²C₅ |
| B. | ¹⁶C₄ * ⁴C₄ |
| C. | 15! * 4 |
| D. | ¹⁵C₄ * ⁵C₃ * 7! |
| Answer» E. | |
| 34. |
Determine all possibilities for the solution set of the homogeneous system of 5 equations in 3 unknowns and the rank of the system is 3. |
| A. | more than two |
| B. | only one |
| C. | zero |
| D. | infinite |
| Answer» D. infinite | |
| 35. |
How many ways are there to place 7 differently colored toys into 5 identical urns if the urns can be empty? Note that all balls have to be used. |
| A. | 320 |
| B. | 438 |
| C. | 1287 |
| D. | 855 |
| Answer» E. | |
| 36. |
Determine all possibilities for the solution set of a homogeneous system of 5 equations in 4 unknowns and the rank of the system is 3. |
| A. | finite |
| B. | zero or finitely many |
| C. | only one |
| D. | infinite |
| Answer» E. | |
| 37. |
A nursery teacher has 5 pencil boxes to give out to her five students. Determine the probability that at least one student gets their name tag? |
| A. | 19/30 |
| B. | 26/47 |
| C. | 123/537 |
| D. | 12/79 |
| Answer» B. 26/47 | |
| 38. |
A number lock contains 6 digits. How many different zip codes can be made with the digits 0–9 if repetition of the digits is allowed upto 3 digits from the beginning and the first digit is not 0? |
| A. | 254307 |
| B. | 453600 |
| C. | 458760 |
| D. | 972340 |
| Answer» C. 458760 | |
| 39. |
Determine the value of a₂ for the recurrence relation aₙ = 17aₙ₋₁ + 30n with a₀=3. |
| A. | 4387 |
| B. | 5484 |
| C. | 238 |
| D. | 1437 |
| Answer» E. | |
| 40. |
Determine all possibilities for the solution set of a homogeneous system that has y₁ = 5, y₂ = −3, y₃ = 2 as a solution. |
| A. | one |
| B. | finitely many |
| C. | infinitely many |
| D. | either one or infinitely many |
| Answer» D. either one or infinitely many | |
| 41. |
There are 5 distinct fruits. How many ways can they be planted into identical fruit plants? |
| A. | 87 |
| B. | 52 |
| C. | 76 |
| D. | 128 |
| Answer» C. 76 | |
| 42. |
In how many ways 6 pens can be selected from 15 identical black pens? |
| A. | 9*3! |
| B. | 21 |
| C. | 14! |
| D. | 1 |
| Answer» E. | |
| 43. |
Consider the recurrence relation a₁=4, aₙ=5n+aₙ₋₁. The value of a₆₄ is _________ |
| A. | 10399 |
| B. | 23760 |
| C. | 75100 |
| D. | 53700 |
| Answer» B. 23760 | |
| 44. |
Calculate sum of divisors of n = 1900. |
| A. | 6530 |
| B. | 5346 |
| C. | 3387 |
| D. | 4123 |
| Answer» E. | |
| 45. |
A group of 20 girls plucked a total of 200 oranges. How many oranges can be plucked one of them? |
| A. | 24 |
| B. | 10 |
| C. | 32 |
| D. | 7 |
| Answer» B. 10 | |
| 46. |
In earlier days, there was a chance to make a telephone call would be of 0.6. Determine the probability when it could make 11 successes in 20 attempts of phone call. |
| A. | 0.2783 |
| B. | 0.2013 |
| C. | 0.1597 |
| D. | 3.8561 |
| Answer» D. 3.8561 | |
| 47. |
There are 5 different-colored boxes in a room each with a distinct cover. Find out the number of ways so that these covers can be put on the boxes such that none of the boxes can have right covers on it? (Assume that all the covers must be on the boxes). |
| A. | 208 |
| B. | 137 |
| C. | 239 |
| D. | 24 |
| Answer» E. | |
| 48. |
Determine the coefficient of the x⁵y⁷ term in the polynomial expansion of (m+n)¹². |
| A. | 792 |
| B. | 439 |
| C. | 382 |
| D. | 630 |
| Answer» B. 439 | |
| 49. |
The linear system Cx = d is known as _________ if d! = 0. |
| A. | homogeneous |
| B. | heterogeneous |
| C. | nonhomogeneous |
| D. | augmented system |
| Answer» D. augmented system | |
| 50. |
Determine the 7th term in the expansion of (x-2y)¹². |
| A. | 6128y⁷ |
| B. | 59136y⁶ |
| C. | 52632x⁶ |
| D. | 39861y⁵ |
| Answer» C. 52632x⁶ | |