1.
In how many different ways can the letters of the word 'SCHOOL' be arranged so that the vowels always come together?
Answer: Option 'C'
'SCHOOL' contains 6 different letters.
vowels OO are always together
we have to arrange the letters (OO)SCHL
Now 5 letters can be arranged in 5! = 120 ways
The vowels (OO) can be arranged 2! = 2 ways.
= (120 x 2) = 240
again you have to divided 2 common vowels so answer is 120.
2.
If all the numbers 2, 3, 4, 5, 6, 7, 8 are arranged, find the number of arrangements in which 2, 3, 4, are together?
Answer: Option 'A'
Answer: Option 'A'
If (2 3 4) is one.
we must arrange (2 3 4), 5, 6, 7, 8 in
5P5 = 5! = 120 ways
2, 3, 4 can be arranged in 3P3 = 3! = 6
120 × 6 = 720.
3.
In how many different number of ways a combination of 3 persons can be selected from 4 men and 2 women.
Answer: Option 'B'
6C3 × 5C2
6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20.
5C2
= 5!/(3! . 2!)
= 5 × 2 = 10
= 20 × 10 = 200.
4.
Find 10P6
Answer: Option ''
Answer: Option 'B'
10P6 = 10!/4! = 10 × 9 × 8 × 7 × 6 × 5
= 151200.
5.
In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
Answer: Option 'D'
Answer: Option 'D'
7p3 = 7 × 6 × 5 = 210