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:

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :

If the four complex numbers $$z,\overline z ,\overline z - 2{\mathop{\rm Re}\nolimits} \left( {\overline z } \right)$$ and $$z-2Re(z)$$ represent the vertices of a square of side 4 units in the Argand plane, then $$|z|$$ is equal to :