Let C₁ be the curve obtained by the solution of differential equation

$$2xy{{dy} \over {dx}} = {y^2} - {x^2},x > 0$$. Let the curve C₂ be the

solution of $${{2xy} \over {{x^2} - {y^2}}} = {{dy} \over {dx}}$$. If both the curves pass through (1, 1), then the area enclosed by the curves C₁ and C₂ is equal to :

Let P(x) = x² + bx + c be a quadratic polynomial with real coefficients such that $$\int_0^1 {P(x)dx} $$ = 1 and P(x) leaves remainder 5 when it is divided by (x $$-$$ 2). Then the value of 9(b + c) is equal to :

Let A = {2, 3, 4, 5, ....., 30} and '$$ \simeq $$' be an equivalence relation on A $$\times$$ A, defined by (a, b) $$ \simeq $$ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to :

If (x, y, z) be an arbitrary point lying on a plane P which passes through the points (42, 0, 0), (0, 42, 0) and (0, 0, 42), then the value of the expression
$$3 + {{x - 11} \over {{{(y - 19)}^2}{{(z - 12)}^2}}} + {{y - 19} \over {{{(x - 11)}^2}{{(z - 12)}^2}}} + {{z - 12} \over {{{(x - 11)}^2}{{(y - 19)}^2}}} - {{x + y + z} \over {14(x - 11)(y - 19)(z - 12)}}$$ is equal to :