Discussion
Home ‣ Aptitude ‣ Permutation and Combination See What Others Are Saying!
- Question
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options- A. 159
- B. 194
- C. 205
- D. 209
- E. None of these
- Correct Answer
- 209
ExplanationWe may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).∴ Required number
of ways= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4) = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2) = (6 x 4) + ❨ 6 x 5 x 4 x 3 ❩ + ❨ 6 x 5 x 4 x 4 ❩ + ❨ 6 x 5 ❩ 2 x 1 2 x 1 3 x 2 x 1 2 x 1 = (24 + 90 + 80 + 15) = 209.
More questions
- 1. 64, 71, 80, 91, 104, 119, 135, 155
Options- A. 71
- B. 80
- C. 104
- D. 119
- E. 135 Discuss
Correct Answer: 135
Explanation:
Go on adding 7, 9, 11, 13, 15, 17, 19 respectively to obtain the next number.So, 135 is wrong.
- 2. 15, 16, 34, 105, 424, 2124, 12756
Options- A. 16
- B. 34
- C. 105
- D. 424
- E. 2124 Discuss
Correct Answer: 2124
Explanation:
2nd term = (1st term) x 1 + 1 = 15 x 1 + 1 = 16.3rd term = (2nd term) x 2 + 2 = 16 x 2 + 2 = 34.
4th term = (3th term) x 3 + 3 = 34 x 3 + 3 = 105.
5th term = (4th term) x 4 + 4 = 105 x 4 + 4 = 424
6th term = (5th term) x 5 + 5 = 424 x 5 + 5 = 2125
∴ 6th term should 2125 instead of 2124.
- 3. 196, 169, 144, 121, 100, 80, 64
Options- A. 169
- B. 144
- C. 121
- D. 100
- E. 80 Discuss
Correct Answer: 80
Explanation:
Numbers must be (14)2, (13)2, (12)2, (11)2, (10)2, (9)2, (8)2.So, 80 is wrong.
- 4. What time will be taken by a boat to cover a distance of 128 km along the stream, if speed of a boat in still water is 24 km/h and speed of stream is 8 km/h?
Options- A. 8 km/h
- B. 4 km/h
- C. 7 km/h
- D. 6 km/h Discuss
Correct Answer: 8 km/h
Explanation:
Downstream speed of boat = Speed of boat in still water + Speed of stream
= 24 + 8 = 32 km/h
? Required time = Distance/Speed downstream
= 128/32 = 4 km/h- 5. A boat goes 12 km in 1 h in still water. It takes thrice time in covering the same distance against the current. Find the speed of the current.?
Options- A. 8 km/h
- B. 12 km/h
- C. 6 km/h
- D. 7 km/h Discuss
Correct Answer: 8 km/h
Explanation:
Speed of a boat in still water = distance / time = 12/1 = 12 km/h
Speed against the current = 12/3 km/h
Let the speed of the current = x km/h
According to the question,
12 - x = 4
? x = 8 km/h- 6. A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9km/hr and the speed of the current is 3 km/hr the distance between A and B is?
Options- A. 4 km
- B. 6 km
- C. 8 km
- D. 12 km Discuss
Correct Answer: 12 km
Explanation:
Speed downstream = (9 + 3) km/hr = 12km/hr
Speed upstream = = (9 - 3) km/hr = 6km/hr
Let the distance AB = d km
Then, d/6 + d/12 = 3
? 2d + d = 36
? d = 12
? Distance AB = 12 km- 7. If the first day of June is Saturday, them the date on which the last Saturday of that month falls, is?
Options- A. 22
- B. 28
- C. 29
- D. 30 Discuss
Correct Answer: 29
Explanation:
If the first Saturday of June is in lst. Then, next Saturday will be on 8th, 15th , 22nd and 29th. So , last Saturday will be on 29th.
- 8. A boat goes 48 km downstream in 20 h. It takes 4 h more to cover the same distance against the stream. What is the speed of the boat in still water?
Options- A. 2.2 km/h
- B. 2 km/h
- C. 4 km/h
- D. 4.2 km/h Discuss
Correct Answer: 2.2 km/h
Explanation:
Speed downstream = 48/20 = 2.4 km/h
Speed upstream = 48/24 = 2 km/h
? Speed of boat in still water = (Speed downstream + Speed upstream)/2
= (2.4 + 2)/2 = 4.4/2 = 2.2 km/h- 9. If the probability that A will live 15 yr is 7/8 and that B will live 15 yr is 9/10, then what is the probability that both will live after 15 yr?
Options- A. 1/20
- B. 63/80
- C. 1/5
- D. None of these Discuss
Correct Answer: 63/80
Explanation:
Required probability = P(A) x P(B)
= (7/8) x (9/10)
= 63/80- 10. Keshav can row 60 km downstream and 36 km upstream, taking 10 h each time. What is the velocity of the current?
Options- A. 3 km/h
- B. 2. 2 km/h
- C. 4 km/h
- D. 1.2 km/h Discuss
Correct Answer: 1.2 km/h
Explanation:
Speed upstream = Distance/Time = 60/10 = 6 km/h
Speed upstream = Distance/Time = 36/10 = 3.6 km/h
? Velocity of the current = (speed downstream - Speed upstream)/2
= (6 - 3.2)/2 = 1.2 km/h
Comments
There are no comments.
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.