How many 4-digit positive integers, which are divisible by 3, can be formed using the digits {1, 3, 4, 6, 7}, with the condition that no digit is used more than once in any number?
What is the sum of the following infinite series?
In a recent election, the allocation of valid votes among the four candidates A, B, C, and D is depicted in the accompanying pie chart. The total number of votes cast in this election was 1,15,000, of which 5,000 were invalid.
Based on the information provided, what is the combined total of valid votes received by candidates B and C?
If 6 men can accomplish half of a task in 12 days by working for 8 hours each day, how many men will be required to complete the entire task in 8 days while working 9 hours a day?
Which of the following options depicts the reflection of the figure shown below when the mirror is placed on the left side?
Consider two identical right circular cones arranged such that one is inverted and placed atop the other, both sharing a common circular base. If a cutting plane intersects the apexes of the stacked cones, what form will the outer edge of the resultant cross-section take?
Which of the following accurately depicts the order of atomic size?
Which of the following acts as the ultimate electron acceptor in the electron transport chain during the process of aerobic respiration?
The following table presents the techniques utilized for the removal of particles in a rapid sand filter, along with their corresponding descriptions.
Determine the correct association.
In a specific area, the temperature of the environment increases by 6°C for every kilometer in altitude. What is the state of atmospheric stability at this location?
As per the Sustainable Development Agenda established by the United Nations in September 2015, what is the total count of Sustainable Development Goals (SDGs), and what is the target year set for their completion?
Which of the following claims regarding the Montreal Protocol is NOT correct?
According to the regulations set forth by the United Nations Environmental Programme (UNEP) in 2004, what is the largest size that microplastics can be?
Considering that the ranks of the square matrices A and B are 3 and 4 respectively, which of the following statements is correct?
In a frequency distribution that exhibits positive skewness, which of the following statements is correct?
Which of the following statements regarding the settling of particles in wastewater treatment systems is/are correct?
The boundary between soap bubbles and air exhibits a surface tension of 0.054 N/m. Determine the internal pressure (in N/m2, rounded to two decimal places) within a soap bubble that has a diameter of 6 cm.
Given the two regression lines defined by the equations 3x - 2y 1 = 0 and 2x - y - 2 = 0, find the means of the x and y variables, respectively.
A gravity settling chamber with a height of ‘H’ and a length of ‘L’ is designed to address particulate air pollution. Within this chamber, the horizontal airflow velocity is ‘Vh’ and the terminal settling velocity of the given particle is ‘Vt’. Which of the following equations correctly illustrates the principle used to ascertain the minimum size of the target particle that can be removed with 100% efficiency?
Water is flowing entirely through a rectangular channel with dimensions of 3 m (width) × 2 m (height). The average flow velocity is 1 m/s. The frictional head loss is 1 m per kilometer. Assume the acceleration due to gravity (g) is 10 m/s². Which of the following statement(s) is/are correct?
Analyze the following initial value problem. What is the value of y when x is equal to ln2 (rounded to one decimal place)?
dy/dx = 2x − y, y(0) = 1
The equations of the regression lines are expressed as
3x - 2y - 10 = 0, 3y - 4x 24 = 0
What is the value of the correlation coefficient, rounded to two decimal places?
Calculate the final BOD of the sample in mg/l (rounded to two decimal places) given that the initial DO of a 10% diluted sample is 6.7 mg/l. After 5 days, the final DO of the mixture is observed to be 2 mg/l, and the oxygen consumption in the blank is recorded as 0.5 mg/l. Assume that k (base e) is equal to 0.23 day-1.
Considering the watershed and the isohyets depicted in the diagram, what is the average precipitation within the watershed represented in _______ mm (an integer value)?
With reference to the gate shown in the image, this gate will start to open automatically when the water level 'IT' above the hinge reaches _______ m (rounded to two decimal places).
A cyclone separator has a radius of 25 cm, and a particle is traveling alongside a gas stream at a velocity of 18 m/s. Determine the ratio of the centrifugal force to the gravitational force acting on the particle, rounded to two decimal places.
Assume the acceleration due to gravity (g) to be 9.8 m/s².
In a room, there are two sources of noise located adjacent to each other, with sound pressure levels recorded at 30 dB and 40 dB, respectively. What is the cumulative sound pressure level in the room, expressed in __________ dB (rounded to two decimal places)?
Use a reference sound pressure of 20 µPa.
An emissions stack from an industrial source discharges 100 g/s of CO at an effective height of H, with a wind velocity of 5 m/s. At a distance of 3 km downwind, the dispersion coefficients in the y-direction and z-direction are 50 m and 25 m, respectively. The concentration of CO at the centerline of the plume, measured 3 km downwind, is __________ mg/m³ (rounded to two decimal places).
Utilize the Gaussian plume model and assume π = 3.14. For the calculations, disregard any reactions and the impact of the ground on the plume.
An individual consumes 2.5 liters of water daily. A quality assessment of the water indicated that the Pb concentration in the water supply is 0.6 mg/L. Considering that this person has a weight of 75 kg, the amount of Pb exposure from this drinking water source for the individual is __________ mg/kg/day (rounded to 2 decimal places).
In a specific region, the annual gasoline usage is 30.6 million tons. The area required to grow sugarcane to produce enough bioethanol to completely replace the gasoline is __________ km² (an integer value).
The energy equivalence of ethanol is 67% that of gasoline, the density of gasoline is 850 kg/m³, the yield of bioethanol from sugarcane per hectare is 3750 L, and 1 km2 is equivalent to 100 hectares.