Advertisements
Advertisements
प्रश्न
If the middle term of `(1/x + x sin x)^10` is equal to `7 7/8`, then value of x is ______.
पर्याय
`2npi + pi/6`
`npi + pi/6`
`npi + (-1)^n pi/6`
`npi + (-1)^n pi/3`
Advertisements
उत्तर
If the middle term of `(1/x + x sin x)^10` is equal to `7 7/8`, then value of x is `npi + (-1)^n pi/6`.
Explanation:
Given expression is `(1/x + x sin x)^10`
Number of terms = 10 + 1 = 11 odd
∴ Middle term = `(11 + 1)/2` th term = 6th term
T6 = T5+1
= `""^10"C"_5 (1/x)^(10 - 5) (x sin x)^5`
∴ `""^10"C"_5 (1/x)^5 * x^5 * sin^5x = 7 7/8`
⇒ `""^10"C"_5 * sin^5x = 63/8`
⇒ `(10*9*8*7*6)/(5*4*3*2*1) * sin^5x = 63/8`
⇒ `252 * sin^5x = 63/8`
⇒ `sin^5x = 63/(8 xx 252)`
⇒ `sin^5x = 1/32`
⇒ `sin^5x = (1/2)^5`
⇒ sin x = `1/2`
⇒ sin x = `sin pi/6`
∴ x = `"n"pi + (-1)^"n" * pi/6`
APPEARS IN
संबंधित प्रश्न
Write the general term in the expansion of (x2 – y)6
Write the general term in the expansion of (x2 – yx)12, x ≠ 0
Find the middle terms in the expansions of `(3 - x^3/6)^7`
Find the middle terms in the expansions of `(x/3 + 9y)^10`
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 the middle term in the expansion of:
(ii) \[\left( \frac{a}{x} + bx \right)^{12}\]
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:
(i) \[\left( x - \frac{1}{x} \right)^{10}\]
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:
(iii) \[\left( 1 + 3x + 3 x^2 + x^3 \right)^{2n}\]
Find the middle terms(s) in the expansion of:
(vi) \[\left( \frac{x}{3} + 9y \right)^{10}\]
Find the middle terms(s) in the expansion of:
(vii) \[\left( 3 - \frac{x^3}{6} \right)^7\]
Find the term independent of x in the expansion of the expression:
(i) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^9\]
Find the term independent of x in the expansion of the expression:
(iii) \[\left( 2 x^2 - \frac{3}{x^3} \right)^{25}\]
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 \[\left( 2r + 4 \right)\text{ th and } \left( r - 2 \right)\] th terms in the expansion of \[\left( 1 + x \right)^{18}\] 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.
Find a, if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.
Find the coefficient of a4 in the product (1 + 2a)4 (2 − a)5 using binomial theorem.
In the expansion of (1 + x)n the binomial coefficients of three consecutive terms are respectively 220, 495 and 792, find the value of n.
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.
The middle term in the expansion of \[\left( \frac{2 x^2}{3} + \frac{3}{2 x^2} \right)^{10}\] is
If the sum of odd numbered terms and the sum of even numbered terms in the expansion of \[\left( x + a \right)^n\] are A and B respectively, then the value of \[\left( x^2 - a^2 \right)^n\] is
If rth term is the middle term in the expansion of \[\left( x^2 - \frac{1}{2x} \right)^{20}\] then \[\left( r + 3 \right)^{th}\] term is
Find numerically the greatest term in the expansion of (2 + 3x)9, where x = `3/2`.
Find the middle term (terms) in the expansion of `(3x - x^3/6)^9`
If p is a real number and if the middle term in the expansion of `(p/2 + 2)^8` is 1120, find p.
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 middle term in the expansion of (1 – 3x + 3x2 – x3)6 is ______.
