A) 152
B) \[-152\]
C) 252
D) \[-252\]
Correct Answer: D
Solution :
[d] \[n=10=\]even So, number of terms in the given expression \[{{\left( x-\frac{1}{x} \right)}^{10}}\]is 11 i.e. \[{{t}_{6}}\] be constant term of the expression. So, constant term \[{{=}^{10}}{{C}_{5}}.{{(x)}^{5}}.{{\left( -\frac{1}{x} \right)}^{5}}\] \[={{-}^{10}}{{C}_{5}}=\frac{-10\times 9\times 8\times 7\times 6}{5\times 4\times 3\times 2}\] \[=-3\times 2\times 7\times 6=-252\] .Hence, option [d] is correct.
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