AIEEE Questions

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15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)

Odd days in 1600 years = 0 

Odd days in 300 years = 1

46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day 

Jan.   Feb.   Mar.   Apr.   May.   Jun.   Jul.   Aug 

( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days.

Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days. 

Hence, as the number of odd days = 5 , given day is Friday.

Let A, B, C be the respective events of solving the problem and A , B, C be the respective events of not solving the problem. Then A, B, C are independent event

∴A, B, C are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

 PA=12, PB=23, PC= 34

∴ P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  = PA∩B∩C 

                  = PAPBPC         ∵ A, B, C are Independent                       

                  =  12×23×34  

                  = 14  

Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                = 1-14= 3/4

The tropic of cancer passes through 8 Indian states.

They are Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, West Bengal, Jharkand, Tripura and Mizoram.

The fruit content in both the fresh fruit and dry fruit is the same.

Given, fresh fruit has 68% water.so remaining 32% is fruit content. weight of fresh fruits is 100kg

Dry fruit has 20% water.so remaining 80% is fruit content.let weight if dry fruit be y kg.

Fruit % in freshfruit = Fruit% in dryfruit 

Therefore, (32/100) x 100 = (80/100 ) x y 

we get, y = 40 kg.