Question

Match LIST-I with LIST-II (adopting standard notations):\[\begin{array}{|c|c|} \hline \textbf{LIST-I (Parameter)} & \textbf{LIST-II (Formula)} \\ \hline \\ \text{A. Cubic parabola equation} & \text{IV. $\dfrac{X^3}{6RL}$} \\ \\ \hline \\ \text{B. Shift in transition curve} & \text{II. $\dfrac{L^2}{24R}$} \\ \\ \hline \\ \text{C. Length of valley curve} & \text{III. $\dfrac{N S^2}{(1.50 + 0.035S)}$} \\ \\ \hline \\ \text{D. Length of summit curve} & \text{I. $\dfrac{N S^2}{4.4}$} \\ \\ \hline \end{array}\] Choose the most appropriate match from the options given below:

• A. A - I, B - II, C - III, D - IV
• B. A - III, B - IV, C - I, D - II
• C. A - I, B - III, C - II, D - IV
• D. A - IV, B - II, C - III, D - I

Hint:

Remember: Transition curves follow cubic parabola, shift is proportional to $L^2 / R$, and summit/valley curves depend on stopping sight distance.

Answer 1

The Correct Option is D

Step 1: Cubic Parabola Equation Identification. 
The standard cubic parabola equation for a transition curve is: \[ y = \frac{X^3}{6RL} \Rightarrow A \rightarrow IV \]

Step 2: Transition Curve Shift Calculation. 
The shift (S) is determined by: \[ S = \frac{L^2}{24R} \Rightarrow B \rightarrow II \]

Step 3: Valley Curve Length Determination. 
The length of a valley curve is calculated as: \[ L = \frac{N S^2}{(1.5 + 0.035S)} \Rightarrow C \rightarrow III \]

Step 4: Summit Curve Length Calculation. 
The length of a summit curve is given by: \[ L = \frac{N S^2}{4.4} \Rightarrow D \rightarrow I \]

Step 5: Final Conclusion. 
The correct matching is: A - IV, B - II, C - III, D - I. Therefore, the correct answer is (D).