Advertisements
Advertisements
प्रश्न
Write the general term in the expansion of (x2 – y)6
Advertisements
उत्तर
APPEARS IN
संबंधित प्रश्न
Find the 4th term in the expansion of (x – 2y)12 .
Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n–1 .
Find a positive value of m for which the coefficient of x2 in the expansion
(1 + x)m is 6
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 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:
(i) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^9\]
Find the term independent of x in the expansion of the expression:
(ii) \[\left( 2x + \frac{1}{3 x^2} \right)^9\]
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:
(x) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^6\]
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.
Find the coefficient of a4 in the product (1 + 2a)4 (2 − a)5 using binomial theorem.
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.
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 in the expansion of (1 + y)n, the coefficients of 5th, 6th and 7th terms are in A.P., then nis equal to
Find numerically the greatest term in the expansion of (2 + 3x)9, where x = `3/2`.
The ratio of the coefficient of x15 to the term independent of x in `x^2 + 2^15/x` is ______.
If p is a real number and if the middle term in the expansion of `(p/2 + 2)^8` is 1120, find p.
Find the term independent of x in the expansion of (1 + x + 2x3) `(3/2 x^2 - 1/(3x))^9`
The position of the term independent of x in the expansion of `(sqrt(x/3) + 3/(2x^2))^10` is ______.
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 ______.
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 for the 9th term in the binomial expansion of (3 + 6x)n, in the increasing powers of 6x, to be the greatest for x = `3/2`, the least value of n is n0. If k is the ratio of the coefficient of x6 to the coefficient of x3, then k + n0 is equal to ______.
If the coefficient of x10 in the binomial expansion of `(sqrt(x)/5^(1/4) + sqrt(5)/x^(1/3))^60` is 5kl, where l, k ∈ N and l is coprime to 5, then k is equal to ______.
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 ______.
