Permutation and Combination (Algebra, Teaching Exam)

Total Questions: 50

1. There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then: [EMRS PGT-2023]

Correct Answer: (a) N≤100
Solution:

2. A student is to answer 10 questions out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is : [EMRS PGT-2023]

Correct Answer: (a) 196
Solution:

3. How many different groups of 5 men and 2 women can be made out of a total 7 men and 3 women? [Bihar (TRE 2.0)-2023]

Correct Answer: (c) 63
Solution:

4. There are 12 people at a party. They all shake hands exactly once with everyone else in the party. The total number of handshakes took place at the party is [Bihar (TRE 2.0)-2023]

Correct Answer: (c) 66
Solution:

Given, there are 12 people is party and they all shake hand with every one else in the party exactly once
Hence, the total number of hand shake in the party.

5. In how many ways can 10 letters be posted in 5 postboxes, if each of the postboxes can take more than 10 letters? [Bihar (TRE 2.0)-2023]

Correct Answer: (c) 5¹⁰
Solution:

We have to put 10 letter is 5 post boxes Therefore, we can put the first letter in 5 postboxes is 5 ways then the second, third and 10th letter can be put in 5 ways.
Hence, total ways = 5×5×5×...×5 (10times)
So = 5¹⁰

6. A triangle is formed by joining any three noncollinear points in pairs. How many triangles can be formed, if there are n non-collinear points? [Bihar (TRE 2.0)-2023]

Correct Answer: (b)
Solution:

7. Three balls are drawn from a bag containing three red, five white and two yellow balls. The number of ways in which this can be done, if at least two are red is : [KVS PGT 2023]

Correct Answer: (d) 22
Solution:

8. The number of ways in which a team of 11 players can be selected from 20 players always including one of them and excluding 3 of them is: [KVS PGT 2023]

Correct Answer: (c) ¹⁶C₁₀
Solution:If a team of 11 players is to be selected from 20 players always including one of them and excluding three of them, then the required number of ways = ¹⁶C₁₀

9. The number of different four digit numbers that can be formed with the digit 3, 4, 6 and 8 using each digit only once is : [KVS PGT 2023]

Correct Answer: (a) 24
Solution:Required number of ways = 4! = 24 ways

10. Out of 16 points in a plane no three are in straight line except 4 points which are collinear. The number of straight lines that can be formed by joining them is: [KVS PGT 2023]

Correct Answer: (b) 119
Solution:Required number of straight lines = ⁶C₂- 1
= 120 - 1 = 119