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 `1` b. `-1` c. `2` d. `-2`

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

Let n be an integer and x,y,z lt1 . Suppose Delta=|(x^(n+1),x^(n+2),x^(n+3)),(y^(n+1),y^(n+2),y^(n+3)),(z^(n+1),z^(n+2),z^(n+3))| If Delta=(x-y)(y-z)(z-x)x^(2)y^(2)z^(2) then n is equal to

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 |[x^(n-1), x^(n+1), x^(n+2)] ,[y^(n-1), y^(n+1), y^(n+2)], [z^(n-1), z^(n+1), z^(n+2)]|= (x-y)(y-z)(z-x)(x^(-1)+y^(-1)+z^(-1)) then n=

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

If x=a^(m+n),y=a^(n+1) and z=a^(l+m) prove that x^(m)+y^(n)z^(l)=x^(n)y^(l)z^(m)

If x=a^(m+n),y=a^(n+1) and z=a^(l+m) prove that x^(m)+y^(n)z^(l)=x^(n)y^(l)z^(m)

If x=a^(m+n),y=a^(n+l) and z=a^(l+m), prove that x^(m)y^(n)z^(l)=x^(n)y^(l)z^(m)

If y=x^(2)e^(x) ,show that y_(n)=(1)/(2)n(n-1)y_(2)-n(n-2)y_(1)+(1)/(2)(n-1)(n-2)}

|z|=1&z^(2n)+1!=0 then (z^(n))/(z^(2n)+1)-(z^(n))/(z^(2n)+1) is equal to