Statement-1 (Assertion) and Statement-2 ...

Statement-1 (Assertion) and Statement-2 (Reason)
Each of the these examples also has four laternative choices ,
only one of which is the correct answer. You have to select the correct choice as given below .
`(7^(9) + 9^(7)) ` is divisible by 16
Statement-2 ` (x^(y) + y^(x))` is divisible by `(x + y),AA x,y.`

Statement-1 is ture ,Statement-2 is treu, Statement-2 is a correct explanation for Statement-1

Statement-1 is ture ,Statement-2 is treu, Statement-2 is not a correct explanation for Statement-1

Statement-1 is true ,Statement-2 is false

Statement-1 is true ,Statement-2 is ture

Text Solution

Verified by Experts

The correct Answer is:

` 7^(9) + 9^(7) = (8-1)^(9) + (8+1)^(7)`
` = (8^(9) - ""^(9)C_(1) * 8^(8) + ""^(9)C_(2) *8^(7) - ""^(9)C_(3) *8^(6) +...+ ""^(9)C_(8)* 8-1)`
` = (8^(7) - ""^(7)C_(1) * 8^(6) + ""^(7)C_(2) *8^(5) +...+ ""^(7)C_(6)* 8-1)`
`8^(9) - 9*8^(8) + 8^(7)*(""^(9)C_(2) + 1) + 8^(6) (-""^(9)C_(3) + 7)`
`+8^(5) (""^(9)C_(4) + ""^(7)C_(2) + ...+ 8 (""^(9)C_(8) + ""^(7)C_(6))`
` = 64 lambda " " [lambda` is an integer]
` therefore 7^(9) + 9^(7) ` is divisible by 16
` therefore ` Statement-1 is true . Statement-2 is false.

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