Advertisements
Advertisements
प्रश्न
Find the middle terms(s) in the expansion of:
(x) \[\left( \frac{x}{a} - \frac{a}{x} \right)^{10}\]
Advertisements
उत्तर
\[\left( \frac{x}{a} - \frac{a}{x} \right)^{10} \]
\[\text{ Here, n is an even number . } \]
\[ \therefore \text{ Middle term } = \left( \frac{10}{2} + 1 \right)^{th} = 6^{th} \text{ term} \]
\[\text{ Now, we have } \]
\[ T_6 = T_{5 + 1} \]
\[ =^{10}{}{C}_5 \left( \frac{x}{a} \right)^{10 - 5} \left( \frac{- a}{x} \right)^5 \]
\[ = - \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}\]
\[ = - 252\]
APPEARS IN
संबंधित प्रश्न
Find the coefficient of x5 in (x + 3)8
Write the general term in the expansion of (x2 – yx)12, x ≠ 0
Find the 4th term in the expansion of (x – 2y)12 .
In the expansion of (1 + a)m + n, prove that coefficients of am and an are equal.
The coefficients of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1:3:5. Find n and r.
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 terms in the expansion of:
(iii) \[\left( 3x - \frac{2}{x^2} \right)^{15}\]
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:
(ii) \[\left( 1 - 2x + x^2 \right)^n\]
Find the middle terms(s) in the expansion of:
(viii) \[\left( 2ax - \frac{b}{x^2} \right)^{12}\]
Find the term independent of x in the expansion of the expression:
(iii) \[\left( 2 x^2 - \frac{3}{x^3} \right)^{25}\]
Find the term independent of x in the expansion of the expression:
(iv) \[\left( 3x - \frac{2}{x^2} \right)^{15}\]
Find the term independent of x in the expansion of the expression:
(v) \[\left( \frac{\sqrt{x}}{3} + \frac{3}{2 x^2} \right)^{10}\]
Find the term independent of x in the expansion of the expression:
(ix) \[\left( \sqrt[3]{x} + \frac{1}{2 \sqrt[3]{x}} \right)^{18} , x > 0\]
The coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)n are in A.P., find n.
If in the expansion of (1 + x)n, the coefficients of three consecutive terms are 56, 70 and 56, then find n and the position of the terms of these coefficients.
If 3rd, 4th 5th and 6th terms in the expansion of (x + a)n be respectively a, b, c and d, prove that `(b^2 - ac)/(c^2 - bd) = (5a)/(3c)`.
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.
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 \[\left( 1 + x \right)^{2n}\] .
Find the sum of the coefficients of two middle terms in the binomial expansion of \[\left( 1 + x \right)^{2n - 1}\]
In the expansion of \[\left( x^2 - \frac{1}{3x} \right)^9\] , the term without x is equal to
If an the expansion of \[\left( 1 + x \right)^{15}\] , the coefficients of \[\left( 2r + 3 \right)^{th}\text{ and } \left( r - 1 \right)^{th}\] terms are equal, then the value of r is
The middle term in the expansion of \[\left( \frac{2 x^2}{3} + \frac{3}{2 x^2} \right)^{10}\] is
If in the expansion of \[\left( x^4 - \frac{1}{x^3} \right)^{15}\] , \[x^{- 17}\] occurs in rth term, then
In the expansion of \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\] , the term independent of x is
If the sum of odd numbered terms and the sum of even numbered terms in the expansion of \[\left( x + a \right)^n\] are A and B respectively, then the value of \[\left( x^2 - a^2 \right)^n\] is
If rth term is the middle term in the expansion of \[\left( x^2 - \frac{1}{2x} \right)^{20}\] then \[\left( r + 3 \right)^{th}\] term is
Find the middle term in the expansion of `(2ax - b/x^2)^12`.
Find the middle term (terms) in the expansion of `(p/x + x/p)^9`.
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.
Show that the middle term in the expansion of `(x - 1/x)^(2x)` is `(1 xx 3 xx 5 xx ... (2n - 1))/(n!) xx (-2)^n`
The number of terms in the expansion of [(2x + y3)4]7 is 8.
The sum of coefficients of the two middle terms in the expansion of (1 + x)2n–1 is equal to 2n–1Cn.
The last two digits of the numbers 3400 are 01.
If n is the number of irrational terms in the expansion of `(3^(1/4) + 5^(1/8))^60`, then (n – 1) is divisible by ______.
