" 1.(i) "x^(y)+y^(x)=a^(b)

If x ^(y) + y ^(x) = a ^(b) then show that (dy)/(dx) =- ((y x ^(y-1) + y^(x) log y)/( x ^(y) log x + x y ^(x -1)))

Simplify : : ( ( x+(1)/(y)) ^(a) ( x-(1)/(y))^(b))/((y+(1)/(x))^(a) (y-(1)/(x))^(b))

Let (x, y) be such that sin^(-1)(ax)+cos^(-1)(y)+cos^(-1)(bxy)=pi//2 . Match the statements in column I with statements in column II. {:("Column I", "Column II"), ("A) If a = 1 and b = 0, then (x, y)", "p) lies on the circle "x^(2)+y^(2)=1), ("B) If a = 1 and b = 1, then (x, y)", "q) lies on "(x^(2)-1)(y^(2)-1)=0), ("C) If a = 1 and b = 2, then (x, y)", "r) lies on y = x"), ("D) If a = 2 and b = 2, then (x, y)", "s) lies on "(4x^(2)-1)(y^(2)-1)=0):}

Find the square root of (a) -8-6i (b) (x^2)/(y^2)+ (y^2)/(x^2)-(1)/(i) ((x)/(y)-(y)/(x))-(9)/(4) .

If x^(y)=y^(x), then ((x)/(y))^(x/y) is equal to a.x^(y/x) b.x^((x)/(y)-1) c.1d.x^((x)/(y))

The expression ((x+(1)/(y))^(a)*(x-(1)/(y))^(b))/((y+(1)/(x))^(a)*(y-(1)/(x))^(b)) reduces to a.((x)/(y))^(a-b) b.((y)/(x))^(a-b)backslash c((x)/(y))^(a+b)d.((y)/(x))^(a+b)

If _(i-1)(x_(i)^(2)+y_(i)^(2))<=2x_(1)x_(3)+2x_(2)x_(4)+2y_(2)y_(3)+2y_(1)y_(4)sum_(i-1)^(4)(x_(i)^(2)+y_(i)^(2))<=2x_(1)x_(3)+2x_(2)x_(4)+2y_(2)y_(3)+2y_(1)y_(4) the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),(x_(4),y_(4)) are the vertices of a rectangle collinear the vertices of a trapezium none of these

Let x_1, x_2, ...... ,x_n be values taken by a variable X a n d y_1, y_2,.......... ,y_n be the values taken by a variable Y such that y_i=a x_i+b ,i=1,2,3.... Then, (a) Var.(Y)= a^2Var.(X) (b) Var.(X)=a^2Var.(Y) (c) Var.(X)=Var.(X)+b (d) none of these

If z=x+i y, z^(1 / 3)=a-i b and (x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then the value of k=