Advertisements
Advertisements
Question
If p is a real number and if the middle term in the expansion of `(p/2 + 2)^8` is 1120, find p.
Solution
Given expression is `(p/2 + 2)^8`
Number of terms = 8 + 1 = 9 (odd)
∴ Middle term = `(9 + 1)/2` th term = 5th term
∴ T5 = T4+1
= `""^8"C"_4 (p/2)^(8 - 4) (2)^4`
= `""^8"C"_4 p^4/2^4 xx 2^4`
= `""^8"C"_4 p^4`
Now 8C4P4 = 1120
⇒ `(8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 1) "P"^4` = 1120
⇒ 70P4 = 1120
⇒ P4 = `1120/70` = 16
⇒ P4 = 24
⇒ P = ±2
Hence, the required value of P = ±2
APPEARS IN
RELATED QUESTIONS
Find the coefficient of a5b7 in (a – 2b)12
Find a positive value of m for which the coefficient of x2 in the expansion
(1 + x)m is 6
Find the middle term in the expansion of:
(ii) \[\left( \frac{a}{x} + bx \right)^{12}\]
Find the middle term in the expansion of:
(iv) \[\left( \frac{x}{a} - \frac{a}{x} \right)^{10}\]
Find the middle terms(s) in the expansion of:
(iv) \[\left( 2x - \frac{x^2}{4} \right)^9\]
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:
(ii) \[\left( 2x + \frac{1}{3 x^2} \right)^9\]
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:
(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:
(ix) \[\left( \sqrt[3]{x} + \frac{1}{2 \sqrt[3]{x}} \right)^{18} , x > 0\]
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 \[p \neq q\]
If a, b, c and d in any binomial expansion be the 6th, 7th, 8th and 9th terms respectively, then prove that \[\frac{b^2 - ac}{c^2 - bd} = \frac{4a}{3c}\].
Write the middle term in the expansion of \[\left( x + \frac{1}{x} \right)^{10}\]
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
In the expansion of \[\left( x - \frac{1}{3 x^2} \right)^9\] , the term independent of x 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 the middle term (terms) in the expansion of `(x/a - a/x)^10`
Find the middle term (terms) in the expansion of `(3x - x^3/6)^9`
Show that the middle term in the expansion of `(x - 1/x)^(2x)` is `(1 xx 3 xx 5 xx ... (2n - 1))/(n!) xx (-2)^n`
If the middle term of `(1/x + x sin x)^10` is equal to `7 7/8`, then value of x is ______.
The last two digits of the numbers 3400 are 01.
The sum of the real values of x for which the middle term in the binomial expansion of `(x^3/3 + 3/x)^8` equals 5670 is ______.
