If there is a term containing `x^(2r)` in `(x + (1)/(x^(2)))^(n-3)`, then

If there is a term independent of x in (x+(1)/(x^(2)))^(n) ,show that it is equal to (n!)/(((n)/(3))!((2n)/(3))!)

Show that there will be no term containing x^(2r) in the expansion of (x+x^-2)^(n-3) if n-2r is a positive integer but not a multiple of 3.

Show that there will be no term containing x^(2r) in the expansion of (x+x^-2)^(n-3) if n-2r is a positive integer but not a multiple of 3.

If r^(th) term is the middle term in the expansion of (x^(2)-(1)/(2x))^(20), then (r+3)^(th) term is

If the rth term is the middle term in the expansion of (x^(2)-(1)/(2x))^(20) , then the (r+3)th term is:

If there is a term independent of x in ( x+1/x^2)^n , show that it is equal to (n!)/((n/3)! ((2n)/3)! )

If the rth term in the expansion of ((x^(3))/(3)-(2)/(x^(2)))^(10) contains x^(20) .then r=

The number of distinct terms in the expansion of (x^(3)+ 1 + (1)/(x^(3)))^(n) , x in R^(+) and a in N , is

If the 4 th term in the expansion of (a x + (1)/(x))^(n) is (5)/(2) , for all x in R then the values of a and n are respectively

If r^(th) term in the expansion of ((x)/(3)-(2)/(x^(2)))^(10) contains x^(4), then find the value of r