Advertisements
Advertisements
Question
Find the coefficients of x60 in the expansion of `(1/x^2 + x^4)^18`
Advertisements
Solution
Here a = `1/x^2`, b = x4, n = 18
We have, tr+1 = nCr an–r .br
= `""^18"C"_"r"(1/(x^2))^(18-"r") (x^4)^"r"`
= 18Cr x2r–36 .x4r
= 18Cr x6r–36
To get the coefficient of x60, we must have
x6r–36 = x60
∴ 6r – 36 = 60
∴ 6r = 96
∴ r = 16
∴ Coefficient of x60
= 18C16
= `(18!)/(16!2!)`
= `(18 xx 17 xx 16!)/(16! xx 2 xx 1)`
= 153
∴ the coefficient of x60 is 153
APPEARS IN
RELATED QUESTIONS
In the following expansion, find the indicated term.
`((4x)/5 - 5/(2x))^9`, 7th term
Find the constant term (term independent of x) in the expansion of `(x - 2/x^2)^15`
Find the constant term (term independent of x) in the expansion of `(sqrt(x) - 3/x^2)^10`
Find the constant term (term independent of x) in the expansion of `(2x^2 - 5/x)^9`
In the expansion of (k + x)8, the coefficient of x5 is 10 times the coefficient of x6. Find the value of k.
Find the term containing x6 in the expansion of (2 − x) (3x + 1)9
The coefficient of x2 in the expansion of (1 + 2x)m is 112. Find m
Select the correct answer from the given alternatives.
The total number of terms in the expression of (x + y)100 + (x − y)100 after simplification is:
Select the correct answer from the given alternatives.
In the expansion of (x2 − 2x)10, the coefficient of x16 is
Answer the following:
Find third term in the expansion of `(9x^2 - y^3/6)^4`
Answer the following:
Find tenth term in the expansion of `(2x^2 + 1/x)^12`
Find the coefficients of x6 in the expansion of `(3x^2 - 1/(3x))^9`.
Answer the following:
If the coefficient of x2 and x3 in the expansion of (3 + kx)9 are equal, find k
Answer the following:
If the constant term in the expansion of `(x^3 + "k"/x^8)^11` is 1320, find k
Answer the following:
Show that there is no term containing x6 in the expansion of `(x^2 - 3/x)^11`
Answer the following:
Show that there is no constant term in the expansion of `(2x - x^2/4)^9`
Answer the following:
State, first four terms in the expansion of `(1 - (2x)/3)^(-1/2)`
Answer the following:
State, first four terms in the expansion of `(1 - x)^(-1/4)`
Answer the following:
State, first three terms in the expansion of `(5 + 4x) ^(-1/2)`
Answer the following:
(a + bx) (1 − x)6 = 3 − 20x + cx2 + ..... then find a, b, c
Answer the following:
The 3rd term of (1 + x)n is 36x2. Find 5th term
Answer the following:
Suppose (1 + kx)n = 1 − 12x + 60x2 − .... find k and n.
The greatest value of the term independent of x in the expansion of (x sin p + x–1 cos p)10, p ∈ R is ______.
