Permutations and Combinations MCQ AP Inter 1st Year Maths Chapter 6

by

Practice AP Inter 1st Year Maths Study Material Chapter 6 Permutations and Combinations MCQ to identify your strengths and weak areas.

AP Inter 1st Year Maths Permutations and Combinations MCQ

Question 1.
A student has 5 pants and 8 shirts. The number of ways in which he can wear the dress in different combinations as
1) 8P5
2) 8C5
3) 8! × 5!
4) 40
Answer:
4) 40

Explanation:
Student can select a pant from 5 pants in 5 ways and a shirt from 8 shirts in 8 ways.
∴ The number of ways he can wear the dress in different combinations = 5 × 8 = 40.

Question 2.
If nP4 = 1680 then n is
1) 7
2) 8
3) 9
4) 10
Answer:
2) 8

Explanation:
nP4 = 1680 = 8 × 7 × 6 × 5
∴ n = 8

Question 3.
If nPr = 1320, then r is
1) 3
2) 4
3) 5
4) 6
Answer:
1) 3

Explanation:
nPr = 1320 = 12 × 11 × 10
∴ r = 3

Question 4.
A man has 3 sons and 6 schools within his reach. In how many ways he can send his sons to school if no two of his sons are to read in the same school ?
1) 6P3
2) 6P3
3) 63
4) 36
Answer:
1) 6P3

Explanation:
The number of ways that he can send his 3 sons to 6 schools if no two of then are in the same school = 6P3

Permutations and Combinations MCQ AP Inter 1st Year Maths Chapter 6

Question 5.
The number of arrangements that can be formed by talking all the letters {T, U, E, S, D. A, Y}
1) 720
2) 5040
3) 120
4) 40320
Answer:
2) 5040

Explanation:
The number of required arrangements = 7! = 5040

Question 6.
The number of arrangements that can be made out of the letters in expresesion a4b3c5 when written in full length is
1) \(\frac{9!}{3!2!4!}\)
2) \(\frac{7!}{2!3!2!}\)
3) \(\frac{5!}{4!3!2!}\)
4) \(\frac{(12)!}{4!3!5!}\)
Answer:
4) \(\frac{(12)!}{4!3!5!}\)

Explanation:
The required number of arrangements = \(\frac{(12)!}{4!3!5!}\)

Question 7.
The number of permutations of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6 when repitition allowed is
1) 6P4
2) 6C4
3) 64
4) 46
Answer:
3) 64

Explanation:
The number fo 4-digit numbers formed = 64.

Question 8.
The number of ways of arranging 8 men and 4 women in a row is
1) 8!
2) 4!
3) (12)!
4) (11)!
Answer:
3) (12)!

Explanation:
The number of ways of arranging 8 men and 4 women in a row = 12!

Question 9.
The number of positive divisors of 1080 is
1) 8
2) 16
3) 32
4) 40
Answer:
3) 32

Explanation:
1080 = 23 × 33 × 51 ⇒ The number of positive divisors of 1080 is
(3 + 1) (3 + 1) (1 + 1) = 32.

Question 10.
The number of ways of selecting 4 boys and 3 girls from a group of 8 boys and 5 girls is
1) 8C4 + 5C3
2) 8C4 × 5C3
3) 8C3 – 5C3
4) None
Answer:
2) 8C4 × 5C3

Explanation:
The number of ways of selecting 4 boys and 3 girls from a group of 8 boys and 5 girls is 8C4 × 5C3

Question 11.
If 12Cs+1 = 12C2s-5 then the value of S is
1) 4
2) 8
3) 12
4) 6
Answer:
4) 6

Explanation:
12Cs+1 = 12C2s-5 ⇒ S + 1 = 2S – 5 or S + 1 + 2S – 5 = 12
S = 6 or 3S = 16
S = 6 [∵ S is a non-negative integer]

Question 12.
The number of diagonals of a polygon of 10 sides is
1) 35
2) 36
3) 38
4) 39
Answer:
1) 35

Explanation:
Number of diagonals of a polygon of 10 sides = \(\frac{10(10-3)}{2}\) = 35

Permutations and Combinations MCQ AP Inter 1st Year Maths Chapter 6

Question 13.
A polygon has 54 diagonals. Then the number of its sides is
1) 7
2) 9
3) 10
4) 12
Answer:
4) 12

Explanation:
If the number of sides is 4 then the number of diagonals
\(\frac{\mathrm{n}(\mathrm{n}-3)}{2}\) = 54
⇒ n = 12.