JEE Mains · Maths · STD 11 - 7. binomial theoram
Given below 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
- A Both Statement I and Statement II are false.
- B Both Statement I and Statement II are true.
- C Statement I is false but Statement II is true.
- D Statement I is true but Statement II is false.
Answer & Solution
Correct Answer
(B) Both Statement I and Statement II are true.
Step-by-step Solution
Detailed explanation
Statement I : Statement II : \(R =(7+4 \sqrt{3})^{25}= I + f\) \(R^{\prime}=(7-4 \sqrt{3})^{25}=f^{\prime}\) \(\therefore R + R ^{\prime}=2\left[{ }^{25} C _0 7^{25}+{ }^{25} C _2 7^{23}(4 \sqrt{3})^2+\ldots.\right]\) \(I+f+f^{\prime}=\) even integer \(\therefore I =\) odd…
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