Directions(1-5): Find the missing numbers in the given series:
1. 2, 3, 7, 16, 32, _
A. 82
B. 67
C. 72
D. 69
E. None of these
Sol. 2 + 1^2 = 3
3 + 2^2 = 7
7 + 3^2 = 16
16 + 4^2 = 32
32 + 5^2 = 57
2. 6, 4, 5, 11, 39, _
A. 170
B. 185
C. 165
D. 189
E. None of these
Sol. 6*1 - 2 = 4
4*2 - 3 = 5
5*3 - 4 = 11
11*4 - 5 = 39
39*5 - 6 = 189
3. 2, 4, 10, 22, 42, _
A. 65
B. 64
C. 70
D. 72
E. 76
Sol. 2 + 2 = 4
4 + 6 = 10
10 + 12= 22
22 + 20= 42
42 + 30= 72
6 - 2 = 4
12 - 6 = 6
20 - 12= 8
30 - 20= 10
4. 18, 9 , 9, 18, 72, _
A. 624
B. 556
C. 486
D. 576
E. None of these
Sol. 18*0.5 = 9
9*1 = 9
9*2 = 18
18*4 = 72
72*8 = 576
5. 25, 35, 49, 67, 89, _
A. 115
B. 120
C. 105
D. 125
E. None of these
Sol. 35 - 25 = 10
49 - 35 = 14
67 - 49 = 18
89 - 67 = 22
14 - 10 = 4
18 - 14 = 4
22 - 18 = 4
6. A bag contains 4 black balls, 3 red balls and 5 green balls. 2 balls are drawn from the box at random. What is the probability that both the balls are of the same colour?
A. 47/68
B. 1/6
C. 19/66
D. 2/11
E. None of these
Sol. Total no. of balls = 4+3+5 = 12
Ways of selecting two balls from 12 = 12c2 = 12!/10!2! = 66
Ways of selecting two balls of same colour = 4c2 + 3c2 + 5c2 = 19
Thus, the required probability = 19/66.
7. A bag contains 5 green, 4 yellow and 3 white marbles. 3 marbles are drawn at random. What is the probability that they are not of the same colour?
A. 13/44
B. 41/44
C. 13/55
D. 152/55
E. None of these
Sol. No. of ways of selecting 3 balls out of 12 = 12c3 = 220
No. of ways of selecting 3 balls of same colour = 5c3 + 4c3 + 3c3 = 15 ways.
Thus, no. of ways of selecting 3 balls of not same colour = 220 - 15 = 205 ways.
Required probability = 205/220 = 41/44.
8. A committee of 4 is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have number of boys less than number of girls?
A. 1/4
B. 1/5
C. 1/6
D. 1/7
E. None of these
Sol. Selection of 1 boy and 3 girls = 5c1*4c3 = 20
Selection of 0 boy and 4 girls = 5c0*4c4 = 1*1 = 1
Total ways = 20 + 1 = 21 ways.
Selecting 4 members from 9 people = 9c4 = 126 ways
Thus, required probability = 21/126 = 1/6.
9. A bag contains 3 red, 6 blue,2 green and 4 yellow balls. If two balls are picked randomly then the probability that either both are red or both are green is
A. 3/5
B. 4/105
C. 2/7
D. 5/91
E. None of these
Sol. Total ways of selecting 2 balls from 15 = 15c2 = 105
Ways of selecting 2 red balls = 3c2 = 3
Ways of selecting 2 green balls = 2c2 = 1
Thus, required probability = (3+1)/105 = 4/105.
10. Out of 15 students studying in a class, 7 are from M.P., 5 from Kerala and 3 from Gujarat. Four students are to be selected at random. What are the chances that at least one is from Kerala ?
A. 12/13
B. 11/13
C. 100/15
D. 51/15
E. None of these
Sol. P(atleast one from kerala) = 1 - P(no one is from kerala)
= 1 - 10c4/15c4 = 1 - 2/13 = 11/13.
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