Advertisements
Advertisements
Question
In the expansion of (k + x)8, the coefficient of x5 is 10 times the coefficient of x6. Find the value of k.
Advertisements
Solution
We know that, in the expansion of (a+ b)n,
tr+1 = nCr an–r br
Here, n = 8, a = k, b = x
∴ tr+1 = 8Cr (k)8–r xr ...(1)
If this is the term containing x5, then r = 5 and Coefficient of x5 = 8C5k3.
Also, if (1) is the term containing x6, then r = 6 and coefficient of x6 = 8C6k2.
Since, coefficient of x5 = 10 × coefficient of x6
∴ 8C5k3 = 10 × 8C6k2
∴ `(8!)/(5!3!) * "k"^3/"k"^2 = (8!)/(6!2!) xx 10`
∴ k = `(5!3!)/(6!2!) xx 10`
= `(5! xx 3 xx 2!)/(6 xx 5! xx 2!) xx 10`
∴ k = 5
APPEARS IN
RELATED QUESTIONS
In the following expansion, find the indicated term.
`(1/3 + "a"^2)^12`, 9th term
In the following expansion, find the indicated term.
`(3"a" + 4/"a")^13`, 10th term
Find the constant term (term independent of x) in the expansion of `(2x + 1/(3x^2))^9`
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 `(x^2 - 1/x)^9`
Find the constant term (term independent of x) in the expansion of `(2x^2 - 5/x)^9`
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
Select the correct answer from the given alternatives.
The term not containing x in expansion of `(1 - x)^2 (x + 1/x)^10` is
Select the correct answer from the given alternatives.
The number of terms in expansion of (4y + x)8 − (4y − x)8
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:
Find the constant term in the expansion of `((4x^2)/3 + 3/(2x))^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:
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 - x)^(-1/4)`
Answer the following:
State, first three terms in the expansion of `(5 + 4x) ^(-1/2)`
Answer the following:
Find the term independent of x in the in expansion of `(1 - x^2) (x + 2/x)^6`
Answer the following:
The 3rd term of (1 + x)n is 36x2. Find 5th term
The greatest value of the term independent of x in the expansion of (x sin p + x–1 cos p)10, p ∈ R is ______.
