Advertisements
Advertisements
प्रश्न
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
पर्याय
\[^{20}{}{C}_{14} \left( \frac{x}{2^{14}} \right)\]
\[^{20}{}{C}_{12} x^2 2^{- 12}\]
- \[- ^t{20}{}{C}_7 x, 2^{- 13}\]
none of these
Advertisements
उत्तर
So, The middle term in the given expansion is
`= \left( - 1 \right)^{13} "^20C_{13} \frac{x^{14 - 13}}{2^{13}}`
\[ = - ^{20}{}{C}_7 x 2^{- 13}\]
APPEARS IN
संबंधित प्रश्न
Find the coefficient of a5b7 in (a – 2b)12
Write the general term in the expansion of (x2 – y)6
Write the general term in the expansion of (x2 – yx)12, x ≠ 0
Find the middle terms in the expansions of `(3 - x^3/6)^7`
Find the middle terms in the expansions of `(x/3 + 9y)^10`
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 the middle term in the expansion of:
(ii) \[\left( \frac{a}{x} + bx \right)^{12}\]
Find the middle term in the expansion of:
(iii) \[\left( x^2 - \frac{2}{x} \right)^{10}\]
Find the middle term in the expansion of:
(iv) \[\left( \frac{x}{a} - \frac{a}{x} \right)^{10}\]
Find the middle terms in the expansion of:
(ii) \[\left( 2 x^2 - \frac{1}{x} \right)^7\]
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:
(iii) \[\left( 1 + 3x + 3 x^2 + x^3 \right)^{2n}\]
Find the middle terms(s) in the expansion of:
(iv) \[\left( 2x - \frac{x^2}{4} \right)^9\]
Find the term independent of x in the expansion of the expression:
(i) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^9\]
Find the term independent of x in the expansion of the expression:
(vii) \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\]
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 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 \[p \neq q\]
In the expansion of (1 + x)n the binomial coefficients of three consecutive terms are respectively 220, 495 and 792, find the value of 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 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 total number of terms in the expansion of \[\left( x + a \right)^{100} + \left( x - a \right)^{100}\] .
The number of irrational terms in the expansion of \[\left( 4^{1/5} + 7^{1/10} \right)^{45}\] is
The middle term in the expansion of \[\left( \frac{2 x^2}{3} + \frac{3}{2 x^2} \right)^{10}\] is
The total number of terms in the expansion of \[\left( x + a \right)^{100} + \left( x - a \right)^{100}\] after simplification is
The middle term in the expansion of \[\left( \frac{2x}{3} - \frac{3}{2 x^2} \right)^{2n}\] is
Find the term independent of x in the expansion of `(3x - 2/x^2)^15`
Find the coefficient of `1/x^17` in the expansion of `(x^4 - 1/x^3)^15`
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`
If xp occurs in the expansion of `(x^2 + 1/x)^(2n)`, prove that its coefficient is `(2n!)/(((4n - p)/3)!((2n + p)/3)!)`
The last two digits of the numbers 3400 are 01.
The number of rational terms in the binomial expansion of `(4^(1/4) + 5^(1/6))^120` 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 ______.
The coefficient of y49 in (y – 1)(y – 3)(y – 5) ...... (y – 99) is ______.
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 ______.
