List of practice Questions

Let $ \omega_f $ be the excitation frequency of a sinusoidal load and $ \omega_n $ be the natural frequency of a single degree of freedom system. Then the dynamic response of the system is highly affected by the stiffness of the system when:

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.
If the security guard does not move around the posted location and has a 360° view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery?

Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.
Which one of the following is the correct logical inference based on the information in the above passage?

Consider the following inequalities.
\text{(i) } 2x - 1 $>$ 7
\text{(ii) } 2x - 9 $<$1
Which one of the following expressions below satisfies the above two inequalities?

Four points $ P(0, 1), Q(0, -3), R(-2, -1), $ and $ S(2, -1) $ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?

In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below. Statement of P: R has copied in the exam.
Statement of Q: S has copied in the exam.
Statement of R: P did not copy in the exam.
Statement of S: Only one of us is telling the truth.
Statement of T: R is telling the truth.
The investigating team had authentic information that S never lies. Based on the information given above, the person who has copied in the exam is:

A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets ₹1000 more than S, what is the share of Q (in ₹)?

A trapezium has vertices marked as P, Q, R, and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm, and SP = 3 cm. What is the shortest distance between PQ and SR (in cm)?

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a "hole in the interior" that can be formed within the 4 $\times$ 4 grid using the unit squares as building blocks?

The hydrogen index (HI) of a potential source rock is 500. If 400 g of the same rock produces 6000 mg of hydrocarbons during a thermal pyrolysis at the maximum temperature, the calculated total organic content (TOC) of the rock is ____________ weight % (rounded off to one decimal place).

Mr. X speaks __________ Japanese __________ Chinese.

The initial water saturation in an oil reservoir with a free gas cap is 30%. The initial gas saturation is 40%. At the end of water flooding, all the free gases are dissolved due to the elevated pressure and the oil formation volume factor reaches a value of 1.20 rb/stb. The final water saturation at the end of water flooding is 50%. If the two-phase formation volume factor at the initiation of the water flood is 2.3 rb/stb, the pore-to-pore displacement efficiency under the current reservoir condition is ____________ % (rounded off to one decimal place).

The station survey data during the directional drilling at two locations are given below.

\[ \text{Dogleg angle} = \cos^{-1}[\cos\alpha_A \cos\alpha_B + \sin\alpha_A \sin\alpha_B \cos(\beta_A - \beta_B)] \] The calculated dogleg severity (dogleg angle per 100 m drilled section) is ________________ (rounded off to one decimal place).

A sandstone reservoir has the formation top at a depth of 3421 ft from the surface. The MDT tool records a pressure of 1560 psi at 3425 ft depth, and the sampled crude has a density of 35$^\circ$API. Considering a normal hydrostatic gradient (brine density 1.04 g/cc) and capillary displacement pressure of 1.2 psi, find the depth of the oil-water contact (OWC) from the surface (rounded off to two decimal places).

The drill pipes and drill collars with a combined length of 2500 m are held on the hook without rotation and mud flow. The specific gravity of the mud in the annulus is 1.5 and that inside the drill string is 1.4. The material density of the drill pipe and drill collar is 7850 kg/m$^3$. The specifications are given below.

The overall weight acting on the hook is ____________ kN (rounded off to two decimal places).

A drilling rig is designed with 12 lines strung between the crown block and traveling block. The hoisting system has an output power of 650 HP. When the drill string is pulled up at 52.5 ft/min, the fast line tension is 46180 lb. If the drill string is pulled at the same power and the fast line tension becomes 35690 lb, compute the new pullout speed (rounded off to one decimal place).

In a sandstone reservoir, the density log reads 2.11 g/cc and sonic log reads 90 μs/ft. The other parameters are given below: Matrix density ($\rho_{ma}$) = 2.68 g/cc Fluid density ($\rho_{fl}$) = 1.0 g/cc Compressional wave travel time in matrix ($\Delta t_{ma}$) = 54 μs/ft Compressional wave travel time in fluid ($\Delta t_{fl}$) = 189 μs/ft The calculated secondary porosity of the reservoir is ________________ % (rounded off to the nearest integer).

The Waxman–Smits equation to estimate water saturation for shaly sands is given as, \[ C_t = \phi^{m^} S_w^{n^} \left( C_w + \frac{B Q_v}{S_w} \right) \] where $ B $ is cation mobility and $ Q_v $ is cation exchange capacity per pore volume. Given parameters: Porosity ($\phi$) = 0.25
$B Q_v = 17.0\ \Omega^{-1}$
Cementation factor ($m^$) = 2.0
Resistivity of water ($R_w$) = 0.05 $\Omega\cdot m$
True formation resistivity ($R_t$) = 12 $\Omega\cdot m$
As per the dataset, the calculated water saturation ($S_w$) in oil zone is ________________ % (rounded off to the nearest integer).

A crude oil with a flowrate of 1000 kg/hr is to be cooled using water in a double-pipe counter-flow heat exchanger from a temperature of 80$^\circ$C to 40$^\circ$C. The water enters the exchanger at 20$^\circ$C and leaves at 40$^\circ$C. The specific heat capacities of the oil and the water at constant pressure are 2 kJ kg$^{-1}$ K$^{-1}$ and 4.2 kJ kg$^{-1}$ K$^{-1}$, respectively. The overall heat transfer coefficient is 0.25 kW m$^{-2}$ K$^{-1}$. Neglecting the heat loss and using the log mean temperature difference (LMTD) method, the minimum heat exchanger area (m$^2$) required for the operation is ____________ (rounded off to two decimal places).

In an oil reservoir undergoing water flooding, the areal and vertical sweep efficiencies are 0.75 and 0.85, respectively. The average water saturation behind the flood front is 0.63 at breakthrough, and the initial water saturation is 0.17. If the initial volume of in-situ oil at the start of water flooding is 3200 rb, the amount of oil produced during the water flooding is ____________ rb (rounded off to two decimal places).

In a three-dimensional $ xyz $-space, if $ \vec{v} = 3z \hat{i} + 2z \hat{j} + z \hat{k} $, and $ \text{curl}(\vec{v}) = a \hat{i} + b \hat{j} + c \hat{k} $, then the value of $ (a + b + c) $ is ________________ (in integer).

If Z is the standard normal variable having mean 0 and standard deviation 1, then the probability of occurrence of Z in the range of –3 to 3 is ________________ (rounded off to three decimal places). Given: \[ \text{erf}(z) \approx \tanh \left( \frac{167z}{148} + \frac{11z^3}{109} \right) \]

The local minimum value of the real function \[ f(x) = 2x^3 - 21x^2 + 36x - 20 \] is __________ (in integer).

Consider the following ordinary differential equation: \[ \frac{dy}{dx} = x^2y \] The initial value is $ y(0) = 1 $ and the step-size is 0.1. Solving this differential equation by Euler’s first-order method, the value of $ y(0.2) $ is ____________ (rounded off to three decimal places).

In a horizontal circular pipe, liquid and gas are flowing concurrently at the same superficial velocity. However, the average velocity of the gas is greater than the average velocity of liquid. If the slip velocity is equal to the superficial velocity of each of the phases, the fractional liquid holdup is ____________ (rounded off to two decimal places).