Advertisements
Advertisements
प्रश्न
The position of the term independent of x in the expansion of `(sqrt(x/3) + 3/(2x^2))^10` is ______.
Advertisements
उत्तर
The position of the term independent of x in the expansion of `(sqrt(x/3) + 3/(2x^2))^10` is 3rd term.
Explanation:
The given expansion is `(sqrt(x/3) + 3/(2x^2))^10`
Tr+1 = `""^10"C"_r (sqrt(x/3))^(10 - r) (3/(2x^2))^r`
= `""^10"C"_r (x/3)^((10 - r)/2) (3/2)^r * 1/x^(2r)`
= `""^10"C"_r (1/3)^((10 - r)/2) * x^((10 - r)/2) (3/2)^r * 1/x^(2r)`
= `""^10"C"_r (1/3)^((10 - r)/2) * x^((10 - r)/2 - 2r) * (3/2)^r`
= `""^10"C"_r (1/3)^((10 - r)/2) * x^((10 - r - 4r)/2) (3/2)^r`
For independent of x, we get
`(10 - r - 4r)/2` = 0
10 – 5r = 0
r = 2
So, the position of the term independent of x is 3rd term.
APPEARS IN
संबंधित प्रश्न
The coefficients of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1:3:5. Find n and r.
Find a positive value of m for which the coefficient of x2 in the expansion
(1 + x)m is 6
Find the middle terms in the expansion of:
(i) \[\left( 3x - \frac{x^3}{6} \right)^9\]
Find the middle terms in the expansion of:
(iii) \[\left( 3x - \frac{2}{x^2} \right)^{15}\]
Find the middle terms(s) in the expansion of:
(ii) \[\left( 1 - 2x + x^2 \right)^n\]
Find the middle terms(s) in the expansion of:
(ix) \[\left( \frac{p}{x} + \frac{x}{p} \right)^9\]
Find the term independent of x in the expansion of the expression:
(ii) \[\left( 2x + \frac{1}{3 x^2} \right)^9\]
Find the term independent of x in the expansion of the expression:
(iv) \[\left( 3x - \frac{2}{x^2} \right)^{15}\]
Find the term independent of x in the expansion of the expression:
(v) \[\left( \frac{\sqrt{x}}{3} + \frac{3}{2 x^2} \right)^{10}\]
Find the term independent of x in the expansion of the expression:
(x) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^6\]
If the coefficients of (2r + 1)th term and (r + 2)th term in the expansion of (1 + x)43 are equal, find r.
The coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)n are in A.P., find n.
If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)2n are in A.P., show that \[2 n^2 - 9n + 7 = 0\]
If in the expansion of (1 + x)n, the coefficients of pth and qth terms are equal, prove that p + q = n + 2, where \[p \neq q\]
Find the coefficient of a4 in the product (1 + 2a)4 (2 − a)5 using binomial theorem.
If in the expansion of (1 + x)n, the coefficients of three consecutive terms are 56, 70 and 56, then find n and the position of the terms of these coefficients.
If the 6th, 7th and 8th terms in the expansion of (x + a)n are respectively 112, 7 and 1/4, find x, a, n.
If the 2nd, 3rd and 4th terms in the expansion of (x + a)n are 240, 720 and 1080 respectively, find x, a, n.
If p is a real number and if the middle term in the expansion of \[\left( \frac{p}{2} + 2 \right)^8\] is 1120, find p.
Write the middle term in the expansion of `((2x^2)/3 + 3/(2x)^2)^10`.
Find the sum of the coefficients of two middle terms in the binomial expansion of \[\left( 1 + x \right)^{2n - 1}\]
If in the expansion of (a + b)n and (a + b)n + 3, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is
If A and B are the sums of odd and even terms respectively in the expansion of (x + a)n, then (x + a)2n − (x − a)2n is equal to
The number of irrational terms in the expansion of \[\left( 4^{1/5} + 7^{1/10} \right)^{45}\] is
In the expansion of \[\left( x - \frac{1}{3 x^2} \right)^9\] , the term independent of x is
In the expansion of \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\] , the term independent of x is
Find the middle term in the expansion of `(2ax - b/x^2)^12`.
Find numerically the greatest term in the expansion of (2 + 3x)9, where x = `3/2`.
If the term free from x in the expansion of `(sqrt(x) - k/x^2)^10` is 405, find the value of k.
Find the value of r, if the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x)18 are equal.
If xp occurs in the expansion of `(x^2 + 1/x)^(2n)`, prove that its coefficient is `(2n!)/(((4n - p)/3)!((2n + p)/3)!)`
In the expansion of `(x^2 - 1/x^2)^16`, the value of constant term is ______.
Middle term in the expansion of (a3 + ba)28 is ______.
The number of terms in the expansion of [(2x + y3)4]7 is 8.
The sum of coefficients of the two middle terms in the expansion of (1 + x)2n–1 is equal to 2n–1Cn.
If the 4th term in the expansion of `(ax + 1/x)^n` is `5/2` then the values of a and n respectively are ______.
The middle term in the expansion of (1 – 3x + 3x2 – x3)6 is ______.
If the coefficient of x10 in the binomial expansion of `(sqrt(x)/5^(1/4) + sqrt(5)/x^(1/3))^60` is 5kl, where l, k ∈ N and l is coprime to 5, then k is equal to ______.
