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- Question
A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?
Options- A. 3
- B. 5
- C. 3!
- D. 5!
- Correct Answer
- 5
ExplanationThe possible outcomes that satisfy the condition of "at least one house gets the wrong package" are:
One house gets the wrong package or two houses get the wrong package or three houses get the wrong package.
We can calculate each of these cases and then add them together, or approach this problem from a different angle.
The only case which is left out of the condition is the case where no wrong packages are delivered.
If we determine the total number of ways the three packages can be delivered and then subtract the one case from it, the remainder will be the three cases above.
There is only one way for no wrong packages delivered to occur. This is the same as everyone gets the right package.
The first person must get the correct package and the second person must get the correct package and the third person must get the correct package.
1=1
Determine the total number of ways the three packages can be delivered.
3=6
The number of ways at least one house gets the wrong package is:
6?1=5
Therefore there are 5 ways for at least one house to get the wrong package. - 1. ?. x 4 ? 227 = 398
?. y 2 + 321 = 346
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 2. If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
Options- A. Sunday
- B. Saturday
- C. Tuesday
- D. Wednesday Discuss
- 3. 1, 4, 9, 16, 23, 25, 36
Options- A. 9
- B. 23
- C. 25
- D. 36 Discuss
- 4. A sum of money is to be divided equally among P, Q and R in the respective ratio of 5 : 6 : 7 and another sum of money is to be divided between S and T equally. If S got ? 2100 less than P, then how much amount did Q receive?
Options- A. ? 2500
- B. ? 2000
- C. ? 1500
- D. Couldn't be determined Discuss
- 5. If a : b = b : c, then ratio a 4 : b 4 is equal to
Options- A. ac : b2
- B. a2 : c2
- C. c2 : a2
- D. b2 : ac Discuss
- 6. A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed.
Options- A. 3 km/h
- B. 4 km/h
- C. 4.5 km/h
- D. 9 km/h Discuss
- 7. A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 h. How much time will he take to drive both ways?
Options- A. 2 h
- B. 21/2 h
- C. 51/2 h
- D. 4 h Discuss
- 8. Find the least number by which 175760 be devided to make it a perfect cube.
Options- A. 10
- B. 20
- C. 100
- D. 5 Discuss
- 9. The roots of the equation x2 + px + q = 0 are equal if :
Options- A. p2 = 2q
- B. p2 = 4q
- C. p2 = - 4q
- D. p2 = - 2q Discuss
- 10. Two cubes have volumes in the ratio 1: 27, The ratio of their surface areas is?
Options- A. 1 : 3
- B. 1 : 8
- C. 1 : 9
- D. 1 : 18 Discuss
More questions
Correct Answer:
Explanation:
According to question ,we can say that
From equation ?. x4 = 398 + 227 = 625
? x4 = 54
From equation ?. y2 = 346 - 321 = 25
? y2 = 52
Correct Answer: Sunday
Explanation:
The year 2004 is a leap year. So, it has 2 odd days.
But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.
∴ The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
∴ 6th March, 2004 is Sunday (1 day before to 6th March, 2005).
Correct Answer: 23
Explanation:
Correct Answer: Couldn't be determined
Explanation:
Couldn't be determined, since the total amount of money is not given in either of the case
Correct Answer: a2 : c2
Explanation:
Given that a /b = b/c
? b2 = ac
? a4 : b4 = a4 : a2 c2 = a2 : c2
Correct Answer: 4 km/h
Explanation:
Given, A = 6 km/h, B = 3 km/ h
According to the formula, Average speed = 2AB/(A + B)
? Required average speed = 2 x 6 x 3/(6 + 3)
= 36/9 = 4 km/h
Correct Answer: 2 h
Explanation:
Given that, W + D = 6 ...(i)
[ w = Time taken while walking and
D = Time taken while driving ]
From Eq. (i)
5 +D = 6
? D = 1
2D = 2 x 1 = 2
? He will take 2 h to drive both ways.
Correct Answer: 10
Explanation:
175760 = 24 x 5 x 13 3
= 23 x 2 x 5 x 133
To make perfect cube, it must be divided by 2 x 5 = 10
Correct Answer: p2 = 4q
Explanation:
On comparing it with ax2 + bx + c = 0 , we get a = 1, b = p, c = q
The roots of the equation x2 + px + q = 0 are equal if
b2 - 4ac = 0
? p2 - 4q = 0 ? p2 = 4q.
Thus , required answer is option B .
Correct Answer: 1 : 9
Explanation:
Let the volume be x3 and 27x3
? Their edges are x and 3x
Now Ratio of their surface area = 6x2 : 54x2 = 1 : 9
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