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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
How many 5-letter words can be formed from the letters of the word 'MECHANICAL' that word always starts with a consonant?1. 45362. 42443. 44444. 4865 |
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Answer» Correct Answer - Option 1 : 4536 Given: Word is 'MECHANICAL' Number of letters in a word should be = 5 Condition: Word should be start from consonant. Solution: Total number of letters = 10 Repeated letters = 2 Consonant & 2 Vowels Letters available for 1st position = 6 Number of total words formed = (6× 9 × 8× 7× 6)/(2× 2) ⇒ Number of words formed = 4536 ∴5-letter words can be formed from the letters of the word 'MECHANICAL' that word always starts with a consonant are 4536. |
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| 2. |
How many different letter arrangements can be made from the letters of the word ROAST?1. 602. 1203. 7204. 240 |
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Answer» Correct Answer - Option 2 : 120 Given: ROAST = 5 alphabet Calculation: Total 5 alphabet Different number if ways n! 5! = 5 × 4 × 3 × 2 × 1 = 120 ∴ Different letter arrangements can be made from letters of ROAST is 120. |
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| 3. |
What is the number of arrangements of 10 letters the can be formed the letter word of ANNELIDOUS, so that all the vowels are not come together?1. (10!/2!) - {(6!/2!) × 5!}2. 10! - (6!× 4!)3. 10! - 6!4. 7! - (6!× 5!) |
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Answer» Correct Answer - Option 1 : (10!/2!) - {(6!/2!) × 5!} Given: The given word is ANNELIDOUS Calculation: There are 10 letters in ANNELIDOUS in this, there are 5 vowels, that is A, E, I, O andU Assume the (AEIOU) as the single object and the remaining letter or object is 5, now we have 6 objects ⇒ The arrangements of all 6 objects = 6!/2! ⇒ The arrangements of(AEIOU) = 5! ⇒ The number of arrangements all the vowels come together = (6!/2!) × 5! All possible arrangements of 10 letters of wordANNELIDOUS = 10!/2! ⇒ The number of arrangments all the vowels do not come together =All possible arrangements - Number of arrangements all vowels come together ⇒ (10!/2!) - {(6!/2!) × 5!} ∴The number of arrangments all the vowels do not come together is(10!/2!) - {(6!/2!) × 5!}. |
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| 4. |
How many different letter arrangements can be made from the letters of the word RECORD?1. 1202. 3603. 7204. 60 |
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Answer» Correct Answer - Option 2 : 360 Formula used: Number of ways = Total number of word!/Number of Repitition! Calculation: RECORD Total number of words = 6 Number of Repitition = 2 time R Number of ways = Total number of word!/Number of Repitition! ⇒Number of ways = 6!/2! ⇒ (2! × 3 × 4 × 5× 6)/2! = 360 ∴ The required answer will be 360. |
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| 5. |
In how many ways can arrange the letters of the words ALLAHABAD?1. 30242. 50403. 75604. None of these |
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Answer» Correct Answer - Option 3 : 7560 Given: The word ALLAHABAD Formulaused: When alphabets are repeated then we use this formula The number of ways = n!/(p! q! r!) n→ Total number of alphabets p → First type repeated alphabets q→ Second type repeated alphabets r→ Third type repeated alphabets Calculation: In the word ALLAHABAD n = 9→ total letters in ALLAHABAD p = 4→ number of A's q = 2→ number of L's Put values inthe formula ⇒ The number ofarrangements = 9!/(4! × 2!) ⇒ The number ofarrangements = (9× 8× 7× 6× 5 × 4!)/{(2× 1)4!} ⇒ The number ofarrangements = (9× 8× 7× 6× 5 )/2 ⇒ The number ofarrangements = 7560 ∴ Word ALLAHABAD can arrange 7560 ways. |
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| 6. |
How many 4-digit numbers(without repetition) can be formed from the digits 4, 5, 6, 7, 8, 9 which are divisible by 2?1. 2802. 1803. 3404. 4005. None of the above/More than one of the above. |
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Answer» Correct Answer - Option 2 : 180 Given: The given digits are4, 5, 6, 7, 8, 9. Concept Used: For a number to be even, its unit digit must be an even number. Calculation: According to the question, The 4-digit numbers to be formed must be even numbers. For that to happen, the unit digit of the numbers must be even. So, the units place can be filled by 4, 6, and 8 only i.e. there are three ways to fill the units place. After filling units place, there are 5 digits left. So, the 4thplacecan be filled in 5ways. Similarly, the 3rd place and 2nd place can be filled in 4 and 3 ways respectively. The number of 4-digit even numbers formed using digits4, 5, 6, 7, 8, 9 = (5× 4× 3) × 3 ⇒ 180 ∴ The number of 4-digit even numbers that can be formed from the digits 4, 5, 6, 7, 8, 9 is 180. |
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| 7. |
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arrang |
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Answer» 1728 NA |
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| 8. |
How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2? |
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Answer» 210 NA |
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| 9. |
In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions? |
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Answer» 36 NA |
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| 10. |
A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and n |
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Answer» 168 NA |
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| 11. |
Groups, each containing 3 boys are to be formed out of 5 boys, A, B , C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups ? |
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Answer» 7 NA |
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| 12. |
In how many ways, a cricket team of 11 players can be made from 15 players, if a particulars player is always chosen ? |
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Answer» 1001 NA |
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| 13. |
In how many different ways can the letters of the word 'SCHOOL' be arranged so that the vowels always come together? |
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Answer» 120 NA |
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| 14. |
Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it? |
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Answer» 720 NA |
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| 15. |
From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady? |
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Answer» 246 NA |
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| 16. |
In a Plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no lines passes through both points A and |
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Answer» 535 NA |
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| 17. |
In how many different ways can the letters of the word ENTRANCE be arranged? |
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Answer» 10080 NA |
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| 18. |
There are 7 non-collinear points. How many triangles can be drawn by joining these points? |
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Answer» 35 NA |
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| 19. |
Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct. |
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Answer» 65000 NA |
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| 20. |
How many different letter arrangements can be made from the letter of the word RECOVER ? |
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Answer» 1260 NA |
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| 21. |
In a question paper, there are four multiple choice type question. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate wil |
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Answer» 624 NA |
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| 22. |
If nc2 = nc5, find n? |
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Answer» 7 NA |
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| 23. |
A two member committee comprising of one male and one female member is to be constitute out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which |
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Answer» 14 NA |
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| 24. |
In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together? |
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Answer» 48 NA |
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| 25. |
How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once? |
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Answer» 120 NA |
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| 26. |
A box contains 2 white balls and 4 red ball. in how many ways can 3 balls be drawn from the box , if at least one black ball is to be included i the draw ? |
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Answer» 64 NA |
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| 27. |
What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected? |
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Answer» 30 NA |
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| 28. |
Find the value of 9p4? |
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Answer» 3024 NA |
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| 29. |
The number of all possible words that can be formed using the letters of the word 'MATHEMATICS', is |
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Answer»
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| 30. |
In how many different ways can the letters of the word ' cloud' can be arranged? |
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Answer» 120 NA |
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| 31. |
In how many different number of ways the letters of the word 'ENGINEERING' can be arranged. |
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Answer» 277200 NA |
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| 32. |
In how many different ways can the letters of the word 'MACHINE' be arranged? |
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Answer» 5040 NA |
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| 33. |
There are 20 books of which 4 are single volumes and the other are books of 8, 5 and 3 volumes respectively. In how many ways can all these books be arranged on a self so that volumes of the same book |
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Answer»
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| 34. |
A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refu |
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Answer» 8! * 480 NA |
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| 35. |
In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee. |
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Answer» 46 NA |
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| 36. |
A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most -. |
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Answer» 215 NA |
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| 37. |
Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is ? |
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Answer» 12 NA |
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| 38. |
12 people at a party shake hands once with everyone else in the room.How many handshakes took place? |
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Answer» 66 NA |
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| 39. |
Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women. ? |
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Answer» 30 NA |
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| 40. |
Find the value of 5p0? |
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Answer» NONE of these NA |
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| 41. |
How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane? |
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Answer» 3 NA |
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| 42. |
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? |
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Answer» 756 NA |
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| 43. |
There are 10 person among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers , is equal to: |
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Answer»
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| 44. |
In how many different ways can the letters of the word 'ABILITY' can be arranged? |
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Answer» 2520 NA |
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| 45. |
If np3 = 210, find n. |
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Answer» 7 NA |
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| 46. |
In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together? |
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Answer»
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| 47. |
An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair? |
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Answer» 80 NA |
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| 48. |
A library has two books each having three copies and three other books each having two copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not separ |
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Answer» 120 NA |
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| 49. |
20 persons were invited to a party. In how many ways, they and the host can be seated at a circular table ? |
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Answer» 20 !
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| 50. |
In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party. |
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Answer» 15 NA |
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