English

Write the General Term in the Expansion of (X2 – Yx)12, X ≠ 0 - Mathematics

Advertisements
Advertisements

Question

Write the general term in the expansion of (x2 – yx)12x ≠ 0

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Binomial Theorem - Exercise 8.2 [Page 171]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 8 Binomial Theorem
Exercise 8.2 | Q 4 | Page 171

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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


In the expansion of (1 + a)m + n, prove that coefficients of am and an are equal.


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: 

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

 


Find the middle terms in the expansion of: 

(i)  \[\left( 3x - \frac{x^3}{6} \right)^9\]

 


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:

(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 middle terms(s) in the expansion of:

(viii)  \[\left( 2ax - \frac{b}{x^2} \right)^{12}\]

 


Find the term independent of x in the expansion of the expression:

(ii)  \[\left( 2x + \frac{1}{3 x^2} \right)^9\]

 


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.

 
 
 

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 3rd, 4th 5th and 6th terms in the expansion of (x + a)n be respectively a, b, c and d, prove that `(b^2 - ac)/(c^2 - bd) = (5a)/(3c)`.


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


If the 2nd, 3rd and 4th terms in the expansion of (x + a)n are 240, 720 and 1080 respectively, find xan.


Write the middle term in the expansion of  \[\left( x + \frac{1}{x} \right)^{10}\]

 

Write the total number of terms in the expansion of  \[\left( x + a \right)^{100} + \left( x - a \right)^{100}\] .

 

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


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

 

If in the expansion of \[\left( x^4 - \frac{1}{x^3} \right)^{15}\] ,  \[x^{- 17}\]  occurs in rth term, then

 

In the expansion of \[\left( x - \frac{1}{3 x^2} \right)^9\]  , the term independent of x is

 

If in the expansion of (1 + y)n, the coefficients of 5th, 6th and 7th terms are in A.P., then nis equal to


The total number of terms in the expansion of \[\left( x + a \right)^{100} + \left( x - a \right)^{100}\]  after simplification is

 

Find the middle term (terms) in the expansion of `(p/x + x/p)^9`.


Find numerically the greatest term in the expansion of (2 + 3x)9, where x = `3/2`.


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`


Find n in the binomial `(root(3)(2) + 1/(root(3)(3)))^n` if the ratio of 7th term from the beginning to the 7th term from the end is `1/6`


The last two digits of the numbers 3400 are 01.


The sum of the co-efficients of all even degree terms in x in the expansion of `(x + sqrt(x^3 - 1))^6 + (x - sqrt(x^3 - 1))^6, (x > 1)` is equal to ______.


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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×