The value of the term independent of x in the expansion of `(x^(2)-(1)/(x))^(9)` is :A. 9B. 18C. 48D. 84

The value of the term independent of x in the expansion of `(x^(2)-(1)

1.	The value of the term independent of x in the expansion of `(x^(2)-(1)/(x))^(9)` is :A. 9B. 18C. 48D. 84
Answer» Correct Answer - D `(x^(2)-(1)/(x))^(9)` `t_(r+1)=.^(9)C_(r)(x^(2))^(9-r)((-1)/(x))^(r)` `.^(9)C_(r)x^(18-2r).(-1)^(r).x^(-r)` `=.^(9)C_(r)(x)^(18-3r)(-1)^(r)" "...(1)` Term will be independent of x when 18 - 3r = 0 r = 6 Put r = 6, in [1] `t_(7)=.^(9)C_(6)(-1)^(6)=(9!)/(6!3!)=84`

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)`
The number of terms in the expansion of `(x+a)^100+(x-a)^100` after simplificationA. 202B. 101C. 51D. 50
What is the number of non-zero terms in the expansion of `(1+2 sqrt(3)x)^(11) + (1 - 2 sqrt(3)x)^(11)` (after simplification)?A. 4B. 5C. 6D. 11
What is the number of terms in the expansion of `[(2x - 3y)^(2)(2x+3y)^(2)]^(2)`?A. 4B. 5C. 8D. 16
What is the sum of the coefficients in the expansion of `(1+x)^(n)` ?A. `2^(n)`B. `2^(n)-1`C. `2^(n)+1`D. `n+1`
After simplification, what is the number of terms in the expansion of `[(3x+y)^(5)]^(4)-[(3x-y)^(4)]^(5)` ?A. 4B. 5C. 10D. 11
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
What is the sum of the coefficients of all the terms in the expansion of `(45x-49)^(4)` ?A. `-256`B. `-100`C. 100D. 256
In the expansion of `(1 + x)^43` ,the co-efficients of `(2r + 1)th and (r + 2)th` terms are equal. Find `r`.A. 5B. 14C. 21D. 22