Question:
The least value of \( n \) for which the number of integral terms in the Binomial expansion of \( \left( \sqrt{7} + \sqrt{11} \right)^n \) is 183, is:
The least value of \( n \) for which the number of integral terms in the Binomial expansion of \( \left( \sqrt{7} + \sqrt{11} \right)^n \) is 183, is:
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To find the number of integral terms in a binomial expansion with irrational components, use the formula for the terms and solve for \( n \).
Updated On: Mar 20, 2025
- 2196
- 2172
- 2184
- 2148
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The Correct Option is C
Solution and Explanation
The number of integral terms in the binomial expansion of \( ( \sqrt{7} + \sqrt{11} )^n \) is given by the formula for the number of terms in the expansion:
\[
\text{Number of integral terms} = \left( \left\lfloor \frac{n}{2} \right\rfloor + 1 \right).
\]
To find the value of \( n \) that results in 183 terms, solve:
\[
\left( \left\lfloor \frac{n}{2} \right\rfloor + 1 \right) = 183.
\]
Solving this gives \( n = 2184 \).
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