Advertisements
Advertisements
Question
Write the middle term in the expansion of `((2x^2)/3 + 3/(2x)^2)^10`.
Advertisements
Solution
\[\text{ Here, n, i . e . , 10, is an even number .} \]
\[ \therefore \text{ Middle term } = \left( \frac{10}{2} + 1 \right)th \text{ term = 6th term } \]
\[\text{ Thus, we have: } \]
\[ T_6 = T_{5 + 1} \]
\[ =^{10}{}{C}_5 \left( \frac{2 x^2}{3} \right)^{10 - 5} \left( \frac{3}{2 x^2} \right)^5 \]
\[ = \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2} \times \frac{2^5}{3^5} \times \frac{3^5}{2^5}\]
\[ = 252\]
APPEARS IN
RELATED QUESTIONS
Write the general term in the expansion of (x2 – y)6
Find the 4th term in the expansion of (x – 2y)12 .
Find the middle terms in the expansions of `(x/3 + 9y)^10`
In the expansion of (1 + a)m + n, prove that coefficients of am and an are equal.
Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of `(root4 2 + 1/ root4 3)^n " is " sqrt6 : 1`
Find the middle term in the expansion of:
(ii) \[\left( \frac{a}{x} + bx \right)^{12}\]
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:
(vii) \[\left( 3 - \frac{x^3}{6} \right)^7\]
Find the term independent of x in the expansion of the expression:
(vi) \[\left( x - \frac{1}{x^2} \right)^{3n}\]
Find the term independent of x in the expansion of the expression:
(vii) \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\]
If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)2n are in A.P., show that \[2 n^2 - 9n + 7 = 0\]
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 a, if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.
If the 2nd, 3rd and 4th terms in the expansion of (x + a)n are 240, 720 and 1080 respectively, find x, a, n.
Find a, b and n in the expansion of (a + b)n, if the first three terms in the expansion are 729, 7290 and 30375 respectively.
If the term free from x in the expansion of \[\left( \sqrt{x} - \frac{k}{x^2} \right)^{10}\] is 405, find the value of k.
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 coefficient of the middle term in the expansion of \[\left( 1 + x \right)^{2n}\] .
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 middle term (terms) in the expansion of `(p/x + x/p)^9`.
Find the term independent of x, x ≠ 0, in the expansion of `((3x^2)/2 - 1/(3x))^15`
Find the term independent of x in the expansion of `(3x - 2/x^2)^15`
Find the middle term (terms) in the expansion of `(x/a - a/x)^10`
If p is a real number and if the middle term in the expansion of `(p/2 + 2)^8` is 1120, find p.
The number of terms in the expansion of [(2x + y3)4]7 is 8.
The last two digits of the numbers 3400 are 01.
If the expansion of `(x - 1/x^2)^(2n)` contains a term independent of x, then n is a multiple of 2.
If the 4th term in the expansion of `(ax + 1/x)^n` is `5/2` then the values of a and n respectively are ______.
The middle term in the expansion of (1 – 3x + 3x2 – x3)6 is ______.
