IBPS Clerk Mains 2016-17 (Important Questions-3)
1. A bag contains 3 red balls, 4 green balls and 3 yellow balls. Three balls are randomly selected, find the probability that all the three balls are not of the same colour.
A. 1/20
B. 19/20
C. 1/10
D. 1/2
E. None of these
Sol. Probability that all 3 balls are of same colour = (3c3 + 4c3 + 3c3)/10c3 = 6/120 = 1/20
Hence prob. that all 3 ball are not of same colour = 1 - 1/20 = 19/20.
2. A box contains 10 balls out of which 3 are red and the rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
A. 105
B. 168
C. 189
D. 120
E. None of these
Sol. 6 balls can be selected in following ways
1 red + 5 blue or 2 red + 4 blue .
Total no. of ways = 3c1*7c5 + 3c2*7c4 = 63 + 105 = 168.
3. A large solid metallic cylinder whose radius and height are equal to each other is to be melted and 48 identical solid balls are to be recast from the liquid metal so formed. What is the ratio of the radius of a ball to the radius of the cylinder?
A. 1 : 16
B. 1 : 12
C. 1 : 8
D. 1 : 4
E. None of these
Sol. Suppose radius of the cylinder is R and that of the spherical ball is r, then according to the given condition,
Ï€R²×R = 48×(4Ï€/3)×r³
R³/r³ = 64 or R:r = 4:1.
4. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is the difference between R and Q’s age?
A. 1 year
B. 2 years
C. 25 years
D. Data inadequate
E. None of these
Sol. Sol. R – Q = R – T => Q = T. Also, R + T = 50
R + Q = 50
So, (R – Q) cannot be determined.
5. 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?
A. 20/3
B. 6
C. 19/3
D. 22/3
E. None of these
Sol. 10 men's 1 day work = 1/15
15 women's 1 day work = 1/12
(10men + 15 women)'s 1 day work = (1/15 + 1/12) = 9/60 = 3/20.
Therefore 10 men and 15 women will complete the work in = 20/3 days.
Directions (1-5): What will come in place of (_) in the following number series ?
6. 108, 189, 253, 302, 338, _
A. 368
B. 374
C. 363
D. 354
E. None of these
Sol. 189 - 108 = 81
253 - 189 = 64
302 - 253 = 49
338 - 302 = 36
Thus, 338 + 25 = 363.
7. 756, 535, 348, 195, 76, _
A. 17
B. -8
C. 12
D. -9
E. None of these
Sol. 756 - 535 = 221
535 - 348 = 187
348 - 195 = 153
195 - 76 = 119
221 - 187 = 34
187 - 153 = 34
153 - 119 = 34
Thus, 153 - 34 = 85
Therefore, 76 - 85 = -9.
8. 705, 728, 774, 843, 935, 1050, _
A. 1190
B. 1188
C. 1185
D. 1187
E. None of these
Sol. 728 - 705 = 23
774 - 728 = 46
843 - 774 = 69
935 - 843 = 92
1050 - 935 = 115
Thus, 1050 + 138 = 1188.
9. 13, 16, 20, 22, 34, _, 55, 52, 83
A. 34
B. 38
C. 42
D. 43
E. 46
Sol. A
20 - 13 = 7
34 - 20 = 14
55 - 34 = 21
22 - 16 = 6
34 - 22 = 12
52 - 34 = 18
10. 102, 99, 104, 97, 106, _
A. 96
B. 95
C. 100
D. 94
E. None of these
Sol. 104 - 102 = 2
106 - 104 = 2
97 - 99 = -2
Thus, 97 - 2 = 95.
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