In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively?


We analyze the logic based on letter-number patterns. Let's look at the structure row-wise: 
Top Row:
N (14), U (21), F (6), (i) = ? 
Bottom Row:
H (8), L (12), O (15), (?) = ? 
Now map letters to positions in the alphabet: \[ N = 14, \quad U = 21, \quad F = 6, \quad H = 8, \quad L = 12, \quad O = 15 \] Compare these with the numbers in the second row: \[ 21 \leftrightarrow N = 14 \Rightarrow 14 + 7 = 21 \] \[ 14 \leftrightarrow U = 21 \Rightarrow 21 - 7 = 14 \] \[ 9 \leftrightarrow F = 6 \Rightarrow 6 + 3 = 9 \] \[ 6 \leftrightarrow (i) = ? \Rightarrow \text{To balance pattern} \Rightarrow (i) = L (12) \Rightarrow 12 - 6 = 6 \quad \checkmark \] 
Now the second row: \[ H = 8, \quad 12 \Rightarrow 8 + 4 = 12 \] (iv) = 8 ✔️ \[ L = 12, \quad (ii) = ? \Rightarrow 12 + 3 = 15 \Rightarrow (ii) = K (11) ✔️ \] \[ (iii) = 12 \Rightarrow O = 15 \Rightarrow 15 - 3 = 12 ✔️ \] So the correct set is: \[ (i) = L, \quad (ii) = K, \quad (iii) = 12, \quad (iv) = 8 \] Thus, the correct option is (D).
Shown below is an arrangement of closely stacked spheres. Assume each one to be in contact with its immediate neighbour. What is the total number of points where the spheres touch each other?
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is:
The words given below are written using a particular font. Identify the digit that does not belong to the same font.
Two soils of permeabilities \( k_1 \) and \( k_2 \) are placed in a horizontal flow apparatus, as shown in the figure. For Soil 1, \( L_1 = 50 \, {cm} \), and \( k_1 = 0.055 \, {cm/s} \); for Soil 2, \( L_2 = 30 \, {cm} \), and \( k_2 = 0.035 \, {cm/s} \). The cross-sectional area of the horizontal pipe is 100 cm², and the head difference (\( \Delta h \)) is 150 cm. The discharge (in cm³/s) through the soils is ........ (rounded off to 2 decimal places).

The most suitable test for measuring the permeability of clayey soils in the laboratory is ___________.
 
Consider the beam ACDEB given in the figure. Which of the following statements is/are correct:

For the beam and loading shown in the figure, the second derivative of the deflection curve of the beam at the mid-point of AC is given by \( \frac{\alpha M_0}{8EI} \). The value of \( \alpha \) is ........ (rounded off to the nearest integer).
