If `y=x^m`, then `y_n` is equal to:
a) `(m!)/((m-n)!)x^(m-n)`
b) `(m!)/((n-m)!)x^(m-n)`
c) `(n!)/((m+n)!)x^(m+n)`
a) `(n!)/((n-m)!)x^(m-n)`

if y= x^m then Y n is equal to: (A) frac{m!}{m-n!} x^(m-n) (B) frac{m!}{n-m!} x^(m-n) (C) frac{n!}{m+n!} x^(m+n) (D) frac{n!}{n-m!} x^(m-n)

Simplify : ((a^(m))/(a^(n)))^(m+n)((a^(n))/(a^(l)))^(n+l)((a^(l))/(a^(m)))^(l+m)

Show that : ((a^(m))/(a^(-n)))^(m-n)xx((a^(n))/(a^(-1)))^(n-1)xx((a^(l))/(a^(-m)))^(l-m)=1

Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-l)))^(1//(l-m))*(x^((n+l)/(l-m)))^(1//(m-n)) wrt x is

If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient of x^m is a. ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

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

IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n (a) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx (b) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx (c) I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx (d) I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx

If y=(x-a)^(m)(x-b)^(n) , prove that (dy)/(dx)=(x-a)^(m-1)(x-b)^(n-1)[(m+n)x-(an+bm) ].

A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local maximum value of the function is (m ,n in N) (a) 1 (b) m^n.n^m (c) (m^m n^n)/((m+n)^(m+n)) (d) ((m n)^(m n))/((m+n)^(m+n))

The number of ways in which we can distribute m n students equally among m sections is given by a. ((m n !))/(n !) b. ((m n)!)/((n !)^m) c. ((m n)!)/(m ! n !) d. (m n)^m