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Engineering Mathematics(8)Core(47)General Aptitude(10)

Engineering Mathematics

8 Questions

GATE→2025→Engineering Mathematics→Probability and Statistics

Q1

MCQ[1 Mark]

Four fair coins are tossed simultaneously. The probability that at least one tail turns up is

(A)

$\frac{1}{16}$

(B)

$\frac{15}{16}$

(C)

$\frac{7}{8}$

(D)

$\frac{1}{2}$

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q2

MCQ[1 Mark]

Let $\vec{A} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + \hat{j}$ where $\hat{i}$, $\hat{j}$, and $\hat{k}$ are unit vectors. The projection of $\vec{B}$ on $\vec{A}$ is

(A)

$\frac{1}{\sqrt{12}}$

(B)

$\frac{1}{\sqrt{6}}$

(C)

$\sqrt{6}$

(D)

$\frac{1}{\sqrt{2}}$

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q3

MCQ[1 Mark]

The value of $\lim_{x \to \pi/2} \left( \frac{\cos x}{x - \frac{\pi}{2}} \right)$ is

(A)

1

(B)

-1

(C)

0

(D)

$\pi$

Explanation

GATE→2025→Engineering Mathematics→Complex Variables

Q4

NAT[1 Mark]

The product of the roots of the equation $x^4 + 1 = 0$ is (answer in integer).

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q5

MCQ[2 Marks]

If $\frac{dy}{dx} + y = x$ and $y(0) = 0$, then the value of $y(1)$ is

(A)

e

(B)

$\frac{1}{e}$

(C)

1

(D)

-1

Explanation

GATE→2025→Engineering Mathematics→Numerical Methods

Q6

MCQ[2 Marks]

Let $f(x) = \ln x$. The first derivative $f'(x)$ is to be calculated at $x=1$ using numerical differentiation. $f'(1)$ is calculated using first order forward difference ($f_{FD}'$), first order backward difference ($f_{BD}'$), and second order central difference ($f_{CD}'$), using interval width $h=0.1$. The CORRECT order of the values of $f_{FD}'$, $f_{BD}'$, and $f_{CD}'$ is

(A)

$f_{FD}' > f_{CD}' > f_{BD}'$

(B)

$f_{CD}' > f_{BD}' > f_{FD}'$

(C)

$f_{BD}' > f_{FD}' > f_{CD}'$

(D)

$f_{BD}' > f_{CD}' > f_{FD}'$

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q7

MCQ[2 Marks]

The eigenvalues of the matrix $\begin{bmatrix} 3 & -1 & 1 \\ -1 & 5 & -1 \\ 1 & -1 & 3 \end{bmatrix}$ are $\lambda_1$, $\lambda_2$, and $\lambda_3$. The value of $\lambda_1 \lambda_2 \lambda_3 (\lambda_1 + \lambda_2 + \lambda_3)$ is

(A)

11

(B)

45

(C)

495

(D)

135

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q8

MSQ[2 Marks]

If a function $f(x)$ is continuous in the closed interval $[a, b]$ and the first derivative $f'(x)$ exists in the open interval $(a, b)$, then according to Lagrange's mean value theorem $\frac{f(b) - f(a)}{b-a} = f'(c)$. If $a=0$, $b=1.5$, and $f(x) = x(x-1)(x-2)$, then the value(s) of $c$ in $[a, b]$ is/are

(A)

0.50

(B)

0.75

(C)

1.00

(D)

1.50

Explanation

Core

47 Questions

GATE→2025→Core→Oil and Gas Well Testing

Q9

MCQ[1 Mark]

Which ONE of the following CANNOT be obtained from pressure transient analysis in well testing?

(A)

Formation damage

(B)

Average reservoir pressure

(C)

Solution gas-oil ratio

(D)

Drainage pore volume

Explanation

GATE→2025→Core→Petroleum Production Operations

Q10

MCQ[1 Mark]

The primary objective of the electrostatic grid in electrostatic heater-treater used in crude oil processing is to

(A)

separate sand particles.

(B)

promote coalescence of water droplets.

(C)

generate electrical energy from the kinetic energy of the feed.

(D)

prevent corrosion by the cathodic protection.

Explanation

GATE→2025→Core→Petroleum Production Operations

Q11

MCQ[1 Mark]

The maximum Polished Rod Load (PRL) in the operation of the sucker rod pump is observed near the

(A)

top of the stroke and the traveling valve is open.

(B)

top of the stroke and the traveling valve is closed.

(C)

bottom of the stroke and the traveling valve is open.

(D)

bottom of the stroke and the traveling valve is closed.

Explanation

GATE→2025→Core→Reservoir Engineering

Q12

MCQ[1 Mark]

Four curves designated as I, II, III, and IV are shown in the figure. $P_b$ is the bubble point pressure of a crude oil at the given temperature. Which ONE of the following options correctly depicts the solubility of asphaltene ($q_a$) in the crude oil with pressure ($P$) at a given temperature?

(A)

I

(B)

II

(C)

III

(D)

IV

Explanation

GATE→2025→Core→Oil and Gas Well Testing

Q13

MCQ[1 Mark]

$C_1$, $C_2$, and $C_3$ are the Dietz shape factors of three reservoirs with circular ($C_1$), square ($C_2$), and rectangular ($C_3$) shape of drainage area, respectively. The well is located at the geometric center of the reservoir. Which ONE of the following options is CORRECT about the shape factors?

(A)

$C_3 < C_2 < C_1$

(B)

$C_2 < C_1 < C_3$

(C)

$C_1 < C_2 = C_3$

(D)

$C_1 = C_2 < C_3$

Explanation

GATE→2025→Core→Oil and Gas Well Testing

Q14

MCQ[1 Mark]

Four curves designated as I, II, III, and IV are shown in the figure. $q_f$ is the bottomhole oil flow rate, $q_s$ is the surface oil flow rate, and $B_o$ is the oil formation volume factor. Which ONE of the following curves depicts the minimum wellbore storage effect?

(A)

I

(B)

II

(C)

III

(D)

IV

Explanation

GATE→2025→Core→Petroleum Production Operations

Q15

MCQ[1 Mark]

Match the entries in GROUP I with the entries in GROUP II. **GROUP I:** (P) Liquid hold-up (Q) Liquid carryover (R) Gas blowby (S) Gas dehydration **GROUP II:** (I) Water removal (II) Free gas escaping with liquid phase (III) Free liquid escaping with gas phase (IV) Fraction of pipe volume occupied by liquid

(A)

P-III; Q-IV; R-I; S-II

(B)

P-IV; Q-III; R-II; S-I

(C)

P-I; Q-II; R-IV; S-III

(D)

P-IV; Q-II; R-III; S-I

Explanation

GATE→2025→Core→Petroleum Formation Evaluation

Q16

MCQ[1 Mark]

Which ONE of the following rocks shows the highest reading in the natural gamma ray log?

(A)

Dolomite

(B)

Anhydrite

(C)

Oil Shale

(D)

Limestone

Explanation

GATE→2025→Core→Reservoir Engineering

Q17

MCQ[1 Mark]

Crude oil denser than pure water has the API gravity

(A)

less than $10^\circ$

(B)

between $10^\circ$ and $20^\circ$

(C)

between $20^\circ$ and $60^\circ$

(D)

more than $60^\circ$

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q18

MCQ[1 Mark]

Which ONE of the following options is CORRECT in relation to the standard drill pipe?

(A)

Nominal weight is equal to the actual weight.

(B)

Nominal weight is less than the actual weight.

(C)

Nominal weight is greater than the actual weight.

(D)

Nominal weight is twice the actual weight.

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q19

MCQ[1 Mark]

Four different multilateral well patterns (Forked, Branched, Dual opening and Splayed) are shown in the figure. Which ONE of the following options correctly identifies the multilateral well patterns?

(A)

I - Forked; II - Branched; III - Dual Opening; IV - Splayed

(B)

I - Dual Opening; II - Branched; III - Forked; IV - Splayed

(C)

I - Dual Opening; II - Splayed; III - Forked; IV - Branched

(D)

I - Branched; II - Dual Opening; III - Splayed; IV - Forked

Explanation

GATE→2025→Core→Reservoir Engineering

Q20

MCQ[1 Mark]

For a hydrocarbon reservoir, the following parameters are used in the general material balance equation (MBE): $N$ = Initial oil in place, stb $G$ = Initial volume of gas cap, scf $m$ = Ratio of initial gas cap volume to initial oil volume, rb/rb $S_{wi}$ = Initial water saturation $S_{oi}$ = Initial oil saturation $B_{oi}$ = Initial oil formation volume factor, rb/stb $B_{gi}$ = Initial gas formation volume factor, rb/scf The total pore volume (in rb) of the reservoir is

(A)

$\frac{G B_{gi} (1+m)}{1 - S_{oi}}$

(B)

$\frac{N B_{oi} (1-m)}{1 - S_{oi}}$

(C)

$\frac{N B_{oi} (1+m)}{1 - S_{wi}}$

(D)

$\frac{G B_{gi} (1-m)}{1 - S_{wi}}$

Explanation

GATE→2025→Core→Reservoir Engineering

Q21

MSQ[1 Mark]

Which of the following statement(s) is/are CORRECT?

(A)

Gradient of temperature is a vector.

(B)

Gradient of pressure is a vector.

(C)

Divergence of velocity is a vector.

(D)

Gradient of velocity is a scalar.

Explanation

GATE→2025→Core→Petroleum Production Operations

Q22

MSQ[1 Mark]

Which of the following statement(s) is/are CORRECT about the chemicals used for the processing of sour crude oil and natural gas?

(A)

Amine solutions cannot be regenerated after removal of $H_2S$ from natural gas.

(B)

Amine solutions in liquid form absorb $H_2S$ from natural gas.

(C)

Glycols become corrosive in the presence of oxygen.

(D)

Iron sponges cannot be used for $H_2S$ removal.

Explanation

GATE→2025→Core→Oil and Gas Well Testing

Q23

MSQ[1 Mark]

Consider the following diffusivity equation for the radial flow of a fluid in an infinite and homogeneous reservoir: $$\frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial P}{\partial r} \right) = \frac{1}{\eta} \frac{\partial P}{\partial t}$$ where $P$ denotes pressure, $r$ is radial distance, $t$ is time, and $\eta$ is diffusivity constant. Initial reservoir pressure is $P_i$. The condition(s) used in the derivation of analytical solution of the above equation for pressure transient analysis in an infinite acting reservoir is/are:

(A)

At time $t=0$, $P=P_i$ for all r.

(B)

Wellbore is treated as a line source.

(C)

As $r \to \infty$, $P \to P_i$ for all t.

(D)

At any radius r and time t, the pressure gradient $\frac{\partial P}{\partial r}$ is constant.

Explanation

GATE→2025→Core→Offshore Drilling and Production Practices

Q24

MSQ[1 Mark]

Which of the following offshore drilling platform(s) has/have legs on the seabed?

(A)

Jack up

(B)

Tension leg

(C)

Concrete gravity

(D)

Semi-submersible

Explanation

GATE→2025→Core→Enhanced Oil Recovery Techniques

Q25

MSQ[1 Mark]

Which of the following statement(s) is/are CORRECT about polymer flooding?

(A)

Viscous fingering in the reservoir decreases.

(B)

Viscosity of the displaced fluid increases.

(C)

Mobility of the displacing fluid increases.

(D)

Mobility ratio decreases.

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q26

NAT[1 Mark]

The hoisting system of a drilling rig contains 7 lines strung (ideal sheaves) with hook load of $3.0 \times 10^5\text{ kg}$. The static derrick load is ______ $\times 10^5\text{ kg}$ (rounded off to one decimal place).

Explanation

GATE→2025→Core→Reservoir Engineering

Q27

NAT[1 Mark]

Reservoir Quality Index (RQI) based on Kozeny-Carman equation as a function of permeability ($k$ in mD) and porosity ($\phi$ in fraction) is given by: $$RQI = C \sqrt{\frac{k}{\phi}}$$ where $C$ is a constant with a value of 0.0314. If a carbonate reservoir has the permeability of 152 mD and the porosity of 0.18, then the RQI is ______ $\mu m$ (rounded off to two decimal places).

Explanation

GATE→2025→Core→Enhanced Oil Recovery Techniques

Q28

NAT[1 Mark]

The ratio of number of production to injection wells for a regular Seven-Spot pattern is ______ (rounded off to one decimal place).

Explanation

GATE→2025→Core→Reservoir Engineering

Q29

NAT[1 Mark]

Natural gas is produced at a flow rate of $2\text{ MMscf/day}$ at the wellhead having temperature and pressure of $560^\circ\text{R}$ and $200\text{ psi}$, respectively. The apparent molecular weight and the compressibility factor ($z$) of the gas are estimated to be $20\text{ g/g-mole}$ and 0.8, respectively, at wellhead conditions. The gas formation volume factor ($B_g$) at the wellhead condition is ______ $\times 10^{-2}\text{ ft}^3/\text{scf}$ (rounded off to one decimal place).

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q30

MCQ[2 Marks]

Three different pressure profiles are shown in the figure. CSD is Casing Setting Depth. Match the entries in GROUP I with the entries in GROUP II: **GROUP I:** (P) Profile 1 (Q) Profile 2 (R) Profile 3 **GROUP II:** (I) Reduced wellbore integrity due to weak formation (II) Reduced wellbore integrity due to weak casing (III) Full wellbore integrity

(A)

P-I; Q-II; R-III

(B)

P-II; Q-III; R-I

(C)

P-III; Q-I; R-II

(D)

P-II; Q-I; R-III

Explanation

GATE→2025→Core→Petroleum Formation Evaluation

Q31

MCQ[2 Marks]

Match the well logging methods in GROUP I with their corresponding measured parameters in GROUP II. **GROUP I:** (P) Neutron log (Q) Density log (R) Microspherically Focused Log (MSFL) (S) Sonic log **GROUP II:** (I) Resistivity in the flushed/invaded zone (II) Hydrogen ion concentration in the formation (III) Interval transit time of a compressional wave (IV) Electron density of the formation

(A)

P-IV; Q-I; R-II; S-III

(B)

P-II; Q-IV; R-I; S-III

(C)

P-II; Q-III; R-IV; S-I

(D)

P-III; Q-IV; R-I; S-II

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q32

MCQ[2 Marks]

A drilling fluid with time-dependent rheology is used for the rotary drilling of a reservoir. The following equation describes the dependence of shear stress ($\tau$) on shear rate ($\dot{\gamma}$): $$\tau + \frac{\mu_0}{\alpha} \frac{d\tau}{dt} = \mu_0 \dot{\gamma}$$ where $\mu_0$ and $\alpha$ are constants. If the rotation of the drill pipe is stopped at time $t=0$ (so $\dot{\gamma} = 0$), then the relaxation behavior of the fluid stress with time is

(A)

$\tau \propto e^{-\frac{\mu_0 t}{\alpha}}$

(B)

$\tau \propto e^{\frac{\mu_0 t}{\alpha}}$

(C)

$\tau \propto e^{-\frac{\alpha t}{\mu_0}}$

(D)

$\tau \propto e^{\frac{\alpha t}{\mu_0}}$

Explanation

GATE→2025→Core→Petroleum Exploration

Q33

MCQ[2 Marks]

Classification of kerogen is based on the relative amount of Carbon (C), Hydrogen (H) and Oxygen (O). Which ONE of the following options is CORRECT about Type II kerogen?

(A)

It is low in aliphatic compounds and H:C ratio < 0.84.

(B)

It is rich in aliphatic compounds and H:C ratio < 0.84.

(C)

It is low in aliphatic compounds and H:C ratio > 1.0.

(D)

It is rich in aliphatic compounds and H:C ratio > 1.0.

Explanation

GATE→2025→Core→Offshore Drilling and Production Practices

Q34

MCQ[2 Marks]

A stationary tank is cylindrical in shape with two hemispherical ends and is horizontal, as shown in the figure. $R$ is the radius of the cylinder as well as of the hemispherical ends. The tank is half filled with an oil of density $\rho$ and the rest of the space in the tank is occupied by air. The air pressure, inside the tank as well as outside it, is atmospheric. The acceleration due to gravity ($g$) acts vertically downward. The net horizontal force applied by the oil on the right hemispherical end (shown by the bold outline in the figure) is

(A)

$\frac{1}{2} \rho g R^3$

(B)

$\frac{2}{3} \rho g R^3$

(C)

$\frac{3}{4} \rho g R^3$

(D)

$\frac{1}{3} \rho g R^3$

Explanation

GATE→2025→Core→Petroleum Formation Evaluation

Q35

MSQ[2 Marks]

Which of the following logging tool(s) underestimate(s) porosity in a gas-bearing formation?

(A)

Neutron log

(B)

Nuclear Magnetic Resonance (NMR) log

(C)

Sonic log

(D)

Density log

Explanation

GATE→2025→Core→Reservoir Engineering

Q36

MSQ[2 Marks]

The effect of pressure on various properties of black oil is shown in the figure. The bubble point pressure is $P_b$. Which of the following option(s) is/are CORRECT?

(A)

Curve 1 represents solution gas-oil ratio.

(B)

Curve 2 represents oil viscosity.

(C)

Curve 3 represents oil formation volume factor.

(D)

Curve 3 represents oil density.

Explanation

GATE→2025→Core→Health Safety and Environment in Petroleum Industry

Q37

MSQ[2 Marks]

Which of the following definition(s) related to fire and explosion is/are CORRECT?

(A)

Fire point is the lowest temperature at which the vapour above a liquid will continue to burn once ignited.

(B)

Deflagration is the explosion in which the reaction front moves at a speed greater than the speed of sound in the unreacted medium.

(C)

Detonation is the explosion in which the reaction front moves at a speed less than the speed of sound in the unreacted medium.

(D)

Flash point of a liquid is the lowest temperature at which it gives enough vapour to form an ignitable mixture with air.

Explanation

GATE→2025→Core→Oil and Gas Well Testing

Q38

MSQ[2 Marks]

Which of the following option(s) is/are CORRECT for well testing analysis of a reservoir?

(A)

Permeability, skin and reservoir geometry are calculated using data from pseudo steady state.

(B)

Permeability, skin and reservoir geometry are calculated using data from transient state.

(C)

Reservoir geometry is calculated using data from pseudo steady state.

(D)

Absolute open flow potential is calculated from back pressure test for a gas well.

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q39

MSQ[2 Marks]

In a capillary rise experiment with a capillary tube of length $l_1$, water rises to a height $h$ such that $h < l_1$. If the capillary tube is cut to a length $l_2$ such that $l_2 < h$ and the experiment is repeated, which of the following statements is/are CORRECT?

(A)

Water overflows from the top of the tube.

(B)

Water does not overflow from the top of the tube.

(C)

At equilibrium, radius of curvature of meniscus are same in both the experiments.

(D)

At equilibrium, radius of curvature of meniscus are different in both the experiments.

Explanation

GATE→2025→Core→Petroleum Formation Evaluation

Q40

NAT[2 Marks]

The formation resistivity factor ($F$) is related to the formation porosity ($\phi$) in a water-bearing carbonate formation by the following correlation: $$F = 0.9 \phi^{-2}$$ where $\phi$ is in fraction. The resistivity of the invaded zone of the formation obtained by the Microspherically Focused Log (MSFL) is $4.5\text{ }\Omega\text{m}$, and the resistivity of the mud-filtrate is $0.05\text{ }\Omega\text{m}$. The formation porosity is ______ % (rounded off to one decimal place).

Explanation

GATE→2025→Core→Reservoir Engineering

Q41

NAT[2 Marks]

The drainage oil-water capillary pressure data for a core retrieved from a homogeneous isotropic reservoir is listed in the table (at WOC = 4100 ft, $P_c = 0$). Assume densities of water and oil are $1.04\text{ g/cc}$ and $0.84\text{ g/cc}$, $g = 980\text{ cm/s}^2$, $\sigma = 35\text{ dynes/cm}$, $\theta = 0^\circ$. The depth of free-water level (FWL) is at ______ ft (rounded off to one decimal place).

Explanation

GATE→2025→Core→Petroleum Formation Evaluation

Q42

NAT[2 Marks]

The porosity of a formation with matrix density of $2.65\text{ g/cc}$ and fluid density of $1.0\text{ g/cc}$ is 0.15. The formation has shear modulus of 30 GPa and bulk modulus of 36 GPa. The compressional wave velocity in the formation is ______ $\times 10^3\text{ m/s}$ (rounded off to two decimal places).

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q43

NAT[2 Marks]

The hydrostatic pressure gradient in a vertical well drilled in a relaxed depositional basin is $0.452\text{ psi/ft}$. Assume that the gradient of effective horizontal stress with depth is constant in the drilling zone and has a value of $9.96 \times 10^{-2}\text{ psi/ft}$. The casing shoe is at 4000 ft depth. While drilling the bore hole below the casing shoe with 10 ppg mud, the maximum allowed standpipe pressure is ______ psi (rounded off to one decimal place).

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q44

NAT[2 Marks]

A vertical well is drilled up to a depth of 4000 ft. Further drilling starts with 10 ppg of fresh mud and $50000\text{ lbf}$ weight on bit (WOB). An equivalent circulation density (ECD) of 10.75 ppg was recorded. The total circulation pressure loss is estimated to be 110 psi. The decrease in hook load is ______ lbf (rounded off to one decimal place).

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q45

NAT[2 Marks]

A horizontal well is planned with two radial sections to land the target at an angle of $90^\circ$. The total vertical depth (TVD) between the surface and the target is 8000 ft. The buildup rate is $6^\circ$ per 100 ft in the first section and $9^\circ$ per 100 ft in the second section. The total angle built by the second section is $30^\circ$. The distance of the first kickoff point from the surface is ______ ft (rounded off to one decimal place).

Explanation

GATE→2025→Core→Reservoir Engineering

Q46

NAT[2 Marks]

The laboratory analysis data obtained from the core is as follows: Weight of clean dry core in air = $30\text{ g}$ Weight of core completely saturated with oil = $32\text{ g}$ Weight of saturated core completely immersed in oil = $24\text{ g}$ If the density of oil used for saturation of core during the experiment is $0.88\text{ g/cc}$, then the effective porosity of the core is ______ % (rounded off to two decimal places).

Explanation

GATE→2025→Core→Reservoir Engineering

Q47

NAT[2 Marks]

The Buckley Leverett frontal advance theory is employed to evaluate the performance of the water flooding operation in a horizontal reservoir. Given: Cross-sectional flow area = $40000\text{ ft}^2$ Payzone thickness = $20\text{ ft}$ Porosity = 20% Water injection rate = $1000\text{ rb/day}$ Distance between injection and production well = $1000\text{ ft}$ Cumulative pore volume of water injected (PVWI) at breakthrough = 0.5 The time of breakthrough is ______ days (rounded off to one decimal place). [Use: 1 acre = $43560\text{ ft}^2$ and $1\text{ bbl} = 5.615\text{ ft}^3$]

Explanation

GATE→2025→Core→Petroleum Production Operations

Q48

NAT[2 Marks]

A hydraulically fractured vertical well has fracture permeability of $4000\text{ mD}$, reservoir permeability of $80\text{ mD}$, fracture width of $0.12\text{ in}$, and fracture half-length of $1000\text{ ft}$. Dimensionless fracture conductivity is ______ $\times 10^{-4}$ (rounded off to one decimal place).

Explanation

GATE→2025→Core→Petroleum Production Operations

Q49

NAT[2 Marks]

An electrical submersible pump is to be installed to lift oil of $30^\circ\text{API}$ in a $10000\text{ ft}$ deep well. The oil formation volume factor ($B_o$) is $1.25\text{ rb/stb}$. The desired flow rate is $8000\text{ stb/day}$. Minimum suction pressure of the chosen pump is 200 psi. Inflow performance relationship shows a flowing bottomhole pressure of 2820 psi at the desired flow rate. Assuming casing pressure and weight of the gas in the annulus to be negligible, the minimum pump setting depth is ______ ft (rounded off to one decimal place).

Explanation

GATE→2025→Core→Oil and Gas Well Testing

Q50

NAT[2 Marks]

Log-log plot of pressure drop ($\Delta p$) versus time ($t$) obtained using well test data is matched with one of the Grigarten type curves. Thereafter, a point on the type curve is chosen with $P_D = 10$ and $t_D/C_D = 100$, where $P_D$, $t_D$, and $C_D$ are dimensionless pressure, dimensionless time, and dimensionless wellbore storage, respectively. The corresponding match point on the log-log plot is $\Delta p = 250\text{ psi}$ and $t = 10\text{ hrs}$. Oil flow rate is $500\text{ rb/day}$. Viscosity of oil is $1.5\text{ cP}$. Thickness of the reservoir is $10\text{ ft}$ and formation volume factor of oil is $1.2\text{ rb/stb}$. The permeability of the reservoir is ______ mD (rounded off to one decimal place).

Explanation

GATE→2025→Core→Oil and Gas Well Testing

Q51

NAT[2 Marks]

Correlation equations for gas compressibility factor ($z$) and viscosity ($\mu$) as functions of pressure ($p$) are given as below: $$z = C_1 p^{-0.25} ; \quad \mu = C_2 p^{1.25}$$ where $C_1$ and $C_2$ are constants, consistent with field units ($p$ in psi, $\mu$ in cP), with values 1.96 and $7 \times 10^{-4}$, respectively. Real gas pseudo pressure corresponding to a pressure of 2500 psi is ______ $\times 10^6\text{ psi}^2/\text{cP}$ (rounded off to two decimal places).

Explanation

GATE→2025→Core→Reservoir Engineering

Q52

NAT[2 Marks]

An isotropic and homogeneous oil reservoir has a porosity of 20%, thickness of 20 ft and total compressibility of $15 \times 10^{-6}\text{ psi}^{-1}$. Variation of flowing bottomhole pressure ($p_{wf}$) with time ($t$) under pseudo steady state of a drawdown test in the well (under radial flow condition) is given as: $$p_{wf} = 2850 - 5t$$ where pressure is in psi and time is in hours. During the well test, the oil flow rate is $1800\text{ rb/day}$. The drainage area of the reservoir is ______ acres (rounded off to two decimal places). [Use: 1 acre = $43560\text{ ft}^2$]

Explanation

GATE→2025→Core→Petroleum Production Operations

Q53

NAT[2 Marks]

A production tubing string of length $1500\text{ m}$ is tightly held by packers to prevent any expansion in either direction. Production of hot gases from the reservoir increases the temperature of the tubing by $20^\circ\text{C}$. The Young's modulus of elasticity of the tubing material is $3000\text{ N/m}^2$, and the linear coefficient of thermal expansion is $5 \times 10^{-6}$ per °C. Assuming no radial expansion, and neglecting the weight of the gas in the tubing and its viscosity, the increase in the stress of the tubing due to temperature rise is ______ $\text{N/m}^2$ (rounded off to two decimal places).

Explanation

GATE→2025→Core→Petroleum Exploration

Q54

NAT[2 Marks]

A homogeneous rock layer Q of density $2600\text{ kg/m}^3$ is lying below homogeneous rock layer P of density $2400\text{ kg/m}^3$. A compressional wave travels from P to Q. On reaching the interface of P and Q, this wave is incident normally and gets reflected and refracted. The velocity of the compressional wave is $2.7\text{ km/s}$ in the rock layer P and $3.5\text{ km/s}$ in layer Q. The ratio of reflection coefficient to the transmission coefficient at the interface is ______ (rounded off to two decimal places).

Explanation

GATE→2025→Core→Oil and Gas Well Drilling Technology

Q55

NAT[2 Marks]

A Newtonian fluid is transported through a smooth horizontal pipe of diameter $1\text{ m}$ at a flow rate of $3.14\text{ m}^3/\text{s}$. The length of the pipe is $1\text{ km}$. The viscosity of the oil is $0.02\text{ Pa}\cdot\text{s}$ and its density is $800\text{ kg/m}^3$. Consider the Darcy friction factor ($f$) for turbulent flow in a smooth pipe is given as: $$f = \frac{0.316}{Re^{0.25}}$$ Assuming fully-developed flow in the pipe, the pressure drop due to the frictional effect is ______ kPa (rounded off to two decimal places).

Explanation

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

Fish : Shoal :: Lion : _____ Select the correct option to complete the analogy.

(A)

Pride

(B)

School

(C)

Forest

(D)

Series

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q57

MCQ[1 Mark]

Identify the grammatically correct sentence:

(A)

It is I who am responsible for this fiasco.

(B)

It is myself who is responsible for this fiasco.

(C)

It is I who is responsible for this fiasco.

(D)

It is I who are responsible for this fiasco.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of $25\text{ km/h}$ and car Q travels East with a speed of $30\text{ km/h}$. Car P travels continuously but car Q stops for some time after travelling for one hour. If both the cars are at the same distance from X at 11:30 AM, for how long (in minutes) did car Q stop?

(A)

10

(B)

12

(C)

15

(D)

18

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

The ceiling function of a real number $x$, denoted by $ce(x)$, is defined as the smallest integer that is greater than or equal to $x$. Similarly, the floor function, denoted by $fl(x)$, is defined as the largest integer that is smaller than or equal to $x$. Which one of the following options is NOT correct for all possible values of $x$?

(A)

$ce(x) \ge x$

(B)

$fl(x) \le x$

(C)

$ce(x) \ge fl(x)$

(D)

$fl(x) < ce(x)$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches and lost 5% of the matches. If they play 3 more matches, what is the probability of P winning exactly 2 of these 3 matches?

(A)

$\frac{48}{125}$

(B)

$\frac{16}{125}$

(C)

$\frac{16}{25}$

(D)

$\frac{25}{48}$

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could. Q. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts and inimical local lords all of which would reduce their chances of getting gold to almost zero. R. All of them thought that easily they could lay their hands on gold and become wealthy overnight. S. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.

(A)

$P \to Q \to R \to S$

(B)

$Q \to S \to R \to P$

(C)

$S \to Q \to P \to R$

(D)

$S \to P \to R \to Q$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

If HIDE and CAGE are coded as 19-23-7-11 and 5-2-17-11 respectively, then what is the code for HIGH?

(A)

5-17-1-2

(B)

17-19-13-17

(C)

13-3-1-2

(D)

19-23-17-19

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q63

MCQ[2 Marks]

The given figure is reflected about the horizontal dashed line and then rotated clockwise by $90^\circ$ about an axis perpendicular to the plane of the figure. Which one of the following options correctly shows the resultant figure?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?

(A)

Circle; Square; Equilateral triangle; Isosceles triangle

(B)

Isosceles triangle; Equilateral triangle; Square; Circle

(C)

Equilateral triangle; Isosceles triangle; Square; Circle

(D)

Isosceles triangle; Square; Equilateral triangle; Circle

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

A final year student appears for placement interview in two companies, S and T. Based on her interview performance, she estimates the probability of receiving job offers from companies S and T to be 0.8 and 0.6, respectively. Let $p$ be the probability that she receives job offers from both the companies. Select the most appropriate option.

(A)

$0 \le p \le 0.2$

(B)

$0.4 \le p \le 0.6$

(C)

$0.2 \le p \le 0.4$

(D)

$0.6 \le p \le 1.0$

Explanation