Let `x^2+y^2+x y+1geqa(x+y)AAx ,y in R ,` then the number of possible integer (s) in the range of `a` is___________.

If (y^(2)-5 y)(x^(2)+2 x+4) lt 2 , for all x in R , then number of integers in the range of y is

Let y be an element of the set A={1,2,3,4,5,6,10,15,30} and x_(1) , x_(2) , x_(3) be integers such that x_(1)x_(2)x_(3)=y , then the number of positive integral solutions of x_(1)x_(2)x_(3)=y is

If R={(x,y): x,y in W, x ^(2)+y^(2)=25} , then find the domain and range or R.

Let z(x,y) =x^(2)y + 3xy^(4), x,y in R . Find the linear approximation for z at (2,-1).

If f(x+y)=f(x)+f(y)-x y-1AAx , y in Ra n df(1)=1, then the number of solution of f(n)=n , n in N , is 0 (b) 1 (c) 2 (d) more than 2

If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then find the interval in which y lies.

Let f(x+1/y) +f(x-1/y) =2f(x) f(1/y) AA x, y in R , y!=0 and f(0)=0 then the value of f(1) +f(2)=

If tan^(2) {pi(x+y)}+cot^(2) {pi (x+y)}=1+sqrt((2x)/(1+x^(2))) where x, y in R , then find the least possible value of y.

Let R="{"x , y")": x , y in R ,x^2+y^2lt=25} and R^(prime)={(x , y): x , y in R , ygeq4/9x^2}dot Then find the domain and range of RnnR^(prime)dot