(1+x)17 (1 + x)19 (1 + x)23 If f(x) |(l + x)23 (l + x)29 (l + x)341 = A + Bx + Cr + ..., then (1+x)41 (l+x)43 (1+x)47 A

If x+ (1)/(x)=1 , find x^(23) + (1)/(x^(23))=

If |{:((1+x)^(17),(1+x)^(19),(1+x)^(23)),((1+x)^(23),(1+x)^(29),(1+x)^(34)),((1+x)^(41),(1+x)^(43),(1+x)^(47)):}|=Ax^2+Bx+C then value of A = "........."

If f(x)=|((1+x)^(17),(a+x)^(19),(1+x)^(23)),((a+x)^(23),(a+x)^(29),(1+x)^(34)),((1+x)^(41),(1+x)^(43),(1+x)^(47))| =A+Bx+Cx^(2)+………. then A is equal to………….

If f(x)=|((1+x)^(17),(a+x)^(19),(1+x)^(23)),((a+x)^(23),(a+x)^(29),(1+x)^(34)),((1+x)^(41),(1+x)^(43),(1+x)^(47))| =A+Bx+Cx^(2)+………. then A is equal to………….

If function f(x) = (x - l)/(x+1), x ne -1 is invertible in its domain, then find f^-1 (x) .

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).

If f(x) = (x^l/x^m)^(l+m) (x^m/x^n)^(m+n) (x^n/x^l)^(n+l) , then find f'(x).

Evaluate int (1)/(x l (x ) l^(2) (x ) ....l^(n) (x)) dx where l^(n) (x) = log_(e) log_(e) ....... Log_(e) (x ) (n times)