Advertisements
Advertisements
प्रश्न
In the following expansion, find the indicated term.
`((4x)/5 - 5/(2x))^9`, 7th term
उत्तर
We know that the (r + 1)th term in the expansion of (a + b)n is
tr+1 = nCr an–r br
Hence a = `(4x)/5` b = `-5/(2x)`, n = 9 and for t7, r = 6
∴ 7th term in the expansion of `((4x)/5 - 5/(2x))^9`
= t7 = `""^9"C"_6((4x)/5)^(9 - 6) ((-5)/(2x))^6`
= `(9!)/(6! 3!) xx ((4x)/5)^3 xx ((-5)/(2x))^6`
...[∵ nCr = nCn–r]
= `(9 xx 8 xx 7)/(3 xx 2 xx 1) xx (4^3.x^3)/5^3 xx 5^6/(2^6.x^6)`
= `(9 xx 8 xx 7)/(3 xx 2 xx 1) xx (64.x^3)/125 xx 15625/(64.x^6)`
= `504/6 xx 125/(x^3)`
= `84 xx 125/(x^3)`
= `10500/x^3`
APPEARS IN
संबंधित प्रश्न
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 `(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.
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
Find the constant term in the expansion of `(2x^2 - 1/x)^12`
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:
The 3rd term of (1 + x)n is 36x2. Find 5th term
