STATEMENT I : The integral part of (8+37)20 is an even integer STATEMENT II : (8+37)20+(8−37)20 is an even integer

Let I+F=(8+37)20, I is integer 0<F<1Let f=(8−37)20 0<f<1I + F + f = even integer & F + f =1⇒I is odd integer

STATEMENT I : The integral part of (8+37)20 is an even integer STATEMENT II : (8+37)20+(8−37)20 is an even integer

Let I+F=(8+37)20, I is integer 0<F<1Let f=(8−37)20 0<f<1I + F + f = even integer & F + f =1⇒I is odd integer

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STATEMENT I : The integral part of ${(8 + 3 \sqrt{7})}^{20}$ is an even integer
STATEMENT II : ${(8 + 3 \sqrt{7})}^{20} + {(8 - 3 \sqrt{7})}^{20}$ is an even integer

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Statement-1 is true, Statement-2 is true. Statement-2 is not a correct explanation for Statement-1

Statement-1 is false, Statement-2 is true

Statement-1 is true, Statement-2 is false

Statement-1 is true, Statement-2 is true. Statement-2 is a correct explanation for Statement-1

answer is D.

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Detailed Solution

Let $I + F = {(8 + 3 \sqrt{7})}^{20},$ I is integer $0 < F < 1$

Let $f = {(8 - 3 \sqrt{7})}^{20} 0 < f < 1$

I + F + f = even integer & F + f =1

$\Rightarrow$ I is odd integer

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STATEMENT I : The integral part of (8+37)20 is an even integer STATEMENT II : (8+37)20+(8−37)20 is an even integer

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STATEMENT I : The integral part of ${(8 + 3 \sqrt{7})}^{20}$ is an even integer
STATEMENT II : ${(8 + 3 \sqrt{7})}^{20} + {(8 - 3 \sqrt{7})}^{20}$ is an even integer