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In the binomial expansion of (1 + x)^(10) , the coefficeents of (2m + 1)^(th) and (4m + 5)^(th) terms are equal. Value of m is

In the expansion of (a+x)^(n) , find the coefficent of rth term from end.

Show that the coefficient of the middle term of (1+x)^(2m) is equal to the sum of the coefficents of the two middle terms of (1+x)^(2m-1) .

Prove that the coefficents of x^(n) in the expansion of (1+x)^(2n) is twice the coefficent of x^(n) in the expansion of (1+x)^(2n-1) .

If n is a positive integer, show that, in the expansion of (1+x)^(n) the sum of the coefficents of terms in the odd positions is equal to the sum of the cofficients of term in the even positions and each sum is equal to 2^(n-1) .

If the coefficents of x^(3) and x^(4) in the expansion of (1+ax + bx^(2)) (1-2x)^(18) in powers of x and both zero then (a,b) is equal to

If "(dy)/(dx)+(2y)/(x)=0 ,y(1)=1" then y(2)=(1)/(n') "(n in N)" .value of "n" is

If X""=""{4^n-3n-1"":""n in N}""a n d""Y""=""{9(n-1)"": n in N} , where N is the set of natural numbers, then XuuY is equal to (1) N (2) Y - X (3) X (4) Y

For the natural number m, n, if ( 1- y ) ^(m) (1 + y) ^( n) =1 + a _(1) y + a _(2) y ^(2) + ...+ a _( m + n) y ^( m +n) and a _(1) = a _(2) = 10, then the value of (m+n) is equal to :