If `m=a^x` and n=a^y,then `m^y,n^x=`

Find whether the following statements are true or false. If the statement is false, then write its correct statement: (i) If P={m,n} and Q={n,m},then PxxQ={(m,n),(n,m)} . (ii) If A and B are non-empty sets, then AxxB is a non-empty set of the ordered pairs (x,y) such that x in A and y in B .

Let S={(x,y)|x,y in R, x^2+y^2-10x+16=0} . The largest value of y/x can be put in the form of m/n where m, n are relatively prime natural numbers, then m^2+n^2=

If 1/ (m+i n) - (x-iy)/(x+iy) =0, where x,y,m,n are real and x+iy!=0 and m+i n!=0 , prove that m^2+n^2=1 .

If m and n are the order and degree of the differential equation (y'')^(5)+4 . ((y'')^(3))/(y''')+y'''=sin x, then

If x and y vary inversely, find the values of l, m and n :

If x and y vary inversely, find the values of l, m and n :

For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a_1y+a_2y^2+... , and a_1=a_2=10 , then a. m n c. m+n=80 d. m-n=20

Determine the values of m and n so that the following system of linear equations have infinite number of solutions: (2m-1)x+3y-5=0 . 3x+(n-1)y-2=0

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

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