If `D=|[1, 1, 1], [1, 1+x, 1], [1, 1, 1+y]|` for `x!=0, y!=0` then `D` is (1) divisible by neither x nor y (2) divisible by both x and y (3) divisible by x but not y (4) divisible by y but not x

If D = |{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

Prove that x^(2n-1)+y^(2n-1) is divisible by x+y

Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9). Let R_1 be a relation in X given by R_1 = {(x, y) : x - y is divisible by 3} and R, be another relation on X given by R_2 = {(x, y) : {x, y}sub {1, 4, 7}} or {x,y} sub{2,5,8} or {x,y} sub {3,6,9} . Show that R_1 = R_2 .

If (x+1, y-2)=(3,1), find the values of x and y.

The point (1,2) lies inside the circle x^(2) + y^(2) - 2x + 6y + 1 = 0 .

Minimize Z=x+y subject to x-yle1, -x+yle1, x,y ge0

If A ={(x,y} ,x^2 +y^2 le 1 and y^2 le 1 -x} then the area of A is …..Sq. units .

x^(2)dy+(xy + y^(2))dx = 0, y = 1 when x = 1

Evaluate |{:(1,x,y),(1,x+y,y),(1,x,x+y):}|

[x sin^(2)((y)/(x)) - y] dx + x dy = 0, y = (pi)/(4) when x = 1