Binomial coefficients basic relation |Term independent | Pascal identity

Binomial coefficients relations and their problems

In the expansion of (7^(1/3)+11^(1/9))^(6561) (a)there are exactly 730 rational term (bthere are exactly 5831 irrational term (bthe term which involves greatest binomial coefficients is irrational (d)the term which involves greatest binomial coefficients is rational

What are binomial coefficients in (a+b)^(7) ?

Properties OF binomial coefficient ,questions on properties OF binomial coefficient

In the expansion of (x+y)^(n) ,if the binomial coefficient of the third term is greater by 9 then that of the second term,then the sum of the binomial coefficients of the terms occupying to odd places is

In the expansion of (3^(-(x)/(4))+3^((5x)/(4)))^(n) the sum of the binomial coefficients is 256 and four xx the term with greatest binomial coefficient exceeds the square of the third coefficient then find 4x.

If the sum of the binomial coefficients in the expansion of (x+ 1/x)^n is 64, then the term independent of x is equal to (A) 10 (B) 20 (C) 30 (D) 40