| Group-I | Group-II | ||
| P | Trilobite | 1 | Periproct |
| Q | Brachiopod | 2 | Hypostome |
| R | Bivalve | 3 | Deltidial plate |
| S | Echinoid | 4 | Lunule |
A hydrocarbon \( C_n H_m \) is burnt in air (O\(_2\) + 3.78N\(_2\)). The stoichiometric fuel to air mass ratio for this process is
Note: Atomic Weight: C(12), H(1) Effective Molecular Weight: Air(28.8)
While doing Bayesian inference, consider estimating the posterior distribution of the model parameter (m), given data (d). Assume that Prior and Likelihood are proportional to Gaussian functions given by \[ {Prior} \propto \exp(-0.5(m - 1)^2) \] \[ {Likelihood} \propto \exp(-0.5(m - 3)^2) \] 
The mean of the posterior distribution is (Answer in integer)
Consider a medium of uniform resistivity with a pair of source and sink electrodes separated by a distance \( L \), as shown in the figure. The fraction of the input current \( (I) \) that flows horizontally \( (I_x) \) across the median plane between depths \( z_1 = \frac{L}{2} \) and \( z_2 = \frac{L\sqrt{3}}{2} \), is given by \( \frac{I_x}{I} = \frac{L}{\pi} \int_{z_1}^{z_2} \frac{dz}{(L^2/4 + z^2)} \). The value of \( \frac{I_x}{I} \) is equal to 
Suppose a mountain at location A is in isostatic equilibrium with a column at location B, which is at sea-level, as shown in the figure. The height of the mountain is 4 km and the thickness of the crust at B is 1 km. Given that the densities of crust and mantle are 2700 kg/m\(^3\) and 3300 kg/m\(^3\), respectively, the thickness of the mountain root (r1) is km. (Answer in integer)