English

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

Advertisements
Advertisements

Question

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`

Advertisements

Solution

It is given that the ratio of the fifth term from the beginning to the fifth term from the end is `sqrt6 : 1`. Therefore, from (1) and (2), we obtain

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

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


The coefficients of the (r – 1)thrth 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 terms in the expansion of:

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

 


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:

(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:

(ix)  \[\left( \frac{p}{x} + \frac{x}{p} \right)^9\]

 


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: 

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

 


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 in the expansion of (1 + x)n, the coefficients of pth and qth terms are equal, prove that p + q = n + 2, where  \[p \neq q\]

 


Find the coefficient of a4 in the product (1 + 2a)4 (2 − a)5 using binomial theorem.

 

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  \[\left( x + \frac{1}{x} \right)^{10}\]

 

Write the coefficient of the middle term in the expansion of \[\left( 1 + x \right)^{2n}\] . 

 

If an the expansion of \[\left( 1 + x \right)^{15}\]   , the coefficients of \[\left( 2r + 3 \right)^{th}\text{  and  } \left( r - 1 \right)^{th}\]  terms are equal, then the value of r is

 

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


Find the middle term (terms) in the expansion of `(3x - x^3/6)^9`


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


The number of terms in the expansion of [(2x + y3)4]7 is 8.


The last two digits of the numbers 3400 are 01.


The coefficient of x256 in the expansion of (1 – x)101(x2 + x + 1)100 is ______.


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