English

The total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is ______. - Mathematics

Advertisements
Advertisements

Question

The total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is ______.

Options

  • 102

  • 25

  • 26

  • None of these

MCQ
Fill in the Blanks
Advertisements

Solution

The total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is 26.

Explanation:

Since the total number of terms are 52 of which 26 terms get cancelled.

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Binomial Theorem - Solved Examples [Page 139]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 8 Binomial Theorem
Solved Examples | Q 16 | Page 139

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Expand the expression: (1– 2x)5


Expand the expression (1– 2x)5


Expand the expression: `(2/x - x/2)^5`


Expand the expression: (2x – 3)6


Expand the expression: `(x/3 + 1/x)^5`


Using Binomial Theorem, evaluate of the following:
(102)5


Find (a + b)4 – (a – b)4. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`


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


If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer.

[Hint: write an = (a – b + b)n and expand]


Find the value of `(a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 -1))^4`


Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.


If n is a positive integer, prove that \[3^{3n} - 26n - 1\]  is divisible by 676.

 
 

Using binomial theorem determine which number is larger (1.2)4000 or 800?

 

Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.

 

Show that  \[2^{4n + 4} - 15n - 16\]  , where n ∈  \[\mathbb{N}\]  is divisible by 225.

 
  
  

Find the rth term in the expansion of `(x + 1/x)^(2r)`


Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`


Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?


Which of the following is larger? 9950 + 10050  or 10150


If a1, a2, a3 and a4 are the coefficient of any four consecutive terms in the expansion of (1 + x)n, prove that `(a_1)/(a_1 + a_2) + (a_3)/(a_3 + a_4) = (2a_2)/(a_2 + a_3)`


If (1 – x + x2)n = a0 + a1 x + a2 x2 + ... + a2n x2n , then a0 + a2 + a4 + ... + a2n equals ______.


The number of terms in the expansion of (a + b + c)n, where n ∈ N is ______.


Find the coefficient of x15 in the expansion of (x – x2)10.


If the coefficient of second, third and fourth terms in the expansion of (1 + x)2n are in A.P. Show that 2n2 – 9n + 7 = 0.


In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that 4OE = (x + a)2n – (x – a)2n 


The number of terms in the expansion of (x + y + z)n ______.


The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is ______.


If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is ______.


Let `(5 + 2sqrt(6))^n` = p + f where n∈N and p∈N and 0 < f < 1 then the value of f2 – f + pf – p is ______. 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×