हिंदी

Write the Total Number of Terms in the Expansion of ( X + a ) 100 + ( X − a ) 100 .

Advertisements
Advertisements

प्रश्न

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

 
Advertisements

उत्तर

The total number of terms are 101 of which 50 terms get cancelled.

Hence, the total number of terms in the expansion of 

\[\left( x + a \right)^{100} + \left( x - a \right)^{100}\]  is 51.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 18: Binomial Theorem - Exercise 18.3 [पृष्ठ ४६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 18 Binomial Theorem
Exercise 18.3 | Q 17 | पृष्ठ ४६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


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


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


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 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: 

(iii) \[\left( x^2 - \frac{2}{x} \right)^{10}\]

 


Find the middle term in the expansion of: 

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

 


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:

(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:

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

 


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: 

(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: 

(vii)  \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\]

 


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 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  \[p \neq q\]

 


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


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 \[\left( 1 + x \right)^{2n}\] . 

 

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

 

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

 

The ratio of the coefficient of x15 to the term independent of x in `x^2 + 2^15/x` is ______.


Find the term independent of x in the expansion of `(3x - 2/x^2)^15`


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


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


In the expansion of `(x^2 - 1/x^2)^16`, the value of constant term is ______.


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


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


The last two digits of the numbers 3400 are 01.


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


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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×