A man starts walking from the point P($$-$$3, 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $$50\left( {{{(PR)}^2} + {{(RQ)}^2}} \right)$$ is equal to ____________.

A cube is placed inside an electric field, $$\overrightarrow E = 150{y^2}\widehat j$$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :

A square loop of side 20 cm and resistance 1$$\Omega$$ is moved towards right with a constant speed v₀. The right arm of the loop is in a uniform magnetic field of 5T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4$$\Omega$$. What should be the value of v₀ so that a steady current of 2 mA flows in the loop?

The temperature of an ideal gas in 3-dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at 300 K, is :

[m_e = mass of electron = 9 $$\times$$ 10^$$-$$31 kg, h = Planck constant = 6.6 $$\times$$ 6.6 $$\times$$ 10^$$-$$34 Js, k_B = Boltzmann constant = 1.38 $$\times$$ 10^$$-$$23 JK^$$-$$1]