11. A bag contains 4 red balls, 3 blue balls and 6 green balls. If two balls are drawn at random, then what is the probability that either both are red or both are blue?

A. 1/26
B. 1/13
C. 3/26
D. 2/13
E. None of these

Option “C” is correct.

Required probability = (4C2 + 3C2 )/13C2

= 3/26
12. A bag contains 15 balls marked 1 to 15. If one ball is drawn at random, then what is the probability that is marked with a number divisible by 2?

A. 3/20
B. 7/10
C. 1/5
D. 1/4
E. None of these

Option “E” is correct.

Number of marked balls divisible by 2=2, 4, 6, 8, 10, 12, 14

Required probability=7/15
13. If the bag contains 5 red balls and 5 green balls, if 2 balls are drawn randomly, then what is the probability that both are green balls?

A. 2/9
B. 1/8
C. 4/5
D. 3/8
E. None of these

Option “A” is correct.

Required probability=5C2 /10C2   

=5 * 4/10 * 9

=2/9
14. The box has 3 red balls, 4green balls and 2 blue balls. If three balls are drawn at random, what is the probability of drawing exactly 2 green balls?

A. 3/14
B. 2/7
C. 5/14
D. 3/7
E. None of these

Option “C” is correct.

Required probability = (4C2 * 5C1)/9C3

= ((4 * 3/1 * 2) * 5)/(9 * 8 * 7/1 * 2 * 3)

= 5/14
15. If the bag contains 3 red balls and 5 green balls, what is the probability of the picking two balls of the same color?

A. 11/28
B. 13/28
C. 15/28
D. 17/28
E. None of these

Option “B” is correct.

Required probability = (3C2 + 5C2 )/ 8C2     

= (6 + 20) / 56

= 13/28
16. In how many different ways can the letters of the word “SERIES” be arranged in such a way that the vowels always come together?

A. 36
B. 72
C. 24
D. 48
E. None of these

Option “A” is correct.

Total letters = 6

Total vowels = E, I, E = 3

Required ways = 4! * 3!/2!2!

= 36
17. In how many ways the word “DETAILS” be arranged so that all vowels and consonants come together?

A. 144
B. 196
C. 72
D. 288
E. None of these

Option “D” is correct.

Number of vowels=E, A, I=3

Number of consonants=D, T, L, S=4

Number of ways=3! * 4! * 2!

=288
18. In how many ways the word “PRIDE” be arranged so that all vowels and consonants come together?

A. 12
B. 18
C. 24
D. 32
E. None of these

Option “C” is correct.

Number of vowels=2

Number of consonants=3

Number of ways=2! * 3! * 2!

=24
19. In how many ways a selection of 4 students having at least 2 boys can be selected from 4 boys and 5 girl students?

A. 36
B. 72
C. 80
D. 81
E. None of these

Option “D” is correct.

Number of ways = 5C2 * 4C2 + 4C3 * 5C1+4C4

= 10 * 6 + 4 * 5 + 1

= 60 + 20 + 1

= 81
20. In how many different ways can the letters of the word “OXFORD” be arranged in such a way that the vowels always come together?

A. 120
B. 240
C. 720
D. 360
E. None of these

Option “A” is correct.

Total letters = 6

Total vowels = 2

Required ways = 5! * 2!/2!

= 120
Pages: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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