Permutation and Combination (Algebra, Teaching Exam Part-3)

Total Questions: 68

1. A polygon has 170 diagonals. How many sides will it have? [PGT 2010]

Correct Answer: (c) 20
Solution:

2. How many words can be formed by the word VOWELS if word starts from E? [PGT 2009]

Correct Answer: (c) 120
Solution:

3. The number of ways in which 5 male and 2 female members of a committee can be seated around tables so that the two females are not seated together is? [PGT 2009/TGT 2011]

Correct Answer: (a) 480
Solution:

4. The chances of throwing 6 with 4, 3 or 2 dice respectively are in the ratio of [PGT 2005]

Correct Answer: (b) 1:3:9
Solution:The chances of throwing 6 with 4, 3, or 2 dice respectively with the ratio is

5. Solve the following equation? [PGT 2005 ]

Correct Answer: (b) 2ⁿ-1
Solution:

6. Let Tₙ denote the number of triangles which can be formed joining the vertices of a regular polygon of n sides. If Tₙ₊₁-Tₙ = 21, then n equals [PGT 2005]

Correct Answer: (b) 7
Solution:The number of triangle that can be formed by using the vertices of a regular polygons = ⁿC3

7. The total number of words which can be formed out of the letters, a, b, c, d, e, f taken three together, each word containing at least one vowel, is [PGT 2005]

Correct Answer: (d) 16
Solution:

8. 3 bulbs are chosen at random from 20 bulbs, out of which 4 are defective. The probability that the room is lighted, will be [PGT 2004]

Correct Answer: (c) 284/285
Solution:

9. If in the expansion of (1 + x)²⁰, the coeffecients of rᵗʰ and (r + 4)th terms are equal, then the value of r is? [PGT 2004]

Correct Answer: (c) 9
Solution:

10. Number of triangles formed by joining 12 points, 7 to which lie on a straight line is [PGT 2004/ TGT 1999]

Correct Answer: (b) 185
Solution: