The area of the region bounded by y $$-$$ x = 2 and x² = y is equal to :

Let y = y(x) be the solution of the differential

equation (x $$-$$ x³)dy = (y + yx² $$-$$ 3x⁴)dx, x > 2. If y(3) = 3, then y(4) is equal to :

The value of

$$\mathop {\lim }\limits_{x \to 0} \left( {{x \over {\root 8 \of {1 - \sin x} - \root 8 \of {1 + \sin x} }}} \right)$$ is equal to :

Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals of the parallelogram is 11x + 7y = 9, then other diagonal passes through the point :