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Question 1 of 65
1. Question
For the matrix, AA^{T} is
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Question 2 of 65
2. Question
The mean of a numerical datase is and the standard deviation is S. If a number K is added to each term in the dataset then the mean and standard deviation become.
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Question 3 of 65
3. Question
If f(x) = e^{x} then at x = 0, the function f(x) is
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Question 4 of 65
4. Question
The pressure (P) versus volume (V) diagram given below represents reversible isothermal curves at temperatures, T1, T2 and T3
Considering one mole of ideal gas for all the three isothermal processes, which one of the following is TRUE?
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Question 5 of 65
5. Question
For the electrochemical reaction, Cu^{2+} + Zn = Zn^{2+} + Cu, the standard cell potential at 25℃ and 1 atm pressure is:
(Given : E° (Cu^{2+}/Cu) = 0.337 V and E° (Zn^{2+}/Zn) = −0.763 V)
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Question 6 of 65
6. Question
The rate of dissolution of Al particles in liquid steel is proportional to concentration difference (∆C). ∆C is defined by:
(Given: (i) C_{b} = bulk concentration of dissolved Al in liquid steel, (ii) C^{*} = saturation concentration of Al in liquid steel at the given temperature, (iii) C_{m} = Density of Al(Atomic weight of Al.)
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Question 7 of 65
7. Question
Hydrogen dissolves in Pd by the reaction H_{2} = 2[H]. At 300℃ and the solubility of hydrogen in Pd is 1.64 × 10^{4} mm^{3} (STP) per kg of Pd. At 300℃ and the solubility of hydrogen in Pd in mm^{3} (STP) per kg of Pd is _________(answer up to one decimal place)
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Question 8 of 65
8. Question
The sieve analysis of ground quartz particles is given in the table below :
Sieve size Mass fraction of ground product
(mm) retained on each sieve
4.76 0.0
3.36 0.2
2.38 0.4
1.68 0.3
1.19 0.08
<1.19 0.02
The cumulative mass fraction of particles of size less than 1.68 mm is ____ (answer up to two decimal places)
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Question 9 of 65
9. Question
The sequence of precipitation to each stable equilibrium during ageing of Al4.5 wt.% Cu alloy is:
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Question 10 of 65
10. Question
Tungsten powder is pressed at 150 MPa to green density of 55%. After sintering, the compact attains 86.5% of its theoretical density. Assuming uniform shrinkage, the linear shrinkage (in%) is _______ (answer up to two decimal places)
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Question 11 of 65
11. Question
For a FCC metal, radius of the largest sphere that can fit in the tetrahedral void (in nm) is ______ (answer up to three decimal places)
(Given : lattice parameter = 0.401 nm)
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Question 12 of 65
12. Question
In an ironcarbon alloy containing 0.35 wt.% C, the mass fraction of pearlite just below the eutectoid temperature is _____(answer up to two decimal places)
(Given: eutectoid composition = 0.8 wt.% carbon; and carbon content in ferrite is 0.025 wt.%)
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NAT Type Question

Question 13 of 65
13. Question
A cubic metal has a density of 19000 kg.m^{−3}, lattice parameter of 0.4 nm and atomic weight of 183. The effective number of atoms in an unit cell of this metal is ______
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Question 14 of 65
14. Question
Primary mechanisms of accommodating plastic strain at low temperatures in crystalline metals are:
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Question 15 of 65
15. Question
Spherical α phase particles are depicted in the hypothetical microstructure section shown below. Using the superimposed grid on the microstructure, the estimated volume fraction of α phase is _______(answer up to three decimal places)
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Question 16 of 65
16. Question
A brittle material (Young’s modulus = 60 GPa and surface energy = 0.5 J.m^{−2}) has a surface crack of length 2 μm. The fracture strength (in MPa) of this material is ________(answer up to two decimal places)
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Question 17 of 65
17. Question
Both creep resistance and tensile strength of a metal can be enhanced by
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Question 18 of 65
18. Question
Stress required to operate a FrankRead source of length L is approximately given by:
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Question 19 of 65
19. Question
The second peak in the powder Xray diffraction pattern of a FCC metal occurs at a Bragg angle θ (in degrees) = _______(answer up to two decimal places)
(Given: λ_{CuKα} = 0.154 nm; lattice parameter of the metal = 0.36 nm)
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Question 20 of 65
20. Question
A rod is elastically deformed by a uniaxial stress resulting in a strain of 0.02. If the Poisson’s ratio is 0.3, the volumetric strain is _______(answer up to three decimal places)
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Question 21 of 65
21. Question
Four alloys, C1, C2, C3, C4, shown in the phase diagram are poured at temperature T_{1} in a mold. During solidification, which one of these alloys is expected to have the highest fluidity?
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Question 22 of 65
22. Question
A material, which shows power law behavior, is being wire drawn. The maximum strain per pass in annealed condition (assume ideal work and efficiency η = 1) is ______ (answer up to two decimal places)
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Question 23 of 65
23. Question
Schematic diagram shows rolling of a slab. P and Q are points on the surface of the workpiece near entrance and exit, respectively. With reference to the work piece, which one of the following statements is TRUE?
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Question 24 of 65
24. Question
Which one of the following manufacturing techniques is used for making window glass?
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Question 25 of 65
25. Question
Dye penetrant test is based on the principle of
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Question 26 of 65
26. Question
Assume that the probability of South Africa against India is 1/3. If South Africa plays a 3 match cricket series against India, the probability that South Africa wins only one match is (assume that no matches are tied or abandoned)______(answer up to three decimal places)
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Question 27 of 65
27. Question
The function f(x) = x^{3} – 3x has a minimum at x = _______
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Question 28 of 65
28. Question
The definite integral, is to be evaluated numerically. Divide the integration interval into exactly 2 subintervals of equal length. Applying the trapezoidal rule, the approximate value of the integral is _______(answer up to two decimal places)
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Question 29 of 65
29. Question
For the second order linear ordinary differential equation,
the following function is a solution:
y = e^{λ}^{x}
Which one of the following statements is NOT TRUE?
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Question 30 of 65
30. Question
Using the bisection method, the root of the equation x^{3} + x – 1 = 0 after thre iterations is ______(answer up to two decimal places)
(Assume starting values of x = −1 and +1)
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Question 31 of 65
31. Question
T_{1} and T_{2} are the melting points of pure metal A and pure stoichiometric oxide AO_{2}, respectively, and T_{1} < T_{2}. The stoichiometric metal oxidation reaction A(s) + O_{2}(g) = AO_{2}(s) is in equilibrium at 1 atm pressure at temperature less than T_{1}. If the temperature increases, which schematic represents the correct standard free energy change versus temperature plot?
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Question 32 of 65
32. Question
A continuous cast steel slab, 1 m × 1 m ×1 m, at 1298 K cools in air. The initial rate of heat loss (in kW) from the top surface of slab by radiation and convection is ______(answer up to two decimal places)
Given: (i) Ambient temperature = 298 K, (ii) emissivity of steel = 0.8, (iii) convective heat transfer coefficient = 4.6 W. m^{−2}. K^{−1}, (iv) StefanBlotzmann constant (σ) = 5.7 × 10^{−8} W.m^{−2}.K^{−4}
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Question 33 of 65
33. Question
The Pourbaix plot of the reaction Al^{3+} + 2H_{2}O = AlO_{2}^{−} + 4H^{+} in potential (E) versus pH diagram is :
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Question 34 of 65
34. Question
During the end blow period in LD steelmaking, the decarburization rate is expressed by the equation : . Here , c and c^{*} are the instantaneous and equilibrium concentration of carbon in steel respectively, in units of wt.% Given that c^{*} = 0.04 wt.% and c(t = 0 min) = 0.4 wt.%, the concentration of carbon in steel (in wt.%) at t = 1 min is ______(answer up to three decimal places)
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NAT Type Question

Question 35 of 65
35. Question
CaCO_{3}(s) dissociate in a closed system according to the reaction :
CaCO_{3}(s) = CaO(s) + CO_{2}(g)
Assuming the reaction is in thermodynamic equilibrium, the degree(s) of freedom, F = ____
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Question 36 of 65
36. Question
A ladle containing molten steel is being discharged. The relevant forces are listed in Column I Match them with their corresponding expressions in Column II.
Column I Column II
[P] Pressure force [1] μUL
[Q] Inertial force [2] ρgL^{3}
[R] Gravity force [3] ρU^{2}L^{2}
[S] Viscous force [4] PL^{2}
μ = viscosity, U = characteristic velocity, L = characteristic length,
g = acceleration due to gravity, P = pressure.
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Question 37 of 65
37. Question
In primary steelmaking, dissolved oxygen (O) reacts with carbon (C) to produce CO(g), at 1 atm pressure according to the reaction: C + C = CO(g). The equilibrium constant for this reaction is: where T is in Kelvin. Assuming Henrian activity coefficient of both O and C to be unity, the dissolved oxygen content (in wt.%) of a plain carbon steel melt with 0.7 wt.% C at 1600℃ is ______ (answer up to four decimal places)
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Question 38 of 65
38. Question
A stoichiometric mixture of CO and pure oxygen at 1 atm and 25℃ flows into a combustion reactor. The molar flow rate of CO entering the reactor is 1 kgmol.h^{−}^{1}. The adiabatic flame temperature (in K) for the combustion of CO with stoichiometric oxygen is:_____
Given: C_{P}(CO_{2}) = 44 kJ.(kgmol K)^{−1}.
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Question 39 of 65
39. Question
A solution contains 10^{−3} M of Fe^{3+} at 25℃. The solubility product of Fe(OH)_{3} is 10^{−39}. Assuming activity equals concentration, the minimum pH at which Fe^{3+} will precipitate as Fe(OH)_{3} is ______(answer up to two decimal places)
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Question 40 of 65
40. Question
A zinc elctrowinning cell is being operated at a current of 400 A, voltage of 3.5 V, and a cathodic current efficiency of 90%. The specific energy consumption (in kJ.kg^{−}^{1} zinc) is _____
(Atomic weight of Zn = 65)
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Question 41 of 65
41. Question
Pure metals A and B form two real binary solid solutions α and β at temperature T and pressure P. The free energy versus composition plots for both the solutions are shown below.
The condition for chemical equilibrium is:
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Question 42 of 65
42. Question
Pure orthorhombic sulfur transforms to stable monoclinic sulfur above 368.5 K. Applying Third law of thermodynamics, the value of entropy (in J.K^{−}^{1} of transformation at 368.5 K is ______(answer up to two decimal places)
Given:
i. Entropy change associated with heating orthorhombic sulfur from 0 K to 368.5 K is 36.86 J.K^{−}^{1}.
ii. Entropy change associated with cooling monoclinic sulfur from 368.5 K to 0 K is −37.8 J.K^{−1}.
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Question 43 of 65
43. Question
For homogeneous nucleation of solid in a liquid of pure metal, the critical edge length (in nm) of a cube shaped nucleus is _____(answer up to two decimal places)
(Given : surface energy γ = 0.177 J.m^{−2}; change in volume free energy ∆G_{V} = −2.8 × 10^{8} J.m^{−3})
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Question 44 of 65
44. Question
Assuming the solid phases to be pure, the slope of line BC in the predominance area diagram schematically shown below is _____(answer up to two decimal places)
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Question 45 of 65
45. Question
For each of the crystallographic system listed in GroupI, match the corresponding minimum symmetric in GroupII
GroupI GroupII
[P] Tetragonal [1]1 twofold rotation
[Q] Cubic [2]1 threefold rotation
[R] Monoclinic [3] 4 threefold rotation
[S] Rhombohedral [4] 1 fourfold rotation
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Question 46 of 65
46. Question
Arrange the magnetic moment of neighboring atoms in a onedimensional lattice in GroupI to the corresponding magnetic material in GroupII
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Question 47 of 65
47. Question
For an intrinsic semiconductor , all room temperature electrical conductivity is 10^{−6}Ω^{−}^{1}. If the electron and hole mobilities are 0.75 and 0.06 m^{2}V^{−1}s^{−1} respectively, the intrinsic carrier concentration (per m^{3}) at room temperature is:
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Question 48 of 65
48. Question
A steel component is subjected to fatigue loading : σ (maximum) = 200 MPa, σ(minimum) = 0. The component has an initial crack length of 1 mm. Propagation of crack is governed by
where, the crack length a is in meters, N is the number of cycles and ∆K is in Mpa.m^{1/2}. The length of the crack (in m) after one million cycles will be _____(answer up to three decimal places)
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Question 49 of 65
49. Question
During heat treatment of a cold worked metal, recrystallization is 20% complete after 100 s. The transformation (in %) in 400 s is ______(answer up to two decimal places)
(Assume Avrami exponent, n = 2)
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Question 50 of 65
50. Question
At low temperature, two parallel edge dislocations lying on parallel slip planes are shown in different configurations below.
Configuration [P] [1] Dislocations repel
Configuration [Q] [2] Dislocations attract
Configuration [R] [3] Dislocations are in stable equilibrium
Configuration [S] [4] Dislocation are in unstable equilibrium
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Question 51 of 65
51. Question
A single crystal of an FCC metal is subjected to a sufficiently large tensile stress along the [110] direction to activate some of the slip systems. Which one of the following slip systems will be activated.
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Question 52 of 65
52. Question
A perfectly elasticplastic material has a yield stress of 450 MPa and fractures at a strain of 0.45. The ratio of resilience to toughness for this material is _____(answer up to three decimal places)
(Given is Young’s modulus E = 4.5 GPa)
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Question 53 of 65
53. Question
Total time for solidification of a cubic casting of dimensions 5.0 cm ×0 cm × 5.0 cm is 1.6 min. A cylindrical riser with diameter to height ratio 0.5 is required so that the time for solidification of riser is 3.2 min. Applying Chvorinov’s rule, the height of the riser (in cm) is ______(answer up to two decimal places)
(Assume that exponent (n) in Chvorinov’s equation is 2)
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Question 54 of 65
54. Question
A 250 mm thick slab of a nickel alloy is subjected to cold rolling using a roll of diameter 450 mm. If the angle of bite during rolling is 10°, the maximum possible reduction (in mm) during rolling is ______(answer up to two decimal places)
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Question 55 of 65
55. Question
WNi compact is prepared by liquid phase sintering at 1500℃. If the size of tungsten grains is 40 μm and the interfacial tungsten tungsten and tungstennickel energies are 0.52 and 0.30 J.m^{−}^{2} respectively, the predicted average neck size (in μm) of sintered tungsten grain is :
(Melting points of tungsten and nickel are 3410℃ and 1453℃, respectively)
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Question 56 of 65
56. Question
The ninth and the tenth of this month are Monday and Tuesday _______.
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Question 57 of 65
57. Question
It is _______ to read this year’s textbook ______ the last year’s
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Question 58 of 65
58. Question
A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?
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Question 59 of 65
59. Question
Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and in which direction should she go to reach point P?
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Question 60 of 65
60. Question
500 students are taking one or more courses out of Chemistry, Physics and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?
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Question 61 of 65
61. Question
“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”
Which of the following statements best reflects the author’s opinion?
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Question 62 of 65
62. Question
Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?
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Question 63 of 65
63. Question
1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?
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Question 64 of 65
64. Question
The number of 3digit numbers such that the digit 1 is never to the immediate right of 2 is
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Question 65 of 65
65. Question
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of geographical region. Contour lines are shown at 25 m intervals in this plot.
Which of the following is the steepest path leaving from P?
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