In how many different ways can the letters of the word MULTIPLE be arranged so that the vowels always come together?

In how many different ways can the letters of the word MULTIPLE be arranged so that the vowels always come together?
a) 4320
b) 2160
c) 1080
d) 40320
e) 20160
by

1 Answer

Answer :

We consider all the three vowels (U, I, E) as one letter, so total number of letters = 6,
and three vowels can be arranged in 3! Ways among themselves. However, the letter ‘L’
comes twice.
:. Total number of ways = (6! × 3!)/2! = 720 × 3 = 2160
Answer is: b)
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Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? A.8 B.11 C.13 D.16 E.None of theseSix bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? A.8 B.11 C.13 D.16 E.None of these

Description : Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? A.8 B.11 C.13 D.16 E.None of these

Last Answer : Answer – D (16) Explanation – L.C.M. of 2, 4, 6, 8, 10, 12 is 120.So, the bells will toll together after every 120 seconds, i.e, 2 minutes.In 30 minutes, they will toll together 30/2 + 1 = 16

Two pipes A and B can fill a tank in 5 and 6hrs.Pipe C can empty it in 12hrs.If all the 3 pipes are opened together,then the tank will be filled in 1)1(13/17)hrs 2)2(8/11)hours. 3)3(9/17)hrs 4)4(1/2)hrs

Description : Two pipes A and B can fill a tank in 5 and 6hrs.Pipe C can empty it in 12hrs.If all the 3 pipes are opened together,then the tank will be filled in 1)1(13/17)hrs 2)2(8/11)hours. 3)3(9/17)hrs 4)4(1/2)hrs

Last Answer : 3)3(9/17)hrs Exp:Net part filled in 1hr=>(1/5+1/6-1/12)=17/60 Tank filled in=60/17=3(9/17).

A tank can be filled by a tap in 6 hours and emptied by an outlet pipe in 8 hours. How long will it take to fill the cistern if both the taps are opened together? 1. 24 hours 2. 22 hours 3. 21 hours 4. 18 hours 5. 20 hours

Description : A tank can be filled by a tap in 6 hours and emptied by an outlet pipe in 8 hours. How long will it take to fill the cistern if both the taps are opened together? 1. 24 hours 2. 22 hours 3. 21 hours 4. 18 hours 5. 20 hours

Last Answer : 1;

What is the total number of illiterate people in city B & C together? 1) 57.34 lakh 2) 58.12 lakh 3) 59.64 lakh 4) 60.62 lakh 5) 61.32 lakh

Description : What is the total number of illiterate people in city B & C together? 1) 57.34 lakh 2) 58.12 lakh 3) 59.64 lakh 4) 60.62 lakh 5) 61.32 lakh

Last Answer : 4) 60.62 lakh

What is the average number of products manufactured by the company over all the years together ? (1) 36550 (2) 39480 (3) 41220 (4) 43330 (5) 34420

Description : What is the average number of products manufactured by the company over all the years together ? (1) 36550 (2) 39480 (3) 41220 (4) 43330 (5) 34420

Last Answer : (4) 43330

What is the total number of students enrolled in all the three classes together ? (1) 150 (2) 125 (3) 140 (4) 160 (5) None of these

Description : What is the total number of students enrolled in all the three classes together ? (1) 150 (2) 125 (3) 140 (4) 160 (5) None of these

Last Answer : (5) None of these

The letters ofthe word ‘NATIONAL’are arranged atrandom. What is the probability that the last letter will be T ? -Maths 9th

Description : The letters ofthe word ‘NATIONAL’are arranged atrandom. What is the probability that the last letter will be T ? -Maths 9th

Last Answer : (c) \(rac{1}{8}\)Let S be the sample space.Then n(S) = Total number of ways in which the letters of word NATIONAL can be arranged= \(rac{8!}{2!\,2!}\) (∵There are 2A s and 2N's in 8 letters)Let E : Event of ... !}{2!\,2!}}\) = \(rac{7!}{8!}\) = \(rac{7!}{8 imes7!}\) = \(rac{1}{8}\).