Back to Years

Type:ALLMCQNATMSQ

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

Engineering Mathematics

8 Questions

GATE→2023→Engineering Mathematics→Complex Variables

Q1

MCQ[1 Mark]

Let $z_1$ and $z_2$ be two arbitrary complex numbers with non-zero modulus. Which of the following conditions is FALSE?

(A)

$|z_1 + z_2| > |z_1| + |z_2|$

(B)

$0 \le |z_1 + z_2| < \infty$

(C)

$|z_1 + z_2| \le |z_1| + |z_2|$

(D)

$|z_1 z_2| = |z_1| |z_2|$

Explanation

GATE→2023→Engineering Mathematics→Numerical Methods

Q2

MCQ[1 Mark]

In the $4^{th}$ order Runge-Kutta method for solving ordinary differential equations with step size $h < 1$, the ratio of the order of local truncation error to the order of global error is

(A)

h

(B)

$h^2$

(C)

$\frac{1}{h}$

(D)

$\frac{1}{h^2}$

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q3

NAT[1 Mark]

Let $X$ be a $3 \times 3$ matrix with $\det(X) = 5$. The determinant of matrix $Y$ obtained by multiplying row 2 by 2 and row 3 by 3 is

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q4

NAT[1 Mark]

Consider a vector field $\vec{V} = x^3 \hat{i} + 2y^2 x \hat{j} + 0.5z \hat{k}$. The divergence of $\vec{V}$ at the point $(1, 2, 1)$ is (rounded to one decimal place).

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q5

MCQ[2 Marks]

The value of $\int_{0}^{\pi} \int_{-1}^{1} r^2 \sin^2 \theta \, dr \, d\theta$ is

(A)

$\frac{\pi}{4}$

(B)

$\frac{\pi}{8}$

(C)

$\frac{\pi}{16}$

(D)

$\frac{\pi}{3}$

Explanation

GATE→2023→Engineering Mathematics→Numerical Methods

Q6

NAT[2 Marks]

Using Simpson's one-third rule (with step size $h = 0.25$), the area under the curve $y = e^{-x^3}$, from $x = 0$ to $x = 1$ is (rounded to two decimal places).

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q7

NAT[2 Marks]

The directional derivative of $f = x^3 + 4y^2 + z^2$ at the point $P(2, 1, 3)$ in the direction of the vector $\vec{V} = 3\hat{i} - 4\hat{k}$ is (rounded to one decimal place).

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q8

NAT[2 Marks]

A switch-over event in a producing well occasionally results in a reportable oil leak with probability 1 in 500. With 10 switch-over events per day following a Poisson distribution, the number of days in a 365-day year with no reportable oil leaks is (rounded to nearest integer).

Explanation

Core

47 Questions

GATE→2023→Core→Petroleum Formation Evaluation

Q9

MCQ[1 Mark]

Which of the following instruments can measure contact angle of a liquid drop placed on a surface?

(A)

Goniometer

(B)

Pycnometer

(C)

Soxhlet apparatus

(D)

Rheometer

Explanation

GATE→2023→Core→Petroleum Production Operations

Q10

MCQ[1 Mark]

Which of the following is the primary role of proppants in hydraulic fracturing?

(A)

Keep the fractures open during production

(B)

Decrease the viscosity of fracturing fluid

(C)

Decrease the density of fracturing fluid

(D)

Reduce the viscosity of crude oil in reservoir

Explanation

GATE→2023→Core→Health Safety and Environment in Petroleum Industry

Q11

MCQ[1 Mark]

A mixture of a flammable gas and air can ignite ONLY if

(A)

the gas concentration is below the limiting oxygen concentration

(B)

the gas concentration is above the upper flammable limit

(C)

the gas concentration is between the lower and upper flammable limits

(D)

the gas concentration is below the lower flammable limit

Explanation

GATE→2023→Core→Reservoir Engineering

Q12

MCQ[1 Mark]

Which of the following relations defines the coefficient of isothermal compressibility ($C_g$) for a gas? (Here, $p, T$, and $v$ represent pressure, temperature, and volume)

(A)

$C_g = -\frac{1}{v} \left(\frac{\partial v}{\partial p}\right)_T$

(B)

$C_g = -\frac{1}{v} \left(\frac{\partial p}{\partial v}\right)_T$

(C)

$C_g = -\frac{1}{p} \left(\frac{\partial v}{\partial p}\right)_T$

(D)

$C_g = -\frac{1}{p} \left(\frac{\partial p}{\partial v}\right)_T$

Explanation

GATE→2023→Core→Reservoir Engineering

Q13

MCQ[1 Mark]

Consider an ideal liquid-vapor mixture at equilibrium having liquid phase mole fraction $x_i$ and gas phase mole fraction $y_i$. For an ideal solution (Raoult's law), the equilibrium ratio ($k_i$) is given by

(A)

$k_i = \frac{x_i}{y_i} = \frac{P_{vi}}{P}$

(B)

$k_i = \frac{x_i}{y_i} = \frac{P}{P_{vi}}$

(C)

$k_i = \frac{y_i}{x_i} = \frac{P_{vi}}{P}$

(D)

$k_i = \frac{y_i}{x_i} = \frac{P}{P_{vi}}$

Explanation

GATE→2023→Core→Enhanced Oil Recovery Techniques

Q14

MCQ[1 Mark]

In-situ combustion method for enhanced oil recovery is commonly used for

(A)

gas condensate reservoirs

(B)

light oil reservoirs

(C)

brown oil reservoirs

(D)

heavy oil reservoirs

Explanation

GATE→2023→Core→Petroleum Exploration

Q15

MCQ[1 Mark]

Which of the following is a sedimentary rock?

(A)

Amphibolite

(B)

Chalk

(C)

Gabbro

(D)

Schist

Explanation

GATE→2023→Core→Petroleum Exploration

Q16

MCQ[1 Mark]

Kerogen classification (Van Krevelen diagram) plots atomic ratios. Which of the following represents the X-axis and Y-axis, respectively?

(A)

H:C ratio and O:C ratio

(B)

O:C ratio and H:C ratio

(C)

C:H ratio and C:O ratio

(D)

C:O ratio and C:H ratio

Explanation

GATE→2023→Core→Petroleum Formation Evaluation

Q17

MCQ[1 Mark]

The response of a four-arm caliper log in a drilled section is shown. The borehole features associated with the three identified sections P, Q, and R are

(A)

P: washout; Q: in-gauge hole; R: key-seat

(B)

P: key-seat; Q: in-gauge hole; R: washout

(C)

P: under-gauge hole; Q: in-gauge hole; R: washout

(D)

P: dog-leg; Q: in-gauge hole; R: key-seat

Explanation

GATE→2023→Core→Petroleum Formation Evaluation

Q18

MCQ[1 Mark]

Which of the following is necessary for the generation of electrokinetic (streaming potential) across well-bore and permeable rock formation?

(A)

Salinity gradient

(B)

Pressure gradient

(C)

Shale membrane

(D)

Mud cake

Explanation

GATE→2023→Core→Petroleum Formation Evaluation

Q19

MCQ[1 Mark]

A first arrival amplitude of the Cement Bond Log (CBL) of a cased hole section is given. The identified depth intervals P, Q, and R represent

(A)

P: not cemented; Q: partially cemented; R: well-cemented

(B)

P: not cemented; Q: well-cemented; R: partially cemented

(C)

P: partially cemented; Q: not cemented; R: well-cemented

(D)

P: well-cemented; Q: not cemented; R: partially cemented

Explanation

GATE→2023→Core→Reservoir Engineering

Q20

MCQ[1 Mark]

Contact angle measurements are performed on smooth surfaces. The interfacial tensions between solid-liquid, liquid-air, and air-solid are $\gamma_{SL}$, $\gamma_{LA}$, and $\gamma_{AS}$, respectively. Which of the following expressions describes Young's equation for the contact angle, $\Theta$?

(A)

$\cos \Theta = \frac{\gamma_{AS} - \gamma_{SL}}{\gamma_{LA}}$

(B)

$\cos \Theta = \frac{\gamma_{SL} - \gamma_{AS}}{\gamma_{LA}}$

(C)

$\cos \Theta = \frac{\gamma_{LA} - \gamma_{AS}}{\gamma_{SL}}$

(D)

$\cos \Theta = \frac{\gamma_{LA} - \gamma_{SL}}{\gamma_{AS}}$

Explanation

GATE→2023→Core→Offshore Drilling and Production Practices

Q21

MCQ[1 Mark]

Which of the following offshore rigs has the HIGHEST water depth operating capability?

(A)

Submersible drilling barge

(B)

Jackup rig

(C)

Jacket platform

(D)

Semi-submersible rig

Explanation

GATE→2023→Core→Oil and Gas Well Testing

Q22

MCQ[1 Mark]

Consider an immiscible liquid mixture of n-decane and water containing fully dissociated NaCl. Using Gibbs Phase Rule ($F = C - P + 2$), the number of degrees of freedom for this system is

(A)

3

(B)

4

(C)

5

(D)

2

Explanation

GATE→2023→Core→Reservoir Engineering

Q23

MSQ[1 Mark]

The mean free path of the gas molecule is $10^{-6}\text{ mm}$, while the pore size of the rock is $10^{-3}\text{ mm}$. Which of the following statements is TRUE?

(A)

The Knudsen number is $10^3$ and the continuum principle would be applicable

(B)

The Knudsen number is $10^{-3}$ and the continuum principle would be applicable

(C)

The Knudsen number is $10^3$ and the continuum principle would not be applicable

(D)

The Knudsen number is $10^{-3}$ and the continuum principle would not be applicable

Explanation

GATE→2023→Core→Health Safety and Environment in Petroleum Industry

Q24

MSQ[1 Mark]

Which of the following is/are the route(s) by which a toxic substance may enter a human body?

(A)

Ingestion

(B)

Inhalation

(C)

Perspiration

(D)

Asphyxiation

Explanation

GATE→2023→Core→Health Safety and Environment in Petroleum Industry

Q25

MSQ[1 Mark]

Select ALL the safety system(s) that is/are required in an offshore platform.

(A)

Permit to work system

(B)

Fire and gas alarms

(C)

Lock out-tag out

(D)

Financial monitoring system

Explanation

GATE→2023→Core→Enhanced Oil Recovery Techniques

Q26

MSQ[1 Mark]

Polymer flooding enhances oil recovery from an oil reservoir by

(A)

increasing the mobility ratio

(B)

reducing the mobility ratio

(C)

reducing the viscous fingering

(D)

increasing the viscous fingering

Explanation

GATE→2023→Core→Petroleum Production Operations

Q27

MSQ[1 Mark]

Which is/are the thermodynamic inhibitor(s) for natural gas hydrate?

(A)

Tetrahydrofuran

(B)

Sodium chloride

(C)

Ethylene glycol

(D)

Tetra n-butyl ammonium bromide

Explanation

GATE→2023→Core→Petroleum Exploration

Q28

MSQ[1 Mark]

Which of the following hydrocarbon trap(s) is/are a result of sedimentary facies changes (stratigraphic traps)?

(A)

Salt dome

(B)

Unconformity

(C)

Pinch out

(D)

Sand lens

Explanation

GATE→2023→Core→Oil and Gas Well Drilling Technology

Q29

MSQ[1 Mark]

Which of the following option(s) is/are indication(s) of a well kick?

(A)

Decrease in mud pit volume

(B)

Increase in mud pit volume

(C)

Decrease in pump pressure

(D)

Increase in pump pressure

Explanation

GATE→2023→Core→Health Safety and Environment in Petroleum Industry

Q30

MCQ[2 Marks]

Consider an industrial accident scenario involving a drain connection failure, vapor cloud formation, ignition, and eventual burnout. Match the three steps of the accident (P: Initiation, Q: Propagation, R: Termination) to the events: (I) Formation of vapor cloud (II) Failure of drain connection (III) Consumption of all combustibles

(A)

P-I; Q-III; R-II

(B)

P-II; Q-I; R-III

(C)

P-II; Q-III; R-I

(D)

P-I; Q-II; R-III

Explanation

GATE→2023→Core→Petroleum Production Operations

Q31

MCQ[2 Marks]

A centrifugal pump running at $500 \text{ rpm}$ delivers $60 \text{ liters/minute}$ with a head of $50 \text{ m}$. At the same efficiency, if the rotational speed is increased to $1000 \text{ rpm}$, the discharge rate and head would respectively be

(A)

$120 \text{ liters/minute}$ and 200 m

(B)

$120 \text{ liters/minute}$ and 100 m

(C)

$60 \text{ liters/minute}$ and 200 m

(D)

$60 \text{ liters/minute}$ and 100 m

Explanation

GATE→2023→Core→Oil and Gas Well Testing

Q32

MCQ[2 Marks]

Match the flow regimes associated with a vertically fractured well in a reservoir: (P) Formation Linear Flow (Q) Fracture Linear Flow (R) Bilinear Flow (S) Pseudo-Radial Flow\nwith their corresponding schematic flow descriptions.

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2023→Core→Reservoir Engineering

Q33

MCQ[2 Marks]

Match the organic solid phase deposition regions (I, II, III) around the bubble point curve with Wax, Hydrate, and Asphaltene.

(A)

I - Wax; II - Hydrate; III - Asphaltene

(B)

I - Hydrate; II - Asphaltene; III - Wax

(C)

I - Asphaltene; II - Hydrate; III - Wax

(D)

I - Hydrate; II - Wax; III - Asphaltene

Explanation

GATE→2023→Core→Petroleum Production Operations

Q34

MCQ[2 Marks]

Match the pure gas hydrate phase diagrams (I, II, III, IV) with the corresponding gases: $CH_4$, $CO_2$, $H_2S$, and $N_2$.

(A)

$I-CH_4; II-N_2; III-CO_2; IV-H_2S$

(B)

$I-H_2S; II-CH_4; III-CO_2; IV-N_2$

(C)

$I-N_2; II-CH_4; III-H_2S; IV-CO_2$

(D)

$I-N_2; II-CH_4; III-CO_2; IV-H_2S$

Explanation

GATE→2023→Core→Petroleum Exploration

Q35

MCQ[2 Marks]

Match the seismic data processing terms in Group-I with their objectives/features in Group-II: **Group-I:** (P) Stacking (Q) Multiple (R) Bow tie (S) Deconvolution **Group-II:** (I) Synform (II) Noise reduction (III) Resolution enhancement (IV) Echo

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2023→Core→Oil and Gas Well Testing

Q36

MSQ[2 Marks]

Which of the following statement(s) is/are TRUE regarding Horner plot regions (ETR, MTR, LTR) in a pressure build-up test?

(A)

Early Time Region (ETR): Pressure build-up data is affected by reservoir boundaries and other reservoir heterogeneities such as sealing faults

(B)

Middle Time Region (MTR): Pressure build-up data is reached after end of the wellbore storage and the pressure transient has entered the virgin reservoir

(C)

Late Time Region (LTR): Pressure build-up data is affected by reservoir boundaries and other reservoir heterogeneities such as sealing faults

(D)

Middle Time Region (MTR): Pressure build-up data is affected by reservoir boundaries and other reservoir heterogeneities such as sealing faults

Explanation

GATE→2023→Core→Health Safety and Environment in Petroleum Industry

Q37

MSQ[2 Marks]

Select the statement(s) that is/are TRUE regarding combustion, fire, and explosion fundamentals.

(A)

Combustion always occurs in the vapor phase

(B)

Combustion cannot occur if air/oxidizer is absent

(C)

Flash point is the lowest temperature at which a vapor above a liquid will continue to burn once ignited

(D)

The distinction between a fire and explosion is in their rate of energy release

Explanation

GATE→2023→Core→Offshore Drilling and Production Practices

Q38

NAT[2 Marks]

Figure shows an inextensible catenary mooring cable in still water. Submerged weight per unit length $w = 100 \text{ kg/m}$, anchor radius $x = 50 \text{ m}$, horizontal tension $T_h = 1600 \text{ kg}$. The catenary length (AB) is m (rounded to two decimal places).

Explanation

GATE→2023→Core→Offshore Drilling and Production Practices

Q39

NAT[2 Marks]

An empty steel pipeline with massless endcaps has an outer diameter $D$ and thickness $t$. Steel density $\rho_s = 7850 \text{ kg/m}^3$, seawater density $\rho_w = 1025 \text{ kg/m}^3$. The critical $D/t$ ratio at which the pipeline starts floating is (rounded to two decimal places).

Explanation

GATE→2023→Core→Reservoir Engineering

Q40

NAT[2 Marks]

Consider the flow of oil and water in a 1D porous medium, with $k_{ro}^o = 1$, $k_{rw}^o = 0.2$, $S_{wr} = 0.2$, $S_{or} = 0.4$, $\mu_o = 5 \text{ cP}$, $\mu_w = 1 \text{ cP}$. The total relative mobility ($\lambda_{total} = k_{ro}/\mu_o + k_{rw}/\mu_w$) at $S_w = 0.4$ is $\text{cP}^{-1}$ (rounded to one decimal place).

Explanation

GATE→2023→Core→Reservoir Engineering

Q41

NAT[2 Marks]

A binary mixture of n-butane ($C_4H_{10}$) and n-pentane ($C_5H_{12}$) is at $180^\circ\text{F}$ and $95 \text{ psia}$. Vapor pressures are $160 \text{ psia}$ and $54 \text{ psia}$, respectively. Assuming ideal solution behavior (Raoult's and Dalton's laws), the mole fraction of n-butane in the gas phase is (rounded to three decimal places).

Explanation

GATE→2023→Core→Reservoir Engineering

Q42

NAT[2 Marks]

A highly permeable reservoir with initial pressure of $3000 \text{ psi}$ is under active water drive. Stabilized pressure is $2500 \text{ psi}$. Oil production rate = $30,000 \text{ STB/day}$, water production = 0, $B_o = 1.5 \text{ bbl/STB}$, $B_g = 0.0007 \text{ bbl/scf}$, $B_w = 1$, $GOR = 850 \text{ scf/STB}$, $R_s = 700 \text{ scf/scf}$? (Given $R_s = 700 \text{ scf/STB}$). The water influx rate is bbl/day (rounded to nearest integer).

Explanation

GATE→2023→Core→Reservoir Engineering

Q43

NAT[2 Marks]

A volumetric undersaturated solution gas drive reservoir has initial water saturation of 15% (unchanged). After production of 10% of initial oil ($N_p = 0.1 N$), $B_o$ changes from $1.4$ to $1.2 \text{ bbl/STB}$. The final gas saturation in percentage is (rounded to one decimal place).

Explanation

GATE→2023→Core→Oil and Gas Well Testing

Q44

NAT[2 Marks]

After well completion, a discovery well in an oil reservoir is produced and then closed for a pressure build-up test. Production history: $500 \text{ STB/day}$ for $5 \text{ days}$, $550 \text{ STB/day}$ for $7 \text{ days}$, $400 \text{ STB/day}$ for $8 \text{ days}$. Horner's pseudo-producing time $t_{pH}$ is hr (rounded to nearest integer).

Explanation

GATE→2023→Core→Petroleum Formation Evaluation

Q45

NAT[2 Marks]

A compressional acoustic wave takes $55 \text{ }\mu\text{s}$ to travel $0.3048 \text{ m}$ through a rock formation having bulk modulus $K = 37.5 \text{ GPa}$ and shear modulus $G = 31 \text{ GPa}$. The bulk density of the rock is $\text{kg/m}^3$ (rounded to two decimal places).

Explanation

GATE→2023→Core→Petroleum Formation Evaluation

Q46

NAT[2 Marks]

A gamma ray log run across a sand-shale sequence recorded maximum (shale) and minimum (clean sand) values of $70 \text{ API}$ and $30 \text{ API}$, respectively. A bed has a gamma log value of $50 \text{ API}$. Assuming a linear relationship, the volume fraction of shale ($V_{sh}$) in the bed is (rounded to one decimal place).

Explanation

GATE→2023→Core→Petroleum Formation Evaluation

Q47

NAT[2 Marks]

Flushed zone resistivity $R_{xo} = 20 \text{ }\Omega\cdot\text{m}$, 100% brine saturated core resistivity $R_0 = 6 \text{ }\Omega\cdot\text{m}$, brine resistivity $R_w = 0.6 \text{ }\Omega\cdot\text{m}$, mud filtrate resistivity $R_{mf} = 0.9 \text{ }\Omega\cdot\text{m}$, saturation exponent $n = 2$. The estimated residual hydrocarbon saturation ($S_{hr} = 1 - S_{xo}$) in percentage is (rounded to two decimal places).

Explanation

GATE→2023→Core→Enhanced Oil Recovery Techniques

Q48

NAT[2 Marks]

Consider a micellar displacement process in a reservoir with porosity $\phi = 0.30$. Microemulsion slug volume = 4% of pore volume, with 4 vol% surfactant. Rock density $\rho_{rock} = 2.7 \text{ g/cm}^3$, surfactant density $\rho_{surf} = 1.1 \text{ g/cm}^3$. Average surfactant adsorption = $0.25 \text{ mg/g}$ of rock. The fraction of injected surfactant adsorbed is (rounded to two decimal places).

Explanation

GATE→2023→Core→Oil and Gas Well Drilling Technology

Q49

NAT[2 Marks]

A kill mud density is required such that bottomhole pressure equals formation pressure. Shut-in pressure (SIDPP) = $6.8 \times 10^6 \text{ Pa}$ at $3500 \text{ m}$ depth. Original mud density $\rho_1 = 1100 \text{ kg/m}^3$. The kill mud density $\rho_2$ is $\text{kg/m}^3$ (rounded to two decimal places).

Explanation

GATE→2023→Core→Oil and Gas Well Drilling Technology

Q50

NAT[2 Marks]

A non-Newtonian drilling fluid obeying Bingham plastic model ($\tau_{yx} = \mu_p \dot{\gamma} + \tau_{yx}^o$) is placed between two flat parallel plates of area $10 \text{ cm}^2$ separated by $1 \text{ cm}$. Force to initiate motion (yield stress) = $300 \text{ dyne}$. Force to keep upper plate moving at $10 \text{ cm/s}$ = $600 \text{ dyne}$. The Bingham plastic viscosity $\mu_p$ is $\text{dyne}\cdot\text{s/cm}^2$ (rounded to nearest integer).

Explanation

GATE→2023→Core→Petroleum Production Operations

Q51

NAT[2 Marks]

Crude oil ($\rho = 850 \text{ kg/m}^3$, $\mu = 2 \times 10^{-3} \text{ Pa}\cdot\text{s}$) flows at $V = 0.35 \text{ m/s}$ through a horizontal capillary tube ($D = 2.5 \times 10^{-3} \text{ m}$, $L = 0.30 \text{ m}$). With Fanning friction factor $f = 16 / Re$, the pressure drop across the capillary tube is Pa (rounded to one decimal place).

Explanation

GATE→2023→Core→Reservoir Engineering

Q52

NAT[2 Marks]

An oil droplet is to be mobilized by water injection. Rear radius of curvature $r_A = 25 \times 10^{-6} \text{ m}$, forward radius of curvature $r_B = 5 \times 10^{-6} \text{ m}$, wetting contact angle = $0^\circ$, interfacial tension $\sigma = 0.025 \text{ N/m}$. The magnitude of the minimum capillary pressure drop required to mobilize the droplet is $\text{N/m}^2$ (rounded to nearest integer).

Explanation

GATE→2023→Core→Offshore Drilling and Production Practices

Q53

NAT[2 Marks]

A four-column semi-submersible floater has column diameter $D = 5 \text{ m}$ each ($N = 4$ columns). Total displaced weight = $4000 \text{ tonnes} = 4 \times 10^6 \text{ kg}$. Added mass = 50% of mass ($m_a = 0.5 m$), $\rho_w = 1025 \text{ kg/m}^3$, $g = 9.81 \text{ m/s}^2$. The natural period of oscillation in heave mode is seconds (rounded to one decimal place).

Explanation

GATE→2023→Core→Petroleum Production Operations

Q54

NAT[2 Marks]

A shell and tube heat exchanger cools crude oil ($3650 \text{ kg/h}$, $C_p = 2.5 \text{ kJ/kg}\cdot\text{K}$) from $400 \text{ K}$ to $360 \text{ K}$. Water ($1600 \text{ kg/h}$, $C_p = 4.187 \text{ kJ/kg}\cdot\text{K}$) enters at $310 \text{ K}$. Countercurrent flow, $U = 300 \text{ W/m}^2\cdot\text{K}$. The heat transfer area required is $\text{m}^2$ (rounded to one decimal place).

Explanation

GATE→2023→Core→Offshore Drilling and Production Practices

Q55

NAT[2 Marks]

An underwater riser with outer diameter $D_o = 250 \text{ mm}$ and wall thickness $t = 20 \text{ mm}$ (inner diameter $D_i = 210 \text{ mm}$) is subjected to effective tension $T_{eff} = 1200 \text{ kN}$, internal pressure $P_i = 25 \text{ MPa}$, and external pressure $P_o = 6 \text{ MPa}$. The true wall tension in the riser is (in $\times 10^6 \text{ N}$, rounded to two decimal places).

Explanation

General Aptitude

10 Questions

GATE→2023→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

The village was nestled in a green spot, ______ the ocean and the hills.

(A)

through

(B)

in

(C)

at

(D)

between

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q57

MCQ[1 Mark]

Disagree : Protest :: Agree : _____ (By word meaning)

(A)

Refuse

(B)

Pretext

(C)

Recommend

(D)

Refute

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

A 'frabjous' number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?

(A)

125

(B)

720

(C)

60

(D)

80

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

Which one among the following statements must be TRUE about the median of a set of scores (such as candidates appearing for GATE)?

(A)

The median is at least as large as the mean.

(B)

The mean is at least as large as the median.

(C)

At most half the candidates have a score that is larger than the median.

(D)

At most half the candidates have a score that is larger than the mean.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

In the given diagram, ovals are marked at different heights ($h$) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

Residency is a housing complex where all well-established residents are academicians, and most of these academicians are authors of best-selling books. Which statement can be logically inferred with certainty?

(A)

Some residents of the complex who are well established in their fields are also authors of some best-selling books.

(B)

All academicians residing in the complex are well established in their fields.

(C)

Some authors of best-selling books are residents of the complex who are well established in their fields.

(D)

Some academicians residing in the complex are well established in their fields.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

Ankita has to climb 5 stairs starting at the ground by moving either 1 or 2 stairs up at a stage without moving down. Let $F(N)$ denote the number of possible ways to reach the $N^{th}$ stair ($F(1)=1, F(2)=2, F(3)=3$). The value of $F(5)$ is

(A)

8

(B)

7

(C)

6

(D)

5

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q63

MCQ[2 Marks]

Based on the text stating that only about 2% of human DNA consists of coding regions used to produce proteins, which statement can be logically inferred with certainty?

(A)

only (i)

(B)

only (ii)

(C)

both (i) and (ii)

(D)

neither (i) nor (ii)

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

Which one of the given figures P, Q, R and S represents the graph of the function $f(x) = ||x+2| - |x-1||$?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

An opaque cylinder is suspended in the path of a parallel beam of light to cast a shadow. Which of the shadow shapes P, Q, R, and S is NOT possible?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation