Let x, y are integers such that `81^ y -4^ x` =77. then 2x + 3y is -

The number of solutions (x, y) where x and y are integers, satisfying 2x^(2) + 3y^(2) + 2x + 3y=10 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

Let x, y, in R satisfy the condition such that sin x sin y + 3 cos y +4 sin y cos x=sqrt(26) . The value of tan^(2)x + cot^(2)y is equal to

If x and y are integers, what is x + y ? (1) 3^x = 81 (2) 5^x = (25)/(5^y)

Let [a] denotes the larger integer not exceeding the real number a if x and y satisfy the equations y=2[x]+3 and y=3[x-2[ simultaneously determine [x+y]

Let f(x) and g(x) be functions which take integers as arguments. Let f(x + y) =f(x)+ g(y) + 8 for all intege x and y. Let f(x) = x for all negative integers x and let g (8) = 17 . Find f(0).

Let x, y be real variable satisfying x^(2) + y^(2) + 8x - 10y - 59 = 0 Let a = max {(x-3)^(2) + (y-4)^(2) and b = min {(x-3)^(2) + (y-4)^(2)) , then a + b + 2010 is ______ .

How many integer pairs (x,y) satisfy x^(2) + 4y^(2) -2xy -2x - 4y -8=0 ?

Let x and y be positive real numbers and theta an angle such that theta!=(npi)/2 for any integer ndot Suppose (sintheta)/x=(costheta)/y and (cos^4theta)/(x^4)+(sin^4theta)/(y^4)=(97sin2theta)/(x^3y+x y^3), then the value of x/y+y/x is

Let A = {x_(1),x_(2),x_(3),x_(4), x_(5), x_(6),x_(7), x_(8)}, B= { y_(1), y_(2), y_(3), y_(4) } . The total number of function f : A to B that are onto and there are exactly three elements x in A such that f(x) = y_(1) is :