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Engineering Mathematics(10)Core(45)General Aptitude(5)

Engineering Mathematics

10 Questions

GATE→2022→Engineering Mathematics→Calculus

Q1

MCQ[1 Mark]

The value of $\lim_{x \to 0} \left[ \frac{1}{x} \ln(1+x) \right]$ is

(A)

e

(B)

1

(C)

0

(D)

$\frac{1}{e}$

Explanation

GATE→2022→Engineering Mathematics→Differential Equations

Q2

MCQ[1 Mark]

The second order ordinary differential equation $\frac{d^2 y}{dx^2} + \frac{dy}{dx} = 5y$ has boundary conditions $y(0) = 0$ and $y(1) = 1$. The type of these boundary conditions is

(A)

Neumann

(B)

Dirichlet

(C)

Cauchy

(D)

Robin

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q3

MCQ[1 Mark]

Let $\vec{F}(x,y) = e^x \sin x \hat{i} + x \hat{j}$. If $C$ is the circle $x^2 + y^2 = 4$ oriented anticlockwise, then $\int_{C} \vec{F} \cdot d\vec{R}$ equals

(A)

$4\pi$

(B)

$6\pi$

(C)

$7\pi$

(D)

$8\pi$

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q4

MSQ[1 Mark]

Which of the following properties of Matrix $A = \begin{bmatrix} 1 & 0.5 & 0 \\ 0.5 & 1 & 0.5 \\ 0 & 0.5 & 1 \end{bmatrix}$ are CORRECT?

(A)

Singular

(B)

Positive definite

(C)

Symmetric

(D)

Diagonal

Explanation

GATE→2022→Engineering Mathematics→Numerical Methods

Q5

MSQ[1 Mark]

Simpson's one-third rule will give the exact value of polynomial integrals up to what degree $n$?

(A)

1

(B)

2

(C)

3

(D)

4

Explanation

GATE→2022→Engineering Mathematics→Differential Equations

Q6

MCQ[2 Marks]

A real gas is produced at constant temperature $30^\circ\text{C}$ with $(\partial Z / \partial P)_T = Z^2$. The difference in compressibility between the real gas and an ideal gas is

(A)

Z

(B)

$Z^2$

(C)

$\sqrt{Z}$

(D)

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

Explanation

GATE→2022→Engineering Mathematics→Probability and Statistics

Q7

NAT[2 Marks]

If $Z$ is standard normal variable, the probability $P(-3 \le Z \le 3)$ is (rounded off to three decimal places).

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q8

NAT[2 Marks]

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

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q9

NAT[2 Marks]

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

Explanation

GATE→2022→Engineering Mathematics→Differential Equations

Q10

NAT[2 Marks]

Given $\frac{dy}{dx} = x^2 y$ with $y(0) = 1$ and step size $h = 0.1$. Using Euler's first-order method, the value of $y(0.2)$ is (rounded to three decimal places).

Explanation

Core

45 Questions

GATE→2022→Core→Petroleum Production Operations

Q11

MCQ[1 Mark]

The general production decline equation is $\frac{1}{q} \frac{dq}{dt} = -b q^d$. Match the value of $d$ (Group 1: I. $d=0$, II. $d=1$, III. $0<d<1$) with decline types (Group 2: P. Harmonic, Q. Exponential, R. Hyperbolic).

(A)

I-P; II-Q; III-R

(B)

II-R; I-P; III-Q

(C)

III-P; I-Q; II-R

(D)

I-Q; II-P; III-R

Explanation

GATE→2022→Core→Petroleum Production Operations

Q12

MCQ[1 Mark]

In project economic evaluation, present value of cash flow discounted at rate $i$ over $m$ years with annual incremental revenue $\Delta R_n$ is given by

(A)

$NPV_R = \sum_{n=1}^m \frac{(1+i)^n}{\Delta R_n}$

(B)

$NPV_R = \sum_{n=1}^m \frac{\Delta R_n}{(1+i)^{n-1}}$

(C)

$NPV_R = \sum_{n=1}^m [\frac{\Delta R_n}{1+i}]^n$

(D)

$NPV_R = \sum_{n=1}^m \frac{\Delta R_n}{(1+i)^n}$

Explanation

GATE→2022→Core→Reservoir Engineering

Q13

MCQ[1 Mark]

The formation volume factors of oil and water are $B_o$ and $B_w$. The CORRECT relationship between surface water cut ($f_{ws}$) and reservoir water cut ($f_w$) is

(A)

$f_{ws} = \frac{B_o f_w}{B_w + B_o}$

(B)

$f_{ws} = \frac{B_o f_w}{B_w + B_o f_w}$

(C)

$f_{ws} = \frac{B_w}{B_o(\frac{1}{f_w}-1) + B_w}$

(D)

$f_{ws} = \frac{B_o}{B_w(\frac{1}{f_w}-1) + B_o}$

Explanation

GATE→2022→Core→Petroleum Production Operations

Q14

MCQ[1 Mark]

Which ONE of the following is used to anchor and support a packer against the casing while expanding its rubber sealing element?

(A)

Blast joints

(B)

Slips

(C)

Landing nipples

(D)

Side pocket mandrels

Explanation

GATE→2022→Core→Offshore Drilling and Production Practices

Q15

MCQ[1 Mark]

'Cupola' offshore storage tank is an example of

(A)

floating storage type.

(B)

above-water storage type.

(C)

submerged storage type.

(D)

platform storage type.

Explanation

GATE→2022→Core→Reservoir Engineering

Q16

MCQ[1 Mark]

The liquid shrinkage curves for different types of crude oil are shown. Which curve represents the Black Oil?

(A)

I

(B)

II

(C)

III

(D)

IV

Explanation

GATE→2022→Core→Oil and Gas Well Drilling Technology

Q17

MCQ[1 Mark]

The dynamic mud inflow and outflow rate profiles are shown. Identify 'Hole ballooning' and 'Lost circulation' cases.

(A)

Case 1 - Hole ballooning; Case 3 - Lost circulation

(B)

Case 2 - Lost circulation; Case 3 - Hole ballooning

(C)

Case 1 - Lost circulation; Case 2 - Hole ballooning

(D)

Case 2 - Hole ballooning; Case 3 - Lost circulation

Explanation

GATE→2022→Core→Health Safety and Environment in Petroleum Industry

Q18

MCQ[1 Mark]

What is the maximum permissible limit of 'oil and grease' in discharged wastewater from a petroleum industry as per CPCB India guidelines?

(A)

5 ppm

(B)

10 ppm

(C)

30 ppm

(D)

50 ppm

Explanation

GATE→2022→Core→Petroleum Formation Evaluation

Q19

MCQ[1 Mark]

The Timur chart for estimating permeability is a log-log plot between

(A)

Porosity and Water Saturation

(B)

True Resistivity and Water Saturation

(C)

Porosity and Irreducible Water Saturation

(D)

Porosity and True Resistivity

Explanation

GATE→2022→Core→Petroleum Formation Evaluation

Q20

MSQ[1 Mark]

The logging tool(s) preferred for measuring formation resistivity in a well drilled with oil-based mud (non-conductive mud) is/are

(A)

Dual Laterolog

(B)

Compensated Neutron Log

(C)

Compensated Density Log

(D)

Induction Log

Explanation

GATE→2022→Core→Petroleum Production Operations

Q21

MSQ[1 Mark]

Which of the following statements are NOT CORRECT during the operating cycle of a 'sucker rod pump'?

(A)

Standing valve is open during the upward stroke.

(B)

Standing valve is closed during the upward stroke.

(C)

Travelling valve is closed during the upward stroke.

(D)

Travelling valve is open during the upward stroke.

Explanation

GATE→2022→Core→Enhanced Oil Recovery Techniques

Q22

MSQ[1 Mark]

Which of the following statements related to the 'enriched gas drive' are CORRECT?

(A)

The enriching components are transferred from the oil to the gas.

(B)

The enriched gas drive is an example of immiscible enhanced oil recovery.

(C)

A miscible zone is formed between the injected gas and the reservoir oil.

(D)

In enriched gas drive, the viscous fingering results in poor sweep efficiency.

Explanation

GATE→2022→Core→Enhanced Oil Recovery Techniques

Q23

MSQ[1 Mark]

Select the CORRECT statements for the injection-production well patterns.

(A)

Inverted 5-spot drive includes four injectors at the corners and the producer at the centre.

(B)

Regular 7-spot drive includes six injectors at the corners and the producer at the centre.

(C)

Staggered-line drive involves staggered injectors and producers.

(D)

Crestal injection involves positioning of the wells along the periphery of the reservoir.

Explanation

GATE→2022→Core→Health Safety and Environment in Petroleum Industry

Q24

MSQ[1 Mark]

The flammable gas detector works on which of the following phenomena/sensor technologies?

(A)

Catalytic

(B)

Paramagnetic

(C)

Electrochemical

(D)

Photoionisation

Explanation

GATE→2022→Core→Oil and Gas Well Drilling Technology

Q25

MSQ[1 Mark]

A drilling mud with high gel strength is undesirable because it

(A)

retards the separation of cuttings and entrained gas at the surface.

(B)

leads to the lost circulation.

(C)

creates swabbing action beneath the bit while pulling the string.

(D)

leads to the hole ballooning.

Explanation

GATE→2022→Core→Petroleum Formation Evaluation

Q26

MSQ[1 Mark]

Which of the following Logging tool combinations are required to estimate Hydrocarbon Initial in Place (HCIP) requiring porosity and water saturation ($S_w$)?

(A)

Resistivity Log, Neutron Log and Gamma Ray Log

(B)

Sonic Log, Neutron Log and Gamma Ray Log

(C)

Resistivity Log, Density Log and Gamma Ray Log

(D)

Neutron Log, Density Log and Sonic Log

Explanation

GATE→2022→Core→Oil and Gas Well Testing

Q27

NAT[1 Mark]

A homogeneous sandstone reservoir is under radial steady state flow. Wellbore radius $r_w = 0.1 \text{ m}$. Formation damage radius $r_s = 1.0 \text{ m}$. Permeability ratio $k/k_s = 5$. The value of skin factor is (rounded off to two decimal places).

Explanation

GATE→2022→Core→Reservoir Engineering

Q28

NAT[1 Mark]

A reservoir produces oil at $7000 \text{ stb/day}$ with producing GOR = $2000 \text{ scf/stb}$. Maintained at $2500 \text{ psi}$ by water injection. Given $B_o = 1.2 \text{ rb/stb}$, $B_w = 1.0 \text{ rb/stb}$, $B_g = 0.0012 \text{ rb/scf}$, solution $R_s = 300 \text{ scf/stb}$. The water injection rate (stb/day) required is (rounded off to nearest integer).

Explanation

GATE→2022→Core→Oil and Gas Well Drilling Technology

Q29

NAT[1 Mark]

An oil well is drilled using an $8.5\text{-inch}$ drill bit at ROP = $30 \text{ ft/hr}$. Rotary speed $N = 20 \text{ rpm}$, WOB $W = 3500 \text{ lb}$. The value of the 'd' exponent is (rounded off to two decimal places).

Explanation

GATE→2022→Core→Oil and Gas Well Drilling Technology

Q30

NAT[1 Mark]

A vertical wellbore is drilled with a $12.25\text{-inch}$ bit, drilling $385 \text{ ft}^3$ of rock in $6.5 \text{ hr}$. The washed-out hole diameter is $12.49 \text{ inches}$. The average rate of penetration (ROP) in $\text{ft/hr}$ is (rounded off to two decimal places).

Explanation

GATE→2022→Core→Petroleum Production Operations

Q31

MCQ[2 Marks]

A brine solution is injected downward through tubing of diameter $d$ inclined at angle $\theta$ from vertical. The condition such that the ratio of frictional pressure drop to gravitational pressure drop equals $4f$ (where $f$ is Fanning friction factor) is

(A)

$u = (2gd)^{1/2}$; $\theta = 30^\circ$

(B)

$u = gd$; $\theta = 30^\circ$

(C)

$u = (gd)^{1/2}$; $\theta = 60^\circ$

(D)

$u = gd^{1/2}$; $\theta = 30^\circ$

Explanation

GATE→2022→Core→Health Safety and Environment in Petroleum Industry

Q32

MCQ[2 Marks]

Match the contaminants (Group I) with their effluent wastewater treatment techniques (Group II): I. Suspended solids II. Biodegradable organics III. Heavy metals IV. Suspended oil and grease Techniques: (P) Ion exchange, (Q) Filtration, (R) Trickling filters, (S) Flocculation

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2022→Core→Reservoir Engineering

Q33

MCQ[2 Marks]

Capillary pressure ($P_c$) vs water saturation ($S_w$) curves for different sandstone reservoirs (I, II, III, and IV) are given. Which reservoir has the most uniform pore size distribution (indicated by a flat/plateau-like median portion)?

(A)

I

(B)

II

(C)

III

(D)

IV

Explanation

GATE→2022→Core→Oil and Gas Well Testing

Q34

MCQ[2 Marks]

Flow tests are conducted for oil wells in reservoirs P, Q, R, and S with given parameters. Identify the reservoir in which the pressure transient reaches earliest at a point $2000 \text{ ft}$ away from the wellbore (highest hydraulic diffusivity $\eta = \frac{k}{\phi \mu c_t}$).

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2022→Core→Oil and Gas Well Testing

Q35

MCQ[2 Marks]

Identify the CORRECT match for flow regimes (Group 1) with pressure derivative log-log slopes (Group 2): I. Spherical flow II. Linear flow III. Bilinear flow IV. Boundary dominated flow Slopes: (P) 1, (Q) 1/4, (R) -1/2, (S) 1/2

(A)

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

(B)

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

(C)

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

(D)

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

(E)

I-R; II-S; III-Q; IV-P (Option C check)

Explanation

GATE→2022→Core→Petroleum Formation Evaluation

Q36

MCQ[2 Marks]

The log data obtained for a well section (Gamma Ray, Density, Neutron logs) are shown. Identify the CORRECT interpretations for Zones 1, 2, 3, and 4.

(A)

Zone 1 - shale, Zone 2 - clean sand with oil, Zone 3 - clean sand with gas, Zone 4 - clean sand with water

(B)

Zone 1 - clean sand with gas, Zone 2 - clean sand with oil, Zone 3 - clean sand with water, Zone 4 - shale

(C)

Zone 1 - shale, Zone 2 - clean sand with gas, Zone 3 - clean sand with oil, Zone 4 - clean sand with water

(D)

Zone 1 - clean sand with water, Zone 2 - clean sand with oil, Zone 3 - clean sand with gas, Zone 4 - shale

Explanation

GATE→2022→Core→Oil and Gas Well Testing

Q37

MSQ[2 Marks]

Well testing is to be conducted on bounded sandstone reservoirs with different well locations (Reservoirs 1, 2, 3). Which of the following statements are CORRECT?

(A)

Pseudo steady flow regime will develop first in Reservoir 1.

(B)

Infinite acting behavior will stop first in Reservoir 2.

(C)

Infinite acting behavior will sustain the longest in Reservoir 1.

(D)

Pressure depletion will be the fastest in Reservoir 3.

Explanation

GATE→2022→Core→Petroleum Exploration

Q38

MSQ[2 Marks]

An exploratory well is planned in a basin up to $5000 \text{ m}$. Surface temperature $T_s = 30^\circ\text{C}$, geothermal gradient $G = 0.025^\circ\text{C/m}$. Select the possible depth range(s) corresponding to the oil window ($60^\circ\text{C}$ to $120^\circ\text{C}$ / $90^\circ\text{C}$ to $150^\circ\text{C}$).

(A)

800 m to 950 m

(B)

1500 m to 1650 m

(C)

3100 m to 3150 m

(D)

4550 m to 4600 m

Explanation

GATE→2022→Core→Oil and Gas Well Testing

Q39

NAT[2 Marks]

For an oil well drawdown test with total compressibility $c_t = 20 \times 10^{-6} \text{ psi}^{-1}$, porosity $\phi = 15\%$, wellbore radius $r_w = 0.25 \text{ ft}$, wellbore fluid volume $V_w = 180 \text{ rb}$, oil viscosity $\mu = 2 \text{ cP}$, thickness $h = 50 \text{ ft}$, permeability $k = 30 \text{ mD}$, skin $S = 0$, the duration of the wellbore storage effect ($t_{wbs}$) in hours is

Explanation

GATE→2022→Core→Reservoir Engineering

Q40

NAT[2 Marks]

During core analysis, lab conditions: $\sigma_{lab} = 35 \text{ dynes/cm}$, $\phi_{lab} = 30\%$, $k_{lab} = 100 \text{ mD}$, $P_{c,lab} = 50 \text{ psi}$. Reservoir conditions: $\sigma_{res} = 25 \text{ dynes/cm}$, $\phi_{res} = 25\%$, $k_{res} = 80 \text{ mD}$. The calculated capillary pressure at reservoir condition using Leverett J-function is psi (rounded off to two decimal places).

Explanation

GATE→2022→Core→Oil and Gas Well Testing

Q41

NAT[2 Marks]

Total oil production rate from a volumetric reservoir is $q = 200 \text{ bbl/day}$ at initial FBHP = $3000 \text{ psi}$. Reservoir properties: $h = 10 \text{ ft}$, $\phi = 18\%$, $c_t = 50 \times 10^{-6} \text{ psi}^{-1}$, $k = 35 \text{ mD}$, $r_w = 0.25 \text{ ft}$, $S = 0$, $r_e = 1000 \text{ ft}$, $\mu = \dots$ (or derived). Considering pseudo steady state, the bottomhole pressure after $180 \text{ days}$ is psi (rounded off to two decimal places).

Explanation

GATE→2022→Core→Reservoir Engineering

Q42

NAT[2 Marks]

An incompressible fluid (density $\rho = 40 \text{ lb/ft}^3$) flows through a linear porous media: $L = 1500 \text{ ft}$, $k = 150 \text{ mD}$, $H = 15 \text{ ft}$, $\mu = 1.5 \text{ cP}$, $P_1 = 1600 \text{ psi}$, $P_2 = 1590 \text{ psi}$, width $W = 30 \text{ ft}$, dip angle $\theta$. The absolute difference between actual fluid interstitial velocity at $\theta = 0^\circ$ and $\theta = 10^\circ$ is (rounded off to three decimal places).

Explanation

GATE→2022→Core→Petroleum Production Operations

Q43

NAT[2 Marks]

An oil well ($r_w = 0.5 \text{ in} = 0.04167 \text{ ft}$) in a heavy oil reservoir ($r_e = 745 \text{ ft}$, $\mu_1 = 500 \text{ cP}$) operates at $q = 200 \text{ rb/day}$ and $P_{wf} = 150 \text{ psi}$ under steady state. Steam stimulation reduces viscosity to $\mu_2 = 35 \text{ cP}$ in the stimulated zone up to $r_s = 65 \text{ ft}$. The new production rate at downhole conditions is rb/day (rounded off to two decimal places).

Explanation

GATE→2022→Core→Petroleum Production Operations

Q44

NAT[2 Marks]

In a horizontal circular pipe, liquid and gas flow concurrently at the same superficial velocity $u_{sl} = u_{sg} = u_s$. The average gas velocity $u_g$ is greater than liquid velocity $u_l$. If slip velocity $u_s = u_g - u_l$ equals the superficial velocity of each phase ($u_s$), the fractional liquid holdup $H_l$ is (rounded to two decimal places).

Explanation

GATE→2022→Core→Reservoir Engineering

Q45

NAT[2 Marks]

A 1 kg-mol bottled gas mixture ($50\%$ Ethane, $45\%$ n-Butane, $5\%$ Propane) is at $30^\circ\text{C}$. Vapor pressures are Ethane $10 \text{ bar}$, n-Butane $40 \text{ bar}$, Propane $3 \text{ bar}$. Equilibrium vapor mole composition of n-Butane in mol% is (rounded to two decimal places).

Explanation

GATE→2022→Core→Petroleum Production Operations

Q46

NAT[2 Marks]

Crude oil ($\dot{m}_o = 1000 \text{ kg/hr}$, $C_{po} = 2 \text{ kJ/kg}\cdot\text{K}$) is cooled from $80^\circ\text{C}$ to $40^\circ\text{C}$ using water ($\dot{m}_w$, $C_{pw} = 4.2 \text{ kJ/kg}\cdot\text{K}$) entering at $20^\circ\text{C}$ and leaving at $40^\circ\text{C}$ in counter-flow. Overall heat transfer coefficient $U = 0.25 \text{ kW/m}^2\cdot\text{K}$. The minimum heat exchanger area ($m^2$) is (rounded off to two decimal places).

Explanation

GATE→2022→Core→Enhanced Oil Recovery Techniques

Q47

NAT[2 Marks]

During waterflooding, areal sweep $E_a = 0.75$, vertical sweep $E_i = 0.85$. Average water saturation behind front $S_{wf} = 0.63$, initial water saturation $S_{wi} = 0.17$. Initial oil volume = $3200 \text{ rb}$. The amount of oil produced at breakthrough is rb (rounded off to two decimal places).

Explanation

GATE→2022→Core→Enhanced Oil Recovery Techniques

Q48

NAT[2 Marks]

Initial water saturation $S_{wi} = 30\%$, initial gas saturation $S_{gi} = 40\%$. At end of waterflooding, free gas dissolves, $B_o = 1.20 \text{ rb/stb}$, and final water saturation $S_{wf} = 50\%$. Two-phase FVF at initiation was $2.3 \text{ rb/stb}$. The pore-to-pore displacement efficiency is % (marked MTA / standard evaluation).

Explanation

GATE→2022→Core→Oil and Gas Well Drilling Technology

Q49

NAT[2 Marks]

Station survey data: A ($4499 \text{ m}$, $\alpha_1 = 14.8^\circ$, $\beta_1 = 19^\circ$), B ($4530 \text{ m}$, $\alpha_2 = 13.5^\circ$, $\beta_2 = 10^\circ$). Using the provided dogleg formula, the dogleg severity per $100 \text{ m}$ is (rounded off to one decimal place).

Explanation

GATE→2022→Core→Petroleum Formation Evaluation

Q50

NAT[2 Marks]

Sandstone reservoir top at $3421 \text{ ft}$. At $3425 \text{ ft}$, pressure is $1560 \text{ psi}$, oil API = $35^\circ$. Brine density = $1.04 \text{ g/cc}$ ($0.451 \text{ psi/ft}$), displacement pressure = $1.2 \text{ psi}$. The Oil-Water Contact (OWC) depth is ft from surface (rounded off to two decimal places).

Explanation

GATE→2022→Core→Oil and Gas Well Drilling Technology

Q51

NAT[2 Marks]

Drill string length = $2500 \text{ m}$ ($2000 \text{ m}$ drill pipe at $30 \text{ kg/m}$, $500 \text{ m}$ drill collar at $870 \text{ kg/m}$). Annulus mud SG = 1.5, internal mud SG = 1.4. Steel density = $7850 \text{ kg/m}^3$. The overall buoyant weight acting on the hook is kN (rounded off to two decimal places).

Explanation

GATE→2022→Core→Oil and Gas Well Drilling Technology

Q52

NAT[2 Marks]

A drilling rig has 12 lines strung, output power = $650 \text{ HP}$. At pullout speed $v_1 = 52.5 \text{ ft/min}$, fast line tension $F_1 = 46180 \text{ lb}$. If fast line tension $F_2 = 35690 \text{ lb}$ at the same power and constant efficiency, the new pullout speed $v_2$ is ft/min (rounded off to one decimal place).

Explanation

GATE→2022→Core→Petroleum Formation Evaluation

Q53

NAT[2 Marks]

Sandstone reservoir with density log reading $\rho_b = 2.11 \text{ g/cc}$ and sonic log reading $\Delta t = 90 \text{ }\mu\text{s/ft}$. Given $\rho_{ma} = 2.68$, $\rho_{fl} = 1.0$, $\Delta t_{ma} = 54$, $\Delta t_{fl} = 189$. The calculated secondary (vuggy/fracture) porosity $\phi_2 = \phi_{sonic} - \phi_{density}$ in % is (rounded to nearest integer).

Explanation

GATE→2022→Core→Petroleum Formation Evaluation

Q54

NAT[2 Marks]

Waxman-Smits shaly sand equation with $\phi = 0.25$, $BQ_v = 17.0$, $m^* = n^* = 2.0$, $R_w = 0.05 \text{ }\Omega\cdot\text{m}$ ($C_w = 20 \text{ }\Omega^{-1}\text{m}^{-1}$), $R_t = 12 \text{ }\Omega\cdot\text{m}$ ($C_t = 1/12$). Calculated water saturation $S_w$ in % is (marked MTA).

Explanation

GATE→2022→Core→Petroleum Exploration

Q55

NAT[2 Marks]

Hydrogen index (HI) of a source rock is $500 \text{ mg HC/g TOC}$. If $400 \text{ g}$ of rock produces $6000 \text{ mg}$ of hydrocarbons during pyrolysis, the total organic carbon (TOC) in weight% is (rounded off to one decimal place).

Explanation

General Aptitude

5 Questions

GATE→2022→General Aptitude→Verbal Ability

Q56

MCQ[2 Marks]

Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear "lost", it was found that wallets with money are more likely to be returned than wallets without money. Similarly, wallets that had a key and money are more likely to be returned than wallets with the same amount of money alone. This suggests that the primary reason for this behavior is compassion and empathy. Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A)

Wallets with a key are more likely to be returned because people do not care about money

(B)

Wallets with a key are more likely to be returned because people relate to suffering of others

(C)

Wallets used in experiments are more likely to be returned than wallets that are really lost

(D)

Money is always more important than keys

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q57

MCQ[2 Marks]

A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle that can be inscribed within the rhombus?

(A)

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

(B)

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

(C)

$\sqrt{2}$

(D)

$2\sqrt{2}$

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q58

MCQ[2 Marks]

An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters (circumferences) of the equilateral triangle to square to circle?

(A)

$3\sqrt{3}:2:\sqrt{\pi}$

(B)

$3\sqrt{3}:2:\sqrt{\pi}$

(C)

$3\sqrt{3}:4:2\sqrt{\pi}$

(D)

$3\sqrt{3}:2:2\sqrt{\pi}$

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q59

MCQ[2 Marks]

Given below are three conclusions drawn based on the statements: 1. All teachers are professors. 2. No professor is a male. 3. Some males are engineers. Which conclusions can be logically inferred?

(A)

Only conclusion III is correct

(B)

Only conclusion I and conclusion II are correct

(C)

Only conclusion II and conclusion III are correct

(D)

Only conclusion I and conclusion III are correct

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q60

MCQ[2 Marks]

In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration?

(A)

11

(B)

12

(C)

144

(D)

2

Explanation