English

Find a Positive Value of M for Which the Coefficient of X2 in the Expansion (1 + X)M is 6

Advertisements
Advertisements

Question

Find a positive value of m for which the coefficient of x2 in the expansion

(1 + x)m is 6

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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


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


Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of `(root4 2 + 1/ root4 3)^n " is " sqrt6 : 1`


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: 

(iii) \[\left( 3x - \frac{2}{x^2} \right)^{15}\]

 


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: 

(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 middle terms(s) in the expansion of:

(x)  \[\left( \frac{x}{a} - \frac{a}{x} \right)^{10}\]

 


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: 

(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)n are in A.P., then find the value of 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.

 

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


Find a, b and n in the expansion of (a + b)n, if the first three terms in the expansion are 729, 7290 and 30375 respectively.


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

 

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


The number of irrational terms in the expansion of \[\left( 4^{1/5} + 7^{1/10} \right)^{45}\]  is

 

The middle term in the expansion of \[\left( \frac{2 x^2}{3} + \frac{3}{2 x^2} \right)^{10}\] is 

 

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

 

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


Find the middle term (terms) in the expansion of `(x/a - a/x)^10`


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)!)`


The sum of coefficients of the two middle terms in the expansion of (1 + x)2n–1 is equal to 2n–1Cn. 


If the expansion of `(x - 1/x^2)^(2n)` contains a term independent of x, then n is a multiple of 2.


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


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×