Advertisements
Advertisements
प्रश्न
Write the middle term in the expansion of \[\left( x + \frac{1}{x} \right)^{10}\]
उत्तर
\[\text{ Here, n, i . e . , 10, is an even number } \]
\[ \therefore \text{ Middle term } = \left( \frac{10}{2} + 1 \right)\text{ th term = 6th term } \]
\[\text{ Thus, we have: } \]
\[ T_6 = T_{5 + 1} \]
\[ = ^{10}{}{C}_5 \left( x \right)^{10 - 5} \times \left( \frac{1}{x} \right)^5 \]
\[ = ^{10}{}{C}_5 \]
APPEARS IN
संबंधित प्रश्न
Find the coefficient of x5 in (x + 3)8
Write the general term in the expansion of (x2 – y)6
Find the 4th term in the expansion of (x – 2y)12 .
Find the 13th term in the expansion of `(9x - 1/(3sqrtx))^18 , x != 0`
Find the middle terms in the expansions of `(x/3 + 9y)^10`
Find the middle term in the expansion of:
(i) \[\left( \frac{2}{3}x - \frac{3}{2x} \right)^{20}\]
Find the middle term in the expansion of:
(iii) \[\left( x^2 - \frac{2}{x} \right)^{10}\]
Find the middle terms(s) in the expansion of:
(i) \[\left( x - \frac{1}{x} \right)^{10}\]
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:
(vii) \[\left( 3 - \frac{x^3}{6} \right)^7\]
Find the middle terms(s) in the expansion of:
(ix) \[\left( \frac{p}{x} + \frac{x}{p} \right)^9\]
Find the middle terms(s) in the expansion of:
(x) \[\left( \frac{x}{a} - \frac{a}{x} \right)^{10}\]
If the coefficients of \[\left( 2r + 4 \right)\text{ th and } \left( r - 2 \right)\] th terms in the expansion of \[\left( 1 + x \right)^{18}\] are equal, find r.
If the coefficients of (2r + 1)th term and (r + 2)th term in the expansion of (1 + x)43 are equal, find r.
Prove that the term independent of x in the expansion of \[\left( x + \frac{1}{x} \right)^{2n}\] is \[\frac{1 \cdot 3 \cdot 5 . . . \left( 2n - 1 \right)}{n!} . 2^n .\]
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 a, b, c and d in any binomial expansion be the 6th, 7th, 8th and 9th terms respectively, then prove that \[\frac{b^2 - ac}{c^2 - bd} = \frac{4a}{3c}\].
Write the middle term in the expansion of `((2x^2)/3 + 3/(2x)^2)^10`.
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
The middle term in the expansion of \[\left( \frac{2 x^2}{3} + \frac{3}{2 x^2} \right)^{10}\] is
Find the middle term in the expansion of `(2ax - b/x^2)^12`.
Find numerically the greatest term in the expansion of (2 + 3x)9, where x = `3/2`.
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 the middle term of `(1/x + x sin x)^10` is equal to `7 7/8`, then value of x is ______.
Middle term in the expansion of (a3 + ba)28 is ______.
The coefficient of x256 in the expansion of (1 – x)101(x2 + x + 1)100 is ______.
The number of rational terms in the binomial expansion of `(4^(1/4) + 5^(1/6))^120` is ______.
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 ______.
Let the coefficients of the middle terms in the expansion of `(1/sqrt(6) + βx)^4, (1 - 3βx)^2` and `(1 - β/2x)^6, β > 0`, common difference of this A.P., then `50 - (2d)/β^2` is equal to ______.
The term independent of x in the expansion of `[(x + 1)/(x^(2/3) - x^(1/3) + 1) - (x - 1)/(x - x^(1/2))]^10`, x ≠ 1 is equal to ______.
