If the tangent to the curve, y = x³ + ax – b at the point (1, –5) is perpendicular to the line, –x + y + 4 = 0, then which one of the following points lies on the curve ?

If the line y = mx + 7$$\sqrt 3 $$ is normal to the hyperbola $${{{x^2}} \over {24}} - {{{y^2}} \over {18}} = 1$$ , then a value of m is :

Let S = {$$\theta $$ $$ \in $$ [–2$$\pi $$, 2$$\pi $$] : 2cos²$$\theta $$ + 3sin$$\theta $$ = 0}. Then the sum of the elements of S is

The value of cos²10° – cos10°cos50° + cos²50° is