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प्रश्न
Find the coefficient of x2 and the coefficient of x6 in `(x^2 -1/x^3)^6`
उत्तर
General term Tr+1 = `""^6"C"_"r" (x^2)^(6 - "r") ((-1)/x^3)^"r"`
= `""^6"C"_"r" x^(12 - 2"r") (- 1)^"r" 1/(x^(3"r"))`
= `""^6"C"_"r" (- 1)^"r" x^(12 - 2"r" - 3"r")`
= `""^16"C"_"r" ( 1)^"r"x^(12 - 5"r")`
To find coefficient of x6
12 – 5r = 6
12 – 6 = 5r
⇒ 5r = 6
⇒ r = `6/5` which is not an integer.
∴ There is no term involving x6.
To find coefficient of x2
12 – 5r = 2
5r = 12 – 2 = 10
⇒ r = 2
So coefficient of x2 is `""^6"C"_2 (- 1)^2 = (6 xx 5)/(2 xx 1)(1)` = 15
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