If $${3^{2\sin 2\alpha - 1}}$$, 14 and $${3^{4 - 2\sin 2\alpha }}$$ are the first three terms of an A.P. for some $$\alpha $$, then the sixth terms of this A.P. is:

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

Let $$\lambda \in $$ R . The system of linear equations
2x₁ - 4x₂ + $$\lambda $$x₃ = 1
x₁ - 6x₂ + x₃ = 2
$$\lambda $$x₁ - 10x₂ + 4x₃ = 3
is inconsistent for:

The product of the roots of the
equation 9x² - 18|x| + 5 = 0 is :