Firstranker's choice
GATE 2015
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Q. 1 – Q. 25 carry ONE mark each
Q.1
Consider the following five readings from an experiment: 19, 17, 15, 13, 11. The standard deviation of the readings is
Q.2
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y(x+h)-y(x) is a numerical approximation for
h
(A) dy/dx (B) dy/dh (C) ? y dx (D) ? x dy
Q.3 If A and B are matrices, (AB)T =
(A) AT B (B) BT A (C) AT BT (D) BT AT
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Q.4
Which of the following properties is intensive?
(A) Volume (B) Gibbs free energy (C) Chemical potential (D) Entropy
Q.5
In an Ellingham diagram, the standard free energy change ?G° for the oxidation reaction of a metal M given by: xM(s) + O2(g) ? MxO2(s), is plotted as a function of temperature. The slope of this line is positive because
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(A) ?Sº is positive (B) ?Sº is negative (C) ?Hº is positive (D) ?H° is negative
Q.6
In froth flotation, hydrophobic mineral particles ascend with air bubbles preferentially over hydrophilic mineral particles. The figure below shows a schematic of a water droplet placed on the surfaces of two mineral P and Q.
Given this information, pick the CORRECT statement from the following:(A) Mineral P ascends with air bubbles preferentially over mineral Q.
(B) Mineral Q ascends with air bubbles preferentially over mineral P.
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(C) Both minerals P and Q ascend with the air bubbles without preference.
(D) Both minerals P and Q sink to the bottom.
Q.7
Which of the following oxide addition results in polymerization (i.e., network formation) in a silicate slag?
(A) CaO (B) MgO (C) P2O5 (D) Na2O
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Q.8
Zn is commercially extracted from which of the following minerals?
(A) Sphalerite (B) Magnetite (C) Chalcopyrite (D) Galena
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Q.9 Self supporting arches for furnace roofs can be fabricated using silica bricks but not using magnesia bricks. Why?
(A) Silica has a significantly lower thermal expansion coefficient than magnesia at high temperatures.
(B) Silica has a significantly higher thermal conductivity than magnesia at high temperatures.
(C) Silica has a significantly lower melting point than magnesia.
(D) Silica is significantly more acidic than magnesia.
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Q.10 A species can diffuse through the lattice (diffusion coefficient, DL), along grain boundaries (diffusion coefficient, DGB), and along free surfaces (diffusion coefficient, DS). Which of the following relations is CORRECT?
(A) DL > DGB > DS (B) DS > DL > DGB (C) DGB > DS > DL (D) DS > DGB > DL
Q.11 Select the CORRECT plot of Gibbs free energy (G) vs. temperature (T) for a single component system from the following:
Q.12 If ?x represents adherent oxide layer thickness and t is time, which of the following curves represents diffusion-controlled oxidation kinetics? T T T? T T(A) P (B) Q (C) R (D) S
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Q.12 If ?x represents adherent oxide layer thickness and t is time, which of the following curves represents diffusion-controlled oxidation kinetics?
t X t(A) P (B) Q (C) R (D) S
Q.13 Based on the standard galvanic series, select the CORRECT sequence of metals in the increasing order of anodic behaviour:
(A) Zn, Fe, Pt, Cu (B) Pt, Zn, Cu, Fe (C) Fe, Pt, Cu, Zn (D) Pt, Cu, Fe, Zn
Q.14 In a conventional unit cell of a crystal, a = b ? c and a = ß = ? = 90°. This crystal belongs to which of the following systems?
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(A) Cubic (B) Tetragonal (C) Orthorhombic (D) Triclinic
Q.15 In an X-Ray powder pattern of a simple cubic crystal, the 2nd peak corresponds to
(A) (111) (B) (100) (C) (200) (D) (110)
Q.16 When boron (trivalent) is doped to silicon, the resulting material is
(A) a p-type semiconductor. (B) an n-type semiconductor.
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(C) a superconductor. (D) an insulator.
Q.17 Which of the following metal working operations can be categorized as an indirect compression process?
(A) Forging (B) Wire drawing (C) Extrusion (D) Stretch forming
Q.18 Which of the following is a typical rolling defect?
(A) Buckling (B) Edge cracking (C) Cold shut (D) Porosity
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Q.19 Which of the following manufacturing processes is NOT used for producing fine grained metals?
(A) Electrodeposition (B) Czochralski method
(C) Equi-Channel Angular Pressing (ECAP) (D) Sintering of milled powders
Q.20 Which of the following metal forming techniques is used to produce soft drink cans from aluminium sheets?
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(A) Rolling (B) Forging (C) Deep drawing (D) Extrusion
Q.21 Which of the following is NOT a solid state metal joining technique?
(A) Ultrasonic welding (B) Friction welding (C) Diffusion bonding (D) Electroslag welding
Q.22 The stress required for Orowan dislocation bypass is 200 MPa in an alloy when the inter-precipitate spacing is 500 nm. In the same alloy, if the inter-precipitate spacing is reduced to 200 nm, the stress required (in MPa) is ______.
Q.23 Which of the following Mohr's circles of a plane-stress condition corresponds to equi-biaxial tension?
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| (A) P | (B) Q |
| (C) R | (D) S |
Q.24 Select the INCORRECT statement related to the effect of a small amount of carbon addition on mechanical properties of iron.
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(A) Ductile-Brittle-Transition-Temperature (DBTT) increases.
(B) Hardenability increases.
(C) Toughness increases.
(D) Yield point phenomenon occurs.
Q.25 In polymers such as epoxies, creep resistance can be enhanced by
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(A) increasing the bulkiness of side groups.
(B) increasing the cross-link density.
(C) addition of plasticizers.
(D) annealing.
Q. 26 – Q. 55 carry TWO marks each
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Q.26
One of the eigenvalues of the matrix [ -2 1 1; 1 -2 1; 1 1 -2 ] is -3. The other eigenvalue is ______.
Q.27 Consider the scalar function f = xyz. The magnitude of the gradient, i.e. |?f| at the point (0,2,2) is ______.
Q.28
The determinant of the matrix [ cos ? sin ? 0; sin ? cos ? 0; 0 0 1] is ______.
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Q.29
The solution of the ordinary differential equation dy/dx = 5x for y|x=0 = 0 is
(A) 5 (B) 5x (C) 5x2/2 (D) e5x
Q.30 The maximum value of the function f(x) = -x² + 2x is ______.
Q.31 C (s) + CO2 (g) ? 2CO (g) is an important reaction in iron making. Given ?H298 = 172000 joules per mole of CO2, which of the following conditions will favour the forward reaction?
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(A) Increasing both temperature and pressure.
(B) Decreasing temperature and increasing pressure.
(C) Decreasing both temperature and pressure.
(D) Increasing temperature and decreasing pressure.
Q.32 Consider the reaction: Fe3O4 (solid, pure) + CO (gas, 1 atm) ?3FeO (solid, pure) + CO2 (gas, 1 atm)
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For this reaction, ?G1200 = -8000 joules per mole of CO and R = 8.314 J mol-1K-1.
The equilibrium ratio, PCO2/PCO for the reaction at 1200 K and 1 atm is ______.
Q.33 An iron blast furnace produces hot metal containing 95% Fe. The iron ore charged into the furnace contains 95% Fe2O3 and the rest is gangue. Assume that all the iron in the ore goes to hot metal. The amount of iron ore (in kg) required for producing 1000 kg of hot metal is ______.
(Atomic weight of Fe = 56 g mol-1 and that of Fe2O3 = 160 g mol-1)
Q.34 The figure below shows water flowing through a pipe. The pressure difference between points P and Q measured using a water-over-mercury manometer is
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