Given below are two statements:Statement I: 2 | vedclass

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(B) Statement $I$: We have $25^{13} + 3^{13} + 20^{13} + 8^{13}$.Since $a^n + b^n$ is divisible by $(a + b)$ when $n$ is odd, we have:$25^{13} + 3^{13

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Both Statement $I$ and Statement $II$ are true.

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(B) Statement $I$: We have $25^{13} + 3^{13} + 20^{13} + 8^{13}$.Since $a^n + b^n$ is divisible by $(a + b)$ when $n$ is odd, we have:$25^{13} + 3^{13}$ is divisible by $(25 + 3) = 28$, which is divisible by $7$.$20^{13} + 8^{13}$ is divisible by $(20 + 8) = 28$, which is divisible by $7$.Thus, the sum is divisible by $7$. Statement $I$ is true.Statement $II$: Let $R = (7 + 4\sqrt{3})^{25} = I + f$, where $I$ is the integral part and $0 Let $R' = (7 - 4\sqrt{3})^{25} = f'$, where $0 Since $7^2 - (4\sqrt{3})^2 = 49 - 48 = 1$, $R'$ is a very small positive number.$R + R' = (7 + 4\sqrt{3})^{25} + (7 - 4\sqrt{3})^{25} = 2 \left[ {}^{25}C_0 7^{25} + {}^{25}C_2 7^{23}(4\sqrt{3})^2 + \dots ight]$.This is an even integer. So, $I + f + f' = 	ext{even integer}$.Since $0 Therefore, $I + 1 = 	ext{even integer}$, which implies $I$ is an odd integer. Statement $II$ is true.

Given below are two statements:
Statement $I$: $25^{13} + 20^{13} + 8^{13} + 3^{13}$ is divisible by $7$.
Statement $II$: The integral part of $(7 + 4\sqrt{3})^{25}$ is an odd number.
In the light of the above statements, choose the correct answer from the options given below:

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Given below are two statements:Statement $I$: $25^{13} + 20^{13} + 8^{13} + 3^{13}$ is divisible by $7$.Statement $II$: The integral part of $(7 + 4\sqrt{3})^{25}$ is an odd number.In the light of the above statements, choose the correct answer from the options given below: