Advertisements
Advertisements
प्रश्न
The total number of terms in the expansion of \[\left( x + a \right)^{100} + \left( x - a \right)^{100}\] after simplification is
पर्याय
202
51
50
none of these
Advertisements
उत्तर
51
Here, n, i.e., 100, is even.
∴ Total number of terms in the expansion =\[\frac{n}{2} + 1 = \frac{100}{2} + 1 = 51\]
APPEARS IN
संबंधित प्रश्न
In the expansion of (1 + a)m + n, prove that coefficients of am and an are equal.
Find the middle term in the expansion of:
(iii) \[\left( x^2 - \frac{2}{x} \right)^{10}\]
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:
(ii) \[\left( 1 - 2x + x^2 \right)^n\]
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:
(vi) \[\left( \frac{x}{3} + 9y \right)^{10}\]
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 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:
(ix) \[\left( \sqrt[3]{x} + \frac{1}{2 \sqrt[3]{x}} \right)^{18} , x > 0\]
If the coefficients of (2r + 1)th term and (r + 2)th term in the expansion of (1 + x)43 are equal, find r.
If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)n are in A.P., then find the value of n.
Find a, if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.
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 middle term in the expansion of \[\left( x + \frac{1}{x} \right)^{10}\]
Write the coefficient of the middle term in the expansion of \[\left( 1 + x \right)^{2n}\] .
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
In the expansion of \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\] , the term independent of x is
Find the middle term in the expansion of `(2ax - b/x^2)^12`.
The ratio of the coefficient of x15 to the term independent of x in `x^2 + 2^15/x` is ______.
If the term free from x in the expansion of `(sqrt(x) - k/x^2)^10` is 405, find the value of k.
Find the value of r, if the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x)18 are equal.
Middle term in the expansion of (a3 + ba)28 is ______.
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.
The sum of coefficients of the two middle terms in the expansion of (1 + x)2n–1 is equal to 2n–1Cn.
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 ______.
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 ______.
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 coefficient of y49 in (y – 1)(y – 3)(y – 5) ...... (y – 99) 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 ______.
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 ______.
