`x` and `y` are natural numbers such that `y<=6` .If `x_(1)` and `x_(2)` be two possible values of `x` for which `x^(2)y+x+y` is divisible by `xy^(2)+y+7` ; then find the value of `(x_(1)+x_(2))`

If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x , y , z) that satisfy the equation is 0 (b) 1 (c) 2 (d) Infinite solutions

Write down the domain and range of the relation (x,y): x=3y and x and y are natural numbers less than 10.

If x and y are positive real numbers such that x^(2)y^(3)=32 then the least value of 2x+3y is

If x and y are positive real numbers such that 2log(2y - 3x) = log x + log y," then find the value of " x/y .

If x and y are real numbers such that 16^(x^(2)+y)+16^(x+y^2)=1 , then find the values of x and y.

If a, b, x, y are positive natural numbers such that (1)/(x) + (1)/(y) = 1 then prove that (a^(x))/(x) + (b^(y))/(y) ge ab .

If x, y, z, t are odd natural numbers such that x + y + z +t=20 then find the number of values of ordered quadruplet (x, y, z, t).

If x, y, z, t are odd natural numbers such that x + y + z +w=20 then find the number of values of ordered quadruplet (x, y, z, t).

If x, y are rational numbers such that (x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1)sqrt(5) then

For oxyacid HClO_(x) , if x=y=z (x,y and z are natural numbers), then calculate the value of |x+y+z|. Where x=number of 'O' atoms y=total number of lone pairs at central atom z=total number of pi (pi) electrons in the oxyacid.