Advertisements
Advertisements
Question
Find the middle term in the expansion of `(2ax - b/x^2)^12`.
Solution
Since the power of binomial is even, it has one middle term which is the `(12 + 2)^"th"/2` term and it is given by
T7 = `""^12"C"_6 (2ax)^6 ((-b)/x^2)^6`
= `""^12"C"_6 (2^6 a^6 x^6 * (-b)^6)/x^12`
= `""^12"C"_6 (2^6 a^6 b^6)/x^6`
= `(59136a^6b^6)/x^6`
APPEARS IN
RELATED QUESTIONS
Find the coefficient of x5 in (x + 3)8
Write the general term in the expansion of (x2 – yx)12, x ≠ 0
Find the 13th term in the expansion of `(9x - 1/(3sqrtx))^18 , x != 0`
Find the middle terms in the expansions of `(3 - x^3/6)^7`
Find the middle term in the expansion of:
(i) \[\left( \frac{2}{3}x - \frac{3}{2x} \right)^{20}\]
Find the middle terms(s) in the expansion of:
(ii) \[\left( 1 - 2x + x^2 \right)^n\]
Find the middle terms(s) in the expansion of:
(iv) \[\left( 2x - \frac{x^2}{4} \right)^9\]
Find the middle terms(s) in the expansion of:
(v) \[\left( x - \frac{1}{x} \right)^{2n + 1}\]
Find the middle terms(s) in the expansion of:
(vi) \[\left( \frac{x}{3} + 9y \right)^{10}\]
Find the middle terms(s) in the expansion of:
(x) \[\left( \frac{x}{a} - \frac{a}{x} \right)^{10}\]
If in the expansion of (1 + x)n, the coefficients of pth and qth terms are equal, prove that p + q = n + 2, where \[p \neq q\]
Find the coefficient of a4 in the product (1 + 2a)4 (2 − a)5 using binomial theorem.
If a, b, c and d in any binomial expansion be the 6th, 7th, 8th and 9th terms respectively, then prove that \[\frac{b^2 - ac}{c^2 - bd} = \frac{4a}{3c}\].
If the coefficients of three consecutive terms in the expansion of (1 + x)n be 76, 95 and 76, find n.
If p is a real number and if the middle term in the expansion of \[\left( \frac{p}{2} + 2 \right)^8\] is 1120, find p.
Write the middle term in the expansion of \[\left( x + \frac{1}{x} \right)^{10}\]
Write the total number of terms in the expansion of \[\left( x + a \right)^{100} + \left( x - a \right)^{100}\] .
If A and B are the sums of odd and even terms respectively in the expansion of (x + a)n, then (x + a)2n − (x − a)2n is equal to
In the expansion of \[\left( x^2 - \frac{1}{3x} \right)^9\] , the term without x is equal to
Find the term independent of x in the expansion of `(3x - 2/x^2)^15`
Find n in the binomial `(root(3)(2) + 1/(root(3)(3)))^n` if the ratio of 7th term from the beginning to the 7th term from the end is `1/6`
If xp occurs in the expansion of `(x^2 + 1/x)^(2n)`, prove that its coefficient is `(2n!)/(((4n - p)/3)!((2n + p)/3)!)`
Find the term independent of x in the expansion of (1 + x + 2x3) `(3/2 x^2 - 1/(3x))^9`
Middle term in the expansion of (a3 + ba)28 is ______.
The number of terms in the expansion of [(2x + y3)4]7 is 8.
The coefficient of x256 in the expansion of (1 – x)101(x2 + x + 1)100 is ______.
The sum of the co-efficients of all even degree terms in x in the expansion of `(x + sqrt(x^3 - 1))^6 + (x - sqrt(x^3 - 1))^6, (x > 1)` is equal to ______.
