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- Question
A box contains 4 different black balls, 3 different red balls and 5 different blue balls. In how many ways can the balls be selected if every selection must have at least 1 black ball and one red ball ? A) 24 - 1 B) 2425-1 C) (24-1)(23-1)25 D) None
Options- A. A
- B. B
- C. C
- D. D
- Correct Answer
- C
ExplanationIt is explicitly given that all the 4 black balls are different, all the 3 red balls are different and all the 5 blue balls are different. Hence this is a case where all are distinct objects.
Initially let's find out the number of ways in which we can select the black balls. Note that at least 1 black ball must be included in each selection.
Hence, we can select 1 black ball from 4 black balls
or 2 black balls from 4 black balls.
or 3 black balls from 4 black balls.
or 4 black balls from 4 black balls.Hence, number of ways in which we can select the black balls
= 4C1 + 4C2 + 4C3 + 4C4
= ........(A)Now let's find out the number of ways in which we can select the red balls. Note that at least 1 red ball must be included in each selection.
Hence, we can select 1 red ball from 3 red balls
or 2 red balls from 3 red balls
or 3 red balls from 3 red ballsHence, number of ways in which we can select the red balls
= 3C1 + 3C2 + 3C3
= ........(B)Hence, we can select 0 blue ball from 5 blue balls (i.e, do not select any blue ball. In this case, only black and red balls will be there)
or 1 blue ball from 5 blue balls
or 2 blue balls from 5 blue balls
or 3 blue balls from 5 blue balls
or 4 blue balls from 5 blue balls
or 5 blue balls from 5 blue balls.Hence, number of ways in which we can select the blue balls
= 5C0 + 5C1 + 5C2 + ? + 5C5
= ..............(C)From (A), (B) and (C), required number of ways
= - 1. The last day of century cannot be either
I. Tuesday
II. Thursday
III. Saturday
IV. Sunday
Options- A. I and II
- B. I and IV
- C. I, II and III
- D. I,III and IV Discuss
- 2. In a ?ABC, if 2?A = 3?B = 6?C, Then ?A is equal to:
Options- A. 60°
- B. 30°
- C. 90°
- D. 120° Discuss
- 3. How many times in a day (24 Hrs), are the hands of a clock in straight line but opposite in direction?
Options- A. 20
- B. 22
- C. 24
- D. 48 Discuss
- 4. Which of the following two months in a particular year will have same calendar.
Options- A. January and August
- B. January and October
- C. March and November
- D. None of these Discuss
- 5. In a circle of radius 21 cm an arc subtends an angle of 72° at the centre. The length of the arc is?
Options- A. 13.2 cm
- B. 19.8 cm
- C. 21.6 cm
- D. 26.4 cm Discuss
- 6. If in a particular year 'X' there are 53 Sundays then how many Sundays will be there in a period of four years X to X + 3 year.
Options- A. 208
- B. 209
- C. 208 or 209
- D. None of these Discuss
- 7. In a game of 80 points, A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60?
Options- A. 12
- B. 10
- C. 8
- D. 6 Discuss
- 8. From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:
Options- A. 75 litres
- B. 100 litres
- C. 150 litres
- D. 120 litres Discuss
- 9. If a - b = 3 and a2 + b2 = 29, find the value of ab.
Options- A. 10
- B. 12
- C. 15
- D. 18 Discuss
- 10. Milk and water are mixed in a vessel A as 4:1 and in vessel B as 3:2. For vessel C, if one takes equal quantities from A and B, find the ratio of milk to water in C.
Options- A. 1:9
- B. 9:1
- C. 3:7
- D. 7:3 Discuss
More questions
Correct Answer: I, II and III
Explanation:
The last day of century cannot be either Tuesday, Thursday or Saturday.
Correct Answer: 90°
Explanation:
Correct Answer: 22
Explanation:
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours.
(Because between 5 and 7 they point in opposite direction at 6 'o clock only). So, in a day, the hands point in the opposite direction 22 times.
Correct Answer: March and November
Explanation:
January and August or October depends on leap year or non leap year. But if we find the number of odd days between March and November we will get number of odd days is 0 hence they will have same calendar.
Correct Answer: 26.4 cm
Explanation:
Arc length = 2?r (?° / 360°)
= 2 x (22/7) x 21 x (72° / 360°) cm
= 26.4 cm
Correct Answer: 209
Explanation:
Let us take two cases
Case (i) : When year start with Sunday then next 4 years will always have 52 Sundays hence total number of Sundays are 53 + 3 x 52 = 209 Sundays
Case (ii) : When year start with Sunday and then we have 53 Sundays that means year is a leap year then next 4 years will always have 52 Sundays hence total number of Sundays are 53 + 3 x 52 = 209 Sundays.
Correct Answer: 8
Explanation:
? B scores 75 points while A 80
? B scores 60 points while A = 80 x 60 / 75 = 64
Again, A scores 80 points while C = 65
? A scores 64 points while C = 65 x 64 / 80 = 52 points
Hence, in a game of 60, B can give C (60 ? 52) = 8 points
Correct Answer: 120 litres
Explanation:
It means (since 343 + 169 = 512)
Thus,
Thus the initial amount of wine was 120 liters.
Correct Answer: 10
Explanation:
2 ab = ( a 2 + b 2 ) - ( a - b ) 2
= 29 - 9 = 20
⟹ab = 10.
Correct Answer: 7:3
Explanation:
Ratio of Milk and water in a vessel A is 4 : 1
Ratio of Milk and water in a vessel B is 3 : 2
Ratio of only milk in vessel A = 4 : 5
Ratio of only milk in vessel B = 3 : 5
Let 'x' be the quantity of milk in vessel C
Now as equal quantities are taken out from both vessels A & B
=> 4/5 : 3/5
x
3/5-x x - 4/5
=> = (equal quantities)
=> x = 7/10
Therefore, quantity of milk in vessel C = 7
=> Water quantity = 10 - 7 = 3
Hence the ratio of milk & water in vessel 3 is 7 : 3
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