What is the middle term in the expansion of `(1-(x)/(2))^(8)` ?A. `(35x^(4))/(8)`B. `(17x^(5))/(8)`C. `(35x^(5))/(8)`D. None of these

What is the middle term in the expansion of `(1-(x)/(2))^(8)` ?A. `(35

1.	What is the middle term in the expansion of `(1-(x)/(2))^(8)` ?A. `(35x^(4))/(8)`B. `(17x^(5))/(8)`C. `(35x^(5))/(8)`D. None of these
Answer» Correct Answer - A Since n = 8 is even number therefore middle term `=((n)/(2)+1)^(th)"term"=(4+1)=5^(th)"term"` Hence, `T_(5)=.^(8)C_(4)(1)^(4)(-(x)/(2))^(4)` `=(8!)/(4!4!)xx(x^(4))/(16)=(8xx7xx6xx5)/(4xx3xx2xx1).(x^(4))/(16)=(70x^(4))/(16)=(35x^(4))/(8)`

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