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- 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. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Options- A. 2 : 3
- B. 1 : 1
- C. 3 : 4
- D. 4 : 3 Discuss
Correct Answer: 4 : 3
Explanation:
5% of A + 4% of B = 2 (6% of A + 8% of B) 3 ⟹ 5 A + 4 B = 2 ❨ 6 A + 8 B ❩ 100 100 3 100 100 ⟹ 1 A + 1 B = 1 A + 4 B 20 25 25 75 ⟹ ❨ 1 - 1 ❩ A = ❨ 4 - 1 ❩ B 20 25 75 25 ⟹ 1 A = 1 B 100 75 A = 100 = 4 . B 75 3 ∴ Required ratio = 4 : 3
- 2. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options- A. 65 sec
- B. 89 sec
- C. 100 sec
- D. 150 sec Discuss
Correct Answer: 89 sec
Explanation:
Speed = ❨ 240 ❩m/sec = 10 m/sec. 24 ∴ Required time = ❨ 240 + 650 ❩sec = 89 sec. 10 - 3. What was the day of the week on 17th June, 1998?
Options- A. Monday
- B. Tuesday
- C. Wednesday
- D. Thursday Discuss
Correct Answer: Wednesday
Explanation:
17 th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)Odd days in 1600 years = 0
Odd days in 300 years = (5 x 3) ≡ 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March April May June (31 + 28 + 31 + 30 + 31 + 17) = 168 days
∴ 168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.
- 4. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
Options- A. 279
- B. 283
- C. 308
- D. 318 Discuss
Correct Answer: 308
Explanation:
Other number = ❨ 11 x 7700 ❩ = 308. 275 - 5. 1872/ ? ? = 234
Options- A. 324
- B. 64
- C. 8
- D. 256 Discuss
Correct Answer: 64
Explanation:
Let 1872/?N = 234.
Then ?N = 1872/234 = 8
? N = 8 x 8 = 64- 6. For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat?
Options- A. 15 : 14
- B. 16 :15
- C. 12 :11
- D. 10 : 9 Discuss
Correct Answer: 16 :15
Explanation:
Let distance covered by dog in 1 leap is x and
Distance covered by cat in 1 leap is y
Then, 3x = 4y
? x= 4/3y
Now, Ratio of speed of dog and cat = Ratio of distance covered by them in the same time = 4x : 5y
= 16/3y : 5y
= 16 : 15- 7. A come of height 7 cm and base radius 3 cm is curved from a rectangular block of wood 10 cm x 5 cm x 2 cm. The percentage of wood wasted is?
Options- A. 34%
- B. 46%
- C. 54%
- D. 66% Discuss
Correct Answer: 34%
Explanation:
Total volume of cuboid = (10 x 5 x 2) cm3
= 100 cm3
Volume curved = 1/3 x (22/7) x 3 x 3 x 7 cm3
= 66 cm3
% of wood wasted = (100 - 66)% = 34 %- 8. 1, 9, 25, 49, 81,?
Options- A. 90
- B. 135
- C. 121
- D. 125 Discuss
Correct Answer: 90
Explanation:
Series pattern
12, 32, 52, 72, 92, 112
So missing term = 112 = 121- 9. An accurate clock shows the time as 3:00 after hour hand has moved 135°, the time would be?
Options- A. 7:30
- B. 6:30
- C. 8:00
- D. 9:30 Discuss
Correct Answer: 7:30
Explanation:
Angle of 360° is covered by hour hand in 12 h .
So, angle of 135° is covered by hour hand in 12/360° x 135° = 4.5 h
Thus, required time = (3 + 4.5)h = 7.5 h = 7 : 30- 10. P.V. Narsihma Rao was elected party leader on 29th may, 1991. What was the day of the week?
Options- A. Tuesday
- B. Friday
- C. Wednesday
- D. Sunday Discuss
Correct Answer: Wednesday
Explanation:
Try yourself. It was Wednesday.
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