If `1,x/2,y` are in harmonic progression `(x,y!=0),` then the number of integral ordered pairs `(X, Y)` is

If, for positive real numbers x, y, z, the numbers x+y, 2y and y + z are in harmonic progression, then which one of the following is correct ?

If x and y satisfy the equations max(|x+y|,|x-y|)=1 and |y|=x-[x] , the number of ordered pairs (x, y).

If x lt 4 " and " x, y in {1, 2, 3, .., 10} , then find the number of ordered pairs (x,y).

If x lt 4 " and " x, y in {1, 2, 3, .., 10} , then find the number of ordered pairs (x,y).

If x lt 4 " and " x, y in {1, 2, 3, .., 10} , then find the number of ordered pairs (x,y).

If 0 le x le 2pi and 2^(cosec^(2)x)sqrt(1/2y^(2)-y+1)lesqrt(2) then the number of ordered pairs of (x,y) is

Consider the system in ordered pairs (x,y) of real numbers sin x+sin y=sin(x+y) , |x|+|y|=1 . The number of ordered pairs (x,y) satisfying the system is

Consider the system in ordered pairs (x,y) of real numbers sin x+sin y=sin(x+y) , |x|+|y|=1 . The number of ordered pairs (x,y) satisfying the system is

If x, y in [0, 2 pi] , then the total number of ordered pairs (x, y) satisfying the equation sinx cos y = 1 is