English

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

Advertisements
Advertisements

Question

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

 
Advertisements

Solution

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
  Is there an error in this question or solution?
Chapter 18: Binomial Theorem - Exercise 18.3 [Page 46]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 18 Binomial Theorem
Exercise 18.3 | Q 17 | Page 46

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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`


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


Find the middle term in the expansion of: 

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

 


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:

(ii)  \[\left( 1 - 2x + x^2 \right)^n\]


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:

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

 


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 2nd, 3rd and 4th terms in the expansion of (1 + x)2n are in A.P., show that  \[2 n^2 - 9n + 7 = 0\]

 


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 a, if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.

 

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 3rd, 4th 5th and 6th terms in the expansion of (x + a)n be respectively a, b, c and d, prove that `(b^2 - ac)/(c^2 - bd) = (5a)/(3c)`.


If the coefficients of three consecutive terms in the expansion of (1 + x)n be 76, 95 and 76, find n.


If the term free from x in the expansion of  \[\left( \sqrt{x} - \frac{k}{x^2} \right)^{10}\]  is 405, find the value of k.

 
 

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

 

If in the expansion of (a + b)n and (a + b)n + 3, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is


In the expansion of \[\left( x^2 - \frac{1}{3x} \right)^9\] , the term without x is 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 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.


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


If the middle term of `(1/x + x sin x)^10` is equal to `7 7/8`, then value of x 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.


If n is the number of irrational terms in the expansion of `(3^(1/4) + 5^(1/8))^60`, then (n – 1) is divisible by ______.


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 ______.


The coefficient of y49 in (y – 1)(y – 3)(y – 5) ...... (y – 99) is ______.


The term independent of x in the expansion of `[(x + 1)/(x^(2/3) - x^(1/3) + 1) - (x - 1)/(x - x^(1/2))]^10`, x ≠ 1 is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×