मराठी

Find the Middle Terms in the Expansions of (X/3 + 9y)^10

Advertisements
Advertisements

प्रश्न

Find the middle terms in the expansions of `(x/3 + 9y)^10`

Advertisements

उत्तर

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the coefficient of x5 in (x + 3)8


Find the 4th term in the expansion of (x – 2y)12 .


Find the middle terms in the expansions of  `(3 - x^3/6)^7`


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: 

(i)  \[\left( \frac{2}{3}x - \frac{3}{2x} \right)^{20}\]

 


Find the middle term in the expansion of: 

(ii)  \[\left( \frac{a}{x} + bx \right)^{12}\]

 


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:

(iv)  \[\left( 2x - \frac{x^2}{4} \right)^9\]


Find the middle terms(s) in the expansion of:

(v) \[\left( x - \frac{1}{x} \right)^{2n + 1}\]

 


Find the middle terms(s) in the expansion of: 

(vi)  \[\left( \frac{x}{3} + 9y \right)^{10}\]

 


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: 

(ix) \[\left( \sqrt[3]{x} + \frac{1}{2 \sqrt[3]{x}} \right)^{18} , x > 0\]

 


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.

 
 
 

If the coefficients of (2r + 1)th term and (r + 2)th term in the expansion of (1 + x)43 are equal, find r.


Prove that the coefficient of (r + 1)th term in the expansion of (1 + x)n + 1 is equal to the sum of the coefficients of rth and (r + 1)th terms in the expansion of (1 + x)n.


Prove that the term independent of x in the expansion of \[\left( x + \frac{1}{x} \right)^{2n}\]  is \[\frac{1 \cdot 3 \cdot 5 . . . \left( 2n - 1 \right)}{n!} . 2^n .\]

 
 

If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)n are in A.P., then find the value of n.


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 coefficients of three consecutive terms in the expansion of (1 + x)n be 76, 95 and 76, find 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.


If the term free from x in the expansion of  \[\left( \sqrt{x} - \frac{k}{x^2} \right)^{10}\]  is 405, find the value of k.

 
 

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.

 
 

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


In the expansion of \[\left( x^2 - \frac{1}{3x} \right)^9\] , the term without x is equal to

 

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

 

 

The number of terms with integral coefficients in the expansion of \[\left( {17}^{1/3} + {35}^{1/2} x \right)^{600}\] is

 

Find the middle term in the expansion of `(2ax - b/x^2)^12`.


Find the term independent of x, x ≠ 0, in the expansion of `((3x^2)/2 - 1/(3x))^15`


If p is a real number and if the middle term in the expansion of `(p/2 + 2)^8` is 1120, find p.


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 xp occurs in the expansion of `(x^2 + 1/x)^(2n)`, prove that its coefficient is `(2n!)/(((4n - p)/3)!((2n + p)/3)!)`


The last two digits of the numbers 3400 are 01.


Let for the 9th term in the binomial expansion of (3 + 6x)n, in the increasing powers of 6x, to be the greatest for x = `3/2`, the least value of n is n0. If k is the ratio of the coefficient of x6 to the coefficient of x3, then k + n0 is equal to ______.


Let the coefficients of the middle terms in the expansion of `(1/sqrt(6) + βx)^4, (1 - 3βx)^2` and `(1 - β/2x)^6, β > 0`, common difference of this A.P., then `50 - (2d)/β^2` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×