`(x/y)^(n-1)=(y/x)^(n-3) then,n=`

(x+y)^(n) + (x-y)^(n) is equal to

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

Let m and n be positive integers and x,y gt 0 and x+y =k, where k is constant. Let f (x,y) = x ^(m)y ^(n), then: (a) f (x,y) is maximum when x= (mk)/(m+n) (b) f (x,y) is maximuim where x =y (c) maximum value of f (x,y) is (m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n)) (d) maximum value of f (x,y) is (k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))

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) ].

The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x +y)]^(n) , is

If |[x^n, x^(n+2), x^(n+3)], [y^n, y^(n+2), y^(n+3)], [z^n, z^(n+2), z^(n+3)]|=(x-y)(y-z)(z-x)(1/x+1/y+1/z), then n equals a. 1 b. -1 c. 2 d. -2

If y=a x^(n+1)+b x^(-n) , then x^2(d^2y)/(dx^2)= n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

If m =! n and (m + n)^(-1) (m^(-1) + n^(-1)) = m^(x) n^(y) , show that : x + y + 2 = 0.

If |[x^n,x^(n+2),x^(n+4)],[y^n,y^(n+2),y^(n+4)],[z^n, z^(n+2),z^(n+4)]|=(1/(y^2)-1/(x^2))(1/(z^2)-1/(y^2))(1/(x^2)-1/(z^2)) then n is __________.

If lta_(n)gtandltb_(n)gt be two sequences given by a_(n)=(x)^((1)/(2^(n)))+(y)^((1)/(2^(n))) and b_(n)=(x)^((1)/(2^(n))) -(y)^((1)/(2^n)) for all ninN . Then, a_(1)a_(2)a_(3) . . . . .a_(n) is equal to