Advertisements
Advertisements
प्रश्न
Answer the following:
If the constant term in the expansion of `(x^3 + "k"/x^8)^11` is 1320, find k
उत्तर
Let tr+1 be the constant term in the expansion of `(x^3 + "k"/x^8)^11`.
We know that, in the expansion of (a + b)n,
tr+1 = nCr, an–r br
Here a = x3, b = `"k"/x^8`, n = 11
∴ tr+1 = `""^11"C"_"r" (x^3)^(11 - "r") ("k"/x^8)^"r"`
= 11Cr x33–3r · kr · x–8r
= 11Cr kr · `x^(33 - 11"r")`
But tr+1 is a constant term
∴ power of x = 0
∴ 33 – 11r = 0
∴ r = 3
∴ constant term = 11C3 k3
= `(11 xx 10 xx 9)/(1xx 2 xx 3) xx "k"^3` = 165k3
But, the constant term = 1320 ...(Given)
∴ 165k3 = 1320
∴ k3 = 8
∴ k = 2
APPEARS IN
संबंधित प्रश्न
In the following expansion, find the indicated term.
`(x^2 - 4/(x^3))^11`, 5th term
In the following expansion, find the indicated term.
`((4x)/5 - 5/(2x))^9`, 7th term
In the following expansion, find the indicated term.
`(1/3 + "a"^2)^12`, 9th term
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`.
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 `(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:
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:
(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.
