Consider the expansion `(x^(2)+(1)/(x))^(15)`. What is the independent term in the given expansion ?A. 2103B. 3003C. 4503D. None of these

Consider the expansion `(x^(2)+(1)/(x))^(15)`. What is the independent

1.	Consider the expansion `(x^(2)+(1)/(x))^(15)`. What is the independent term in the given expansion ?A. 2103B. 3003C. 4503D. None of these
Answer» Correct Answer - B `(x^(2)+(1)/(x))^(15)` `T_(r+1)=.^(15)C_(r)(x^(2))^(15-r)((1)/(x))^(r)` `=.^(15)C_(r)x^(30-2r-r)=.^(15)C_(r)x^(30-3r)` For independent term, `30 - 3r = 0 rArr r = 10` Put r = 10, we get `T_(10+1)=.^(15)C_(10)=(15!)/(10!5!)` `=(15 xx 14 xx 13 xx 12 xx 11 xx 10!)/(10! xx 1 xx 2 xx 3 xx 4 xx 5)=3003`

What is `C(n, r) + 2C(n, r - 1) + C(n, r - 2)` equal to?A. `C(n + 1, r)`B. `C(n -1, r + 1)`C. `C(n, r + 1)`D. `C(n + 2, r)`
In the expansion of `(1+x)^(50),`find the sum of coefficients of odd powers of `xdot`A. `2^(26)`B. `2^(49)`C. `2^(50)`D. `2^(51)`
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Consider the expansion `(x^(2)+(1)/(x))^(15)`. What is the sum of the coefficients of the middle terms in the given expansion ?A. C(15, 9)B. C(16, 9)C. C(16, 8)D. None of these
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