The equation of the normal to the curve
y = (1+x)^2y + cos ²(sin^–1x) at x = 0 is :

If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to :

Let P(h, k) be a point on the curve
y = x² + 7x + 2, nearest to the line, y = 3x – 3.
Then the equation of the normal to the curve at P is :

If the tangent to the curve y = x + sin y at a point
(a, b) is parallel to the line joining $$\left( {0,{3 \over 2}} \right)$$ and $$\left( {{1 \over 2},2} \right)$$, then :