Consider a block kept on an inclined plane (incline at 45$$^\circ$$) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane($$\mu$$) is equal to :

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g = 10 m/s$$^2$$)

Given below are two statements :

Statement I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.

Statement II : Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.

In the light of the above statements, choose the correct answer from the options given below :

Two bodies of masses $$m_{1}=5 \mathrm{~kg}$$ and $$m_{2}=3 \mathrm{~kg}$$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $$\mathrm{m}_{1}$$ will be : [Take $$\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$$