Bissoy.com
Doctors Medicines MCQs Q&A

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: In how many ways can the word ‘DISTURBANCE’ be arranged such that all the consonants are always together? Quantity B: In how many ways can the word ‘DISTURBANCE’ be arranged such that all the vowels are always together?

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: In how many ways can the word ‘DISTURBANCE’ be arranged such that all the consonants are always together? Quantity B: In how many ways can the word ‘DISTURBANCE’ be arranged such that all the vowels are always together? Correct Answer Quantity A < Quantity B

Solving for Quantity A:

The word ‘DISTURBANCE’ contains 11 different letters, comprising of 7 consonants and 4 vowels

When the consonants are always together, they are considered as one letter

Hence, the 5 letters to be arranged are (DSTRBNC) IUAE

No. of ways of arranging them = 5! = 120 ways

The 7 consonants can be arranged in = 7! = 5040 ways

Hence, required no. of ways = 120 × 5040 = 60480

⇒ Quantity A = 60480

Solving for Quantity B:

The word ‘DISTURBANCE’ contains 11 different letters, comprising of 7 consonants and 4 vowels

When the vowels are always together, they are considered as one letter

Hence, the 8 letters to be arranged are DSTRBNC (IUAE)

No. of ways of arranging them = 8! = 40320 ways

The 4 vowels can be arranged in = 4! = 24 ways

Hence, required no. of ways = 24 × 40320 = 967680

⇒ Quantity B = 967680

∴ Quantity A < Quantity B

Related Questions

In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve for the both quantities and choose the correct option. Quantity I – In how many ways letters of MOBILE can be arranged when vowels are always together. Quantity II – In how many ways letters of MONDAY can be arranged when vowels are not together.
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: In how many different ways can the letters of the word JUMBLE be arranged? Quantity B: In how many different ways can the letters of the word BOTTLE  be arranged?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: There are two inlet pipes A, B and two outlet pipes C, D inlet pipe B takes 7 hours more to fill the tank when compared to A. Two outlet pipes when working together can empty the tank in 3.5 hours and efficiency of both the pipe is same if all of them working together can fill the tank in 2 hours. Calculate the time taken by A to fill the tank. Quantity B: The ratio of efficiencies of two pipes A and B is in the ratio 3 ∶ 2 and that of pipe B and C is 1 ∶ 3. Pipe A and B are inlet pipes, pipe C is outlet pipe working together they can fill the tank in 7.5 hours. Calculate the time taken by A to fill the tank when working alone.
Given below are two quantities. Based on the given information, you have to determine the relation between the two quantities. Quantity A: Find the number of ways to arrange 7 different books in 5 different bookshelves if bookshelf 1 and 2 contain only one and two number of books respectively and rest of the bookshelves can contain any number of books. Quantity B: How many word having 3 consonants and 2 vowels can be formed out of 5 consonants and 4 vowels?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: A can do a piece of work in 10 days and B can do the same work in 15 days. They start working together and after 4 days, A left the work. Find in how many days the total work will be completed. Quantity B: P can do a piece of work in 15 days and Q can do the same work in 25 days. They start working together and after 5 days, Q left the work. Find in how many days the remaining work will gets completed.
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for both quantities and choose the correct option. Quantity A: In how many ways can 5 boys and 4 girls be seated in a row so that they sit alternately? Quantity B: How many words can be formed using letters of the word EQUITY taken all at a time?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Twelve persons can construct a 320 m long wall in 32 days working 8 hours a day. In how many days can 40 persons construct a 250 m long wall working 10 hours a day? Quantity B: A can finish the work in 15 days and B in 30 days. They both work together for 5 days and then B leaves. How many days will A take to complete the remaining work?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity I: Pipe A alone can fill the tank in 15 hours while pipe B alone can empty the tank in 5 hours. There is a leakage at the bottom which also alone can empty the tank in 4 hours. When pipe A and Pipe B are open simultaneously then in how many hours the tank gets empty? Quantity II: 25 men can complete the work in 20 hours and 30 women can complete the work in 15 hours. If 15 men work for 10 hours then stopped working then remaining work gets completed by all 30 women. In what time total works get completed?
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: P and Q received Rs. 2000 and Rs. 2500 respectively as their wage for a certain work. If P can do the work alone in 15 days, in how many days will Q do the same work alone? Quantity B: R and S worked together and received their wages in the ratio 4 ∶ 5. If R can do a work in 10 days, in how many days will S do the same work?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: The ratio of two numbers is 6 : 11 and their difference is 65. What will be the smaller number among both the numbers? Quantity B: The ratio of two numbers is 5 : 6. If their product is 1470, then what is the sum of both the numbers?