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प्रश्न
Constant term in the expansion of \[\left( x - \frac{1}{x} \right)^{10}\] is
पर्याय
152
−152
−252
252
उत्तर
−252
Suppose (r + 1)th term is the constant term in the given expansion.
Then, we have:
\[T_{r + 1} = ^{10}{}{C}_r (x )^{10 - r} \left( \frac{- 1}{x} \right)^r \]
\[ = ^{10}{}{C}_r ( - 1 )^r x^{10 - r - r} \]
\[\text{ For this term to be constant, we must have: } \]
\[10 - 2r = 0\]
\[ \Rightarrow r = 5\]
\[ \therefore \text{ Required term } = - ^{10}{}{C}_5 = - 252\]
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