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).
The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct? Note:
In the given figure, PQRS is a square of side 2 cm, and PLMN is a rectangle. The corner \( L \) of the rectangle is on the side \( QR \). Side \( MN \) of the rectangle passes through the corner \( S \) of the square. What is the area (in cm\(^2\)) of the rectangle PLMN? Note:
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).
In levelling between two points A and B on the opposite banks of a river, the readings are taken by setting the instrument both at A and B, as shown in the table. If the RL of A is 150.000 m, the RL of B (in m) is ....... (rounded off to 3 decimal places).
A one-way, single lane road has traffic that consists of 30% trucks and 70% cars. The speed of trucks (in km/h) is a uniform random variable on the interval (30, 60), and the speed of cars (in km/h) is a uniform random variable on the interval (40, 80). The speed limit on the road is 50 km/h. The percentage of vehicles that exceed the speed limit is ........ (rounded off to 1 decimal place).