MCQOPTIONS
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MCQOPTIONS
This section includes 258 Mcqs, each offering curated multiple-choice questions to sharpen your Arithmetic Ability knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
How many even integers between 4000 and 7000 have four different digits? |
| A. | 672 |
| B. | 840 |
| C. | 504 |
| D. | 728 |
| Answer» B. 840 | |
| 2. |
If P (n, r) = 2520 and C (n, r) = 21, then what is the value of C (n + 1, r + 1)? |
| A. | 7 |
| B. | 14 |
| C. | 28 |
| D. | 56 |
| Answer» D. 56 | |
| 3. |
If C(20, n + 2) = C(20, n – 2) then what is n equal to? |
| A. | 8 |
| B. | 10 |
| C. | 12 |
| D. | 16 |
| Answer» C. 12 | |
| 4. |
How many three-digit even numbers can be formed using the digits 1, 2, 3, 4 and 5 when repetition of digits is not allowed? |
| A. | 36 |
| B. | 30 |
| C. | 24 |
| D. | 12 |
| Answer» D. 12 | |
| 5. |
If a and b are greatest values of 2nCr and 2n - 1Cr respectively, then |
| A. | a = 2b |
| B. | b = 2a |
| C. | a = b |
| D. | a2 = 2b2 |
| Answer» B. b = 2a | |
| 6. |
In what number of ways can the letters of the word 'ABLE' be arranged so that the vowels occupy even places? |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» C. 6 | |
| 7. |
In how many ways the letter of the word BALLOON be arranged so that two L do not come together? |
| A. | 1260 |
| B. | 360 |
| C. | 900 |
| D. | 1060 |
| Answer» D. 1060 | |
| 8. |
A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to: |
| A. | 28 |
| B. | 27 |
| C. | 25 |
| D. | 24 |
| Answer» D. 24 | |
| 9. |
Let (x + 10)50 + (x - 10)50 = a0 + a1 x + a2 x2 +…+ a50 x50, for all x ∈ R; then \(\frac{{{a_2}}}{{{a_0}}}\) is equal to: |
| A. | 12.5 |
| B. | 12 |
| C. | 12.25 |
| D. | 12.75 |
| Answer» D. 12.75 | |
| 10. |
Out of 15 points in plane, n points are in the same straight line, 445 triangles can be formed by joining these points. What is the value of n? |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 11. |
How many words can be formed using all the letters of the word ‘NATION’ so that all the three vowels should never come together? |
| A. | 354 |
| B. | 348 |
| C. | 288 |
| D. | None of the above |
| Answer» D. None of the above | |
| 12. |
If different words are formed, with all the letters of the word ‘AGAIN’ and are arranged alphabetically among themselves as in a dictionary, the word at the 50th place will be |
| A. | NAAGI |
| B. | NAAIG |
| C. | IAAGN |
| D. | IAANG |
| Answer» C. IAAGN | |
| 13. |
Naresh has 10 friends, and he wants to invite 6 of them to a party. How many times will 3 particular friends never attend the party? |
| A. | 8 |
| B. | 7 |
| C. | 720 |
| D. | 35 |
| Answer» C. 720 | |
| 14. |
If all the words, with or without meaning, are written using the letters of the word QUEEN add are arranged as in English Dictionary, then the position of the word QUEEN is |
| A. | 47th |
| B. | 44th |
| C. | 45th |
| D. | 46th |
| Answer» E. | |
| 15. |
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is: |
| A. | 180 |
| B. | 175 |
| C. | 160 |
| D. | 162 |
| Answer» B. 175 | |
| 16. |
From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist? |
| A. | 209 |
| B. | 210 |
| C. | 246 |
| D. | 242 |
| Answer» D. 242 | |
| 17. |
9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is |
| A. | 18720 |
| B. | 18270 |
| C. | 17280 |
| D. | 12780 |
| Answer» D. 12780 | |
| 18. |
In how many ways can the leter of the word 'SCALE' be arranged, so that the vowels do not come together? |
| A. | 72 |
| B. | 36 |
| C. | 48 |
| D. | 60 |
| Answer» B. 36 | |
| 19. |
How many different permutations can be made out of the letters of the word ‘TESTBOOK' ? |
| A. | \(\frac{{8!}}{{4!}}\) |
| B. | \(\frac{{8!}}{{2! \times 2!}}\) |
| C. | \(\frac{{8!}}{{2! \times 3!}}\) |
| D. | None of these |
| Answer» C. \(\frac{{8!}}{{2! \times 3!}}\) | |
| 20. |
If nPr = 720 and nCr = 120, then the value of r is: |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 21. |
Evaluate the expression: \(\frac{{\left( {12!} \right) - \left( {10!} \right)}}{{9!}}\) |
| A. | 1210 |
| B. | 1610 |
| C. | 1130 |
| D. | 1310 |
| Answer» E. | |
| 22. |
If n and r are integers such that 1 ≤ r ≤ n, then the value of \(n(^{n-1}C_{r-1})\) is |
| A. | \(^nC_r\) |
| B. | \(r(^nC_r)\) |
| C. | \(n(^nC_r)\) |
| D. | \((n-1)(^nC_r)\) |
| Answer» C. \(n(^nC_r)\) | |
| 23. |
Let n be the number of different 5 digits numbers, divisible by 4 that can be formed with the digits 1, 2, 3, 4, 5 and 6 , with no digit being repeated. What is the value of n? |
| A. | 144 |
| B. | 168 |
| C. | 192 |
| D. | 222 |
| Answer» D. 222 | |
| 24. |
How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed? |
| A. | 35 |
| B. | 53 |
| C. | 120 |
| D. | 60 |
| Answer» E. | |
| 25. |
Let n be the number of different 6 digit numbers, divisible by 4 with the digits 2, 3, 4, 5, 6 and 7, no digit being repeated in the numbers. What is the value of n? |
| A. | 192 |
| B. | 720 |
| C. | 24 |
| D. | 190 |
| Answer» B. 720 | |
| 26. |
In how many ways can 15 members of a council sit along a circular table, when the secretary is to sit on one side of the chairman and the deputy secretary on the other side? |
| A. | 24 |
| B. | 2 × 15! |
| C. | 2 × 12! |
| D. | None of these |
| Answer» D. None of these | |
| 27. |
If \(\rm {^nC_r}={^nC_{r-1}}\) and \(\rm {^nP_r}={^nP_{r+1}}\), then the value of n is: |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 5 |
| Answer» D. 5 | |
| 28. |
If \(\mathop \sum \limits_{{\rm{r}} = 0}^{25} \left\{ {{}_\;^{50}{{\rm{C}}_{\rm{r}}}\cdot50 - {{\rm{r}}_{{{\rm{C}}_{25}} - {\rm{r}}}}} \right\} = {\rm{K}}\left( {{}_\;^{50}{{\rm{C}}_{25}}} \right)\), then K is equal to: |
| A. | 252 |
| B. | 225 - 1 |
| C. | 224 |
| D. | 225 |
| Answer» E. | |
| 29. |
In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is |
| A. | 13 |
| B. | 11 |
| C. | 9 |
| D. | 7 |
| Answer» B. 11 | |
| 30. |
Let Tn denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If Tn+1 - Tn = 21, then n equals: |
| A. | 5 |
| B. | 7 |
| C. | 6 |
| D. | 4 |
| Answer» C. 6 | |
| 31. |
Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is: |
| A. | 500 |
| B. | 200 |
| C. | 300 |
| D. | 350 |
| Answer» D. 350 | |
| 32. |
How many 5-digit prime numbers can be formed using the digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed? |
| A. | 5 |
| B. | 4 |
| C. | 3 |
| D. | 0 |
| Answer» E. | |
| 33. |
In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers? |
| A. | 16 |
| B. | 20 |
| C. | 14 |
| D. | 15 |
| Answer» B. 20 | |
| 34. |
A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is |
| A. | 24 × 8! × 8! |
| B. | (8!)3 |
| C. | 210 × 8! × 8! |
| D. | 16! |
| Answer» D. 16! | |
| 35. |
How many words starting with letter D can be formed by taking all letters from word DELHI, so that the letters are not repeated? |
| A. | 4 |
| B. | 12 |
| C. | 24 |
| D. | 120 |
| Answer» D. 120 | |
| 36. |
A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done? |
| A. | 151200 |
| B. | 75600 |
| C. | 37800 |
| D. | 18900 |
| Answer» B. 75600 | |
| 37. |
Let x be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to |
| A. | 2480 |
| B. | 2481 |
| C. | 2482 |
| D. | 2483 |
| Answer» C. 2482 | |
| 38. |
If 42(nP2) = nP4 then the value of n is |
| A. | 2 |
| B. | 4 |
| C. | 9 |
| D. | 42 |
| Answer» D. 42 | |
| 39. |
If a polygon has 44 diagonals then the number of its sides is |
| A. | 11 |
| B. | 10 |
| C. | 8 |
| D. | 7 |
| Answer» B. 10 | |
| 40. |
If 20C1 + (22) 20C2 + (32) 20C3 +…+ (202) 20C20 =A(2β), then the ordered pair (A, β) is equal to: |
| A. | (420, 19) |
| B. | (420, 18) |
| C. | (380, 18) |
| D. | (380, 19) |
| Answer» C. (380, 18) | |
| 41. |
How many four-digit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition of digits? |
| A. | 24 |
| B. | 36 |
| C. | 44 |
| D. | 64 |
| Answer» B. 36 | |
| 42. |
In how many ways the letter of a word 'SNOWMAN' be arranged so that the word formed starts with a vowel and end with a vowel? The formed word may not certainly have a meaning. |
| A. | 120 |
| B. | 240 |
| C. | 150 |
| D. | 180 |
| Answer» B. 240 | |
| 43. |
Out of 8 Americans and 5 Indians, in how many ways a committee of 6 members can be formed if it should have at least 3 Indians? |
| A. | 560 |
| B. | 708 |
| C. | 140 |
| D. | None of these |
| Answer» C. 140 | |
| 44. |
A bag contains 3 black, 4 white and 2 red balls, all the balls being different. The number of selections of at most 6 balls containing balls of all the colours is |
| A. | 42 × 4! |
| B. | 26 × 4! |
| C. | (26 - 1) × 4! |
| D. | None of these |
| Answer» B. 26 × 4! | |
| 45. |
If nCn-2 = 28, n>0, then n = ? |
| A. | 28 |
| B. | 7 |
| C. | 8 |
| D. | 27 |
| Answer» D. 27 | |
| 46. |
If n! has 17 zeros, then what is the value of n? |
| A. | 95 |
| B. | 85 |
| C. | 80 |
| D. | No such value of n exists |
| Answer» E. | |
| 47. |
A five-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition of digits. What is the number of ways this can be done? |
| A. | 96 |
| B. | 48 |
| C. | 32 |
| D. | 216 |
| Answer» E. | |
| 48. |
How many words can be formed with the letters of the word "POSTMAN", if every word begins with P and ends with N? |
| A. | 720 |
| B. | 5040 |
| C. | 120 |
| D. | 4320 |
| Answer» D. 4320 | |
| 49. |
In how many different ways can the letters of the word "CORPORATION" be arranged so that all the vowels always come together? |
| A. | 810 |
| B. | 1440 |
| C. | 2880 |
| D. | 50400 |
| Answer» E. | |
| 50. |
In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player? |
| A. | 42 |
| B. | 35 |
| C. | 21 |
| D. | 20 |
| Answer» D. 20 | |