Binomial Theore...

The coefficient of second, third and fourth terms in the binomial expansion of  (1+x)ⁿ (‘n ’, a + ve integer) are in A.P.., if n is equal to

The coefficient of  x³ in the binomial expansion of   

The coefficient of  x¹⁷ in the expansion of (x- 1) (x- 2) …..(x –18) is

If the coefficients of (r +1)th term and (r + 3)th term in the expansion of  (1+x)²ⁿ be equal then

If  x = 99⁵⁰ +100⁵  and  y = (101)⁵⁰ , then

The greatest coefficient in the expansion of  (1+x)¹²  is

In the expansion of  (1+x)⁶⁰ , the sum of coefficients of odd powers of x is

Let n  ∈ Q an n  ∉N,n ≠0, a  > 0, then the expansion of  (a+x)ⁿ in powers of x is valid if

The expansion of  , in powers of x, is valid if

The middle term in the expansion of  (1+x)²ⁿ is

The coefficient of x⁹⁹  in (x+1)(x+3)(x+5)………..(x+199) is

If the expansion of in powers of x contains the term  x^2r , then n −2r is

If rth ,(r+1)th and (r+2)th terms in the expansion of  (1+x)ⁿ are in A.P. then

Coefficient of  a² b⁵ in the expansion of  (a+b)³ (a −2b)⁴ is

In the expansion of(1+x)¹¹ , the  5^th term is 24 times the  3^rd term . The value of x is

The sum of coefficients in the expansion of  (x+2y+z)ⁿ  is (n being a positive integer)

If the rth term in the expansion of   contains  x⁴  then r is equal to

If a + b = 1, then   is equal to  

The 1st three terms in the expansion of (4 + x)^3/2  are

The coefficients of  xⁿ in the expansion of  (1+2x + 3x² + ........)^1/2 is  

If z =   + ........, then z² + 2z is equal to

The index of the power of x that occurs in the  7^th term from the end in the expansion of  

The index of the power of x that occurs in the  6^th term in the expansion of  

If in the expansion of(1+x)⁴³ , the coefficients of (2r+1)th and (r+2)th  terms are equal, then r is equal to