Author: Vidhyarthi Darpan

GATE 2020 Statistics Previous Year Paper 

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q.No. 1 Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world champion in boxing, recently in a ceremony the Rashtrapati Bhawan (the President’s official residence) in New Delhi. 

(A)with,

(B)at on,

(C)on, at

(D)to, at

Q.No. 2 Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are 

(A) slim

(B) bright

(C) obvious

(D) uncertain

Q.No. 3 Select the word that fits the analogy: 

Cover : Uncover :: Associate : 

(A) Unassociate

(B) Inassociate 

(C) Misassociate

(D) Dissociate

Q.No. 4 Hit by floods, the kharif (summer sown) crops in various parts of the country have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period. 

Which of the following statements can be inferred from the given passage?

(A)Officials declared that the food-grain production target will be met due to good rains.

(B)Officials want the food-grain production target to be met by the November-February period.

(C)Officials feel that the food-grain production target cannot be met due to floods.

(D)Officials hope that the food-grain production target will be met due to a good rabi produce.

Q.No. 5 The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is _____________

(A) n²

(B) n² + n

(C) 2n² – n

(D) 2n² +n

Q6 – Q10 carry two marks each. 

Q.No. 6 Repo rate is the rate at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks. 

Which of the following statements can be inferred from the above passage? 

(A)Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks. 

(B)Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks. 

(C)Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks. 

(D)Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Q.No. 7 P, Q, R, S, T, U, V, and W are seated around a circular table. 

I. S is seated opposite to W. 

II. U is seated at the second place to the right of R. 

III. T is seated at the third place to the left of R. 

IV. V is a neighbour of S. 

Which of the following must be true? 

(A) P is a neighbour of R.

(B) Q is a neighbour of R.

(C) P is not seated opposite to Q. 

(D) R is the left neighbour of S.

Q.No. 8 The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other? 

(A) 66.6

(B) 75.2

(C) 88.2

(D) 116.5

Q. No. 9 For a matrix M = [m_ij]; i, j = 1,2,3,4, the diagonal elements are all zero and m_ij = -m_ij: The minimum number of elements required to fully specify the matrix is______ 

(A) 0

(B) 6

(C) 12

(D) 16

Q.No. 10 The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 – 2018 is Company P Company Q 

(A) 15:17

(B) 16:17

(C) 17:15

(D) 17:16

Q1 – Q25 carry one mark each. 

Q.No. 1 Let M be a 3 × 3 non-zero idempotent matrix and let I₃ denote the 3 × 3 identity matrix. Then which of the following statements is FALSE? 

(A) The eigenvalues of M are 0 and 1

(B) Rank(M) = Trace(M)

(C) I₃ – M^-1 is idempotent

(D) (I₃ + M)^-1 = I₃ – 2M

Q.No.2 Let C denote the set of all complex numbers. Consider the vector space 

V = {(a,b,c): a,b,c e C, a + 5 = 0, b + c = 0}, 

over the field of real numbers, where for any complex number z, z denotes its complex conjugate. If i = √-1, then a basis of V is 

(A){(1,-1,1),(i,i,i)}

(B){(1,-1,1), (i, -i,i)}

(C){(1, -i, 1), (i,1,1)}

(D){(1, -i,1),(i,1,-1)}

Q.No. 3 Let S = {(x, y) E R R: x² – y² = 4} and f: S ⟶ R be defined by f(x,y) = 6 x + y2, where R denotes the set of all real numbers. Then 

(A) f is bounded on S

(B) the maximum value off on S is 13

(C) the minimum value of f on S is -14

(D) the minimum value off on S is -13

Q.No. 4 Let f: R XR → R be defined by 

Where R denotes the set of all real numbers and c E R is a fixed constant. Then, which of the following statements is TRUE? 

(A) There does NOT exist a value of c for which f is continuous at (0,0)

(B) f is continuous at (0,0) if c = 0 

(C) f is continuous at (0,0) if c = 10

(D) f is continuous at (0,0) if c = 16

Q.No. 5 The moment generating function of a random variable X is given by 

Then P(X ≤ 2) equals 

(A) 1/3

(B) 1/6

(C) 1/2

(D)5/6

Q.No. 6 Consider the following two-way fixed effects analysis of variance model 

Where ε_ijk‘s are independently and identically distributed N(0,0%) random variables, .

Let SSE denote the sum of squares due to error. For any positive integer v and any ∝ € (0,1), let X_V²∝ denote the (1 – ∝)-th quantile of the central chi-square distribution with v degrees of freedom. Then a 95% confidence interval for σ² is given by SSE x? 

Q.No. 7 Let X₁,…,X₂₀ be independent and identically distributed random variables with the common probability density function 

Then the distribution of the random variable is

(A) central chi-square with 10 degrees of freedom 

(B) central chi-square with 20 degrees of freedom 

(C) central chi-square with 30 degrees of freedom 

(D) central chi-square with 40 degrees of freedom 

Q.No. 8 Let X₁, …, X₁₀ be a random sample from a Weibull distribution with the probability density function 

where For any positive integer v and any a the quantile of the central chi-square distribution with v degrees of freedom. Then, a 90% confidence interval for θ is 

Q.No. 9 Let X₁, …, X_n be a random sample of size n (≥ 2) from a uniform distribution on the interval [-θ, θ], where θ ε (θ,∞). A minimal sufficient statistic for θ is 

Q.No. 10 Let X₁, …, X_n be a random sample of size n (≥ 2) from N(θ,2θ²) distribution, where θ ε (0,∞). Which of the following statements is TRUE? 

Q.No. 11 Let be a Poisson process with rate λ= 2. Given that N(3) = 1, the expected arrival time of the first event of the process is 

(A) 1

(B) 3/2 

(C) 2/3

(D) 3

Q.No. 12 Consider the regression model 

where β₀ and β₁ are unknown parameters and εi’s are random errors. Let y_i be the observed value of Y_i, i = 1, …, n. Using the method of ordinary least squares, the estimate of β₁ is 

Q.No. 13 Let In be a random sample of size n (≥2) from N_p (0, Σ) distribution, where is a positive definite matrix. Define 

where for any column vector U, U^t denotes its transpose. Then the distribution of the statistic is 

Q.No. 14 Consider a two-way fixed effects analysis of variance model without interaction effect and one observation per cell. If there are 5 factors and 4 columns, then the degrees of freedom for the error sum of squares is 

(A) 20

(B) 19

(C) 12

(D) 11

Q.No. 15 Let X₁, …, X_n be a random sample of size n (≥2) from an exponential distribution with the probability density function 

where Consider the problem of testing against based on X₁, …, X_n. Which of the following statements is TRUE? 

(A) Likelihood ratio test at level leads to the same critical region as the corresponding most powerful test at the same level. 

(B) Critical region of level likelihood ratio test is is the a-th quantile of the central chi-square distribution with 2n degrees of freedom 

(C) Likelihood ratio test for testing H₀ against H₁ does not exist 

(D) At any fixed level , the power of the likelihood ratio test is lower than that of the most powerful test 

Q.No. 16 The characteristic function of a random variable X is given by 

Q.No. 17 Let the random vector X = (X₁, X₂, X₃, X₄) follow N₄(μ, ∑) distribution, where 

Then P(X₁ + X₂ + X₃ + X₄ > 0) = _______________ (correct up to one decimal place).

Q.No. 18 Let {X_n}_n≥0 be a homogeneous Markov chain with state space {0,1} and one 

step transition probability matrix , then 27 × E(X₂) ______________= (correct up to two decimal places). 

Q. No. 19 Let E, F and G be mutually independent events with P(E) = 1/2, P(F) = 1/3 and P(G) = 1/4. Let p be the probability that at least two of the events among E,F and G occur. Then 12 × p = __________ (correct up to one decimal place). 

Q.No. 20 Let the joint probability mass function of (X,Y,Z) be 

where k = 10 – x – y – z; x, y, z = 0,1, … , 10; x + y + z ≤ 10. Then the variance of the random variable Y + Z equals _____________ (correct up to one decimal place). 

Q.No. 21 The total number of standard 4 X 4 Latin squares is___________

Q.No. 22 Let X be a 4 × 1 random vector with E(X) = 0 and variance-covariance matrix 

Let Y be the 4 × 1 random vector of principal components derived from ∑. The proportion of total variation explained by the first two principal components equals __________ (correct up to two decimal places). 

Q.No. 23 Let X₁, …,X_n be a random sample of size n (≥2) from an exponential distribution with the probability density function 

Q.No. 24 Let where x_i‘s are fixed covariates and εi’s are independent and identically distributed random variables with mean zero and finite variance. Suppose that α and β are the least squares estimators of α and β, respectively. Given the following data: 

where y_i is the observed value of Y_i, i = 1, …, 7. Then the correlation coefficient between and equals 

Q.No. 25 Let {0,1,2,3} be an observed sample of size 4 from N(θ,5) distribution, where θ ε [2,∞). Then the maximum likelihood estimate of θ based on the observed sample is _________.

Q26 – Q55 carry two marks each. 

Q.No. 26 Let f: × → be defined by 

where denotes the set of all real numbers. Then 

Q.No. 27 Consider the linear transformation T: ³ → ³ defined by 

Where is the set of all complex numbers and ³ = × × . Which of the following statements is TRUE? 

(A) There exists a non-zero vector X such that T(X) = -X 

(B) There exist a non-zero vector Y and a real number λ ≠ 1 such that T(Y) = λY 

(C) T is diagonalizable 

(D) T² = I₃, where I₃ is the 3 × 3 identity matrix 

Q.No. 28 For real numbers a, b and c, let 

Then, which of the following statements is TRUE? 

(A) Rank(M) = 3 for every a, b, c ∈

(B) If a + c = 0 then M is diagonalizable for every b ∈

(C) M has a pair of orthogonal eigenvectors for every a,b,c ∈

(D) If b = 0 and a + c = 1 then M is NOT idempotent 

Q.No. 29 Let M be a 4 × 4 matrix with (x – 1)²(x – 3)² as its minimal polynomial. Then, which of the following statements is FALSE? 

(A) The eigenvalues of M are 1 and 3 

(B) The algebraic multiplicity of the eigenvalue 1 is 3 

(C) M is NOT diagonalizable 

(D) Trace(M) = 8 

Q.No. 30 Let f: × → be defined by 

f(x.y)=|y-2||x-1|,      (x,y) ×

where denotes the set of all real numbers. Then which of the following statements is TRUE? 

(A) f is differentiable at (1,2) 

(B) f is continuous at (1,2) but NOT differentiable at (1,2) 

(C) The partial derivative of f, with respect to x, at (1,2) does NOT exist 

(D) The directional derivative of f at (1,2) along u=12,12equals 1

Q.No. 31 Which of the following functions is uniformly continuous on the specified domain? 

Q.No. 32 Let the random vector X = (X₁, X₂,X₃) have the joint probability density 

function 

Which of the following statements is TRUE? 

(A) X₁, X₂ and X₃ are mutually independent 

(B) X₁, X₂, and X₃ are pairwise independent 

(C) (X₁, X₂) and X₃ are independently distributed 

(D) Variance of X₁ + X₂ is π² 

Q.No. 33 Suppose that P₁ and P₂ are two populations having bivariate normal distributions with mean vectors respectively, and the same variance-covariance matrix be two new observations. If the prior probabilities for P₁ and P₂ are assumed to be equal and the misclassification costs are also assumed to be equal then, according to linear discriminant rule, 

(A) Z₁ is assigned to P₁ and Z₂, is assigned to P₂ 

(B) Z₁ is assigned to P₂ and Z₂ is assigned to P₁ 

(C) both Z₁ and Z₂ are assigned to P₁ 

(D) both Z₁ and Z₂ are assigned to P₂ 

Q.No. 34 Let X₁, …, X_n be a random sample of size n (≥2) from an exponential distribution with the probability density function 

where Which of the following statements is TRUE?

Q.No. 35. Let the joint distribution of (X, Y) be bivariate normal with mean vector and variance-covariance matrix where -1 < p < 1. Then E[max (X , Y)] equals 

Q.No. 36 Let X₁, X₂, …, X₁₀ be independent and identically distributed N₃(0,I₃) random vectors, where I₃ is the 3 × 3 identity matrix. Let 

where J₃ is the 3 × 3 matrix with each entry 1 and for any column vector U, U^t denotes its transpose. Then the distribution of T is 

(A) central chi-square with 5 degrees of freedom 

(B) central chi-square with 10 degrees of freedom 

(C) central chi-square with 20 degrees of freedom 

(D) central chi-square with 30 degrees of freedom 

Q.No. 37 Let be independent and identically distributed random vectors, where is a positive definite matrix. Further, let matrix, where for any matrix M, M^t denotes its transpose. If W_m(n, ∑) denotes a Wishart distribution of order m with n degrees of freedom and variance covariance matrix 2, then which of the following statements is TRUE? 

Q.No. 38 Let the joint distribution of the random variables where 

Then which of the following statements is TRUE? 

(A) X₁ – X₂ + X₃ and X₁ are independent 

(B) X₁ + X₂ and X₃ – X₁ are independent 

(C) X₁ – X₂ + X₃ and X₁ + X₂ are independent 

(D) X₁ – 2X₂ and 2X₁ + X₂ are independent 

Q.No. 39 Consider the following one-way fixed effects analysis of variance model 

Q.No. 40 Let X₁, …, X_n be a random sample of size from N(θ,1) distribution, where θ∈ (-∞,∞). Consider the problem of testing Ho: θ ∈ [1,2] against H:θ <1 or θ > 2, based on X₁, …,X_n. Which of the following statements is TRUE? 

Q.No. 41 In a pure birth process with birth rates λ_n = 2ⁿ, n ≥ 0, let the random variable T denote the time taken for the population size to grow from 0 to 5. If Var(T) denotes the variance of the random variable T, then 256 ×Var(T) = _____________

Q.No. 42 Let {X_n]_n≥0 be a homogeneous Markov chain whose state space is {0,1,2} and TO 1 01 whose one-step transition probability matrix is Then nP(X2n=2|X0=2)= ________________(correct up to one decimal place). 

Q.No. 43 Let (X,Y) be a random vector such that, for any y > 0, the conditional probability density function of X given Y = y is 

If the marginal probability density function of Y is 

then E(Y|X = 1) = ________  (correct up to one decimal place). 

Q.No. 44 Let (X,Y) be a random vector with the joint moment generating function 

Let Φ(.) denote the distribution function of the standard normal distribution and and Φ (1.5) = 0.9332 then the value of 2 p + 1 (round off to two decimal places) equals _______

Q.No. 45 Consider a homogeneous Markov chain {X_n}_n≥0 with state space {0,1,2,3} and one-step transition probability matrix 

Assume that P(X₀ = 1) = 1. Let p be the probability that state 0 will be visited before state 3. Then 6 × p = __________

Q.No. 46 Let (X,Y) be a random vector with joint probability mass function 

where Then the variance of Y equals ____________

Q.No. 47 Let X be a discrete random variable with probability mass function f ∈{f₀, f₁}, 

where 

The power of the most powerful level α = 0.1 test for testing H₀: X ~ f₀ against H₁:X ~ f₁, based on X, equals ___________ (correct up to two decimal places). 

Q.No. 48 Let X = (X₁,X₂,X₃) be a random vector following N₃ (0, ∑) distribution, 

where . Then the partial correlation coefficient between X₂ and X₃, with fixed X₁, equals _______ (correct up to two decimal places). 

Q.No. 49 Let X₁, X₂, X₃ and X₄ be a random sample from a population having probability density function and f(-x) = f(x), for all For testing H₀: θ = 0 against H₁ : θ <0, let T⁺ denote the Wilcoxon Signed-rank statistic. Then under H₀, 

Q.No. 50 A simple linear regression model with unknown intercept and unknown slope is fitted to the following data 

using the method of ordinary least squares. Then the predicted value of y corresponding to x = 5 is _________

Q.No. 51 Let where denotes the set of all real numbers. If then 84 × 1 = _____________________________

Q.No. 52 Let the random vector (X,Y) have the joint distribution function 

Let Var(X) and Var(Y) denote the variances of random variables X and Y, respectively. Then 16 Var(x) + 32 Var(Y) = _________________

Q.No. 53 Let {X_n}_n≥1 be a sequence of independent and identically distributed random variables with Further, let 

where Φ (.) denotes the cumulative distribution function of the standard normal distribution, then c² = _______________(correct up to one decimal place). 

Q.No. 54 Let the random vector X = (X₁, X₂, X₃) have the joint probability density function 

Then the variance of the random variable X₁ + X₂ + X₃ equals _____________. (correct up to one decimal place). 

Q.No. 55 Let X₁, …,X₅ be a random sample from a distribution with the probability density function 

where For testing H₀: θ = 0 against   the sign test statistic, where 

 otherwise Then the size of the test, which rejects H, if and only if equals _______________ (correct up to one decimal place). 

GATE 2020 Textile Engineering and Fibre Science Previous Year Paper

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q.1 This book, including all its chapters____interesting. The students as well as the, instructor __________in agreement about it. 

(A)is, was

(B)are, are

(C)is, are

(D)were, was

Q.2 their vehicles near the entrance of the main administrative People were prohibited building 

(A)to park

(B)from parking

(C)parking

(D)to have parked

Q.No.3 Select the word that fits the analogy: 

Do: Undo :: Trust : 

(A)Entrust

(B)Intrust

(C)Distrust

(D)Untrust

Q.No.4 Stock markets ________ at the news of the coup. 

(A) poised

(B) plunged

(C) plugged

(D) probed

Q.5 If P,Q,R,S are four individuals, how many teams of size exceeding one can be formed, with Q as a member? 

(A) 5

(B) 6

(C) 7

(D) 8

 Q6 – Q10 carry two marks each. 

Q.No.6 Non-performing Assets (NPAs) of a bank in India is defined as an asset, which remains unpaid by a borrower for a certain period of time in terms of interest, principal, or both. Reserve Bank of India (RBI) has changed the definition of NPA thrice during 1993-2004, in terms of the holding period of loans. The holding period was reduced by one quarter each time. In 1993, the holding period was four quarters (360 days).

(A) √2

(B) √3

(C) 2

(D) 3

Q.10 The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was _______

(A) 32.7
(B) 33.7
(C) 34.1
(D) 35.1

TF: Textile Engineering and Fibre Science 

Q1-Q25 carry one mark each. 

Q.1 For the matrix , the eigenvalues of the matrix AP are

(A)1,0,1

(B)1,0,0

(C)1, 1,0

(D)1,1,1

Q.2 The integrating factor of the differential equation dy/dx + y = e-x is 

(A)ex

(B)e-x

(C)xe-x

(D)xex

Q.3 Laplace transform of cosh(t) is 

(A)1/S2 – 1

(B)S/S-1

(C)S/S2 – 1

(D)S/S2+1

Q.4 In wool, the sulfur containing amino acid is 

(A)Alanine

(B)Cystine

(C)Glycine

(D)Serine

Q.5 Viscose rayon is soluble in 

(A) Acetone

(B) Chloroform

(C) Formic 85% (v/v)

(D) acid Sulfuric acid 59% (w/w)

Q.6 In carding, the highest draft is kept between 

(A) Lap roller and feed roller

(B) Feed roller and licker-in

(C) Licker-in and cylinder

(D) Cylinder and doffer

Q.7 The spinning system in which one revolution of twisting element imparts several turns to the fibre strand is 

(A) Ring

(B) Rotor

(C) Friction

(D) Wrap

Q.8 The technology that does NOT produce a nonwoven fabric is 

(A) Spunbonding

(B) Hydroentangling

(C) Melt Blowing

(D) Braiding

Q.9 For the same yarn and fabric sett, the weave that gives the maximum tearing strength is 

(A) Plain

(B) 2×2 matt

(C) 5-end satin

(D) 2/1 twill 

Q.10 Two yarns have variance of strength as V1 and V2. If Vi< V2, the variance ratio F would be 

(A)V2 /V1

(B)V1 /V2

(C)V12 /V22

(D)V22 /V12

Q.11 Cotton fibre length parameter that CANNOT be obtained from Baer Sorter diagram is 

(A) Mean length

(B) Dispersion

(C) Uniformity ratio

(D) Modal length

Q.12 The purpose of carbonization of wool fibres is to remove 

(A) Waxy matter

(B) Surface scales

(C) Vegetable matter

(D) Ortho-cortex

Q.13 Biopolishing of cotton fabrics is done using 

(A) Cellulase

(B) Amylase

(C) Proteinase

(D) Esterase

Q.14 For the given system of linear equations, 2x -z = 1; 5x + y = 7; y + 3z = 5, the sum of x, y and z is _______________.

Q.15 If F = xi + yj + zk, then the magnitude of 7x F is ______________.

Q.16 A polypropylene filament is drawn in two stages with draw ratios of 1.5 and 2 respectively. The overall draw ratio is ___________.

Q.17 The refractive indices of a filament in axial and radial directions are 1.58 and 1.52 respectively. The birefringence of the filament (correct up to 2 decimal places) is._____________

Q.18 A twin-delivery drawframe, running at a delivery speed of 800 m/min with an efficiency of 95%, is producing 5.9 ktex sliver. The rate of production of the draw frame in kg/h (rounded off to 2 decimal places) is _____________

Q.19 The diameter (mm) of a yarn having twist of 700 turns per meter and surface twist angle of 20° (rounded off to 2 decimal places) is _________________

Q.20 A magazine creel has 800 package holders. The effective creel capacity (number) is ___________

Q.21 A shuttle loom is running at 180 picks per minute. The angular velocity of crank shaft (degree/second) is _____________

Q.22 The length (km) of 5 kg of 30 Ne yarn (rounded off to the nearest integer) is __________

Q.23 The limit irregularity and measured irregularity of a yarn are 8.4% and 9.6%, 

respectively. The Index of Irregularity (rounded off to 2 decimal places) is __________

Q.24 A padding mangle is processing a fabric at 1320 m/h. The bottom bowl of the mangle is rotating at 25 rpm. Assuming zero slippage at the nip, the diameter (cm) of this bowl is ___________

Q.25 A Procion H (monochlorotriazine based) reactive dye used for printing of cotton has a molecular weight of 471. Taking the atomic weight of H=1, C=12, N=14, O=16, CI=35.5, the molecular weight of the fully hydrolyzed dye (correct up to 1 decimal place) would be ____________

Q26 – Q55 carry two marks each. 

Q.26 Let L = lim(sin x) tanx. The value of L is 

(A) 0

(B) 1

(C) 2

(D) ∞

Q.27 The solution of the differential equation = 0, which satisfies the conditions, y(0) = 0, y'(0) = 3 is

(A) e-x 

(B) ex

(C) ex + e-2x 

(D) ex – e-2x

Q.28 In melt spinning of poly(ethylene terephthalate), pre-drying of polymer chips is essential to avoid 

(A) Hydrolytic degradation

(B) Oxidative degradation

(C) Microbial degradation

(D) Photo-induced degradation

Q.29 Determine the correctness or otherwise of the following Assertion (a) and Reason 

[a]: Caprolactam is polymerized in the presence of a small amount of water to produce fibre grade nylon 6. 

Im I 

[r]: Water acts as a catalyst and converts caprolactam to aminocaproic acid. 

(A) Both [a] and [1] are true and [7] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(C) Both [a] and [r] are false 

(D) [a] is true but [r] is false 

Q.30 Determine the correctness or otherwise of the following Assertion [a] and Reason 

[r] 

[a]: Melting point of nylon 66 fibre is much higher than that of polyethylene fibre. 

[r]: The molecular weight of nylon 66 fibre is significantly higher than that of polyethylene fibre. 

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(C) Both [a] and [1] are false

(D) [a] is true but [r] is false

Q.31 Carding of polyester fibres requires that the values of wire-point density 

(points/inch2) of 

(P) Licker-in 

(Q) Cylinder 

(R) Flat 

follow the order 

(A) P<Q R 

(B) P<R<Q 

(C) Q<R<P

(D) Q<P<R

Q.32 For combing with forward feed, the given parameters are: Detachment setting = 15 mm, Length of feed per combing cycle=6 mm, Longest fiber length = 30 mm. According to Gégauff’s theory, the noil (%) would be 

(A) 9

(B) 16

(C) 30

(D) 49

Q.33 Determine the correctness or otherwise of the following Assertion (a) and Reason 

[r] 

[a]: Open-loop auto levelling system needs a signal storage device with time delay 

function. 

[r]: The signal must be stored until the material reaches the adjusting point. 

(A) Both [a] and [r] are true and [r] is the correct reason for [a] 

(B) Both [a] and [1] are true but [r] is not the correct reason for [a] 

(C) Both [a] and [r] are false

(D) [a] is true but [r] is false

Q.34 If both the concentration (%, w/w) of size paste and target add-on are 12%, the total wet pick-up (kg) by 12 kg bone-dry warp sheet is 

(A) 6

(B) 12

(C) 18

(D) 24

Q.35 At front centre (0°) and at back centre (180°) of a shuttle loom, 

(A)The sley velocities are the same but accelerations are different.

(B)The sley velocities are different but accelerations are the same.

(C)The sley velocities are the same and also accelerations are the same.

(D)The sley velocities are different and also accelerations are different. 

Q.36 Match the looms listed in Group I with the corresponding components given in Group II. The correct option is 

Group I                                         Group II 

P. Multiphase                         1. Matched cam 

Q. Projectile                            2. Profile reed 

R. Air-jet                                    3. Crank shaft 

S. Shuttle 4. Weaving rotor

(A) P-1, Q-4, R-2, S-3

(B) P-1, Q-2, R-4, S-3

(C) P-4, Q-1, R-2, S-3

(D) P-3, Q-1, R-2, S-4

Q.37 Consider two yarns, one 100% wool and the other 100% cotton, each containing 100 fibres in the yarn cross-section. The respective limit irregularities (%) of wool and cotton yarns will approximately be 

(A) 11.2 and 10.6

(B) 10.6 and 11.2

(C) 11.8 and 11.2

(D) 11.8 and 10.6

Q.38 If the numerical value X of yarn linear density, expressed in denier is the same as that expressed in English (Ne) system, then X approximately is 

(A) 24.3

(B) 48.6

(C) 72.9

(D) 97.2

Q.39 Determine the correctness or otherwise of the following Assertion [a] and Reason 

[r] 

[a]: Sodium chlorite is a bleaching agent for cotton. 

[r]: Sodium chlorite is an effective reducing agent. 

(A)Both [a] and [] are true and [r] is the correct reason for [a] 

(B)Both [a] and [r) are true but [r] is not the correct reason for [a]

(C)Both [a] and [r] are false

(D)[a] is true but [r] is false

Q.40 Determine the correctness or otherwise of the following Assertion (a) and Reason 

[a]: Acrylic fibres are dyed with basic dyes in acidic medium. 

[r]: In acidic medium the acrylic fibre acquires positive charge. 

(A) Both [a] and [r] are true and [r] is the correct reason for [a] 

(B)Both [a] and [r] are true but [r] is not the correct reason for [a] 

(C) Both (a) and rare false

(D) [a] is true but [r] is false

Q.41 Determine the correctness or otherwise of the following Assertion (a) and Reason 

[a]: Foam finishing significantly reduces the energy consumed in drying. 

[r]: The specific heat of air is significantly lower than that of water. 

(A) Both [a] and [f] are true and [r] is the correct reason for [a] 

(B) Both [a] and [r] are true but [r] is not the correct reason for [a] 

(C) Both [a] and [r] are false

(D) [a] is true but [7] is false

Q.42 If the probability density function of a continuous random variable X is given by f(x) = e-*, 0<x<co, the mean of random variable X is _____________

Q.43 Assuming the step size h = 1, the numerical value of the definite integral r2 x2 Jo 1+x3 dx obtained using Trapezoidal rule (rounded off to 2 decimal places) is_____

Q.44 In the production of PET, diglycol terephthalate (DGT) is an intermediate. Taking the atomic weights of H=1, C=12, 0=16, the molecular weight of DGT is _____

Q.45 In wet spinning of acrylic filament yarn, the volumetric flow rate of the spinning dope per spinneret hole is 0.1 cm3/min. If the surface speed at the first take up roller is 1.5 m/min and the diameter of spinneret hole is 0.02 cm, then the jet stretch (rounded off to 2 decimal places) is _____________

Q.46 Two types of polyester staple fibers of fineness 3 and 6 denier and having the  same length are mixed in a ratio of 2:3 by weight. The mean fibre fineness (denier) of the mix (rounded off to 2 decimal places) is ______________

Q.47 Two rovings, each with a mass CV of 10%, are fed to a ring spinning machine that adds a mass CV of 20%. The mass CV (%) of the yarn (rounded off to 2 decimal places) is ________________

Q.48 In a drum-driven winder, the grooved drum having a width of 20 cm is rotating at 1000 rpm. If the drum makes 5 revolutions per double traverse, the traverse speed (m/min) is _____________

Q.49 The whale constant and course constant are 4.2 and 5.04 respectively. If the loop length is 4.2 mm, then stitch density (number/cm’) is _________

Q.50 A cotton fibre has a degree of cell wall thickening (O) of 0.9 and perimeter of 40 um. The actual cross-sectional area of the wall (um) of the fibre (rounded off to 1 decimal place) is __________

Q.51 A fabric with mass per unit area of 250 g/m2 has flexural rigidity of 275 uN-m. The bending length (mm) of the fabric (rounded off to 2 decimal places) is _______

Q.52 The ‘standard machine rate of loading of a tensile tester, working on pendulum lever principle, is 440 N/cm. As the pendulum lever swings from 30° 10 45°, the *machine rate of loading’ (N/cm), reduces by___________ (rounded off to 2 decimal places) 

Q.53 Under a load of 500 cN, the extension of a yarn of 300 mm length is 10%. If the elastic recovery is 90%, then the length (mm) of the yarn after removal of load is_____ 

Q.54 Given that one gram mole of a gas occupies 22.4 L of volume at STP, the atomic weights of H=1, and that of O=16, the concentration (g/L) of hydrogen peroxide solution of 25 volume strength (rounded off to 2 decimal places) is ______________

Q.55 The work of adhesion (Ws) depends on the surface tension (Ylv) of the liquid and the contact angle (6) formed on a surface and is expressed as Yuv(1 + cose). The Wsz for a given fabric and a liquid is reduced to 1/3rd of the original value after oil repellent treatment. If the measured contact angle of the untreated fabric is 60°, the percent change in the contact angle after the treatment is ____________

ANSWER KEY

GATE 2020 Metallurgical Engineering Previous Year Paper 

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q. 1He is known for his unscrupulous ways. He always sheds __________tears to deceive people.

(A)fox’s
(B)crocodile’s
(C)crocodile
(D)fox 

Q. 2 Jofra Archer, the England fast bowler, is __________than accurate. 

(A) more fast
(B) faster
(C) less fast 

(D) more faster

Q.No.3 Select the word that fits the analogy: 

Build : Building :: Grow: 

(A) Grown
(B) Grew
(C) Growth

(D) Growed

Q. 4 I do not think you know the case well enough to have opinions. Having said that, I agree with your other point. What does the phrase “having said that” mean in the given text? 

(A) as opposed to what I have said
(B) despite what I have said
(C) in addition to what I have said 

(D) contrary to what I have said 

Q. 5 Define [x] as the greatest integer less than or equal to x, for each x € (-00,00). If y = [x], then area under y for x € [1,4] is 

(A) 1
(B) 3
(C) 4

(D) 6

Q6 – Q10 carry two marks each. 

Q. 6 Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project. 

Based on the above paragraph, which of the following is correct about crowd funding? 

(A) Funds raised through unwilling contributions on web-based platforms.
(B) Funds raised through large contributions on web-based platforms.
(C) Funds raised through coerced contributions on web-based platforms.

(D) Funds raised through voluntary contributions on web-based platforms. 

Q. 7 P, Q, R and S are to be uniquely coded using a and B. If P is coded as aa and Q as aß, then R and S, respectively, can be coded as 

(A) Ba and aß
(B) BB and ac
(C) aß and BB

(D) Ba and BB 

Q. 8 The sum of the first n terms in the sequence 8, 88,888, 8888, … is 

Q. 9 Select the graph that schematically represents BOTH y = x” and y = x1/m properly in the interval OS X < 1, for integer values of m, where m > 1. 

Q. 10 The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates in percentage) of these four schools is 

(A) 58.5 %
(B) 58.8%
(C) 59.0 %

(D) 59.3%

MT: Metallurgical Engineering 

Q1 – Q 25 carry one mark each. 

Q. 1 The general solution to the following homogeneous ODE, 

The values of λ₁ and λ, are: 

(A) -1 and -3
(B) -3 and -3
(C) 1 and -3

(D) 1 and 3

Q. 2 The number of independent elastic constants of an isotropic material is: 

(A) 1
(B) 2
(C) 3 

(D) 4

Q. 3 A slip system consists of a slip plane and a slip direction. Which one of the following is NOT a valid slip system in a FCC copper crystal? 

(A) (111)[110]
(B) (111)[011]
(C) (111)[101]

(D) (111)[101]

Q. 4 A dielectric material is: 

(A) Electrical conductor

(B) Metallic magnet

(C) Two coupled electrical conductors

(D) Electrical insulator

Q. 5 Which one of the following processes is an example of an electrolytic cell? 

(A) Corrosion of a metal rod in ambient atmosphere

(B) Charging of a rechargeable battery

(C) Discharging of a rechargeable battery

(D) Sacrificial cathodic protection system

Q. 6 Which one of the following statements regarding selective leaching of a binary alloy is TRUE? 

(A) The lower atomic weight element is leached.

(B) The element having higher diffusivity is leached.

(C) The more electronegative element is leached. 

(D) The element with lower density is leached. 

Q. 7 In green sand casting, which one of the following is NOT a part of the gating system? 

(A) Runner

(B) Sprue

(C) Riser

(D) Pouring basin

Q. 8 For a material to exhibit superplasticity, one of the requirements is: 

(A) Coarse-grained microstructure

(B) High strain-rate sensitivity

(C) Low strain-hardening exponent

(D) High modulus of elasticity

Q. 9 The dye penetrant test for detecting flaws is based on: 

(A) Magnetism

(B) Sound propagation

(C) X-ray absorption

(D) Capillary action

Q. 10 When 1 mole of C3H8 at 300 K is burnt with a stoichiometric amount of oxygen at 300 K to form CO2 and H20, the adiabatic flame temperature is 5975 K. If C3Hg is burnt under the same conditions but with excess oxygen, the adiabatic flame temperature will be 

(A) equal to 5975 K irrespective of the amount of excess oxygen.

(B) higher than 5975 K irrespective of the amount of excess oxygen.

(C) lower than 5975 K irrespective of the amount of excess oxygen. 

(D) higher or lower than 5975 K depending on the amount of excess oxygen.

Q. No. 11 Two solid spheres X and Y of identical diameter are made of different materials having thermal diffusivities 100 x 10-6 m?s-1 and 25 x 10-6 ms-1 respectively. Both spheres are heated in a furnace maintained at 1000 K. If the center of the sphere X reaches 800 K in 1 hour, time required for the center of sphere Y to reach 800 K is

(A) 1 hour

(B) 2 hours.

(C) 4 hours.

(D) 16 hours.

Q. 12 Select the correct spectra (shown on a log-log scale in the figures) for emission from a gray surface and a black body, both maintained at 1000 K. 

Q. 13 Given the three vectors X =-i-j+k, Y=-i+2j + k and Z= i + k, which one of the following statements is TRUE? 

(A) X, Y and Z are mutually perpendicular.

(B) X, Y and Z are coplanar.

(C) X makes an angle of 30° with the normal to the plane containing Y and Z.

(D) Z makes an angle of 60° with the normal to the plane containing X and Y.

Q. 14 Angle between two neighboring tetrahedral bonds in Si having a diamond cubic structure is: 

(A) 102.5°

(B) 109.50

(C) 120⁰

(D) 135.5⁰

Q. 15 The sequence of precipitation during aging of Al – 4 wt% Cu alloy is: 

Q. 16 The indenter used in Rockwell hardness measurements on C scale is

(A) diamond cone.

(B) 10 mm steel ball.

(C) diamond pyramid.

(D) 1/16-in. steel ball

Q. 17 For the function y=a*, the derivative, at x = 1 is: 

(A) 1
(B) a
(C) a² 

(D) alna

Q. 18 Cupola is a furnace used to produce 

(A) cast irons.
(B) plain carbon steels.
(C) copper alloys

(D) aluminium alloys.

Q. 19 The functions y = e* and y = e-* intersect at the point: 

(A) (1,3)
(B) (-2, 2)
(C) (0, 1)

(D) (-1,-1)

Q. 20 A heavily cold-worked metal will 

(A) yield a coarser recrystallized grain size.
(B) possess a lower driving force for recrystallization.
(C) have a higher energy barrier for nucleation of recrystallized grains. 

(D) recrystallize at lower temperatures. 

Q. 21 For the function f(x) given in the figure, the value of S(1 – f(x)) dx is_______(round off to one decimal place). 

Q. 22 A component subjected to tensile stress in a mechanical device is monitored periodically for cracks by NDT. The NDT technique can only detect cracks (both surface and internal) which are larger than 1 mm. Keeping a 10% margin of safety, the maximum allowed tensile stress on the component will be______—–MPa (round off to the nearest integer). 

Given, fracture toughness Kic=30 MPa m12 and assume crack geometry factor of unity. 

Q. 23 An iron plate with a total exposed surface area of 50 cm2 undergoes atmospheric corrosion. If 200 g of weight is lost over a period of 10 years, then the corrosion rate is ________kg.m2 year” (round off to the nearest integer). 

Q. 24 In cold-rolling, for the sheet to be drawn into rolls, the angle of contact (or angle of bite) should be less than or equal to _______degree (round off to one decimal place). 

Given, the coefficient of friction between sheet and roll is 0.1 

Q. 25 The number of atoms per unit area in (100) plane of Pb is _______(round off to the nearest integer). 

Given, crystal structure and atomic radius of Pb are FCC and 0.175 nm respectively. 

Q26 – Q55 carry two marks each. 

Q. 26 In the edge dislocation configuration given in the figure, dislocations X and Y  are fixed and separated by a distance 2h on the same slip plane. Dislocation Z is free to glide on a parallel slip plane. The two slip planes are separated by a distance h. Which one of the following statements is TRUE regarding the stability of dislocation Z at positions 1, 2 and 3? 

Assume all dislocations have identical Burgers vector. 

(A) Position 1: unstable equilibrium; Position 2: unstable; Position 3: unstable
(B) Position 1: stable equilibrium; Position 2: unstable; Position 3: unstable
(C) Position 1: unstable equilibrium; Position 2: stable; Position 3: unstable

(D) Position 1: stable equilibrium; Position 2: unstable; Position 3: stable

Q. 27 Which one of the following dislocation reactions is NOT feasible in a FCC crystal? 

Q. 28 A galvanic cell is formed by connecting Zn (E2n2+/Zn = -0.76 V) and Fe (Efez+/Fe = -0.44 V) wires immersed in their respective ion solutions. The cell discharges spontaneously with a voltage of 0.5 V. The ratio of the concentration of [Fe2+] to [Zn2+] ions in the cell is of the order of: 

Given, R = 8.314 J.mol-‘.K!, F = 96500 C.mol-‘, T = 298 K 

(A) 10^-6
(B) 10^-5
(C) 10⁶

(D) 10⁷

Q. 29 The divergence of the vector field (x3 + y3)i + 3xy?j + 3zyak is: 

Q. 30 Match the products in Column I with the manufacturing processes in Column II. 

(A) P-1, Q-2, R-3, S-4
(B) P-2, Q-3, R-1, S-4
(C) P-4, Q-1, R-2, S-3

(D) P-4, Q-2, R-1, S-3

Q. 31 f(x) = x ln(x) + (1 – x) In(1 – x) + 3 x (1 – x) has______at x = 0.5 

(A) a local minimum
(B) a local maximum
(C) a point of inflection

(D) a non-zero slope 

Q. 32 Match the processes in Column I with the most appropriate mechanisms in Column II. 

(A) P-1, Q-4, R-2, S-3
(B) P-3, Q-1, R-2, S-4
(C) P-3, 0-4, R-2, S-1

(D) P-1, Q-2, R-3, S-4

Q. 33 Match the reactors in Column I with the corresponding products in Column II. 

(A) P-1, Q-3, R-2, S-4
(B) P-3, Q-4, R-2, S-1
(C) P-3, Q-1, R-2, S-4

(D) P-3, Q-1, R-4, S-2

Q. 34 X-ray diffraction pattern from an elemental metal with a FCC crystal structure shows the first peak at a Bragg angle 0 = 24.650. The lattice parameter of this metal is ___________nm. 

Given, the wavelength of the X-ray used is 0.1543 nm. 

(A) 0.185
(B) 0.262
(C) 0.320 

(D) 0.370

Q. 35 Match the materials in Column I with their common applications in Column II. 

(A) P-1, Q-3, R-2, S-4
(B) P-4, Q-2, R-1, S-3
(C) P-2, Q-1, R-4, S-3

(D) P-2, Q-3, R-1, S-4

Q. 36 The Mg-Sn phase diagram exhibits two eutectics on either side of the high melting intermetallic line compound, Mg2Sn, as given below. 

After the eutectic reaction has gone to completion and equilibrium has been attained at a temperature just below 561°C, the amount of eutectic constituent present in the alloy, Mg-50 wt.% Sn, is approximately ______________(in wt.%). 

Given, atomic weight of Sn is 118.7 and Mg is 24.3 

(A) 25
(B) 38
(C) 68

(D) 75

Q. 37 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r] 

Assertion [a]: Low-alloy steels used for medium-temperature creep resistance often have additions of strong carbide-forming elements. 

Reason [r]: During creep deformation, the particles with higher misfit with the matrix, lose coherency. 

(A) Both [a] and [r] are true and [r] is the correct reason for [a].
(B) Both [a] and [r] are true but [r] is not the correct reason for [a].
(C) Both [a] and [r] are false.

(D) [a] is true but [r] is false.

Q. 38 Determine the correctness or otherwise of the following Assertion [a] and the 

Reason [r] 

Assertion [a]: The rate of homogenization in a dilute substitutional solid solution of B in A is controlled by the diffusivity of B. 

Reason [r]: Atomic migration cannot occur along dislocations and grain boundaries. 

(A) Both [a] and [r) are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false

(D) [a] is true but [r] is false

Q. 39 Match the elements in Column I with their electronic behaviour given in 

(A) P-1, Q-2, R-3, S-4
(B) P-3, Q-4, R-1, S-2
(C) P-4, Q-1, R-2, S-3

(D) P-4, Q-3, R-1, S-2

Q. 40 Radius of the largest interstitial atom that can be accommodated in an octahedral void in BCC iron without distorting the lattice is_________nm (round off to three decimal places). 

Assume hard sphere model and radius of Fe atom as 0.124 nm. 

Q. 41 The production process of cylindrical pipes results in a statistical scatter in their diameter which is modelled by a normal distribution with a mean value of 10 mm. If the area under the normal curve between 9 mm and 10 mm is 0.35, then the probability of producing pipes of diameter greater than 11 mm is________(round off to two decimal places). 

Q. 42 The solution (using trapezoidal rule) of the integral 

by dividing the range 0 to 1 into two equal intervals is_______(round off to two decimal places). 

Q. 43 Iron is corroding in fresh water which has dissolved oxygen concentration of 15 mM. The anodic current density at an overpotential of 120 mV is________A.cm2 (round off to three decimal places). 

Given: 

1. Anodic Tafel slope is 0.06 V. 

2. Diffusion coefficient of oxygen is 2.42 x 10^-5 cm².s^-1 

3. Diffusion layer thickness is 0.06 cm. 

Q. 44 A metal oxidizes at 1200 K with a parabolic rate constant of 3×10-6 g².cm^-4.s^-1 Time taken for the oxide film to grow to a thickness of 2 um is_______s (round off to two decimal places). 

Given, the density of oxide is 6.5 g.cm^-3. 

Q.No.45 Two plates of composition, Fe^-10 wt.% Ni and Fe^-20 wt.% Cr^-5 wt% Ni are fusion-welded using a filler rod of composition 20 wt.% Ni-80 wt.% Cr. Contribution to dilution of the weld pool is 20% from each plate. The Ni content in the weld pool is________w t.% (round off to the nearest integer). 

Q. 46 Figure shows schematic of a venturimeter. The cross sectional area is 100 mm at A and is 50 mm at B. If air is flowing through the venturimeter at a flow rate of 10-3 mos’, the height H in the air-over-water manometer is mm_____________ (round off to the nearest integer). 

Assume: 

1. Incompressible flow with no friction losses. 

2. Density of air is 1 kg m^-3. 

3. Density of water is 1000 kg m^-3. 

4. Acceleration due to gravity is 9.8 m s^-2. 

Q. 47 For effective communication in a ball mill, it is desired that the balls travelling along the mill wall leave the wall at point C and travel freely in air along the path CDA, as shown in the figure. If ZBOC is 120°, the rotational speed of the mill is _____ rpm (rounded off to one decimal place) by performing suitable force balance at point C. 

Assume: 

1. There is no slip between the ball and mill wall. 

2. O is the rotational axis of the mill and OB is parallel to the vector g. 

3. Inner diameter of ball mill is 3.26 m. 

4. Acceleration due to gravity g is 9.8 m s2. 

Q. 48 If liquid copper is cooled to 1353 K, the magnitude of the driving force for liquid to transform to solid is_______J.mol^-1 (round off to one decimal place). 

Given, melting temperature and enthalpy of melting of copper are 1356 K and 13 kJ.mol^-1 respectively. 

Q. 49 1000 kg of liquid steel containing 0.03 wt.% S needs to be desulphurized using a slag to bring the sulphur content down to 0.015 wt.%. The quantity of slag needed is_________kg (round off to the nearest integer). 

Assume: 

1. Thermodynamic equilibrium 

2. No sulphur in the slag prior to desulphurization treatment 

Given the equilibrium sulphur partition ratio between slag and steel, is 50. 

Q. 50 Zone refining of Si results in residual P content of 0.1 parts per billion by weight. The electrical conductivity of this zone refined Si is _________22.m-1 (round off to two decimal places). 

Given: 

1. Avogadro number is 6.02×1023. 

2. Density of Si is 2.33 g.cm . 

3. Atomic weight of P is 30.97. 

4. Charge of electron is 1.6×10-19 A.S 

5. Mobility of electron is 0.2 m2.Vol.s! 

Q. 51 The steady state creep rate of a material increases by a factor of 20 when the temperature is increased from 890 K to 980 K. The creep rate at a temperature of______K (round off to the nearest integer) will be 5 times the creep rate at 890 K. 

Q. 52 Crack growth is being continuously measured in a test specimen subjected to constant amplitude cyclic stress with a mean stress of zero. The crack growth rate is related to the stress intensity range, AK as 

where, a is the crack length and N is the number of cycles. When the crack length increases by a factor of two, the crack growth rate will increase by a factor of_______(round off to one decimal place). 

Q. 53 In a top gated mold, liquid metal enters the mold cavity as a freely falling stream under gravity from a height of 0.5 m. Ignore the fluid friction due to viscosity and the drag due to changes in the direction of flow. If the volume of the mold cavity is 10 m, then the time required to fill the mold is__________ (round off to nearest integer). 

Given: 

1. Acceleration due to gravity is 9.8 m.s². 2. Cross-sectional area of the gate is 0.2 m2. 

Q. 54 A Basic Oxygen Furnace operator, at the end of oxygen blow, measures the dissolved oxygen content in the steel as 0.03 wt.% and the steel temperature as 1800 K. The carbon content [C] in the steel is ___________wt.% (round off to two decimal places). 

Assume: 

1) Equilibrium between dissolved carbon (C), dissolved oxygen [O], and 

CO (gas) at 1 atmosphere. 

2) Henry’s law is valid for both [C] and [O] 

Given: 

[C]1 wt.% Henrian Std. State + [O]1 wt.% Henrian Std. State → (CO)1 atm. Std. State 

△G° = -19840 – 40.65 T J 

R= 8.314 J.mol^-1.K^-1 

Q. 55 M and N are 3 x 3 matrices. If the det(M) is -9 and the det(N) is -14, then the det(NM) is ______________(round off to the nearest integer). 

Answer Key –

GATE 2020 Mining Engineering Previous Year Paper

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q. 1 Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world champion in boxing, recently in a ceremony the Rashtrapati Bhawan (the President’s official residence) in New Delhi.
(A) with,
(B) at on,
(C) on, at
(D) to, at

Q. 2 Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are

(A) slim
(B) bright
(C) obvious
(D) uncertain

Q. 3 Select the word that fits the analogy: 

Cover : Uncover :: Associate : 

(A) Unassociate
(B) Inassociate
(C)Misassociate
(D) Dissociate

Q. 4 Hit by floods, the kharif (summer sown) crops in various parts of the country have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period. 

Which of the following statements can be inferred from the given passage? 

(A) Officials declared that the food-grain production target will be met due to good rains.
(B) Officials want the food-grain production target to be met by the November-February period.
(C)Officials feel that the food-grain production target cannot be met due to floods.
(D) Officials hope that the food-grain production target will be met due to a good rabi produce. 

Q. 5 The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is _____________

(A) n²
(B) n² + n
(C) 2n² – n
(D) 2n² +n 

Q6 – Q10 carry two marks each. 

Q. 6 Repo rate is the rate at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks. 

Which of the following statements can be inferred from the above passage? 

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.
(B) Increase in repo rate will decrease the cost of borrowing and increase lending byC commercial banks.
(C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.
(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Q. 7 P, Q, R, S, T, U, V, and W are seated around a circular table. 

I. S is seated opposite to W. 

II. U is seated at the second place to the right of R. 

III. T is seated at the third place to the left of R. 

IV. V is a neighbour of S. 

Which of the following must be true? 

(A) P is a neighbour of R.
(B) Q is a neighbour of R.
(C) P is not seated opposite to Q.
(D) R is the left neighbour of S.

Q. 8 The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car How many kilometers the car Q had travelled when the cars crossed each other? 

(A) 66.6
(B) 75.2
(C) 88.2
(D) 116.5

Q. No. 9 For a matrix M = [m_ij]; i, j = 1,2,3,4, the diagonal elements are all zero and m_ij = -m_ij: The minimum number of elements required to fully specify the matrix is______ 

(A) 0
(B) 6
(C) 12
(D) 16

Q. 10 The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 – 2018 is 

Company P Company Q 

(A) 15:17
(B) 16:17
(C) 17:15
(D) 17:16

MN: Mining Engineering 

Q1-Q25 carry one mark each. 

Q. 1 The eigenvalues of the matrix are

(A)6,4
(B)4,5
(C)-2,5
(D)-4, 5

Q. 2 For the electric delay detonator shown in the figure, the components P, Q and R, 

(A) fuse head, delay element, priming charge
(B) fuse head, priming charge, delay element
(C) priming charge, delay element, fuse head
(D) delay element, fuse head, priming charge

Q. 3 Match the following safety arrangements for a surface-to-underground shaft hoist with their corresponding safety functions. 

(A) P-1, Q-2, R – 3
(B) P-3, Q – 1, R – 2
(C) P-2,Q – 3, R – 1
(D) P – 1,Q-3, R – 2

Q.No.4 The fore bearings and back bearings of the lines of an open compass traverse are given below. 

The stations that are free from local attraction are 

(A)P and Q
(B)Q and R
(C)R and S
(D)S and T

Q.No.5 The plane stress condition is given by 

Q. 6 Match the following metals with their corresponding minerals. 

(A) P-4,Q-2, R-1, S – 3
(B) P-4,Q – 1, R-3, S-2
(C) P-3, Q-4, R – 1, S-2
(D) P-2, Q-3, R-4, S – 1

Q. 7 Match the wire rope types with their corresponding cross-sectional diagrams. 

(A) P-3, Q-2, R-4, S-1
(B) P-3, -1, R-2, S-4
(C) P-1, -3, R-4, S-2
(D) P-4, Q-2, R-3, S-1

Q. 8 The “ratchet and pawl’ mechanism in a jack hammer drill 

(A)forces down the piston
(B)provides a twisting force to the drill steel
(C)engages rifle bar with rifle nut
(D)prevents reverse rotation of rifle bar 

Q. 9 Post-pillar method of stoping is a variant of

(A) cut and fill stoping
(B) sublevel stoping
(C) vertical crater retreat method
(D) sublevel caving

Q. 10 “Cross-measure borehole method is used for 

(A) rock slope monitoring
(B) methane drainage
(C) connecting two drifts
(D) subsidence monitoring 

Q. 11 The dry and wet bulb temperatures at the inlet of the airstream are 30 °C and 25 °C, respectively. The corresponding values at the outlet of the airstream are 26 °C and 25 °C, respectively. The psychrometric process that occurs in the airstream is described as 

(A) latent cooling

(B) sensible cooling

(C) condensation

(D) evaporative cooling

Q. 12 For a mixture of inflammable gases, the lower and upper explosibility limits can be computed using 

(A) Dalton’s law

(B) Graham’s law

(C) Le Chatelier relation

(D) Boyle’s law

Q. 13 The code for the lowest category of mineral resources under United Nations Framework Classification (UNFC) system is 

(A) 444
(B) 123
(C) 334
(D) 111

Q. 14 Match the following sampling patterns with the corresponding sampling types. 

(A) P-1,Q – 3, R-2, S-4
(B) P-1,Q – 3, R-4, S-2
(C) P-1,Q – 2, R-3, S-4

(D) P-4,Q-2, R – 1, S-3

Q. 15 In the context of gas testing using flame safety lamp, the correct statement is 

(A) Each accumulation test has to be necessarily followed by percentage test
(B) Accumulation test is always done after percentage test
(C) Either percentage test or accumulation test can be done first
(D) Percentage test is done only in the event of accumulation test giving negative result 

Q. 16 For x in the range of [-3, 3], the maximum value for the function 

Q. 17 A rock sample has a coefficient of thermal diffusivity 1.282×10-6 m/s, specific heat 900 J/(kg °C) and density 2600 kg/m3. The coefficient of thermal conductivity of the rock sample in W/(m °C) is__________(round off to I decimal place). 

Q. 18 A random variable X has the following probability mass function. 

The expected value of the variable X is___________(round off to 1 decimal place). 

Q. 19 A random sample has five observations as shown below. 

The coefficient of variation of the sample is________(round off to 3 decimal places). 

Q. 20 Rock strata has unit weight of 25 kN/m2 and Poisson’s ratio 1/3. At a depth of 200 m, the horizontal stress in MPa is_________(round off to 1 decimal place). 

Q. 21 A shovel of bucket capacity 4.2 m³ makes 900 passes per day with a fill factor of 0.8. If the swell factor of the rock is 1.4, then in-situ volume handled by the shovel in a month of 24 working days in m³ is__________(round off to 1 decimal place). 

Q. 22 A cylindrical sample of granular material has the following measurements: 

Length: 10 cm 

Diameter: 5 cm 

Weight: 350 g 

Assume the sample is completely dry with specific gravity of solid grains 2.8. The void ratio of the sample is__________(round off to 3 decimal places). 

Q. 23 The following consecutive readings were taken at uniform intervals with a level and a levelling staff on continuously sloping ground. 

The number of change points is___________.

Q. 24 The cost of a slurry pump is Rs. 50,000 and it has an estimated life of 7 years. If the salvage value is Rs. 8,000, the annual depreciation following straight-line depreciation method, in Rupees, is___________(round off to I decimal place). 

Q. 25 In a mine bench, the shovel loading time follows exponential distribution with a mean loading time of 5 min per dumper. The arrival rate of dumpers that are identical in capacity, follows Poisson distribution with a mean arrival rate of 8 per hour. The probability that the shovel remains idle is___________(round off to 2 decimal places). 

Q26 – Q55 carry two marks each. 

Q. 26 For , the value of dw/dt is 

Q. 27 For the differential equation y1-x2dy+x1-y2dx=0, assuming the constant of integration to be C, the general solution is 

Q. 28 A belt-drive used for power transmission between two parallel shafts has a belt of mass 1.2 kg/m, and the maximum allowable belt tension is 2250 N. If the centrifugal tension is one third of the maximum allowable belt tension, the speed at which maximum power is transmitted by the belt, in m/s, is 

(A) 46.48
(B) 38.73
(C) 25.00
(D) 35.36

Q.No.29 An air receiver of a compressor, having volume 0.5 m?, supplies air for charging ANFO in drill holes. During the charging process the absolute pressure of the air receiver falls from 900 kPa to 700 kPa. Assuming the entire process is isothermal, the volume of air supplied by the receiver at 100 kPa ambient pressure, in m is 

(A) 1.00
(B) 0.39
(C) 0.64
(D) 4.48

Q. 30 A conveyor belt consumes 60 kW power while running at a speed of 3.0 m/s. The angle of lap is 180o and the coefficient of friction between belt and pulley is 0.2. The  maximum tension (kN) in the belt is 

(A) 21.7
(B) 61.7
(C) 82.9
(D) 42.9

Q. 31 A linear programming problem is stated below. 

Maximize Z = 3x₁ + 5x₂ 

subject to, 2x₁ + x₂ 8 

6x₁ + 8x₂ 30 

x₁, x₂ 0 

The objective function has 

(A) infinite number of solutions
(B) unbounded solution
(C) unique solution
(D) infeasible solution

Q. 32 An explosive mixture has 80 g of ammonium nitrate (NH4NO3) and 14 g of fuel oil (C10H20). The oxygen balance in the mixture is 

(A)surplus by 32 g
(B)deficient by 24 g
(C)surplus by 16 g
(D)deficient by 32 g

Q. 33 A cylindrical sample of cross-sectional area A, length L, and Young’s Modulus E, is subjected to a constant uniaxial load P. Within the elastic limit of loading, the total strain energy stored is 

Q. 34 A surface mine production system along with the reliability of the individual components is shown below. The system reliability is_______(round off to 3 decimal places). 

Q. 35 The selling price of one rock bolt (in Rs.) is given as, S = (200 – 10n-0.5), where n is the number of bolts produced. The manufacturing cost of rock bolts has a fixed component of Rs. 15000, and a variable component of Rs. 100 per bolt. The minimum break-even production, in number of rock bolts, is______(round off to 1 decimal place). 

Q. 36 Two underground mines are separated by a horizontal coal barrier of 60 m thickness. One mine is inundated, whereas the other mine has a blind heading of dimensions 4.0 m wide and 2.5 m height terminating at the barrier. The overall in-situ shear strength of the coal mass is 500 kPa. Assume that the failure mode is in shear. At a factor of safety of 10, the maximum water head that can be withstood by the coal barrier, in m, is____________(round off to 1 decimal place). 

Q. 37 Air enters from ambient atmosphere into a level duct of uniform cross-section area 0.2 m- at a flow rate of 2.0 m³/s and density of 1.2 kg/m³. The entry shock loss factor is 1.0 and the resistance of the duct per meter length is 1.0 Ns²/m⁸. The static pressure measured at a distance of 20 m from the duct entrance in Pa, is___________(round off to 1 decimal place). 

Q. 38 A sealed-off area air sample consists of 16.0% O₂, 3.0% CO₂, and the rest is N₂. Assume that the standard composition of atmospheric air is 21.0% O₂ and 79,0% N₂. The percentage of blackdamp in the air sample is_______(round off to 2 decimal places). 

Q. 39 A diesel loader produces 60 l/s of exhaust fumes containing 5000 ppm of CO. The incoming air has 10 ppm of CO. The minimum amount of air flow in m3/s that is needed at the loader to dilute Co to a permissible level of 50 ppm is___________(round off to 1 decimal place). 

Q. 40 The equation for peak particle velocity (PPV) from blast induced ground vibration is given by , where k and B are site constants. 

In a field study, the following readings are recorded. 

The value of B is______________(round off to 3 decimal places). 

Q. 41 An underground copper mine sends 2500 tonnes of ore per day to the concentrator plant having an average grade of 1.2% Cu. The plant produces concentrate of 25.0% Cu with a recovery of 93.0%. The solids portion of tailings generated from the plant per day in tonnes is_____________(round off to 1 decimal place). 

Q. 42 A mine gallery is supported by regularly placed roof bolts of 100 kN allowable pull force per bolt, as shown below. Assuming unit weight of the immediate roof is 25 kN/m2, the factor of safety of the support system is______(round off to 2 decimal places). 

Q. 43 The slip circle of radius 30.0 m in an overburden slope is shown with the centre of slip circle at point O. The tension crack is completely filled with water. For one meter width of the slope, the moment exerted by the force of water about O in kN-m is____________(round off to 1 decimal place). 

Q. 44 The function values at four points of x are shown in the table. The area under the function, using trapezoidal method, is ______________(round off to 1 decimal place). 

Q. 45 A particle starting from rest moves in a straight line such that after time, 1 (seconds), the acceleration becomes (6 – t/4) cm/s2. When the acceleration becomes zero, the velocity of the particle in cm/s is____________(round off to I decimal place). 

Q. 46 A parallelepiped has edge vectors as shown below. 

The volume of the parallelepiped is 

(round off to 1 decimal place). 

Q. 47 For a development heading, the blasting parameters are 

Cross-section: 6.0 m × 5.0 m 

Total number of holes: 72 

Number of trimmer holes: 30 

Depth of each hole: 3.5 m 

Charge per hole (except trimmers): 3.5 kg 

Charge per trimmer hole: 1.8 kg 

Pull per round: 90% of hole depth 

The powder factor for the development round in my/kg is_________(round off to 2 decimal places). 

Q. 48 The following figure represents the observations from the level survey of an underground gallery. 

If the reduced level of station A is 100.0 m, the reduced level of station D in m is___________(round off to 1 decimal place). 

Q. 49 A tacheometer was setup at station P and the following readings were taken at two stations A and B with the staff held vertical and the line of sight horizontal. 

The additive and multiplying constants of the tacheometer are 0 and 100, respectively. The length of AB in m is _____________ (round off to 1 decimal place). 

Q. 50 The geometry of a simple planar curve (ADB) is shown below. The value of the mid-ordinate of the curve in m is_____________(round off to I decimal place). 

Q. 51 A steel cube of side 50 mm is subjected to a uniform pressure of 200 MPa acting on each face. The Young’s modulus and Poisson’s ratio of the material are 200 GPa and 0.25, respectively. The decrease in the side of the cube in mm is (round off to 3 decimal places). 

Q. 52 In the figure shown below, the friction coefficient between the block and the inclined plane is 0.2, and all the pulleys are weightless. The weight of the block is 10 N. The minimum force P in Newtons that is needed to slide the block up the inclined plane is____________(round off to 2 decimal places). 

Q. 53 An assignment problem is given below with the cost of assignment as shown. 

TL 

If only one task can be assigned to one group, the minimum cost of assignment is ______.

Q. 54 A vertical stoping block of length 60.0 m, height 40.0 m, and average width 1.5 m has sharp boundary walls. However, the mining width of the stopping block is 2.0 m. The tonnage factors are 3.0 tonne/m2 for ore and 2.5 tonne/for wall rocks. The average grade of ore is 10.0%. The overall grade of ore mined on account of dilution in percentage is ____________ (round off to 2 decimal places). 

Q. 55 A bauxite ore body has four boreholes as shown below. For each borehole, the grade of alumina, the thickness of the ore body, and the triangular area of influence are as shown. 

The average grade of ore body in the region ABCD in percentage is_______(round off to 1 decimal place). 

Answer key