हिंदी

Find the 13th Term in the Expansion of (9x - 1/(3sqrtx))^18 , X != 0 - Mathematics

Advertisements
Advertisements

प्रश्न

Find the 13th term in the expansion of `(9x - 1/(3sqrtx))^18 , x != 0`

Advertisements

उत्तर

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Binomial Theorem - Exercise 8.2 [पृष्ठ १७१]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 8 Binomial Theorem
Exercise 8.2 | Q 6 | पृष्ठ १७१

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the coefficient of a5b7 in (a – 2b)12


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 the middle terms in the expansion of: 

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

 


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:

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

 


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

 


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 `((2x^2)/3 + 3/(2x)^2)^10`.


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 \[\left( 1 + x \right)^{2n}\] . 

 

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

 

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

 

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

 

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

 

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


If the term free from x in the expansion of `(sqrt(x) - k/x^2)^10` is 405, find the value of k.


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`


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


Find the term independent of x in the expansion of (1 + x + 2x3) `(3/2 x^2 - 1/(3x))^9`


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


The last two digits of the numbers 3400 are 01.


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


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 ______.


If the 4th term in the expansion of `(ax + 1/x)^n` is `5/2` then the values of a and n respectively are ______.


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 ______.


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×