MCQOPTIONS
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MCQOPTIONS
This section includes 109 Mcqs, each offering curated multiple-choice questions to sharpen your Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The total number of arrangements of the letters in the expression a3b2c4 when written at full length is ? |
| A. | 1260 |
| B. | 2520 |
| C. | 610 |
| D. | None of these |
| Answer» B. 2520 | |
| 2. |
If there are 10 positive real numbers n1 < n2, n3 .... < n10 How many triplets of these numbers (n1, n2, n3) (n2, n3, n4), ... can be generated such that in each triplet the first number is always less than the second number and the second number is always less the third number ? |
| A. | 45 |
| B. | 90 |
| C. | 120 |
| D. | 180 |
| Answer» D. 180 | |
| 3. |
If nCr - 1 = 36, nCr = 84 and nCr + 1 = 126 then ? |
| A. | n = 8, r = 4 |
| B. | n = 9, r = 3 |
| C. | n = 7, r = 5 |
| D. | None of these |
| Answer» C. n = 7, r = 5 | |
| 4. |
If 35Cn + 7 = 35C4n - 2, then all the values of n are given by ? |
| A. | 28 |
| B. | 3, 6 |
| C. | 3 |
| D. | 6 |
| Answer» C. 3 | |
| 5. |
If 2n + 1Pn - 1 : 2n - 1Pn = 3 : 5, then n is equal to ? |
| A. | 4 |
| B. | 6 |
| C. | 3 |
| D. | 8 |
| Answer» B. 6 | |
| 6. |
If nPr= 720 nCr than the value r is ? |
| A. | 6 |
| B. | 5 |
| C. | 4 |
| D. | 7 |
| Answer» B. 5 | |
| 7. |
If 56Pr + 6 : 54Pr + 3 = 30800 : 1 then the value of r is ? |
| A. | 40 |
| B. | 41 |
| C. | 42 |
| D. | None of these |
| Answer» C. 42 | |
| 8. |
If n+2C8 : n- 2P4 = 57 : 16 then the value of n is ? |
| A. | 20 |
| B. | 19 |
| C. | 18 |
| D. | 17 |
| Answer» C. 18 | |
| 9. |
Find the value of 5 P2. |
| A. | 15 |
| B. | 18 |
| C. | 20 |
| D. | 122 |
| Answer» D. 122 | |
| 10. |
If 50cr = 50cr + 2 find r. |
| A. | 24 |
| B. | 23 |
| C. | 22 |
| D. | 21 |
| E. | 20 |
| Answer» B. 23 | |
| 11. |
If nP3 = 9240, then find the value of n. |
| A. | 20 |
| B. | 21 |
| C. | 22 |
| D. | 23 |
| E. | 24 |
| Answer» D. 23 | |
| 12. |
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? |
| A. | 40 |
| B. | 400 |
| C. | 5040 |
| D. | 2520 |
| Answer» D. 2520 | |
| 13. |
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together? |
| A. | 10080 |
| B. | 4989600 |
| C. | 120960 |
| D. | None of these |
| Answer» D. None of these | |
| 14. |
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? |
| A. | 120 |
| B. | 720 |
| C. | 4320 |
| D. | 2160 |
| E. | None of these |
| Answer» C. 4320 | |
| 15. |
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? |
| A. | 159 |
| B. | 194 |
| C. | 205 |
| D. | 209 |
| E. | None of these |
| Answer» E. None of these | |
| 16. |
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? |
| A. | 5 |
| B. | 10 |
| C. | 15 |
| D. | 20 |
| Answer» E. | |
| 17. |
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women? |
| A. | 266 |
| B. | 5040 |
| C. | 11760 |
| D. | 86400 |
| E. | None of these |
| Answer» D. 86400 | |
| 18. |
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? |
| A. | 360 |
| B. | 480 |
| C. | 720 |
| D. | 5040 |
| E. | None of these |
| Answer» D. 5040 | |
| 19. |
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? |
| A. | 210 |
| B. | 1050 |
| C. | 25200 |
| D. | 21400 |
| E. | None of these |
| Answer» D. 21400 | |
| 20. |
In how many ways can the letters of the word 'LEADER' be arranged? |
| A. | 72 |
| B. | 144 |
| C. | 360 |
| D. | 720 |
| E. | None of these |
| Answer» D. 720 | |
| 21. |
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? |
| A. | 564 |
| B. | 645 |
| C. | 735 |
| D. | 756 |
| E. | None of these |
| Answer» E. None of these | |
| 22. |
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women? |
| A. | 63 |
| B. | 90 |
| C. | 126 |
| D. | 45 |
| E. | 135 |
| Answer» B. 90 | |
| 23. |
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? |
| A. | 810 |
| B. | 1440 |
| C. | 2880 |
| D. | 50400 |
| E. | 5760 |
| Answer» E. 5760 | |
| 24. |
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw? |
| A. | 32 |
| B. | 48 |
| C. | 64 |
| D. | 96 |
| E. | None of these |
| Answer» D. 96 | |
| 25. |
In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? |
| A. | 32 |
| B. | 48 |
| C. | 36 |
| D. | 60 |
| E. | 120 |
| Answer» D. 60 | |
| 26. |
In how many ways can the letters of the word 'Director' be arranged so that the three vowels are never together ? |
| A. | 1800 |
| B. | 18000 |
| C. | 16000 |
| D. | 1600 |
| Answer» C. 16000 | |
| 27. |
A mixed doubles tennis game is to be played between two teams ( each team consists of one male and one female). There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played ? |
| A. | 12 |
| B. | 48 |
| C. | 36 |
| D. | 42 |
| Answer» C. 36 | |
| 28. |
There is a 7-digit telephone number with all different digits. If the digit at extreme right and extreme left are 5 and 6 respectively, find how many such telephone number are possible ? |
| A. | 120 |
| B. | 100000 |
| C. | 6720 |
| D. | 30240 |
| E. | None of the above |
| Answer» D. 30240 | |
| 29. |
In how many ways, can 24 persons be seated around a circular table if there are is 13 seats? |
| A. | 24! / [13 x 11! ] |
| B. | 22! / [14 x 12!] |
| C. | 23! / [13 x 11!] |
| D. | 24! / [12 x 12!] |
| E. | None of the above |
| Answer» B. 22! / [14 x 12!] | |
| 30. |
There are 14 points in a plane, out of which 4 are collinear. Find the number of triangles made by these points . |
| A. | 364 |
| B. | 360 |
| C. | 368 |
| D. | 365 |
| Answer» C. 368 | |
| 31. |
Find the number of diagonals formed in hexagon . |
| A. | 12 |
| B. | 10 |
| C. | 6 |
| D. | 9 |
| Answer» E. | |
| 32. |
There is a polygon of 12 sides . How many triangles can be drawn using the vertices of polygon ? |
| A. | 200 |
| B. | 220 |
| C. | 240 |
| D. | 260 |
| E. | 280 |
| Answer» C. 240 | |
| 33. |
There are 10 points in a plan, out of which 5 are collinear. Find the number of straight lines formed by joining them. |
| A. | 36 |
| B. | 45 |
| C. | 30 |
| D. | 35 |
| Answer» B. 45 | |
| 34. |
In how many ways, 12 balls can be divided between 2 boys, one receiving 5 and the other 7 balls ? |
| A. | 1784 |
| B. | 1584 |
| C. | 1854 |
| D. | 1560 |
| E. | None of the above |
| Answer» C. 1854 | |
| 35. |
Find the number of combinations that can be formed with 5 oranges, 4 mangoes and 3 bananas, when one fruit of each kind is taken. |
| A. | 60 |
| B. | 120 |
| C. | 110 |
| D. | 75 |
| E. | None of the above |
| Answer» B. 120 | |
| 36. |
20 persons were invited to a party. In how many ways, they and the host can be seated at a circular table ? |
| A. | 18 ! |
| B. | 19 ! |
| C. | 20 ! |
| D. | Couldn't be determined |
| E. | None of the above |
| Answer» D. Couldn't be determined | |
| 37. |
In how many different ways, 5 boys and 5 girls can sit on a circular table, so that the boys and girls are alternate ? |
| A. | 2880 |
| B. | 2800 |
| C. | 2680 |
| D. | 2280 |
| E. | None of the above |
| Answer» B. 2800 | |
| 38. |
In how many ways, a committee of 3 men and 2 women can be formed out of a total of 4 men and 4 women ? |
| A. | 15 |
| B. | 16 |
| C. | 20 |
| D. | 24 |
| Answer» E. | |
| 39. |
In how many ways, a cricket team of 11 players can be made from 15 players, if a particulars player is always chosen ? |
| A. | 1835 |
| B. | 1001 |
| C. | 1635 |
| D. | 1365 |
| E. | None of the above |
| Answer» C. 1635 | |
| 40. |
How many necklaces of 12 beads can be made from 18 beads of various colours ? |
| A. | [118 x 13!] / 2 |
| B. | [110 x 14! ] / 2 |
| C. | [119 x 13!] / 2 |
| D. | [110 x 12!] / 2 |
| E. | None of the above |
| Answer» D. [110 x 12!] / 2 | |
| 41. |
In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position ? |
| A. | 9 |
| B. | 12 |
| C. | 14 |
| D. | 18 |
| Answer» C. 14 | |
| 42. |
Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they are to be filled with either a red or a blue ball such that no two adjacent boxes can be filled with blue balls Then, how different arrangements are possible, given that all balls of a given colour are exactly identical in all respects ? |
| A. | 8 |
| B. | 10 |
| C. | 15 |
| D. | 22 |
| Answer» E. | |
| 43. |
A child has four pockets and three marbles. In how many ways, the child can put the marbles in the pockets ? |
| A. | 12 |
| B. | 64 |
| C. | 256 |
| D. | 60 |
| E. | None of the above |
| Answer» C. 256 | |
| 44. |
In how many ways, can the letters of the word 'ASSASSINATION' be arranged, so that all the S are together ? |
| A. | 10! |
| B. | 14! (4!) |
| C. | 151200 |
| D. | 3628800 |
| E. | None of the above |
| Answer» D. 3628800 | |
| 45. |
Find the number of ways, in which 12 different beads can be arranged to form a necklace . |
| A. | 11 !/2 |
| B. | 10 !/2 |
| C. | 12 !/2 |
| D. | Couldn't be determined |
| E. | None of the above |
| Answer» B. 10 !/2 | |
| 46. |
Find the number of ways of preparing a chain with 5 different coloured beads ? |
| A. | 18 |
| B. | 24 |
| C. | 12 |
| D. | 30 |
| Answer» D. 30 | |
| 47. |
Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women. ? |
| A. | 30 |
| B. | 20 |
| C. | 10 |
| D. | 25 |
| Answer» B. 20 | |
| 48. |
A department had 8 male and female employees each. A project team involving 3 male and 3 female members needs to be chosen from the department employees. How many different projects teams can be chosen ? |
| A. | 112896 |
| B. | 3136 |
| C. | 720 |
| D. | 112 |
| Answer» C. 720 | |
| 49. |
A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees ? |
| A. | 320 |
| B. | 160 |
| C. | 80 |
| D. | 200 |
| Answer» C. 80 | |
| 50. |
Find the number of ways of arranging the host and 8 guests at a circular table, so that the host always sits in a particular seat ? |
| A. | 4! |
| B. | 8! |
| C. | 6! |
| D. | 9! |
| Answer» C. 6! | |