Advertisements
Advertisements
प्रश्न
In the expansion of `(x^2 - 1/x^2)^16`, the value of constant term is ______.
Advertisements
उत्तर
In the expansion of `(x^2 - 1/x^2)^16`, the value of constant term is 16C8.
Explanation:
Let Tr+1 be the constant term in the expansion of `(x^2 - 1/x^2)^16`
∴ Tr+1 = `""^16"C"_r (x^2)^(16 - r) ((-1)/x^2)^r`
= `""^16"C"_r (x)^(32 - 2r) (-1)^r * 1/x^(2r)`
= `(-1)^r * ""^16"C"_r (x)^(32 - 2r - 2r)`
⇒ `(-1)^r * ""^16"C"_r (x)^(32 - 4r)`
For getting constant term, 32 – 4r = 0
⇒ r = 8
∴ Tr+1 = `(-1)^8 * ""^16"C"_8 = ""^16"C"_8`
APPEARS IN
संबंधित प्रश्न
Find the coefficient of x5 in (x + 3)8
Write the general term in the expansion of (x2 – y)6
Find the 13th term in the expansion of `(9x - 1/(3sqrtx))^18 , x != 0`
Find the middle terms in the expansions of `(x/3 + 9y)^10`
Find a positive value of m for which the coefficient of x2 in the expansion
(1 + x)m is 6
Find the middle term in the expansion of:
(i) \[\left( \frac{2}{3}x - \frac{3}{2x} \right)^{20}\]
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:
(i) \[\left( 3x - \frac{x^3}{6} \right)^9\]
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:
(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 term independent of x in the expansion of the expression:
(vi) \[\left( x - \frac{1}{x^2} \right)^{3n}\]
Find the term independent of x in the expansion of the expression:
(vii) \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\]
If the coefficients of (2r + 1)th term and (r + 2)th term in the expansion of (1 + x)43 are equal, find r.
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 \[2 n^2 - 9n + 7 = 0\]
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 A and B are the sums of odd and even terms respectively in the expansion of (x + a)n, then (x + a)2n − (x − a)2n is equal to
The middle term in the expansion of \[\left( \frac{2 x^2}{3} + \frac{3}{2 x^2} \right)^{10}\] 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
Find the middle term (terms) in the expansion of `(p/x + x/p)^9`.
The ratio of the coefficient of x15 to the term independent of x in `x^2 + 2^15/x` is ______.
Find the term independent of x, x ≠ 0, in the expansion of `((3x^2)/2 - 1/(3x))^15`
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.
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`
If the middle term of `(1/x + x sin x)^10` is equal to `7 7/8`, then value of x 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 the expansion of `(x - 1/x^2)^(2n)` contains a term independent of x, then n is a multiple of 2.
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 ______.
