Advertisements
Advertisements
Question
Answer the following:
If the coefficient of x2 and x3 in the expansion of (3 + kx)9 are equal, find k
Advertisements
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.
`(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`
In the expansion of (k + x)8, the coefficient of x5 is 10 times the coefficient of x6. Find the value of k.
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 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
Find the constant term in the expansion of `(2x^2 - 1/x)^12`
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:
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:
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 ______.
