Which of the following points lies on the tangent to the curve

x⁴e^y + 2$$\sqrt {y + 1} $$ = 3 at the point (1, 0)?

If x = 1 is a critical point of the function
f(x) = (3x² + ax – 2 – a)e^x , then :

If the point P on the curve, 4x² + 5y² = 20 is
farthest from the point Q(0, -4), then PQ² is equal to:

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, y = x²–1 below the x-axis, is :