# Find the term independent of x in the expansion of (3x-2x2)15 - Mathematics

Sum

Find the term independent of x in the expansion of (3x - 2/x^2)^15

#### Solution

Given expression is (3x - 2/x^2)^15

General term "T"_(r + 1) = ""^n"C"_r x^(n - r) y^r

= ""^15"C"_r (3x)^(15 - r) (- 2/x^2)^r

= ""^15"C"_r (3)^(15 - r) * x^(15 - r) (-2)^r * 1/x^(2r)

= ""^15"C"_r (3)^(15 - r) * x^(15 - r - 2r) * (-2)^r

= ""^15"C"_r (3)^(15 - r) * x^(15 - 3r) (-2)^r

For getting a term independent of x

Put 15 – 3r = 0

⇒ r = 5

∴ The required term is ""^15"C"_5 (3)^(15 - 5) (-2)^5

= - ""^15"C"_3 (3)^10 (2)^5

= -(15 xx 14 xx 13 xx 12 xx 11)/(5 xx 4 xx 3 xx 2 xx 1) * (3)^10 (2)^5

= -7 xx 13 xx 3 xx 11 * 3(3)^10  (2)^5

= – 3003 (3)10 (2)5

Hence, the required term = –3003 (3)10 (2)5

Concept: General and Middle Terms
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Chapter 8: Binomial Theorem - Exercise [Page 142]

#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Exercise | Q 4 | Page 142

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