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Engineering Mathematics(9)Core(46)General Aptitude(10)

Engineering Mathematics

9 Questions

GATE→2026→Engineering Mathematics→Probability and Statistics

Q1

MCQ[1 Mark]

Two identical cubic dice are rolled simultaneously. Which of the following is the probability that at least one of the face values of the two dice is greater than 3?

(A)

$\frac{1}{2}$

(B)

$\frac{3}{4}$

(C)

$\frac{1}{4}$

(D)

$\frac{3}{8}$

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q2

MCQ[1 Mark]

Which of the following options is CORRECT for the eigenvalues ($\lambda$) of the given matrix? $$\begin{bmatrix} 8 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 7 \end{bmatrix}$$

(A)

$\lambda = 1, 1, 1$

(B)

$\lambda = 8, 5, 7$

(C)

$\lambda = 0, 0, 0$

(D)

$\lambda = 40, 1, 35$

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q3

MCQ[1 Mark]

For a given matrix $A = \begin{bmatrix} 4 & 4 \\ 0 & 4 \\ -4 & 4 \end{bmatrix}$, and $A^T$ representing its transpose, which of the following options is the CORRECT representation of $A^T A$?

(A)

$\begin{bmatrix} 4 & 0 \\ 0 & -4 \end{bmatrix}$

(B)

$\begin{bmatrix} 32 & 0 \\ 0 & 48 \end{bmatrix}$

(C)

$\begin{bmatrix} 32 & 0 \\ 0 & 0 \\ 0 & 48 \end{bmatrix}$

(D)

$\begin{bmatrix} 4 & 0 \\ 0 & 0 \\ 0 & -4 \end{bmatrix}$

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q4

MCQ[1 Mark]

Given two vectors $\vec{U}$ and $\vec{V}$, which of the following options is CORRECT for the expansion of divergence, $\nabla \cdot (\vec{U} + \vec{V})$?

(A)

$\nabla \times \vec{U} + \nabla \times \vec{V}$

(B)

$\nabla \times \vec{U} - \nabla \times \vec{V}$

(C)

$\nabla \cdot \vec{U} + \nabla \cdot \vec{V}$

(D)

$\nabla \cdot \vec{U} - \nabla \cdot \vec{V}$

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q5

NAT[1 Mark]

The solution of the given expression is: $$\lim_{x \to \pi/2} \frac{\sin(\cos(x)) - \cos(x)}{\left(\frac{\pi}{2} - x\right)}$$

Explanation

GATE→2026→Engineering Mathematics→Complex Variables

Q6

MCQ[2 Marks]

Which of the following is the correct representation of the given expression? $$\frac{(1+i)^8}{(1-i)^6}$$ (A) $2e^{-i\frac{\pi}{2}}$ (B) -1 (C) $2e^{i\frac{\pi}{2}}$ (D) 1

(A)

$2e^{-i\frac{\pi}{2}}$

(B)

-1

(C)

$2e^{i\frac{\pi}{2}}$

(D)

1

Explanation

GATE→2026→Engineering Mathematics→Numerical Methods

Q7

MCQ[2 Marks]

The values of a function $f(x)$ at three different $x$ are given as: $f(0.90) = 7.75$, $f(1.00) = 9.00$, $f(1.10) = 10.35$ Using the central difference approximation method, which of the following is the CORRECT estimate of first differential, $f'(1.00)$ and second differential, $f''(1.00)$, respectively?

(A)

10.00 and 13.00

(B)

13.00 and 10.00

(C)

10.00 and 10.00

(D)

13.00 and 13.00

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q8

MCQ[2 Marks]

Consider a random continuous variable X and its distribution function $f(x)$. Which of the following options describes the Probability Density Function (PDF)?

(A)

$\frac{d}{dx}f(x)$

(B)

$\frac{d^2}{dx^2}f(x)$

(C)

$\int f(x) dx$

(D)

$\int \frac{1}{f(x)} dx$

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q9

NAT[2 Marks]

Consider a vector function $\vec{F} = (y-z+2)\hat{i} + (yz+8)\hat{j} - xz\hat{k}$, on the surface (S) in the XY plane at $z=0$ (as shown in the figure). Considering Stokes' theorem for space, the ABSOLUTE value of surface integral $\iint_{S} (\nabla \times \vec{F}) \cdot \hat{n} ds$ is

Explanation

Core

46 Questions

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q10

MCQ[1 Mark]

Which of the following is the basic mechanism of hydrocyclones and centrifuges used for solids control in a drilling operation?

(A)

Screening

(B)

Forced settling

(C)

Chemical flocculation

(D)

Dilution

Explanation

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q11

MCQ[1 Mark]

Which of the following is the role of stabilizer subs in the rotary drilling process?

(A)

To prevent the drill-string from falling into the wellbore

(B)

To keep casing equidistant from the wellbore wall

(C)

To assist in keeping the drill collars centralized

(D)

To isolate the wellbore fluid from the subsurface formations

Explanation

GATE→2026→Core→Reservoir Engineering

Q12

MCQ[1 Mark]

For a single-phase dry gas reservoir having a well producing only dry gas, E represents gas expansion factor and $B_g$ represents gas formation volume factor. Which of the following options is CORRECT?

(A)

$E \propto \frac{1}{B_g}$

(B)

$E \propto B_g$

(C)

$E \propto B_g^2$

(D)

$E \propto B_g^3$

Explanation

GATE→2026→Core→Latest Trends in Petroleum Engineering

Q13

MCQ[1 Mark]

Choose the correct option by matching the entries in Group X with their description in Group Y. **Group X:** (P) Gas hydrate (Q) Oil shale (R) Coal bed methane (S) Shale oil **Group Y:** (I) Gas is mostly present in adsorbed state (II) Sedimentary rock contains kerogen (III) Oil recovered from shale (IV) Gas is present inside the cages formed by water molecules

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2026→Core→Offshore Drilling and Production Practices

Q14

MCQ[1 Mark]

Which of the following statements is NOT CORRECT in the context of offshore operational environment?

(A)

The motion of ocean's surface can be due to energy transfer from wind to water.

(B)

Lunar tides are caused by the moon.

(C)

Solar tides are caused by the sun.

(D)

The motion of ocean's surface can be due to energy transfer from water to wind.

Explanation

GATE→2026→Core→Petroleum Production Operations

Q15

MCQ[1 Mark]

Which of the following has the most proppant carrying capacity during hydraulic fracturing process?

(A)

Pentane

(B)

Cross-linked gel

(C)

Slickwater

(D)

Untreated formation brine

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q16

MCQ[1 Mark]

A circular shaped reservoir has external radius of $r_e$. A well of radius $r_w$ lies in the centre of the reservoir. The part of the reservoir around the wellbore up to a radius of $r_s$ is damaged, where $r_w < r_s < r_e$. Formation damage causes additional pressure drop $\Delta P(r)$ that varies with radial distance $r$. Which of the following is TRUE about the additional pressure drop at the radial location, $r_s$ due to formation damage?

(A)

$\Delta P(r_s) = \Delta P(r_w)$

(B)

$\Delta P(r_s) = 0$

(C)

$\Delta P(r_s) = 2 \times \Delta P(r_w)$

(D)

$\Delta P(r_s) = 4 \times \Delta P(r_w)$

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q17

MCQ[1 Mark]

In a drawdown test, $P_D$, $t_D$, and $C_D$ are dimensionless pressure, dimensionless time, and dimensionless wellbore storage coefficient, respectively. In the early time of a drawdown test, fluid flow results from wellbore unloading. For this period, which of the following is the CORRECT representation of the relationship among these parameters?

(A)

$t_D = P_D C_D$

(B)

$C_D = P_D t_D$

(C)

$P_D = t_D C_D$

(D)

$t_D = P_D + C_D$

Explanation

GATE→2026→Core→Enhanced Oil Recovery Techniques

Q18

MSQ[1 Mark]

Which of the following is/are conventional Enhanced Oil Recovery method(s)?

(A)

Water flooding

(B)

In-Situ combustion

(C)

Surfactant flooding

(D)

Steam flooding

Explanation

GATE→2026→Core→Petroleum Production Operations

Q19

MSQ[1 Mark]

Which of the following improve(s) the productivity index of a vertical well in an oil reservoir?

(A)

Hydraulic fracturing

(B)

Increasing the perforation length

(C)

Increasing the skin factor

(D)

Reducing the oil viscosity by steam injection

Explanation

GATE→2026→Core→Petroleum Production Operations

Q20

MSQ[1 Mark]

Which of the following methods is/are used to separate water from crude oil-water emulsion?

(A)

Heating

(B)

Centrifugation

(C)

Addition of interfacial tension reducing agents

(D)

Electrostatic coalescence

Explanation

GATE→2026→Core→Offshore Drilling and Production Practices

Q21

MSQ[1 Mark]

Which of the following statements is/are CORRECT about the water injection well platforms?

(A)

These are meant for injection of gas through the injection well.

(B)

Metering devices are not required to determine injection rate of injection wells.

(C)

Metering devices are required to determine injection rate of injection wells.

(D)

Firefighting and life-saving equipment should be present on the platform.

Explanation

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q22

MSQ[1 Mark]

Which of the following options is/are representing the rheological behavior of a conventional drilling fluid?

(A)

Dilatant

(B)

Pseudoplastic

(C)

Thixotropic

(D)

Rheopectic

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q23

MSQ[1 Mark]

Pressure ($p$) as function of radius ($r$) and time ($t$) can be found from the analytical solution of radial diffusivity equation for homogenous and isotropic reservoir following Darcy law. For this solution, if $\frac{\partial p}{\partial t}$ is treated as constant, which of the following correctly describe(s) the state(s) of pressure change?

(A)

Transient

(B)

Pseudo-steady

(C)

Steady

(D)

Unsteady

Explanation

GATE→2026→Core→Offshore Drilling and Production Practices

Q24

MSQ[1 Mark]

Which of the following statements is/are CORRECT about the floating production, storage, and offloading systems (FPSOs)?

(A)

Existing tankers cannot be converted into FPSOs.

(B)

FPSOs can be selected in the absence of any pipeline infrastructure.

(C)

FPSOs cannot process the produced fluids.

(D)

FPSOs can be used for the storage of produced crude oil.

Explanation

GATE→2026→Core→Petroleum Formation Evaluation

Q25

MSQ[1 Mark]

For a radioactive material, if $N$ is the number of nuclei present at time $t$, and $\lambda$ is decay constant, then which of the following is/are CORRECT representation(s) of the rate of decay?

(A)

$-\frac{dN}{dt} = \lambda N^2$

(B)

$-\frac{dN}{dt} = \lambda N$

(C)

$-\frac{dN}{dt} = \frac{\lambda}{N^2}$

(D)

$-\frac{dN}{dt} = \frac{\lambda}{N}$

Explanation

GATE→2026→Core→Petroleum Formation Evaluation

Q26

MSQ[1 Mark]

Which of the following logging methods is/are NOT used for investigation in Cement Bond Logging (CBL)?

(A)

Gamma ray

(B)

Neutron

(C)

Electrical

(D)

Acoustic wave

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q27

NAT[1 Mark]

A circular reservoir with a well in the centre is producing oil at constant rate under pseudo steady state. The rate of pressure change measured at the wellbore is $1.0 \text{ psi/day}$. Pressure at the external radius of the reservoir at a certain time was 3500 psi. After 500 days, the pressure (in psi) at the external radius will be

Explanation

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q28

NAT[1 Mark]

When 92 ml of distilled water (density = $1.0 \text{ g/cm}^3$) is mixed with 23 grams of NaCl salt, the density of the resultant brine solution is $1.15 \text{ g/cm}^3$. The volume of the brine solution (in ml) is

Explanation

GATE→2026→Core→Reservoir Engineering

Q29

NAT[1 Mark]

An oil has a density of $50 \text{ lbm/ft}^3$ at Standard Temperature and Pressure (STP) conditions. The density of the oil (in °API) is [Given: water density is $62.4 \text{ lbm/ft}^3$ at STP]

Explanation

GATE→2026→Core→Petroleum Exploration

Q30

MCQ[2 Marks]

Choose the CORRECT match of the sedimentary rocks in GROUP X with their processes/mechanisms of formation in GROUP Y. **GROUP X:** (P) Evaporite (Q) Sandstone (R) Limestone (S) Siltstones **GROUP Y:** (I) Physical process mainly consisting of lithification or cementation of deposition (II) Chemical process and depositions by marine living organisms (III) Anaerobic deposition of organic materials in mud bed (IV) Evaporation and precipitations of marine water

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

Explanation

GATE→2026→Core→Petroleum Formation Evaluation

Q31

MCQ[2 Marks]

Which of the following "logging methods" in a borehole will provide the highest depth of investigation for a given marine formation?

(A)

Neutron

(B)

Sonic

(C)

Density

(D)

Resistivity

Explanation

GATE→2026→Core→Health Safety and Environment in Petroleum Industry

Q32

MCQ[2 Marks]

Choose the CORRECT match of the fire detection systems in GROUP X with their corresponding working mechanisms in GROUP Y. **GROUP X:** (P) Fusible plug loops (Q) Thermal and smoke detection system (R) Gas detection system **GROUP Y:** (I) Detects rise in temperature caused by fire and visible/invisible particles of combustion. (II) Functions based on drop in pressure that activates fire shutdown. (III) Detects flammables.

(A)

P-I; Q-II; R-III

(B)

P-II; Q-I; R-III

(C)

P-III; Q-I; R-II

(D)

P-II; Q-III; R-I

Explanation

GATE→2026→Core→Petroleum Production Operations

Q33

MCQ[2 Marks]

The sectional view of three different damaged regions (marked as P, Q and R) near the vicinity of a perforation is shown in the figure. Choose the correct option by matching the entries in GROUP X with corresponding terms in GROUP Y. **GROUP X:** P, Q, R **GROUP Y:** (I) Grain fracturing (II) Charge and core debris (III) Compacted pulverized zone

(A)

P-I; Q-II; R-III

(B)

P-II; Q-III; R-I

(C)

P-I; Q-III; R-II

(D)

P-II; Q-I; R-III

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q34

MCQ[2 Marks]

Real gas pseudo pressure is used to derive diffusivity equation for highly compressible fluid for which viscosity ($\mu$) and gas compressibility factor ($Z$) are functions of pressure ($p$). Which of the following represents the partial derivative of the real gas pseudo pressure with respect to time ($t$)?

(A)

$\frac{2p}{\mu Z} \frac{\partial p}{\partial t}$

(B)

$\frac{p^2}{2\mu Z} \frac{\partial p}{\partial t}$

(C)

$\frac{\mu Z}{2p} \frac{\partial p}{\partial t}$

(D)

$\frac{2\mu Z}{p^2} \frac{\partial p}{\partial t}$

Explanation

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q35

MCQ[2 Marks]

Stokes' law is used to calculate the settling rate in the drilling fluid for two batches (P and Q) of barite. The particle (spherical) size of barite from batch P is $75~\mu m$ and that for batch Q is $25~\mu m$. The particle settling rate in the drilling fluid for the batch P is ______ times that for the batch Q.

(A)

Four

(B)

Nine

(C)

Two

(D)

One

Explanation

GATE→2026→Core→Petroleum Formation Evaluation

Q36

MSQ[2 Marks]

Which of the following approaches is/are used to get the response of Formation Micro Scanner (FMS) log?

(A)

Optical

(B)

Electrical

(C)

Thermal

(D)

Nuclear

Explanation

GATE→2026→Core→Petroleum Formation Evaluation

Q37

MSQ[2 Marks]

Which of the following conditions is/are inferred using cross plots of neutron porosity $\phi_N$ and density porosity $\phi_D$?

(A)

Gas zone

(B)

Shale distribution

(C)

Water zone

(D)

Oil zone

Explanation

GATE→2026→Core→Reservoir Engineering

Q38

MSQ[2 Marks]

Which of the following is/are obtained using a core sample?

(A)

Porosity

(B)

Pore size distributions

(C)

Absolute permeability

(D)

Reservoir boundary

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q39

MSQ[2 Marks]

Pressure change and derivative type curves (Bourdet type curves) are used in the well test analysis. Which of the following statements is/are CORRECT about these type curves?

(A)

These curves are on Log-Log plot.

(B)

Horizontal axis is for dimensionless time $t_p$.

(C)

All derivative type curves merge in the middle time region.

(D)

Vertical axis is for dimensionless pressure $P_D$ only.

Explanation

GATE→2026→Core→Health Safety and Environment in Petroleum Industry

Q40

MSQ[2 Marks]

Which of the following is/are objective(s) of a safety system in offshore production platforms?

(A)

To prevent leak or overflow of hydrocarbons.

(B)

To prevent ignition of hydrocarbons released on the platform.

(C)

To prevent water coning in the reservoir.

(D)

To prevent gas coning in the reservoir.

Explanation

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q41

MSQ[2 Marks]

A wellbore has true vertical depth (TVD) of 10000 ft. The pore pressure of the formation fluid in the permeable stratum at the bottom of the wellbore is 6500 psig. Which of the following is/are the acceptable average static mud density value(s) (in lbm/gal) to prevent the flow of the formation fluid from the permeable stratum to the wellbore? [Given: $1 \text{ lbm/gal}$ mud is equivalent to $0.052 \text{ psi/ft}$]

(A)

13.8

(B)

11.3

(C)

11.8

(D)

13.2

Explanation

GATE→2026→Core→Petroleum Production Operations

Q42

MSQ[2 Marks]

Which of the following statements is/are CORRECT about the skin factor?

(A)

Successful hydraulic fracturing increases the skin factor.

(B)

Successful hydraulic fracturing decreases the skin factor.

(C)

Formation damage near wellbore increases the skin factor.

(D)

Formation damage near wellbore decreases the skin factor.

Explanation

GATE→2026→Core→Petroleum Formation Evaluation

Q43

NAT[2 Marks]

For a given reservoir of porosity, $\phi = 0.1$, the water saturation is equal to the irreducible water saturation. The BVI (Bulk Volume Irreducible) water saturation was estimated as 0.04 using NMR (Nuclear Magnetic Resonance) log. The permeability, $k$ in mD is estimated using the relation: $$k = 10^4 \phi^4 \left(\frac{FFI}{\phi - FFI}\right)^2$$ where FFI is the Free Fluid Index. Based on this information, the permeability (in mD) is

Explanation

GATE→2026→Core→Petroleum Production Operations

Q44

NAT[2 Marks]

The Inflow Performance Relationship (IPR) for a vertical well in a single-phase oil reservoir was found to be linear. The flowing bottomhole pressures are 4000 psi and 1000 psi at oil flow rates of 200 STB/day and $600 \text{ STB/day}$ respectively. At the flowing bottomhole pressure of 2875 psi, the value of flow rate (in STB/day) is

Explanation

GATE→2026→Core→Petroleum Production Operations

Q45

NAT[2 Marks]

A matrix acidizing job is planned on a sandstone pay zone at a depth of 7000 ft without formation breakdown by keeping a safety margin of 250 psi with the help of a coil tubing unit. Consider the fracture gradient of $0.7 \text{ psi/ft}$, average specific gravity of the injection fluid as 1.065, and frictional pressure drop of 200 psi. The maximum surface injection pressure (in psi) is [Given: Hydrostatic gradient (psi/ft) = $0.433 \times \text{Specific Gravity}$]

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q46

NAT[2 Marks]

A drawdown test data is analyzed to find out the permeability and skin factor of the reservoir using a semi-log plot. Flowing bottomhole pressure (in psi) is plotted on the linear scale against time (in hours). Flow rate is 1500 STB/day, oil formation volume factor is 1.2 RB/STB, oil viscosity is 1 cP, and thickness of the bed is 10 ft. After plotting, it is found that the slope of the straight line fitting the data in the middle time region is $-60 \text{ psi/log cycle}$. The permeability of the reservoir (in mD) is [RB: Reservoir Barrel; STB: Stock Tank Barrel]

Explanation

GATE→2026→Core→Petroleum Production Operations

Q47

NAT[2 Marks]

A conventional Sucker Rod Pumping (SRP) unit is being used for lifting 25 °API oil from a depth of 5000 ft. The maximum and minimum values of polished rod loads are 14300 lbf and 5200 lbf, respectively. The ideal counter balance load (in lbf) is

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q48

NAT[2 Marks]

Matthews-Brons-Hazebroek (MBH) plots are used to calculate the Dietz shape factor ($C_A$) for reservoirs of various shapes. The MBH plot for a right-angled triangle reservoir with a well in the centre shows a reading of dimensionless pressure $P_{D(MBH)} = 3.0$ at the modified dimensionless time $t_{DA} = 1.0$. The Dietz shape factor of this right-angled triangle reservoir is

Explanation

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q49

NAT[2 Marks]

A drilling fluid following power law model is being circulated in a wellbore at the rate of $600 \text{ gal/min}$. The internal diameter ($D_i$) of the drill-pipe is 4.276 inches. The power law parameter ($n$) for the drilling fluid in the applicable flow regime is 0.67. The wall shear-rate ($\dot{\gamma}_w$) inside the drill-pipe is given by the following equation: $$\dot{\gamma}_w = \left(\frac{3n+1}{4n}\right) \times \frac{8V}{D_i}$$ where $V$ is the average drilling fluid velocity inside the drill-pipe. The value of wall shear-rate inside the drill-pipe (in $\text{s}^{-1}$) is [Given: 1 gallon = $3785.4 \text{ cm}^3$; 1 inch = $2.54 \text{ cm}$]

Explanation

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q50

NAT[2 Marks]

The upper limit of the scale of the dial reading for a given rotational oilfield viscometer is $300^{\circ}$. At the rotational rate of 100 RPM, the highest possible effective (apparent) viscosity measurable (in cP) is [Given: $1^{\circ}$ dial reading is equivalent to $5.11 \text{ dynes/cm}^2$ or $0.511 \text{ Pa}$; $1 \text{ RPM} = 1.703 \text{ s}^{-1}$]

Explanation

GATE→2026→Core→Oil and Gas Well Testing

Q51

NAT[2 Marks]

Three wells are at the corners of an equilateral triangle inside an infinite acting reservoir. The reservoir is horizontal, homogenous and isotropic and has uniform thickness. Initial reservoir pressure is 3000 psi. If only one of the wells had been producing in the transient state, the pressure at the centre of equilateral triangle would have dropped by 100 psi after 60 days. If all the three wells started producing simultaneously in transient state at the same rate, then after 60 days since the start of production, the pressure at the centre of the equilateral triangle (in psi) is

Explanation

GATE→2026→Core→Reservoir Engineering

Q52

NAT[2 Marks]

Oil is being produced from an undersaturated oil reservoir (with no initial gas cap). The reservoir rock compressibility and water saturation are negligible. There is no water influx, and there is no water production from the well. The initial oil formation volume factor was $1.24 \text{ RB/STB}$. After production of oil for a short period of time, the reservoir pressure is still above the bubble-point pressure, and the oil formation volume factor has changed to $1.25 \text{ RB/STB}$. The calculated oil recovery factor (in fraction) is [RB: Reservoir Barrel; STB: Stock Tank Barrel]

Explanation

GATE→2026→Core→Reservoir Engineering

Q53

NAT[2 Marks]

Consider one-dimensional oil flow in a horizontal porous media having length of 2000 ft, constant cross-sectional area of $6000 \text{ ft}^2$ and absolute permeability of 50 mD. Oil of viscosity 2 cP is flowing along the length (perpendicular to the cross section) such that the pressure at the inlet and outlet are 2500 psig and 2200 psig, respectively. Using the Darcy's equation for single phase flow, the flow rate of the oil through this porous media (in bbl/day) is [$1 \text{ bbl} = 5.61 \text{ ft}^3$]

Explanation

GATE→2026→Core→Reservoir Engineering

Q54

NAT[2 Marks]

A gas reservoir has bulk volume of $10000 \text{ ft}^3$, connate water saturation of 0.2 and porosity of 0.2. There is no oil present in the reservoir. The gas formation volume factor, $B_g$ is $0.005 \text{ RCF/SCF}$. The volume of gas in-place for this reservoir (in SCF) is $\times 10^4$.

Explanation

GATE→2026→Core→Oil and Gas Well Drilling Technology

Q55

NAT[2 Marks]

A drill-string placed in a wellbore is composed of 6000 ft of drill-pipe having internal diameter of 4.67 inches. The drilling fluid is being pumped at the rate of 80 cycles/minute and the pump factor is $0.21 \text{ bbl/cycle}$. Assume the amount of drilling fluid in the drill-collar and drill-bit to be negligible. The time required to circulate the drilling fluid from the surface to the drill-bit (in minutes) is [$1 \text{ bbl} = 5.61 \text{ ft}^3$]

Explanation

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

Expedite, Hasten, Hurry, ______ Fill the blank by choosing a word with a meaning similar to that of the words given above.

(A)

Accelerate

(B)

Retard

(C)

Provide

(D)

Disable

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q57

MCQ[1 Mark]

A black square PQRS has been cut into two parts. One part of it is shown in Panel I. Which one of the shapes in Panel II is the other part?

(A)

(i)

(B)

(ii)

(C)

(iii)

(D)

(iv)

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

A day can only be cloudy or sunny. The probability of a day being cloudy is 0.5, independent of the condition on other days. What is the probability that in any given four days, there will be three cloudy days and one sunny day?

(A)

$1/4$

(B)

$3/4$

(C)

$2/3$

(D)

$3/8$

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

The values of Stock A and Stock B on a particular day are Rs. 50 and Rs. 80, respectively. An investor invests Rs. 100 in Stock A and Rs. 80 in Stock B. He sells all the stocks the next day when the value of Stock A is Rs. 55 and Stock B is Rs. 70. The profit made by the investor is Rs.

(A)

0

(B)

5

(C)

10

(D)

20

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q60

MCQ[1 Mark]

'When it is raining, peacocks dance.' Based only on this sentence, which one of the following options is necessarily true?

(A)

Peacocks dance only when it is raining.

(B)

When peacocks dance, it is raining.

(C)

When peacocks are not dancing, it is not raining.

(D)

When it is not raining, peacocks do not dance.

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

Water: P :: Food : Q Choose the P and Q combination from the options below to form a meaningful analogy.

(A)

P = Thirst; Q = Hunger

(B)

P = Drink; Q = Hunger

(C)

P = Thirst; Q = Satiated

(D)

P = Wet; Q = Critic

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

Two tiles are missing in Panel I. Which one of the options in Panel II is the appropriate choice for the missing tiles?

(A)

(i)

(B)

(ii)

(C)

(iii)

(D)

(iv)

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q63

MCQ[2 Marks]

Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the line segments between them represent intercity highways. A salesperson needs to make a trip. She needs to start from a city, visit each of the remaining cities exactly once, and finally return to the same city from which she started. Which one of the following options is then true?

(A)

Such a trip is possible for (i), but not for (ii).

(B)

Such a trip is possible for (ii), but not for (i).

(C)

Such a trip is possible for both (i) and (ii).

(D)

Such a trip is possible neither for (i) nor for (ii).

Explanation

GATE→2026→General Aptitude→Data Interpretation

Q64

MCQ[2 Marks]

The figure in Panel I below is a grid of cells with four rows and four columns. The numbers on the top and on the left represent the number of cells that are to be shaded in that column and row, respectively. Which one of the options shown in Panel II below represents the grid shaded correctly?

(A)

(i)

(B)

(ii)

(C)

(iii)

(D)

(iv)

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice in succession and the number on the top face is recorded each time. The probability that the sum of the two recorded numbers is a prime number is

(A)

$\frac{3}{36}$

(B)

$\frac{13}{36}$

(C)

$\frac{15}{36}$

(D)

$\frac{19}{36}$

Explanation