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- Question
When six fairs coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads ?
Options- A. 15
- B. 42
- C. 16
- D. 40
- Correct Answer
- 42
ExplanationThe question requires you to find number of the outcomes in which at most 3 coins turn up as heads.
i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads or 3 coins turn heads.The number of outcomes in which 0 coins turn heads is =1
The number of outcomes in which 1 coin turns head is = =6
The number of outcomes in which 2 coins turn heads is =15
The number of outcomes in which 3 coins turn heads is =20
Therefore, total number of outcomes =1+6+15+20= 42 outcomes
- 1. Three number are in the ratio 4 : 5 : 6 and their average is 25. The largest number is?
Options- A. 42
- B. 36
- C. 30
- D. 32 Discuss
- 2. A card is drawn at random from a pack of 52 cards. A card is drawn at random. What is the probability that it is neither a heart nor a king?
Options- A. 4/13
- B. 9/13
- C. 2/13
- D. 4/13 Discuss
- 3. If three caps are picked at random, what is the probability that two are red and one is green?
Options- A. 9/22
- B. 6/19
- C. 1/6
- D. 3/22 Discuss
- 4. If three balls are picked at random, what is the probability that atleast one is red?
Options- A. 1/2
- B. 7/12
- C. 11/12
- D. 1/5 Discuss
- 5. 150 m long train running with the speed of 90 km/h to cross a bridge in 26 s .What is the length of the bridge?
Options- A. 500 m
- B. 600 m
- C. 659 m
- D. 550 m Discuss
- 6. If two caps are picked at random, what is the probability that both are blue?
Options- A. 1/6
- B. 1/10
- C. 1/12
- D. None of these Discuss
- 7. If two marbles are picked at random, what is the probability that either both are green or both are yellow?
Options- A. 5/91
- B. 1/35
- C. 1/3
- D. 4/105 Discuss
- 8. 3/5 of 4/7 of 7/9 of 425
Options- A. 121
- B. 118
- C. 113
- D. 110 Discuss
- 9. A horse and a cow were sold for Rs. 12000 each. The horse was sold at a loss of 20% and the cow at a gain of 20%. The entire transaction resulted in?
Options- A. No loss or gain
- B. Loss of Rs . 1000
- C. Gain of Rs.. 1000
- D. Gain of Rs. 2000 Discuss
- 10. A thief running at 8 km/h is chased by a policeman whose speed is 10 km/h. If the thief is 100 m ahead of the policeman, then the time required for the policeman to catch the thief will be
Options- A. 2 min
- B. 3 min
- C. 4 min
- D. 6 min Discuss
More questions
Correct Answer: 30
Explanation:
Let the number be 4N, 5N and 6N
Then, 4N + 5N + 6N/3 = 25
or 15N = 75
or N = 5
Then largest number = 6N = 6 x 5 = 30
Correct Answer: 9/13
Explanation:
There are 13 hearts and 3 more kings
? P(heart or a king) = (13 + 3)/52 = 4/13
? P (neither a heart nor a king) = 1 - 4/13 = 9/13
Correct Answer: 3/22
Explanation:
Total number of caps = 12
? n(S) = 12C3 = 220
n(E1) = Out of 4 red caps, number of ways to pick 2 caps = 4C2 = 6
n(E2) = Out of 5 green caps
Number of ways to pick one cap = 5C1 = 5
P(E) = n(E1) x n(E2)/n(S) = (6 x 5)/220 = 3/22
Correct Answer: 11/12
Explanation:
Total Number of outcomes = 10C3 = 120
Number of outcomes not containing red balls = 5C3 = 10
? Probability that at least one is red = 1 - 10/120 = 11/12
Correct Answer: 500 m
Explanation:
Let length of bridge be L m.
We know, Speed = Distance/Time
According to the question,
90 x 5/18 = 150 + L/26
? 25 x 26 = 150 + L
? 650 = 150 + L
? L = 500 m
Correct Answer: None of these
Explanation:
Total number of caps = 2 + 4 + 5 + 1 = 12
Total number of outcomes = n(S) = 12 C2 = 66
Favorable number of outcomes = n(E) = 2C2 = 1
? Required probability = 1/66
Correct Answer: 4/105
Explanation:
Ways of selection of two green marbles = 2C2 = 1
Ways of selection of two yellow marbles = 3C2 = 3
So, probability (both are green) = 1/15C2 ....(I)
Probability (both are yellow) = 3/15C2 ....(Ii)
Then, required probability = 1/15C2 + 3/15C2 = 4/ 15C2
= 4/105
Correct Answer: 113
Explanation:
? = 3/5 of 4/7 of 7/9 of 425
? ? = 3/5 x 4/7 x 7/9 x 425 = 113.33 = 113
Correct Answer: Loss of Rs . 1000
Explanation:
? Loss% = (20/10)2 = (2)2 = 4%
? Total S.P. = Rs. 24000
? Total C.P. = Rs. (100/96) x 24000 = Rs. 25000
? Loss = Rs. 1000
Correct Answer: 3 min
Explanation:
Relative speed of policeman with thief = (10 - 8) = 2 km/h
Now, time taken to cover 100 m with speed of 2 km/h or 2000 m/h
Now, Speed = Distance / Time
? Time = D/S = 100/2000
= 1/20 h or 60/20 min = 3 min
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