# Which of the following type of numbers are closed under only multiplication?

A. Rational Numbers

B. Integers**C. Whole Numbers**

D. Natural Numbers

A. Rational Numbers

B. Integers**C. Whole Numbers**

D. Natural Numbers

A. 6

B. 24

C. 132**D. 144**

First, arrange the 4 men around the circular table in alternate chairs in (4 – 1)! = 3! ways. Now four alternate chairs are vacant. Each of the 4 women can now be seated in the vacant chairs in 4! ways. The total number of ways = 4! X 3! = 144 ways. Why the** **number of ways for men is 3! and not 4!**?** It is because it is immaterial where the first man is seated. The problem of uniqueness/permutation begins only after the first man is seated.** **Therefore, only three men have to be seated in some order now and they can be seated in the remaining 3 seats in 3! ways !!!

A. 1200, 1800, 1600

B. 1000, 1200, 1500**C. 1600, 2400, 1800**D. 800, 1000, 1400

We will take the ratio of all three

Yaser:Hiba:Ali = 8 : 12 : 9

The sum of the ratio is: 29

Now

In order to take out Yaser’s share:

8*5800⁄29 = 1600

Simplified share of Yaser: 1600

Similarly, follow the same procedure for the rest of the two.

A. 12

B. 4

C. 7**D. 5**

A. 35**B. 50**

C. 65

D. 40

A. 4 : 4: 11

B. 11 : 12: 21**C. 50: 69: 120**

D. 110 : 50: 69

A. 20 Liters

B. 30 Liters

C. 40 Liters**D. 60 Liters**

A. 9000

B. 5000**C. 4000**

D. 2000