Permutation and Combination (Algebra, Teaching Exam)

Total Questions: 50

31. The number of ways of selection of a cricket team of eleven from 17 players in which only 5 players can bowl, if each cricket team of 11 must include exactly 4 bowlers, is: [UKPSC Lecturer (Mains) 2020]

Correct Answer: (a) 3960
Solution:

32. How many numbers can be formed taking only 3 digits together out of the digits: 1, 2, 3, 4, 5 and 6? [UKPSC Lecturer (Mains) 2020]

Correct Answer: (b) 120
Solution:

33. The number of integers greater than 6000 that can be formed using the digits 3,5,6,7 and 8 without repetition is : [Haryana PGT 2019]

Correct Answer: (b) 192
Solution:

The number of 4 digit integers greater than 6000 formed using the digits 3,5,6,7 and 8 without repetition is = 3×4×3×2 = 72.

The number of 5 digit integers greater than 6000 formed using the digits 3, 5, 6, 7 and 8 without repetition is 5! = 120

Hence, total number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition is = 120+72 = 192.

34. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in dictionary; then the position of the word small is: [Haryana PGT 2019]

Correct Answer: (d) 58th
Solution:

35. The number of diagonals of a polygon having 12 sides is: [Haryana TGT 2020]

Correct Answer: (b) 54
Solution:

36. Total number of chords joining 21 points on the circle will be: [UK SSSC LT 2020]

Correct Answer: (b) 210
Solution:

37. Solve the following equation? [Haryana PGT 2020]

Correct Answer: (d)
Solution:


38. Five children take part in a tournament. Each one has to play every other one. How many games must they play? [Haryana PGT 2018]

Correct Answer: (a) 10
Solution:

Total number of games played if each one has to play every other one is = ⁵C2 = 10

39. The straight line 𝓁₁, 𝓁₂, 𝓁₃ are parallel and lie in the same plane. A total number of m points are taken on 𝓁₁, n points on 𝓁₂, k points on 𝓁₃. The maximum number of triangles formed with vertices at these points are: [Haryana PGT 2018]

Correct Answer: (c)
Solution:

To form a triangle, 3 non-collinear points must be chosen in the plane. Hence, total number of triangles formed is given by

40. 20 persons were invited for a party. What is the number of ways in which they and the host can be seated at a circular table such that two particular persons [UKPSC GIC 2018]

Correct Answer: (c) 2(18!)
Solution:

Total number of persons including host to be seated at circular table = 21
Now, if the two particular persons are to be seated on either side of the host then number of ways for all of them to be seated on a circular table with host =
2! (19-1)! = 2(18!)
Since, the ways of two particular persons to be seated on either side of the host is 2!