31. Two unbiased coins are tossed. What is the probability of getting exactly two heads?

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

Option “C” is correct.

Total event={HH, HT, TH, TT}=4

Possible=HH=1

Required probability=1/4
32. A bag contains 5 red balls and 7 blue balls. Find the probability to choose 2 balls in the same color.

A. 1/66
B. 31/66
C. 29/66
D. 1/22
E. 1/33

Option “B” is correct.

Probability = (5C2 + 7C2)/12C2

= [(5 * 4) + (7 * 6)] / (12 * 11)

= 31/66
33. If the box contains 4 red balls and 3 green balls, what is the probability of picking two balls of the same color?

A. 2/5
B. 3/7
C. 4/9
D. 1/5
E. None of these

Option “B” is correct.

Required probability= (4C2+3C2)/7C2

=18/42

=3/7
34. What is the probability of selecting 2 red balls from the bag containing 4 yellow balls and 5 red balls?

A. 1/9
B. 1/6
C. 2/9
D. 5/18
E. None of these

Option “D” is correct.

Required probability = 5C2 / 9C2

= 20/72

= 5/18
35. If the bag contains 3 apples and 4 orange, what is the probability of choosing two oranges?

A. 1/7
B. 2/7
C. 3/7
D. 4/7
E. None of these

Option “B” is correct.

Total fruits = 4 + 3 = 7

Required probability = 4C2/7C2   

= 4 * 3/7 * 6

= 2/7
36. Find the number of ways can the word “COMPASS” can be arranged, so that the vowels always come together.

A. 120
B. 180
C. 360
D. 720
E. None of these

Option “D” is correct.
Required number of ways = 6! * 2!/2! = 6 * 5 * 4 * 3 * 2 = 720
37. In how many ways word “SUMMITS” be arranged in that all vowels and consonants come together?

A. 120
B. 240
C. 720
D. 360
E. 180

Option “A” is correct.

Number of vowels = U, I = 2

Remaining letters = S, M, M, T, S = 5

Number of ways = 2! * 5! * 2!/(2! * 2!)

= 120
38. A teacher and head master are chosen out of a group having 15 persons. How many ways are there?

A. 120
B. 180
C. 210
D. 240
E. 280

Option “C” is correct.
Total number of ways=15 * 14=210
39. Two students are selected from 8 students. How many ways are there to achieve this?

A. 68
B. 64
C. 56
D. 52
E. None of these

Option “C” is correct.
Number of ways=8 * 7=56
40. In how many different ways can the letters of the word “ELECTION” be arranged ?

A. 13440
B. 40320
C. 20160
D. 6720
E. 10080

Option “C” is correct.
Required number of ways = ELECTION = 8!/2! = 20160
Pages: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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