List of practice Questions

Ankit, Arun, and Ankur have one apple each. Ankur also has one banana. Alam has one mango and one kiwi. Ankit has just bought one pineapple. Who has the least number of fruit(s)?

Which one of the following numbers is odd one out?
31541 42651 53791 64871 75981

Let $ f(x, y, z) = x^2 y^3 z $. Then, what is the value of \[ x \frac{\partial f}{\partial x}(x, y, z) + y \frac{\partial f}{\partial y}(x, y, z) + z \frac{\partial f}{\partial z}(x, y, z)? \]

If $ \times $ means $ + $, $ + $ means $ \div $, $ - $ means $ \times $, and $ \div $ means $ - $, then evaluate: 8 $ \times $ 7 $ - $ 8 $ + $ 40 $ \div $ 2.

Given a series $ 5, 8, 11, 14, \dots $, if the $ n $-th term of the given series is 320, then find $ n $ (where $ n \geq 1 $):

Vipul, Ahmad, Santosh, and David are playing Carrom. Vipul and Ahmad are partners sitting opposite to each other. David faces towards South. If Vipul faces towards West, then who faces towards the North?

Consider the function given below and pick one or more CORRECT statement(s) from the following choices.
\[ f(x) = x^3 - \frac{15}{2} x^2 + 18x + 20 \]

Which of the following statements is true in respect of diamagnetic substances?

The limit of $ \lim_{x \to 0} \frac{\sin x}{x} $ is:

Water from a hand pump located near a landfill has 1 mg/L arsenic (oral carcinogenic potency factor = 1.75 (kg-day)/mg). A person who lives nearby drinks 2 L/day of water from this hand pump for 10 years. Assume a body weight of 70 kg and an average life duration of 70 years. The chances of this person getting an excess risk of cancer is ________ × 10^-3 (rounded off to three decimal places).

An industry releases three greenhouse gases (GHGs), CO2 (5 kg/day), CH4 (0.5 kg/day), and N2O (0.1 kg/day). The industry flares the CH4 before it is released to the atmosphere. The Global Warming Potential (GWP) are as follows: CO2 = 1, CH4 = 21, N2O = 310. The annual GWP of GHGs released from the industry is ________ kg CO2 equivalent (rounded off to the nearest integer).

A solid waste of composition $ C_{60}H_{135}O_{50}N_5 $ is to be composted aerobically in a closed vessel mechanical composting facility. Given: all ammonia generated escapes the facility; air contains 23% of Oxygen by weight; 100% excess air requirement for the closed vessel composting facility. The atomic weights: C – 12, H – 1, O – 16, N – 14. The actual air required for composting is:

Length of the streets, in km, are shown on the network. The minimum distance travelled by the sweeping machine for completing the job of sweeping all the streets is ________ km. (rounded off to nearest integer)

An incandescent light bulb operated for two hours per day uses 12.2 kWh of energy per month. Burning of one kg of coal generates 2 kWh of electrical energy and releases 7 g of PM10. The reduction in PM10 emitted per month, if this incandescent bulb is replaced with a light emitting diode (LED) bulb which consumes 1/6th of energy, is ________ g (rounded off to one decimal place).

A particle dispersoid has 1510 spherical particles of uniform density. An air purifier is proposed to be used to remove these particles. The diameter-specific number of particles in the dispersoid, along with the number removal efficiency of the proposed purifier is shown in the following table:

The overall mass removal efficiency of the proposed purifier is ________% (rounded off to one decimal place).

A boiler burns coal at a rate of 1 kg/s. If the coal has 3% sulfur content, assuming that there is no sulfur in ash, SO2 emitted is ________ kg/day. (rounded off to nearest integer)

A common effluent treatment plant with a capacity of 2 million litres per day (MLD) employs reverse osmosis (RO) for water reuse. The RO unit removes 95% of the total dissolved solids (TDS) and the water recovery rate is 70%. If the TDS concentration in the RO feed is 8000 parts per million (ppm), the TDS in the RO reject is ________ g/L. (rounded off to one decimal place)

A circular sewer pipe, having Manning’s coefficient (n) of 0.01, is laid at a bed slope of 1:100. If it is flowing 80% full for a discharge of 2 m$^3$/s, then its diameter is ________ m. (rounded off to three decimal places)

Diameter ($d$) and length ($l$) of each pipe are as presented in figure and all pipes are of same material having friction factor ($f$) of 0.02. Assume acceleration due to gravity ($g$) as 10.0 m/s$^2$. If the head difference between $P$ and $Q$ is 10 m, then the head loss between $Q$ and $R$ is ________ m. (rounded off to two decimal places)

The following table and figure (not to scale) show characteristics of a catchment

The hyetograph resulting from a storm that occurred uniformly over the catchment, is as follows

Assuming a constant base flow of 40 m$^3$/s, the peak of the runoff hydrograph produced by storm for the catchment at the outlet $O$ is ________ m$^3$/s. (rounded off to two decimal places)

The following figure (not to scale) depicts a rainfall hyetograph for a storm over a catchment

If the storm produced a direct runoff of 12.5 mm, then the $\phi$-index of the storm for the catchment is ________ mm/hour. (rounded off to two decimal places)

Aerobic biomass has a yield coefficient value of 0.4 for glucose (molecular weight = 180 g/mole) substrate. The bacteria is represented as $ {C}_5{H}_7{O}_2{N} $ (molecular weight = 113 g/mole). Assume that no endogenous metabolism occurs. The percentage of carbon going into CO2 from 1 mole/L glucose is ________ % (rounded off to two decimal places).

Which of the following expressions can be deduced on the basis of dimensional analysis? (All symbols have their usual meanings)

The value of $ \int_0^\infty \frac{\sin(4x)}{\pi x} \, dx $ is ________

The following is a system of linear equations
x - 2y + z = 34 (1)
2x + y + z = 102 (2)
x + y - 3z = 17 (3)
The value of $ x + y + z $ is ________. (rounded off to two decimal places)