`x^(3m) + x^(3n-1) + x^(3r-2)`, where, `m,n,r in N` is divisible by

If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r) , then the value of a_(r) , where n in N is

If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r) , then the value of a_(r) , where n in N is

if (1-x^3)^n=sum_(r=0)^n a_rx^r (1-x)^(3n-2r), where n epsilonN then find a_r .

if (1-x^3)^n=sum_(r=0)^n a_rx^r (1-x)^(3n-2r), where n epsilonN then find a_r .

If 5x^(3) +Mx+ N, M,N in R is divisible by x^(2) + x+1 , then the value of M +N is

For x in(0,(pi)/(4)). Let S_(n)=sum_(r=1)^(2n)sin(sin^(-1)x^(3r-2)),C_(n)=sum_(r=1)^(2n)cos(cos^(-1)x^(3r-1)) and T_(n)=sum_(r=1)^(2n)tan(tan^(-1)x^(3r)) where n in N and n>=3

For what values of m and n is 2x^(4)-11x^(3)+mx+n is divisible by x^(2)-1 ?

Statement-1 Coefficient of x^49 in (1+ x)(3 +x)(5 +x)......... (99+x) is 2500 and Statement. 2 The coefficient of x^k in (1 +x)l (2 +x)m (3 +x)n where l +m +n -k= 1 is (l+ 2m +3n).

Let f(x)=x^((m)/(n)) for x in R where m and n are integers,m even and n odd and '0