# Find the term independent of x in the expansion of (x3+32x2)10. - Mathematics

Sum

Find the term independent of x in the expansion of (sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10.

#### Solution

Let (r + 1)th term be independent of x which is given by

Tr+1 = ""^10"C"_r  sqrt(x/3)^(10 - r)  sqrt(3)^r/(2x^2)

= ""^10"C"_r  x^((10 - r)/2)/3  3^(r/2)  1/(2^r  x^(2r))

= ""^10"C"_r  3^(r/2 - (10 - r)/2)  2^(-r)  x^((10 - r)/2 - 2r)

Since the term is independent of x, we have

(10 - r)/2 - 2r = 0

⇒ r = 2

Hence 3rd term is independent of x and its value is given by

T3 = ""^10"C"_2  (3^(-3))/4

= (10 xx 9)/(2 xx 1) xx 1/(9 xx 12)

= 5/12

Concept: Binomial Theorem for Positive Integral Indices
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Solved Examples | Q 7 | Page 134
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