Tangents drawn from the point ($$-$$8, 0) to the parabola y² = 8x touch the parabola at $$P$$ and $$Q.$$ If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to :

Muon ($$\mu $$^$$-$$) is a negatively charged (|q| = |e|) particle with a mass m_{$$\mu $$} = 200 m_e, where m_e is the mass of the electron and e is the electronic charge. If $$\mu $$^$$-$$ is bond to a proton to form a hydrogen like atom, identify the correct statements.
(A)   Radis of the muonic orbit is 200 times smaller than that of the electron.
(B)   The speed of the $$\mu $$^$$-$$ in the n^th orbit is $${1 \over {200}}$$ times that of the electron in the n^th orbit.
(C)   The ionization energy of muonic atom is 200 timesmore than of an hydroen atom.
(D)   The momentum of the muon in the n^th orbit is 200 times more than that of the electron.

A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

A man in a car at location Q on a straight highway is moving with speed $$\upsilon $$. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum ?