List of practice Questions

Consider the following statements:

P: According to the National Ambient Air Quality Standards (Central Pollution Control Board, Govt. of India, notification 2009), annual time-weighted average \( \text{PM}_{10} \) standard is more than \( \text{PM}_{2.5} \) standard.

Q: According to the National Air Quality Index released by Govt. of India in 2015, sub-index value of \( \text{PM}_{10} \) can be less than that of \( \text{PM}_{2.5} \).

Choose the correct option from the following:

For flood routing, consider the following statements:
P: Hydrologic routing method uses continuity equation and momentum equation
Q: Hydraulic routing method uses continuity equation and energy equation
Choose the correct option from the following:

Consider the following two series:
\[ \textbf{P: } \sum_{n=1}^{\infty} \frac{1}{n} \qquad \textbf{Q: } \sum_{n=1}^{\infty} \frac{1}{n^2} \]
Choose the correct option from the following:

You conducted a batch experiment in the lab for 10 minutes to degrade a toxic compound, which follows first-order kinetics. The compound degrades from \( 2 \times 10^{-3} \, {M} \) to \( 2 \times 10^{-4} \, {M} \). The information from the lab experiment will be used to design a plug flow reactor in field conditions.
Given field conditions:
• Flow rate of contaminated water to be treated: 1 m\(^3\)/hour
• Concentration of toxic compound in contaminated water: \( 5 \times 10^{-1} \, {M} \)
• Target concentration of toxic compound in treated water: \( 1 \times 10^{-4} \, {M} \)
• Temperature is the same in lab and field conditions.
The required volume of the plug flow reactor is ________ m\(^3\). (rounded off to two decimal places)

A tank has inflow, outflow, and a stirring mechanism. Initially, the tank holds 500 L of a brine solution of concentration 200 g/L. At \( t = 0 \), an inflow of another brine solution of concentration 100 g/L starts entering the tank at the rate of 15 L/minute. At the same time, the outflow of thoroughly stirred mixture also takes place at the same rate so that the volume of brine in the tank remains constant. The brine concentration \( C \) (g/L) in the tank at any time \( t \) (minute) can be expressed by the following differential equation: \[ \frac{dC}{dt} + 0.03 C = 3 \] The brine concentration in the tank at \( t = 1.5 \) hour is ________ g/L. (rounded off to two decimal places)

For a gradually varied flow, consider the following statements:
P: \( y_n>y_c>y \) in M3 surface profile
Q: \( y_n<y_c<y \) in S1 surface profile
where, \( y_n \) is normal depth, \( y_c \) is critical depth, and \( y \) is flow depth.
Choose the correct option from the following: