The tangent and normal to the ellipse 3x² + 5y² = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is :

Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a distance $${3 \over 5}$$ from the origin. Then which one of the following points lies on any of these lines ?

If both the mean and the standard deviation of 50 observations x₁, x₂,..., x₅₀ are equal to 16, then the mean of (x₁ – 4)² , (x₂ – 4)² ,....., (x₅₀ – 4)² is :

If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha $$,where –1 $$ \le $$ x $$ \le $$ 1, – 2 $$ \le $$ y $$ \le $$ 2, x $$ \le $$ $${y \over 2}$$ , then for all x, y, 4x² – 4xy cos $$\alpha $$ + y² is equal to :