मराठी

In the Expansion of (1 + A)M + N, Prove that Coefficients of Am and an Are Equal. - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Binomial Theorem - Exercise 8.2 [पृष्ठ १७१]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 8 Binomial Theorem
Exercise 8.2 | Q 9 | पृष्ठ १७१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Write the general term in the expansion of (x2 – y)6


Find the 13th term in the expansion of `(9x - 1/(3sqrtx))^18 , 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`


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:

(ii) \[\left( 2 x^2 - \frac{1}{x} \right)^7\]

 


Find the middle terms in the expansion of:

(iv)  \[\left( x^4 - \frac{1}{x^3} \right)^{11}\]

 


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: 

(vii) \[\left( 3 - \frac{x^3}{6} \right)^7\]

  


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: 

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

 


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.

 

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 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 a, b, c and d in any binomial expansion be the 6th, 7th, 8th and 9th terms respectively, then prove that \[\frac{b^2 - ac}{c^2 - bd} = \frac{4a}{3c}\].


If the coefficients of three consecutive terms in the expansion of (1 + x)n be 76, 95 and 76, find 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  \[\left( x + \frac{1}{x} \right)^{10}\]

 

Find the sum of the coefficients of two middle terms in the binomial expansion of  \[\left( 1 + x \right)^{2n - 1}\]

 

If 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 \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\] , the term independent of x is

 

The middle term in the expansion of \[\left( \frac{2x}{3} - \frac{3}{2 x^2} \right)^{2n}\] 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 `(3x - x^3/6)^9`


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.


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 position of the term independent of x in the expansion of `(sqrt(x/3) + 3/(2x^2))^10` is ______.


The last two digits of the numbers 3400 are 01.


The number of rational terms in the binomial expansion of `(4^(1/4) + 5^(1/6))^120` is ______.


The middle term in the expansion of (1 – 3x + 3x2 – x3)6 is ______.


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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×