Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m². It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g = 10 m/s²)

Match List I with List II.               

List I                                                                                  List II

(a) Isothermal                                                                 (i) Pressure constant

(b) Isochoric                                                                    (ii) Temperature constant

(c) Adiabatic                                                                   (iii) Volume constant

(d) Isobaric                                                                      (iv) Heat content is constant

Choose the correct answer from the options given below:

The entropy of any system is given by S = ${\alpha }^2\beta \mathcal{l}n\left[\frac{\mu kR}{J{\beta }^2}+3\right]$ <!-- [if gte mso 9]><xml> </xml><![endif]--> Where a and b are the constants. $\mu$ , J, k and R no. of moles, mechanical equivalent of heat, Bolzmann constant and gas constant respectively. <!-- [if gte mso 9]><xml> </xml><![endif]-->  $[TakeS=\frac{dQ}{T}]$

Choose the incorrect option from the following:

In the reported figure, hear energy absorbed by a system in going through a cyclic process is_______ pJ.

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0°C to 50°C when no work is done is___________.  (R is the universal gas constant)