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(8) If the number of terms in 
(x+1+(1)/(x))^(n)(n inI^(+))is 401 , then 
n is greater than
(a) 201
(b) 200
(c) 199
(d) None of these

(88) If the number of terms in (x+1+1x)n(nI+) \left(x+1+\frac{1}{x}\right)^{n}\left(n \in I^{+}\right) is 401401 , then n n is greater than\newline(a) 201201\newline(b) 200200\newline(c) 199199\newline(d) None of these

Full solution

Q. (88) If the number of terms in (x+1+1x)n(nI+) \left(x+1+\frac{1}{x}\right)^{n}\left(n \in I^{+}\right) is 401401 , then n n is greater than\newline(a) 201201\newline(b) 200200\newline(c) 199199\newline(d) None of these
  1. General Term Expansion: The general term in the expansion of (x+1+1x)n(x+1+\frac{1}{x})^n is Tk+1=C(n,k)xnk(1x)kT_{k+1} = C(n, k) \cdot x^{n-k} \cdot \left(\frac{1}{x}\right)^k.
  2. Number of Terms: The number of terms in the expansion is n+1n+1 because the powers of xx range from xnx^n to xnx^{-n}.
  3. Find nn: To find nn when there are 401401 terms, we set n+1=401n+1 = 401.
  4. Solve for n: Solve for n: n=4011n = 401 - 1.
  5. Compare to Options: n=400n = 400.
  6. Compare to Options: n=400n = 400.Compare n=400n = 400 to the options given: (a) 201201, (b) 200200, (c) 199199, (d) None of these.

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