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- Question
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Options- A.
10 21 - B.
11 21 - C.
2 7 - D.
5 7 - Correct Answer
-
10 21
ExplanationTotal number of balls = (2 + 3 + 2) = 7.Let S be the sample space.
Then, n(S) = Number of ways of drawing 2 balls out of 7 = 7C2 ` = (7 x 6) (2 x 1) = 21. Let E = Event of drawing 2 balls, none of which is blue.
∴ n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls. = 5C2 = (5 x 4) (2 x 1) = 10. ∴ P(E) = n(E) = 10 . n(S) 21
More questions
- 1. A Shopkeeper purchased some books from a publication worth ? 750. Because of some reasons, he had to sell two-fifth part of the book at a loss of 15%. On which gain he should sell his rest of the books, so that he gets neither nor loss
Options- A. 10%
- B. 9%
- C. 12%
- D. 15% Discuss
Correct Answer: 10%
Explanation:
Here, A = 2/5, R = 15%
According to the formula
Gain % = AR/(1 - A)%
= [(2/5) x 15]/[1 - (2/5)]%
= (6 x 5)/3%
= 10%- 2. A 200 m long rain is running at a speed of 54 km/hr. On the parallel and a different track, another train 300 m long is running at a speed of 72 km/hr. Both the trains are running in the same direction. Find out how much will it take the train to cross each other?
Options- A. 90 sec
- B. 100 sec
- C. 120 sec
- D. 150 sec Discuss
Correct Answer: 100 sec
Explanation:
We know that, when the trains are moving in the same direction,
Relative speed= Difference between the speed of train
and total distance for crossing each other = Sum of the length of train
Therefore, Relative speed = 72 km/hr - 54 km /hr = 18 km/hr
Relative speed in m/sec = 18 km/hr x 5/18 = 5 m/sec
and Total distance = 200m + 300m = 500m
and Total time taken to cross each other = Total distance in meter/ Relative speed in m/sec
= 500 m / (5 m/sec) = 100 sec- 3. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
Options- A. 5 : 7 : 8
- B. 20 : 49 : 64
- C. 38 : 28 : 21
- D. None of these Discuss
Correct Answer: 20 : 49 : 64
Explanation:
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.Then, 14x : 8y : 7z = 5 : 7 : 8.
Now, 14x = 5 ⟺ 98x = 40y ⟺ y = 49 x 8y 7 20 And, 14x = 5 ⟺ 112x = 35z ⟺ z = 112 x = 16 x. 7z 8 35 5 ∴ x : y : z = x : 49 x : 16 x = 20 : 49 : 64. 20 5 - 4. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Options- A. 40%
- B. 42%
- C. 44%
- D. 46% Discuss
Correct Answer: 44%
Explanation:
Let original length = x metres and original breadth = y metres.Original area = (xy) m2.
New length = ❨ 120 x ❩m = ❨ 6 x ❩m. 100 5 New breadth = ❨ 120 y ❩m = ❨ 6 y ❩m. 100 5 New Area = ❨ 6 x x 6 y ❩m2 = ❨ 36 xy ❩m2. 5 5 25 The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
∴ Increase % = ❨ 11 xy x 1 x 100 ❩% = 44%. 25 xy - 5. In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
Options- A. 20 litres
- B. 30 litres
- C. 40 litres
- D. 60 litres Discuss
Correct Answer: 60 litres
Explanation:
Quantity of milk = ❨ 60 x 2 ❩litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = ❨ 40 ❩ . 20 + x Now, ❨ 40 ❩ = 1 20 + x 2 ⟹ 20 + x = 80
⟹ x = 60.
∴ Quantity of water to be added = 60 litres.
- 6. A certain number of men can do a piece of work in 80 days. If there were 10 men less, it could be finished in 20 days more. How many men are there in the starting?
Options- A. 45
- B. 50
- C. 40
- D. 60 Discuss
Correct Answer: 50
Explanation:
Let the original number of men = N
Time taken by N = 80 days
Now, (N - 10) men can finish the work in the (80 + 20) = 100 days
Here, M1 = N, M2 = (N - 10), D1 = 80 and D2 = 100
According to the formula.
M1D1 = M2D2
? N x 80 = 100 x (N - 10)
? 8N = 10N - 100
? 10N - 8N = 100
? N = 50- 7. When a 192 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available?
Options- A. 52
- B. 68
- C. 62
- D. None of these Discuss
Correct Answer: None of these
Explanation:
No. of pieces = Total length / Length of each piece
= 192/3.2
= 60- 8. The amount instalment will discharge on debit of Rs 3220 due in 4 year at 10 % simple interest?
Options- A. 500
- B. 600
- C. 700
- D. None of these Discuss
Correct Answer: 700
Explanation:
Let the amount instalment be Rs ' x '
Then According to question,
(Amount of 'x' for 3 yrs) + (Amount of 'x' for 2 yrs) + (Amount of 'x' for 1 yrs) + x =3220
or, [x+(x × 10 × 3)/100] + [x+(x × 10 × 2)/100] + [x+(x × 10 × 1)/100] + x=3220
? 4x+ (30x/100)+(20x/100)+(10x/100)=3220
? 460x=322000
? x=Rs 700
? Each Instalment= Rs 700- 9. The sum of the ages of a mother and a daughter is 50 years. Also, 5 years ago, the mother's age was 7 times of the age of her daughter. The present ages of the mother and the daughter respectively are?
Options- A. 35 years, 15 years
- B. 38 years, 12 years
- C. 40 years, 10 years
- D. 42 years, 8 years Discuss
Correct Answer: 40 years, 10 years
Explanation:
Let the daughter's present be x years.
Then, mother's present age = (50 - x) years
Now, 7(x -5) = (50 - x - 5)
? x = 10
So, the present ages of mother and daughter are 40 years and 10 years respectively.- 10. Marks obtained by an student in 5 subjects are given below 25, 26, 27, 28, 29 in these obtained marks 27 is
Options- A. mode
- B. median and mode
- C. mean and median
- D. both (a) and (c) Discuss
Correct Answer: mean and median
Explanation:
27 is in the middle, so is the median and its the mean too.
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