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Mathematics - Permutation Combination

Practise 72 MHTCET previous year questions on Permutation Combination, compiled from papers spanning 2012 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty MHTCET tests.

Permutation Combination has been asked in 7 of the 17 years of MHTCET papers analysed (2007–2026), with 72 questions in all. 29% of them were easy, 64% moderate and 7% tough. Most of its questions came from 2026, with 14 questions that year. In the last three years (2024–2026) it had 41 questions across 59 papers, about 0.7 per paper.

The chapter's 7 topics are not weighted equally: Arrangement under Constraint (23 questions, 32%), Permutation (20 questions, 28%), and Combination (14 questions, 19%) have been asked the most. Arrangement under Constraint has also led over the last five years, with 20 questions. Permutation has produced the most tough questions (2).

  1. 1The number of permutations of the letters of the word INSTITUTION are .......20 Apr, 2026 (E)Permutation
  2. 2Four men and three women are to be arranged at a round table. The number of arrangements in which no two women are together is ....19 Apr, 2026 (M)Circular Permutation
  3. 311 players of the Indian cricket team are sitting at a circular table. The number of ways they can sit so that two players, the wicket keepe18 Apr, 2026 (M)Circular Permutation
  4. 4In a test, there are 7 questions of the type 'True or False'. No student got all the answers correct. If the sequence of answers for every s18 Apr, 2026 (E)Permutation
  5. 5The number of arrangements of the letters in the word SOLAPUR, so that consonants and vowels are placed alternately is17 Apr, 2026 (M)Arrangement under Constraint
  6. 6In a test, there are 5 questions of the 'true or false' type. No student has got all the answers correct and the sequence of answers for eve17 Apr, 2026 (E)Permutation
  7. 7The number of arrangements of the numbers strictly between 10 and 1000 formed with the digits 0, 1, 2, 3, 4, 5, 6 without repetition is16 Apr, 2026 (M)Permutation
  8. 8The number of 4-letter words formed from the English alphabet such that there are exactly 2 vowels and 2 consonants and no vowel is repeated16 Apr, 2026 (E)Permutation
  9. 9The number of five-digit numbers formed using the digits without repetition and which are greater than are15 Apr, 2026 (M)Arrangement under Constraint
  10. 10A bag contains 23 balls, of which 7 are identical. The number of ways of selecting 12 balls from the bag is....15 Apr, 2026 (E)Selection of one or more item
  11. 11If 6 boys and 3 girls are to be seated in a row for a photograph, then the probability that the end seats are occupied by the girls and no t15 Apr, 2026 (E)Arrangement under Constraint
  12. 12The number of cubic equations that can be formed with the coefficients 0, 3, 2, 4, 5, 6 when repetition of coefficients is allowed, is....13 Apr, 2026 (M)Permutation
  13. 13There are boys and girls seated in a row for a photograph. The number of ways in which a photograph can be taken if the girls occupy only od11 Apr, 2026 (M)Permutation
  14. 14The number of ways that 8 beads of different colours can be strung to form a necklace is11 Apr, 2026 (E)Circular Permutation
  15. 15Let denotes the number of ways in which 5 boys and 5 girls can be arranged in a line alternately and n denotes the number of ways in which 527 Apr, 2025 (E)Permutation
  16. 16The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them a26 Apr, 2025 (M)Combination
  17. 17The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl never sit toge26 Apr, 2025 (E)Arrangement under Constraint
  18. 18There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these poin25 Apr, 2025 (E)Combination
  19. 19A family consisting of a mother, father and their 8 children ( 4 boys and 4 girls) are to be seated at a round table in a party. How many wa23 Apr, 2025 (M)Circular Permutation
  20. 2021 friends were invited for a party. Two round tables can accommodate 12 and 9 friends each. The number of ways of the seating arrangements 22 Apr, 2025 (M)Circular Permutation
  21. 21If four digit numbers are formed by using the digits without repetition, then out of these numbers, the numbers exactly divisible by 25 are22 Apr, 2025 (E)Permutation
  22. 22The greatest possible number of points of intersection of 8 distinct straight lines and 4 distinct circles is21 Apr, 2025 (M)Permutation
  23. 23The probability that in a random arrangement of the letters of the word 'UNIVERSITY' , the two 'I' s do not come together is21 Apr, 2025 (M)Permutation
  24. 24If , then21 Apr, 2025 (E)Combination
  25. 25A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are20 Apr, 2025 (M)Combination
  26. 264 red balls and 5 green balls are selected from n balls. If the sum of both the selections is greater then then the value of is equal to20 Apr, 2025 (E)Combination
  27. 27The number of ways, in which 6 boys and 5 girls can sit at a round table, if no two girls are to sit together, is19 Apr, 2025 (M)Arrangement under Constraint
  28. 28Total number of 3-digit numbers, whose g.c.d with 36 is 2 , is19 Apr, 2025 (E)Selection of one or more item
  29. 29Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women choose chairs from amongst the cha16 May, 2024 (M)Permutation
  30. 30A five digit number divisible by 3 is to be formed using the digits without repetition, then the total number of ways this can be done is16 May, 2024 (E)Arrangement under Constraint
  31. 31There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing a15 May, 2024 (E)Permutation
  32. 32numbers greater than a million can be formed with the digits .11 May, 2024 (M)Permutation
  33. 33The number of arrangements, of the letters of the word MANAMA in which two M's do not appear adjacent, is11 May, 2024 (E)Arrangement under Constraint
  34. 34Words of length 10 are formed by using the letters A, B, C, D, E, F, G, H, I, J. Let . be number of such words where no letter is repeated a10 May, 2024 (M)Permutation
  35. 35Consider a group of 5 boys and 7 girls. The number of different teams, consisting of 2 boys and 3 girls that can be formed from this group i09 May, 2024 (E)Arrangement under Constraint
  36. 36The number of ways in which 5 boys and 3 girls can be seated on a round table, if a particular boy and a particular girl never sit adjacent 04 May, 2024 (M)Arrangement under Constraint
  37. 37Five persons and are seated in a circular arangement, if each of them is given a hat of one of the three colours red, blue and green, then t04 May, 2024 (E)Circular Permutation
  38. 38The number of four letter words that can be formed using letters of the word BARRACK is03 May, 2024 (M)Permutation
  39. 39A committee of 11 members is to be formed from 8 males and 5 females. If is the number of ways the committee is formed with at least 6 males03 May, 2024 (E)Arrangement under Constraint
  40. 40If 3 books on Physics, 2 books on Chemistry and 4 books on Mathematics are to be arranged on a shelf so that all the Physics books are toget02 May, 2024 (M)Arrangement under Constraint
  41. 41Number of different nine digit numbers, that can be formed from the digits in the number 223355888 by rearranging its digits, so that the od02 May, 2024 (E)Arrangement under Constraint
  42. 42A linguistic club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this group including the selection of a leader 14 May, 2023 (M)Selection of one or more item
  43. 43If in a regular polygon, the number of diagonals are 54 , then the number of sides of the polygon are14 May, 2023 (E)Combination
  44. 44Five persons and are seated in a circular arrangement. If each of them is given a cap of one of the three colours red, blue and green, then 13 May, 2023 (M)Circular Permutation
  45. 45Five students are selected from n students such that the ratio of number of ways in which 2 particular students are selected to the number o13 May, 2023 (E)Permutation
  46. 46If denotes the number of triangles which can be formed using the vertices of regular polygon of sides and , then12 May, 2023 (M)Permutation
  47. 47The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends with a consonant, are12 May, 2023 (E)Arrangement under Constraint
  48. 48Five students are to be arranged on a platform such that the boy occupies the second position and such that the girl is always adjacent to t11 May, 2023 (M)Arrangement under Constraint
  49. 49Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Then mean of number of tens is11 May, 2023 (E)Combination
  50. 50The teacher wants to arrange 5 students on the platform such that the boy occupies second position and the girls and are always adjacent to 11 May, 2023 (E)Arrangement under Constraint

Frequently Asked Questions

1.How many questions are available for Permutation Combination?

This chapter includes 72 questions compiled from MHTCET papers spanning 2012 to 2026.

2.Are these questions only from MHTCET, or from other exams too?

These are MHTCET questions specifically for the Permutation Combination chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Permutation Combination an important chapter for MHTCET Mathematics?

Permutation Combination has appeared in 7 of the 17 years of MHTCET papers covered here, with 72 questions across 67 papers - about one per paper it appears in.

4.What is the difficulty level of Permutation Combination questions in MHTCET?

Of the 72 questions analysed for this chapter, 29% are easy, 64% moderate and 7% tough. 2026 had the most, with 14 questions.

5.Which topics in Permutation Combination should I focus on?

These topics have carried the most weightage in Permutation Combination:

  • Arrangement under Constraint - 23 questions (32%)
  • Permutation - 20 questions (28%)
  • Combination - 14 questions (19%)
  • Permutation has produced the most tough questions (2).
6.Is Permutation Combination's weightage in MHTCET going up or down?

Across all 67 papers analysed, Permutation Combination has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.