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

Engineering Mathematics

8 Questions

GATE→2024→Engineering Mathematics→Complex Variables

Q1

MCQ[1 Mark]

A complex number is defined as $z = x + iy$ with $i = \sqrt{-1}$. $\overline{z}$ is the complex conjugate of $z$. The imaginary part of $(2z + 4\overline{z} + 4iy)$ is

(A)

6

(B)

2

(C)

2y

(D)

3y

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q2

MCQ[1 Mark]

The solution of the initial value problem given by $y'' + y' - 2y = 0$; $y(0) = 3$, $y'(0) = 6$ is

(A)

$4e^x + e^{-2x}$

(B)

$4e^x - e^{-2x}$

(C)

$4e^x + 3e^{-2x}$

(D)

$4e^{-2x} - 3e^x$

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q3

MSQ[1 Mark]

For the given matrix $Q = \begin{bmatrix} \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ 0 & 1 & 0 \\ -\frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \end{bmatrix}$, which of the following statements is/are true?

(A)

Q is an orthogonal matrix

(B)

$Q^T = Q^{-1}$

(C)

Q is a singular matrix

(D)

Q is a symmetric matrix

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q4

NAT[1 Mark]

If $P = \begin{bmatrix} 2 & -1 \\ 2 & 2 \end{bmatrix}$, the product of the eigenvalues of $P$ is

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q5

NAT[1 Mark]

The number of ways in which a supervisor can choose four workers out of 10 equally competent workers is

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q6

MCQ[2 Marks]

Which ONE of the following is the implicit form of the solution for the differential equation given below? $$\frac{dy}{dx} + \frac{2x + 3y}{3x + 5y} = 0$$

(A)

$x^2 - 3xy - \frac{5y^2}{2} - C = 0$

(B)

$x^2 - 3xy + \frac{5y^2}{2} - C = 0$

(C)

$x^2 + 3xy - \frac{5y^2}{2} - C = 0$

(D)

$x^2 + 3xy + \frac{5y^2}{2} - C = 0$

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q7

MCQ[2 Marks]

Let $r(t) = \frac{\sin 3t}{t} \hat{i} + (t+2)^4 \hat{j} + (t+1)\frac{\sin t}{t} \hat{k}$. The value of $\lim_{t \to 0} r(t)$ is

(A)

0

(B)

$\hat{i} + 32\hat{j} - \hat{k}$

(C)

$3\hat{i} + 16\hat{j} + \hat{k}$

(D)

$3\hat{i} + 16\hat{j}$

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q8

NAT[2 Marks]

The value of $\int_{0}^{2} f(x) dx$ using Simpson's $1/3^{rd}$ rule with only one interior point is (round off to nearest integer) for $f(x) = 2 + 20x + 30x^5$.

Explanation

Core

47 Questions

GATE→2024→Core→Petroleum Production Operations

Q9

MCQ[1 Mark]

Absolute open flow potential of a well is the

(A)

maximum theoretical flow rate of reservoir fluid that a well can deliver.

(B)

minimum theoretical flow rate of reservoir fluid that a well can deliver.

(C)

flow rate of reservoir fluid from a well when the sandface pressure is 100 psia.

(D)

minimum flow rate of reservoir fluid when a well is stimulated.

Explanation

GATE→2024→Core→Reservoir Engineering

Q10

MCQ[1 Mark]

A constant composition expansion (CCE) test is conducted on a slightly compressible reservoir fluid sample in a pressure-volume-temperature (PVT) cell at $130^\circ\text{F}$. The relative fluid volume $(V/V_{sat})$ data is given. The bubble point pressure (psia) of the reservoir fluid is

(A)

2530

(B)

1650

(C)

1250

(D)

1095

Explanation

GATE→2024→Core→Oil and Gas Well Drilling Technology

Q11

MCQ[1 Mark]

Marsh funnel viscosity is reported as number of seconds required for one quart of drilling fluid sample to flow out of a Marsh funnel. The time of efflux of one quart of fresh water from a Marsh funnel at $70 \pm 5^\circ\text{F}$ is ______ seconds.

(A)

$21 \pm 0.5$

(B)

$26 \pm 0.5$

(C)

$31 \pm 0.5$

(D)

$36 \pm 0.5$

Explanation

GATE→2024→Core→Latest Trends in Petroleum Engineering

Q12

MCQ[1 Mark]

From the options given below, identify the process through which coal bed methane is produced.

(A)

Underground coal gasification

(B)

Open cast mining of coal

(C)

Depressurization, using vertical/horizontal wells

(D)

Underground coal combustion

Explanation

GATE→2024→Core→Petroleum Production Operations

Q13

MCQ[1 Mark]

Gas-liquid flow regimes for horizontal pipelines are shown below. Identify the correct pair from the list given below.

(A)

I-Stratified; II-Slug; III-Annular; IV-Bubbly

(B)

I-Slug; II-Bubbly; III-Annular; IV-Stratified

(C)

I-Annular; II-Slug; III-Stratified; IV-Bubbly

(D)

I-Slug; II-Stratified; III-Bubbly; IV-Annular

Explanation

GATE→2024→Core→Offshore Drilling and Production Practices

Q14

MCQ[1 Mark]

The speed of Tsunami is a function of

(A)

only water depth.

(B)

only wave height.

(C)

both water depth and wave height.

(D)

both wind speed and wave height.

Explanation

GATE→2024→Core→Offshore Drilling and Production Practices

Q15

MCQ[1 Mark]

Which ONE of the following is a POSITIVELY BUOYANT floating structure?

(A)

Jacket Platform

(B)

Semi-Submersible

(C)

Tension Leg Platform

(D)

Barge

Explanation

GATE→2024→Core→Reservoir Engineering

Q16

MCQ[1 Mark]

Which ONE of the following methods makes use of the centrifugal force for measuring the interfacial tension between two immiscible phases?

(A)

Pendant drop method

(B)

Spinning drop method

(C)

Du Noüy ring method

(D)

Wilhelmy plate method

Explanation

GATE→2024→Core→Petroleum Production Operations

Q17

MCQ[1 Mark]

Which ONE of the following can result in a negative value of skin factor near the wellbore?

(A)

Hydraulic fracturing

(B)

Fines migration

(C)

Asphaltene deposition

(D)

Clay swelling

Explanation

GATE→2024→Core→Enhanced Oil Recovery Techniques

Q18

MCQ[1 Mark]

For a schematically shown five-spot pattern, what is the ratio of number of production wells to the number of injection wells per pattern unit?

(A)

2

(B)

1

(C)

1/4

(D)

1/2

Explanation

GATE→2024→Core→Petroleum Exploration

Q19

MCQ[1 Mark]

Which ONE of the following options represents the waves generated during partitioning of acoustic energy at an interface inside the Earth?

(A)

Rayleigh waves

(B)

Love waves

(C)

Body waves

(D)

Surface waves

Explanation

GATE→2024→Core→Petroleum Exploration

Q20

MCQ[1 Mark]

"Earth is a low-pass filter". This implies it filters out which ONE of the following parameters in the subsurface?

(A)

Phase

(B)

Amplitude

(C)

Frequency

(D)

Velocity

Explanation

GATE→2024→Core→Petroleum Exploration

Q21

MCQ[1 Mark]

Which ONE is the correct formula for calculation of Foldage of a 2D seismic line?

(A)

$Foldage = (\frac{1}{2})(\text{number of geophones})(\frac{\text{geophone interval spacing}}{\text{shot interval spacing}})$

(B)

$Foldage = (\frac{1}{2})(\text{number of geophones})(\frac{\text{shot interval spacing}}{\text{geophone interval spacing}})$

(C)

$Foldage = (\frac{1}{2})(\text{number of shots})(\frac{\text{shot interval spacing}}{\text{geophone interval spacing}})$

(D)

$Foldage = (\frac{1}{2})(\text{number of shots})(\frac{\text{geophone interval spacing}}{\text{shot interval spacing}})$

Explanation

GATE→2024→Core→Oil and Gas Well Testing

Q22

MCQ[1 Mark]

Well tests can be classified as either 'single well productivity test' or 'descriptive reservoir test'. Which ONE of the following CANNOT be determined from a 'single well productivity test'?

(A)

Characteristics of the formation damage and other source of skin

(B)

Well deliverability

(C)

Characteristics of both vertical and horizontal reservoir heterogeneity

(D)

Identification of produced fluids and their respective volume ratios

Explanation

GATE→2024→Core→Oil and Gas Well Drilling Technology

Q23

MCQ[1 Mark]

Which mud type will have the highest acoustic velocity from the following options?

(A)

Mud with live oil at low temperature

(B)

Mud with dead oil at high temperature

(C)

Mud with live oil at high temperature

(D)

Mud with dead oil at low temperature

Explanation

GATE→2024→Core→Enhanced Oil Recovery Techniques

Q24

MSQ[1 Mark]

Which of the following is/are thermal enhanced oil recovery method(s)?

(A)

Alkali-surfactant-polymer flooding

(B)

In situ combustion

(C)

Steam assisted gravity drainage

(D)

Low salinity water flooding

Explanation

GATE→2024→Core→Health Safety and Environment in Petroleum Industry

Q25

MSQ[1 Mark]

Dilute sodium hydroxide is used in oilfield operations for enhanced oil recovery. For economic reasons, sodium hydroxide is delivered on site as anhydrous solid beads/cakes. This compound must be diluted on site by mixing water. Which of the following precautions must be followed during handling and preparation of dilute sodium hydroxide?

(A)

Use of Personal Protective Equipment (PPE) while handling and processing sodium hydroxide

(B)

Adequate ventilation to avoid exposure of sodium hydroxide aerosols

(C)

Stable supply of hot utility line as sodium hydroxide dilution is an endothermic reaction

(D)

Stable supply of cold utility line as sodium hydroxide dilution is an exothermic reaction

Explanation

GATE→2024→Core→Oil and Gas Well Drilling Technology

Q26

NAT[1 Mark]

A field rotational viscometer containing a drilling fluid gives a dial reading of $12^\circ$ and $20^\circ$ at rotor speeds of 300 rpm and 600 rpm, respectively. The drilling fluid is assumed to obey power law model, $\tau = K\dot{\gamma}^n$. The power law index, $n$, is (round off to two decimal places).

Explanation

GATE→2024→Core→Petroleum Formation Evaluation

Q27

NAT[1 Mark]

Shear wave velocity ($V_s$) in a limestone formation is $3600\text{ m/s}$. Assume that the modulus of incompressibility ($K$) is twice that of the modulus of rigidity ($G$), and the bulk density ($\rho_b$) of the formation is $2700\text{ kg/m}^3$. For this limestone formation, the compressional wave velocity ($V_p$) is ______ m/s.

Explanation

GATE→2024→Core→Reservoir Engineering

Q28

NAT[1 Mark]

Two reservoir sands A and B of same thickness are encountered in a well at different depths. The hydrocarbon in the shallow reservoir sand A is $10^\circ\text{API}$ whereas, in the deeper reservoir sand B, it is $20^\circ\text{API}$. For single phase incompressible systems, it may be assumed that the permeability in the deeper reservoir sand B is half of that of the shallow reservoir sand A, and the viscosity is directly proportional to the specific gravity of oil in respective sands. The ratio of the mobility in reservoir sand A to that of reservoir sand B is (round off to two decimal places).

Explanation

GATE→2024→Core→Reservoir Engineering

Q29

MCQ[2 Marks]

From the following figure, match the CORRECT set of liquid shrinkage curves from GROUP I with various crude oil systems from GROUP II. **GROUP I:** (P) Curve P (Q) Curve Q (R) Curve R (S) Curve S **GROUP II:** (I) High shrinkage crude oil (II) Low shrinkage crude oil (III) Ordinary black oil (IV) Near-critical crude oil

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Core→Reservoir Engineering

Q30

MCQ[2 Marks]

Match the following pressure-volume-temperature (PVT) studies from GROUP I with their objectives from GROUP II. **GROUP I:** (P) Constant composition expansion (Q) Differential liberation (R) Separator test (S) Slim tube experiment **GROUP II:** (I) to determine the minimum miscibility pressure for gas injection (II) to determine the saturation pressure of the crude oil (III) to mimic the reservoir performance during production (IV) to design and optimize the separator conditions

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Core→Reservoir Engineering

Q31

MCQ[2 Marks]

Hydrocarbon fluids usually are classified as dry gas, wet gas, gas condensate and black oil. Which ONE of the following combinations is the CORRECT pressure temperature phase diagram that represents the reservoir fluid type?

(A)

I-dry gas; II-wet gas; III-gas condensate; IV-black oil

(B)

I-dry gas; II-gas condensate; III-wet gas; IV-black oil

(C)

I-black oil; II-wet gas; III-gas condensate; IV-dry gas

(D)

I-gas condensate; II-black oil; III-wet gas; IV-dry gas

Explanation

GATE→2024→Core→Reservoir Engineering

Q32

MCQ[2 Marks]

Which ONE of the following is the CORRECT combination of dimensionless numbers and their force ratios? **Dimensionless Number:** (P) Froude Number (Q) Capillary Number (R) Reynolds Number (S) Bond Number **Ratio of Forces:** (I) Inertia/Gravity (II) Buoyancy/Capillary (III) Inertia/Viscous (IV) Viscous/Capillary

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Core→Offshore Drilling and Production Practices

Q33

MCQ[2 Marks]

From the standard flexible riser configurations shown schematically in the figure, choose the CORRECT combination.

(A)

I-Steep Wave; II-Lazy Wave; III-Steep S; IV-Lazy S

(B)

I-Lazy Wave; II-Steep Wave; III-Lazy S; IV-Steep S

(C)

I-Tethered Wave; II-Tethered S; III-Steep S; IV-Lazy S

(D)

I-Steep Wave; II-Lazy Wave; III-Tethered S; IV-Tethered Wave

Explanation

GATE→2024→Core→Petroleum Exploration

Q34

MCQ[2 Marks]

The figures below show the typical geometry of the subsurface strata in relation to the boundaries of the depositional sequences. Which ONE of the following options CORRECTLY represents the four seismic sequences with their corresponding names?

(A)

I-Onlap; II-Toplap; III-Erosional truncation; IV-Downlap

(B)

I-Onlap; II-Downlap; III-Erosional truncation; IV-Toplap

(C)

I-Erosional truncation; II-Toplap; III-Onlap; IV-Downlap

(D)

I-Erosional truncation; II-Downlap; III-Onlap; IV-Toplap

Explanation

GATE→2024→Core→Oil and Gas Well Testing

Q35

MCQ[2 Marks]

Which of the following tests is/are used to obtain reservoir deliverability ($kh/\mu$) information? 1. Exploration or appraisal well openhole wireline 2. Exploration or appraisal well Drill Stem Test (DST) 3. Development well openhole wireline 4. Development well Drill Stem Test (DST)

(A)

1 only

(B)

3 only

(C)

1 and 3

(D)

2 and 4

Explanation

GATE→2024→Core→Petroleum Formation Evaluation

Q36

MCQ[2 Marks]

The decay of Gamma ray energy in the Earth formation goes through three dominant processes represented by regions I, II, and III in the figure below. Which ONE of the following options is CORRECT?

(A)

I-Photoelectric effect; II-Pair production effect; III-Compton effect

(B)

I-Epithermal effect; II-Pair production effect; III-Photoelectric effect

(C)

I-Photoelectric effect; II-Compton effect; III-Pair production effect

(D)

I-Epithermal effect; II-Photoelectric effect; III-Compton effect

Explanation

GATE→2024→Core→Oil and Gas Well Testing

Q37

MCQ[2 Marks]

Consider single-phase radial flow of a fluid with constant viscosity and low compressibility... Match the flow regime with the CORRECT mathematical relation given in the table. **Flow Regime:** (P) Steady-state flow (Q) Transient flow (R) Pseudosteady-state flow **Mathematical Relation:** (I) $(\partial P / \partial t)_r = 0$ (II) $(\partial P / \partial t)_r = \text{constant}$ (III) $(\partial P / \partial t)_r = f(r,t)$

(A)

P-I; Q-II; R-III

(B)

P-I; Q-III; R-II

(C)

P-II; Q-II; R-I

(D)

P-II; Q-I; R-III

Explanation

GATE→2024→Core→Enhanced Oil Recovery Techniques

Q38

MSQ[2 Marks]

The microbial enhanced oil recovery method helps to recover oil by which one or more of the following phenomena?

(A)

Reducing the interfacial tension due to production of biosurfactants.

(B)

Stimulating the well due to production of acids.

(C)

Increasing the mobility ratio due to production of biopolymers.

(D)

Reducing the viscosity due to production of gases in situ.

Explanation

GATE→2024→Core→Petroleum Production Operations

Q39

MSQ[2 Marks]

Fixed roof tank for storage of organic liquids reduces volatile organic compound (VOC) emissions... The objective(s) of such a vent is/are to

(A)

control pressure build-up in the tank.

(B)

control vacuum generation in the tank.

(C)

add oil to the tank.

(D)

add water to the tank.

Explanation

GATE→2024→Core→Petroleum Production Operations

Q40

MSQ[2 Marks]

A choke is generally installed at the well head and/or downhole. The desired function(s) of the choke is/are to

(A)

protect surface equipment from damage.

(B)

avoid sand ingress problem.

(C)

regulate production rate.

(D)

ensure oil and water coning.

Explanation

GATE→2024→Core→Petroleum Production Operations

Q41

MSQ[2 Marks]

Which of the following options is/are CORRECT about the below mentioned hydrocarbons? LNG: Liquefied Natural Gas; LPG: Liquefied Petroleum Gas; NGL: Natural Gas Liquid; CNG: Compressed Natural Gas

(A)

LNG is primarily methane at approximately 110 K temperature

(B)

LPG is primarily propane and butane at standard temperature and pressure

(C)

NGL is primarily methane at standard temperature and pressure

(D)

CNG is primarily pentane at standard temperature and pressure

Explanation

GATE→2024→Core→Reservoir Engineering

Q42

MSQ[2 Marks]

Consider flow of two immiscible viscous fluids inside a thin slit of width $2B$. The flow rates of both the fluids are such that the planar interface is exactly at the center of the slit ($X=0$). Upper and lower boundaries are at $X=B$ and $X=-B$. $\tau_{XZ}^I$ and $\tau_{XZ}^{II}$ are shear stresses, $v_z^I$ and $v_z^{II}$ are velocities. Which of the following options represent(s) the CORRECT boundary condition(s)?

(A)

$|\tau_{XZ}^I| = |\tau_{XZ}^{II}|$ at $X=0$

(B)

velocity continuity at boundaries

(C)

no-slip condition at solid walls ($X=\pm B$)

(D)

shear stress continuity across fluid-fluid interface

Explanation

GATE→2024→Core→Reservoir Engineering

Q43

NAT[2 Marks]

Porosity and oil saturation of various core samples retrieved from a layered reservoir are given below along with layer thicknesses. Assuming uniform area of cross section for all the layers, the average oil saturation of the reservoir is ______ % (round off to one decimal place). [Layer 1: h=1.0 ft, phi=10%, So=60% Layer 2: h=1.5 ft, phi=15%, So=65% Layer 3: h=2.0 ft, phi=20%, So=70% Layer 4: h=2.5 ft, phi=25%, So=75%]

Explanation

GATE→2024→Core→Oil and Gas Well Drilling Technology

Q44

NAT[2 Marks]

If a weight of $P = 100\text{ N}$ is supported by two massless strings connected to the walls as shown in the figure, the value of $T_1$ is ______ N (round off to one decimal place).

Explanation

GATE→2024→Core→Reservoir Engineering

Q45

NAT[2 Marks]

A natural gas has the following composition: - $CO_2$: mole fraction 0.02, $M = 44$ - $CH_4$: mole fraction 0.93, $M = 16$ - $C_2H_6$: mole fraction 0.03, $M = 30$ - $C_3H_8$: mole fraction 0.02, $M = 44$ Assume $Z = 0.82$, $R = 10.73\text{ psia}\cdot\text{ft}^3/(lb\text{-mole}\cdot^\circ\text{R})$. Density at 2000 psia and $150^\circ\text{F}$ ($610^\circ\text{R}$) is ______ $\text{lb/ft}^3$ (round off to two decimal places).

Explanation

GATE→2024→Core→Enhanced Oil Recovery Techniques

Q46

NAT[2 Marks]

A surfactant enhanced oil recovery process has been employed on a sandstone reservoir: $A = 20\text{ acres}$, $h = 25\text{ ft}$, $\phi = 0.20$, $S_{orw} = 0.30$, $S_{orc} = 0.10$, $B_o = 1.05$, $E_v = 1$, $S_{oi} = 0.75$. The ratio of oil displaced due to surfactant flood to the original oil in place at reservoir condition is (round off to two decimal places).

Explanation

GATE→2024→Core→Petroleum Production Operations

Q47

NAT[2 Marks]

An ideal mixture of benzene and toluene is in equilibrium at a pressure of $750\text{ mm Hg}$ and temperature of $90^\circ\text{C}$. The concentration of benzene in the vapour phase in mole fraction is (round off to two decimal places). [Given Antoine equation: $\log_{10} P_i^0 = A_i - \frac{B_i}{T + C_i}$ with $T$ in $^\circ\text{C}$]

Explanation

GATE→2024→Core→Offshore Drilling and Production Practices

Q48

NAT[2 Marks]

The diameter and draft of a freely floating classical upright spar without moonpool is $30\text{ m}$ and $75\text{ m}$, respectively. The added mass in heave mode is 1.8 times the mass of the spar. The critical damping of the spar in heave mode is ______ $\times 10^6\text{ kg/s}$ (round off to one decimal place).

Explanation

GATE→2024→Core→Offshore Drilling and Production Practices

Q49

NAT[2 Marks]

A long vertical hollow steel pipe used as a column in an offshore structure follows Euler's column theory. The length, outer diameter and thickness of the pipe are $30\text{ m}$, $0.50\text{ m}$, and $0.03\text{ m}$, respectively. The Euler buckling load (assuming no environmental loads) of the pipe pinned at both the ends, is ______ kN (round off to one decimal place).

Explanation

GATE→2024→Core→Petroleum Formation Evaluation

Q50

NAT[2 Marks]

A core sample from a well-consolidated sand has a length of $10\text{ cm}$, diameter of $4\text{ cm}$, and a resistance ($r$) of $100\text{ }\Omega$ at $T_2 = 200^\circ\text{F}$ when completely saturated with brine. The resistivity $R_w(T_1)$ of brine is $0.5\text{ }\Omega\cdot\text{m}$ at $T_1 = 75^\circ\text{F}$. The cementation factor $m=2$ and tortuosity $a=1$. The porosity (in fraction) of the core sample using Archie's/Humble's formula at $200^\circ\text{F}$ is (round off to two decimal places).

Explanation

GATE→2024→Core→Petroleum Formation Evaluation

Q51

NAT[2 Marks]

In an exploratory well, both clean and dirty reservoir sand with quartz as major mineralogy is encountered. The fraction of shale volume ($V_{sh}$) in the dirty reservoir sand is 25% with grain density ($\rho_{sh}$) of $2.7\text{ g/cc}$, quartz grain density ($\rho_q$) of $2.65\text{ g/cc}$. Bulk density of clean sand is $2\text{ g/cc}$ and dirty sand is $2.25\text{ g/cc}$, fluid density $\rho_f = 1\text{ g/cc}$. The difference of porosity $(\phi_{Clean} - \phi_{Dirty})$ in fraction is (round off to three decimal places).

Explanation

GATE→2024→Core→Oil and Gas Well Drilling Technology

Q52

NAT[2 Marks]

The settling velocity ($v_s$) of a spherical particle in a Newtonian fluid using Stokes' law is $v_s = \frac{g d_s^2 (\rho_s - \rho_l)}{18 \mu}$. Density of barite is $4200\text{ kg/m}^3$ and drilled solid particle is $2600\text{ kg/m}^3$. Fluid density is $1300\text{ kg/m}^3$. The diameter of a drilled spherical solid particle that has the same settling velocity as a spherical barite particle of $0.1\text{ mm}$ diameter in the drilling fluid is ______ mm (round off to two decimal places).

Explanation

GATE→2024→Core→Oil and Gas Well Drilling Technology

Q53

NAT[2 Marks]

A two-cylinder reciprocating positive-displacement duplex/double-acting mud pump is used for mud circulation (delivering fluid on both forward and backward strokes, i.e., 2 displacements per cylinder per stroke cycle). Liner diameter = $15\text{ cm}$, piston rod diameter = $6\text{ cm}$, stroke length = $40\text{ cm}$, volumetric efficiency = $85\%$. The total volume of fluid displaced per complete pump cycle (2 cylinders $\times$ both strokes) is ______ $\text{cm}^3$ (round off to nearest integer).

Explanation

GATE→2024→Core→Reservoir Engineering

Q54

NAT[2 Marks]

Consider the displacement of oil by water through a 1D porous medium. $k_{ro}^0 = 0.8$, $k_{rw}^0 = 0.3$, $S_{or} = 0.35$, $S_{wr} = 0.25$, $\mu_w = 1\text{ cP}$, $\mu_o = 8\text{ cP}$. Normalized water saturation $S_w^* = \frac{S_w - S_{wr}}{1 - S_{or} - S_{wr}}$. Relative permeabilities: $k_{ro} = k_{ro}^0(1 - S_w^*)$, $k_{rw} = k_{rw}^0 S_w^*$. The mobility ratio corresponding to $S_w = 0.6$ is (round off to one decimal place).

Explanation

GATE→2024→Core→Petroleum Production Operations

Q55

NAT[2 Marks]

The invasion of a drilling fluid to a radius of $3\text{ ft}$ from the center of the wellbore into the formation has resulted in the development of skin. Permeability of the damaged skin zone is $50\text{ mD}$, unaffected formation permeability is $400\text{ mD}$, and wellbore radius is $0.25\text{ ft}$. The value of the skin factor is (round off to two decimal places).

Explanation

General Aptitude

10 Questions

GATE→2024→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

If '→' denotes increasing order of intensity, then the meaning of the words [drizzle → rain → downpour] is analogous to [______ → quarrel → feud]. Which one of the given options is appropriate to fill the blank?

(A)

bicker

(B)

bog

(C)

dither

(D)

dodge

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q57

MCQ[1 Mark]

Statements: 1. All heroes are winners. 2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes. III. Some winners are heroes. Which of the above inferences can be logically deduced from statements 1 and 2?

(A)

Only I and II

(B)

Only II and III

(C)

Only I and III

(D)

Only II

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

A student was supposed to multiply a positive real number $p$ with another positive real number $q$. Instead, the student divided $p$ by $q$. If the percentage error in the student's answer is 80%, the value of $q$ is

(A)

5

(B)

$\sqrt{2}$

(C)

2

(D)

$\sqrt{5}$

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

If the sum of the first 20 consecutive positive odd numbers is divided by $20^2$, the result is

(A)

1

(B)

20

(C)

2

(D)

$1/2$

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is

(A)

150

(B)

200

(C)

250

(D)

175

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. Yoko Roi stands (i) as an author for standing (ii) as an honorary fellow, after she stood (iii) the freedom of speech. Her writings that stand (iv)

(A)

(i) out, (ii) down, (iii) in, (iv) by

(B)

(i) down, (ii) out, (iii) by, (iv) in

(C)

(i) out, (ii) down, (iii) by, (iv) in

(D)

(i) out, (ii) in, (iii) by, (iv) down

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder. The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is

(A)

5/2

(B)

7/2

(C)

9/2

(D)

7/3

Explanation

GATE→2024→General Aptitude→Data Interpretation

Q63

MCQ[2 Marks]

The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true?

(A)

The risk reduction on increasing the steps/day from 0 to 10000 is less than the risk reduction on increasing the steps/day from 10000 to 20000.

(B)

The risk reduction on increasing the steps/day from 0 to 5000 is less than the risk reduction on increasing the steps/day from 15000 to 20000.

(C)

For any 5000 increment in steps/day the largest risk reduction occurs on going from 0 to 5000.

(D)

For any 5000 increment in steps/day the largest risk reduction occurs on going from 15000 to 20000.

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B. If viewed from direction Y, it will appear as

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation is

(A)

$120^\circ$

(B)

$60^\circ$

(C)

$90^\circ$

(D)

$180^\circ$

Explanation