βThe team ______ more than 300 runs in 20 overs ___________ rains. However, some players needed to improve their batting skills.β Choose the option with the correct sequence of words to fill the blanks.
a.
score; despite
b.
scoring; instead of
c.
scored; despite
Correct Answer
d.
scoring; in spite of
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Q2mcq
If a positive real $x$ satisfies the following equation
log 2 $x$ + log $x$ = 48,
$\sqrt{2}$ then the value of $x$ is _________________
a.
2 16
Correct Answer
b.
4 16
c.
2 14
d.
4 14
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Q3mcq
The next figure (indicated by β?β) in the sequence is
a.
Correct Answer
b.
c.
d.
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Q4mcq
βAll the mangoes in the basket are good.β If the above statement is false, then which one of the following statements is necessarily true?
a.
All the mangoes in the basket are not good.
b.
No mango in the basket is good.
c.
In the basket, some of the mangoes are good and some are not good.
d.
There exists at least one mango in the basket that is not good.
Correct Answer
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Q5mcq
Consider the following statements about four numbers: (S1) The average of the four numbers is 25 (S2) Each number is at most 40 (S3) Each number is at least 20 Choose the option that is necessarily correct.
a.
(S1) and (S2) together imply (S3)
b.
(S2) and (S3) together imply (S1)
c.
(S1) and (S3) together imply (S2)
Correct Answer
d.
(S1) implies (S3)
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Q6mcq
βPeople are crowding around ___ pit into which ___ elephant has fallen. I have never seen an elephant looking more bewildered ___ miserable. Here it is in a most undignified position, thrust into a pit and made to look up ___ a vast, curiosity-stricken crowd.β Choose the option with the correct sequence of words to fill the blanks.
a.
an; a; at; and
b.
a; an; and; at
Correct Answer
c.
and; a; an; at
d.
at; a; an; and
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Q7mcq
The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The following observations were made: (i) The quantity of S sold was twice that of T. (ii) The quantity of R sold was thrice that of T. (iii) The quantity of Q sold was four times that of T. Product P Q R S T Unit selling price (Rs.) 100 50 40 60 60 What is the quantity of product P sold on that day?
a.
40
b.
50
Correct Answer
c.
60
d.
70
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Q8mcq
Consider a string P of length $l$ that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length $x$ they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of $x/l$ is __________
a.
$Ο$
b.
$Ο-1$ $2Ο$ $Ο$
c.
$2(Ο-1)$
Correct Answer
d.
$Ο$ $Ο-1$
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Q9mcq
The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels. They are seated in rows and columns as shown in the figure with exactly one person sitting in each box. It is known that (i) Meritoriusβ daughter and his brother are seated in the same column. (ii) His son is seated diagonally across the sibling of the worst orator. (iii) The best and worst orators are seated in the same row. Who is the best orator?
a.
Meritorius
b.
Meritoriusβ brother
Correct Answer
c.
Meritoriusβ son
d.
Meritoriusβ daughter
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Q10mcq
Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?
a.
P
b.
Q
Correct Answer
c.
R
d.
S
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Given a function f (t) $=$ e $-$ at, where a is a constant. The Laplace transform of the function is [ f (t)] $=$ F (s). Which one of the following options is correct?
β
a.
F (s) $=$ 1
b.
F (s) $=$ s
c.
F (s) $=$ a
d.
F (s) $=$ 1 (s $+$ a)
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Which one of the following options is correct? For Al - 4 % Ag alloy (composition in atom %), the correct sequence of operations involved in precipitation hardening is:
a.
b.
c.
d.
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Which one of the following options is correct? In a convective heat transfer for laminar flow over a flat plate, Nusselt number is a function of Reynolds number and Prandtl number. Similarly, in a convective mass transfer for laminar flow over a flat plate, Sherwood number is a function of:
a.
Schmidt number and Reynolds number
b.
Weber number and Reynolds number
c.
Schmidt number and Weber number
d.
Weber number and Prandtl number
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Which one of the following options is correct? For a solid immersed in a fluid, the convective heat transfer coefficient across the solid-fluid interface is NOT dependent on:
a.
Solid-fluid interfacial area
b.
Thermal conductivity of solid
c.
Roughness of solid surface
d.
Viscosity of fluid
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$ $ Value of scalar triple product a. (b $$ c) is (answer in integer) _____________. $$ a $=$ 2 i $-$ 3 j $+$ 4 k $$ $ $$ $$ b $=$ i $+$ 2 j $-$ 3 k $$ $ $$ $$ c $=$ 3 i $+$ 4 j $-$ k $$ $ $$ Here, $$$ i, $$$ j and k $$$ are mutually orthogonal unit vectors.
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A box contains 20 thermometers, 3 of which are defective. One person randomly draws 2 thermometers from the box, one-by-one, without replacement. The probability in percent (rounded-off to two decimal places) that none of these TWO thermometers is defective, is ________________ %.
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For an equilibrium phase diagram of a binary A-B alloy at a constant pressure as shown in the figure, the degree of freedom at βXβ is (answer in integer) _______________.
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Two parallel plates, with Newtonian incompressible liquid in between, are 2 mm apart. The upper plate is stationary and the lower plate moves with a velocity of 4 m/s. A force per unit area of 5 N/m 2 is applied parallel to the lower plate to maintain its motion. The viscosity of the liquid (rounded off to two decimal places) is $_______$ 10 β3 N.s/m 2
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Match the crystal systems in Column I with the corresponding axial lengths (a, b, c) and interaxial angles (Ξ±, Ξ², $)$ provided in Column II Column I Column II (P) Tetragonal (1) a $=ΜΈ$ b $=ΜΈ$ c, Ξ± = Ξ² = $$ = 90Β° (Q) Rhombohedral (2) a = b $=ΜΈ$ c, Ξ± = Ξ² = $$ = 90Β° (R) Orthorhombic (3) a $=ΜΈ$ b $=ΜΈ$ c, Ξ± = $$ = 90Β° $=ΜΈ$ Ξ² (S) Monoclinic (4) a = b = c, Ξ± = Ξ² = $ =ΜΈ$ 90Β°
a.
P-3, Q-1, R-2, S-4
b.
P-2, Q-3, R-4, S-1
c.
P-4, Q-3, R-2, S-1
d.
P-2, Q-4, R-1, S-3
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Match the concepts listed in Column I with the associated terms listed in Column II Column I Column II (P) Paris Law (1) Creep (Q) Schmid Factor (2) Fatigue (R) Larson - Miller Parameter (3) Dynamic Strain Aging (S) Portevin - Le Chatelier Effect (4) Critical Resolved Shear Stress
a.
P-3, Q-1, R-2, S-4
b.
P-2, Q-4, R-1, S-3
c.
P-2, Q-4, R-3, S-1
d.
P-1, Q-3, R-2, S-4
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Match the descriptions listed in Column I with the corresponding non-destructive testing methods listed in Column II: Column I Column II (P) Internal flaws in railroad wheel (1) Ultrasonic (Q) In-service monitoring of crack (2) Radiography (R) Inclusion in mild steel (3) Dye Penetrant (S) Surface crack in Al-based alloy (4) Acoustic Emission
a.
P-1, Q-4, R-2, S-3
b.
P-3, Q-2, R-4, S-1
c.
P-3, Q-2, R-1, S-4
d.
P-1, Q-3, R-4, S-2
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The equation below represents a steady-state laminar flow of a fluid through a horizontal tube:
$ r$ 0
$dv$ 1 $d dP$
$r dr dr dz$ $P$ is fluid pressure $$ is dynamic viscosity $(r, z):$ coordinates of cylindrical polar system, and $v$ is axial velocity in z-direction Which one of the following statements related to the above case is NOT correct?
a.
The fluid is Newtonian
b.
Shear stress is maximum at the center $(r$ = 0)
c.
Radial velocity is zero
d.
There is no variation of $v$ in z-direction
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Match the terms in Column I with the corresponding attributes in Column II: Column I Column II (P) Wiedemann-Franz law (1) Charge carrier concentration (Q) Neel temperature (2) Paramagnetism (R) Hall voltage (3) Ratio between thermal conductivity and
electrical conductivity of metals (S) Curie law (4) Diamagnetism
(5) Anti-ferromagnetism
a.
P-4, Q-3, R-2, S-1
b.
P-2, Q-5, R-1, S-3
c.
P-3, Q-5, R-1, S-2
d.
P-3, Q-4, R-5, S-2
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Consider a distribution with the following probability density function
0.5, 0 $<$ x $<$ 2 f (x)
$= {$
0.0, Otherwise
. Given that the mean of the above probability distribution is 1, the variance (rounded off to two decimal places) is _______________.
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Taking number of intervals n = 3, the value of the integral $$ e $-$ x 2 dx using
0.3
0 Trapezoidal method, is ________________ (rounded off to two decimal places).
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Solution of the differential equation 10 x 2 d y dy $-$ 20 x $+$ 22.4 y $=$ 0 is
2
2 dx dx y $=$ c 1 x m 1 $+$ c 2 x m 2 where m 1 $$ m 2. The value of m $+$ m (answer in integer) is _____________
1 2
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Iron powder is compacted at room temperature to 75% of its theoretical density. The as-pressed iron compact is sintered in inert-gas atmosphere at 1200 Β°C to 90% of its theoretical density. Assuming isotropic shrinkage, the linear shrinkage (in percent) undergone by the iron compact during sintering (rounded off to one decimal place) is ________________ %
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An alloy having composition W-20 wt.% Ni is prepared by mixing elemental powders. The resulting powder mixture is liquid phase sintered at 1550 Β°C for 1 hour. The liquid phase sintered microstructure consists of interconnected, spherical tungsten grains dispersed in nickel. The tungsten grain size is 70 Β΅m and the W-W interparticle neck diameter is 35 Β΅m. If W-Ni interfacial energy is 0.30 J/m 2, the W-W interfacial energy (in J/m 2), rounded off to two decimal places is ___________________ (Given: melting point of W: 3410 Β°C and melting point of Ni: 1455 Β°C)
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A metal having body-centered cubic structure is analyzed through X-ray diffraction using monochromatic X-ray of wavelength 0.154 nm. The diffraction angle $(2)$ corresponding to {2 0 0} plane is 60Β° (for first order reflection). The atomic radius of this element (rounded off to three decimal places) is _______________nm.
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A cylindrical single crystal of copper having 10 mm diameter is deformed under a uniaxial tensile load of 2200 N. The angle between the normal to the slip plane and the tensile loading axis is $,$ whereas, the angle between slip direction and the tensile axis is $.$ The slip direction is in the plane defined by the stress axis and the normal to the slip plane. If $$ = $,$ the critical resolved shear stress (CRSS), rounded off to one decimal place, is ________ MPa.
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For plane strain fracture toughness (K Ic) testing of Maraging steel, the minimum thickness to achieve valid K Ic is (answer in integer) ______________ mm. (Given: K Ic = 90 $MPam$ and yield stress = 900 MPa)
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The lattice parameter of Ni (face-centered cubic) is 0.35 nm and its shear modulus is 76 GPa. The strain energy per unit length of a screw dislocation in Ni crystal (rounded off to two decimal places) is _________ $$ 10 -9 J/m.
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20 g of gold (Au) and 20 g of silver (Ag) are mixed to form a single-phase solid solution (assume ideal mixing). The atomic weight of Au is 197 g/mol and the atomic weight of Ag is 108 g/mol. The value of universal gas constant R is 8.314 J/mol-K. The total entropy of mixing (rounded off to two decimal places) is ___________ J/K.
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2 moles of an ideal gas is reversibly expanded from 10 liter to 20 liter at isothermal condition. The value of universal gas constant R is 8.314 J/mol-K. If the temperature of the gas is 27 Β°C, the magnitude of work done in the process (rounded off to two decimal places) is ______________ Joules.
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Specific heat capacity at constant pressure $(C$) of a solid metal is given by the following expression: $C in$ J/mol-K 20 5 10 $ T$ (for T= 298 K to 1000 K) At constant pressure, if the temperature (T in K) of 2 moles of metal is increased from 300 K to 600 K, the change in enthalpy of the metal (answer in integer) is ___________ Joules.
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With reference to the Ellingham diagram, the standard Gibbs free energy change for the oxidation of solid metal M (s) and liquid metal M (l) is given below: Reaction I: M (s) + O 2 (g) $$ MO 2 (s) $$ G o = (β 338900 β 15.2T lnT + 247T) Joules; from T = 300 K to melting point. Reaction II: M (l) + O 2 (g) $$ MO 2 (s) $$ G o = (β 390800 β 15.2T lnT + 285.3T) Joules; from melting point to T = 1800 K The melting point of the metal M (rounded off to one decimal place) is _______________ Kelvin.
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A given volume of liquid is undercooled just below the melting temperature to form a spherical solid nucleus (consider homogeneous nucleation). The Gibbs free energy of solidification $(G$ v) is (β 0.5 $$ 10 8) J/m 3. The solid-liquid interfacial energy $()$ is isotropic and its value is 0.1 J/m 2. The critical nucleus size for a stable nucleus is __________ nm (answer in integer).
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A 50 mm flat aluminium plate is reduced in thickness to 25 mm in a single pass cold-rolling operation with the rolling diameter of 1250 mm. For this case, the minimum required coefficient of friction between the plate and the roll (rounded off to two decimal places) is ___________.
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A cylindrical furnace has 0.1 m inner diameter and 0.2 m height. Walls A 1 (inner section of cylindrical surface area) and A 2 (inner section of bottom surface area) are maintained at 1873 K. The sides and bottom are assumed to be black bodies, well insulated and heated electrically. The top area (A 3) is open to atmosphere maintained at 300 K, resulting in loss of heat βqβ. Given: View factors F 13 = 0.1175 and F 23 = 0.06, where F ij is the fraction of radiation leaving surface βiβ that is intercepted by surface βjβ. Stefan-Boltzmann constant = 5.67 $$ 10 -8 W/m 2 - K 4. The power needed to maintain the furnace at 1873 K, is (approximate to the nearest integer) __________________W. `
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During carburizing of a steel, the surface concentration is kept constant at 1.4 wt.% carbon. Diffusivity of carbon for the steel at 950 Β°C is 6.25 $$ 10 -11 m 2 /s. At 950 Β°C, the time required to carburize the steel with an initial composition of 0.2 wt.% carbon to 0.8859 wt.% carbon at a depth of 0.2 mm is ______________ seconds (approximate to the nearest integer). Use the nearest value of the error function from the table given below for your calculation.
z erf (z)
0.3 0.3268
0.4 0.4284
0.5 0.5205
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For the following reaction between methane and stochiometric air having composition 20 vol.% O 2 and 80 vol.% N 2, the estimated adiabatic flame temperature (rounded off to one decimal place) is ________________ Kelvin. CH 4 (g) + 2 O 2 (g) $$ CO 2 (g) + 2 H 2 O (g) Given: $H$ = β 850 kJ/mol at 298 K Assume specific heat at constant pressure (C p) for each reactant and product is 50 J/mol-K and is independent of temperature.
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A copper ore contains 30 wt.% chalcopyrite (CuFeS 2) and remaining gangue material. Assuming no copper in gangue material, the amount of copper in the ore (rounded off to one decimal place) is ______________ wt.%. Given: Atomic weights of Fe, Cu and S are 56, 63.5, and 32 g/mol, respectively.
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A blast furnace produces hot metal with the following composition: 4 wt.% C, 1.5 wt.% Si, and rest Fe. Only input of iron is through iron ore containing 85 wt.% Fe 2 O 3 and 15 wt.% gangue consisting of SiO 2 and Al 2 O 3. 2% of all iron (by weight) is lost in slag. The amount of ore used to produce 1000 kg of hot metal (rounded off to one decimal place) is _________________ kg. Given: Atomic weights of Fe and O are 56 g/mol and 16 g/mol, respectively.
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Al 2 O 3 can be electrolyzed with an inert anode or a carbon anode. Overall reactions are as follows: Reaction I: For inert anode, 2 4 $ GΒ°$ Al 2 O 3 (s) Al (l) + O 2 (g); (in Joules) = 1124800 β 218 T 3 3 Reaction II: For carbon anode, 2 4 $ GΒ°$ Al 2 O 3 (s) + C (s) Al (l) + CO 2 (g); (in Joules) = 730700 β 218 T 3 3 T denotes temperature in Kelvin Given: Faraday constant = 96500 Coulomb If inert anode is replaced by carbon anode during electrolysis of Al 2 O 3 at temperature 1300 K, the decrease in the magnitude of decomposition potential between the two reactions (rounded off to two decimal places) is _________________ Volts.
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Given a scalar field $$ (x, y, z) $=$ x 2 $-$ yz Magnitude of a vector in the direction of the most rapid increase of $$ at a point P (3,4,1), rounded-off to two decimal places, is _______________
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