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प्रश्न
Find the coefficient of a5b7 in (a – 2b)12
उत्तर
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संबंधित प्रश्न
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 4th term in the expansion of (x – 2y)12 .
Find the middle terms in the expansions of `(3 - x^3/6)^7`
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 terms in the expansion of:
(i) \[\left( 3x - \frac{x^3}{6} \right)^9\]
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:
(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:
(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:
(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:
(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:
(x) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^6\]
Prove that the coefficient of (r + 1)th term in the expansion of (1 + x)n + 1 is equal to the sum of the coefficients of rth and (r + 1)th terms in the expansion of (1 + x)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)`.
If the 6th, 7th and 8th terms in the expansion of (x + a)n are respectively 112, 7 and 1/4, find x, a, n.
If the 2nd, 3rd and 4th terms in the expansion of (x + a)n are 240, 720 and 1080 respectively, find x, a, n.
Write the middle term in the expansion of `((2x^2)/3 + 3/(2x)^2)^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 \[\left( 1 + x \right)^{2n - 1}\]
If in the expansion of (a + b)n and (a + b)n + 3, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is
The number of irrational terms in the expansion of \[\left( 4^{1/5} + 7^{1/10} \right)^{45}\] is
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
In the expansion of \[\left( x - \frac{1}{3 x^2} \right)^9\] , the term independent of x is
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 xp occurs in the expansion of `(x^2 + 1/x)^(2n)`, prove that its coefficient is `(2n!)/(((4n - p)/3)!((2n + p)/3)!)`
The position of the term independent of x in the expansion of `(sqrt(x/3) + 3/(2x^2))^10` is ______.
The number of terms in the expansion of [(2x + y3)4]7 is 8.
If the expansion of `(x - 1/x^2)^(2n)` contains a term independent of x, then n is a multiple of 2.
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 ______.
