Advertisements
Advertisements
Question
Answer the following:
If the coefficient of x2 and x3 in the expansion of (3 + kx)9 are equal, find k
Solution
Here a = 3, b = kx, n = 9
We have, tr+1 = nCr, an–r .br
= 9Cr (3)9–r (kx)r
= 9Cr (3)9–r . kr(x)r
For coefficient of x2, r = 2
For coefficient of x3, r = 3
But, coefficient of x2 = coefficient of x3
∴ 9C2 (3)7 . k2 = 9C3. 36 .k3
∴ `(9!)/(2!7!) (3)^7"k"^2 = (9!)/(3!6!) (3)^6 . "k"^3`
∴ `(9 xx 8 xx 7!)/(2 xx 1 xx 7!) (3)^7"k"^2 = (9 xx 8 xx 7 xx 6!)/(3 xx 2 xx 1 xx 6!) (3)^6*"k"^3`
∴ 36 × 37 × k2 = 84 × 36 × k3
∴ `36/84 xx 3` = k
∴ k = `9/7`
APPEARS IN
RELATED QUESTIONS
In the following expansion, find the indicated term.
`(2x^2 + 3/(2x))^8`, 3rd term
In the following expansion, find the indicated term.
`(x^2 - 4/(x^3))^11`, 5th term
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 `(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.
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`.
Find the coefficients of x60 in the expansion of `(1/x^2 + x^4)^18`
Answer the following:
Find the constant term in the expansion of `((4x^2)/3 + 3/(2x))^9`
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:
(a + bx) (1 − x)6 = 3 − 20x + cx2 + ..... then find a, b, c
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 ______.
