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An intrinsic semiconductor has conduction electron concentration, n = 1012 cm3. The mobility of both electrons and holes are identical = 4 104 cm2 V1 s1. If a voltage of 100 V is applied on two parallel end faces of the cube (edge length 1 cm) through Ohmic contacts, the current through the cube would be (in mA) (Given: charge of electron = 1.6 1019 C)
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An infinite plate with a through-thickness crack of length 2 mm is subjected to a tensile stress (as shown in the figure). Assuming the plate to be linear elastic, the fracture stress is ____________ MPa (round off to the nearest whole number) (Given: Fracture toughness, 𝐾𝐼𝐶=25 𝑀𝑃𝑎 √𝑚)
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Mild steel is carburized at 1300 K for 1 hour to obtain a certain case depth. Keeping the time as 1 hour, the case depth can be doubled by increasing the temperature to ______________K (round off to the nearest whole number)
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I n a two-dimensional, incompressible and irrotational flow, stream function ( (x, y) ) and velocity potential ( (x, y) ) exist. The velocities in x and y directions are non-zero.
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T he velocity field and the surface normal vector are given by, V uiˆ v ˆj wkˆ and 1 2 3 n n iˆ n ˆj n kˆ , respectively. If Euler equations are to be solved, the boundary condition that must be satisfied at the wall is,
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If the stream function ( ( , ) xy ) for a two-dimensional incompressible flow field is given as 2 2 2y x y , the corresponding velocity field is
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A pitot-static tube is used to measure air velocity in a duct by neglecting losses. The density of air is 1.2 kg/m3. If the difference between the total and static pressures is 1 kPa, the velocity of air at the measuring location, in m/s, is _______.
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I f the velocity field is 2 ˆˆ4 V xy i xy j m/s, vorticity of the fluid element in the field at (x=1, y=2) in s-1 is ____.
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A two-dimensional laminar viscous liquid film of constant thickness (h) steadily flows down an incline as shown in figure. Acceleration due to gravity is g. If the velocity profile in the liquid film is given as, u ky(2h y); v 0, the value of constant k is
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A water jet of 100 mm diameter issuing out of a nozzle at a speed of 50 m/s strikes a vane and flows along it as shown in figure. The vane is attached to a cart which is moving at a constant speed of 20 m/s on a frictionless track. The jet is deflected at an angle of 30o. Take the density of water as 1000 kg/m3. Neglecting the friction between the vane and the fluid, the magnitude of the force exerted by water on the cart in the x-direction, in N, is ______.
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C apillary waves are generated in the sea. The speed of propagation (C) of these waves is known to be a function of density (ρ), wave length (λ), and surface tension (σ). Assume, ρ and λ to be constant. If the surface tension is doubled, in the functional form of the relevant non-dimensional group, the percentage increase in propagation speed (C) is _______ .
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C onsider a fully developed, two-dimensional and steady flow of a viscous fluid between two fixed parallel plates separated by a distance of 30 mm. The dynamic viscosity of the fluid is 0.01 kg/m-s and the pressure drop per unit length is 300 Pa/m. The fluid velocity at a distance of 10 mm from the bottom plate, in m/s, is ________.
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A 2.6 gram smooth table-tennis (ping-pong) ball has a diameter of 38 mm. Density (ρ) of air is 1.2 kg/m3. Neglect the effect of gravity. Take coefficient of drag as 0.5. If the ball is struck with an initial velocity of 30 m/s, the initial deceleration, in m/s2, is _________.
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O n a flat plate, transition from laminar to turbulent boundary layer occurred at a critical Reynolds number (Recr). The empirical relations for the laminar and turbulent boundary layer thickness are given by m 0.5 5.48 Re la x x and 0.2 0.37 Re turb x x , respectively. The ratio of laminar to turbulent boundary layer thickness, at the location of transition, is 0.3. The value of Recr is _______.
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A (150 mm × 150 mm) square pillar is located in a river with water flowing at a velocity of 2 m/s, as shown in figure. The height of the pillar in water is 8 m. Take density of water as 1000 kg/m3 and kinematic viscosity as 1×106 m/s2. The coefficient of drag of the pillar is 2.0. The drag force exerted by water on the pillar in N is _______.
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A n orifice plate is used to measure flow rate of air (density = 1.23 kg/m3) in a duct of 250 mm diameter as shown in figure. The volume flow rate is 1 m3/s. Flow at sections 1 and 3 is uniform and section 2 is located at vena contracta. The diameter ratio, Dt/D1, is 0.66. The flow area at vena contracta, A2 = 0.65At, where At is area of the orifice. The pressure difference between locations 2 and 3 in N/m2 is ____________.
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I f wale constant and course constant for knitted fabrics are 4.2 and 5.46, respectively, then the value of the loop shape factor, accurate to one decimal place, is ______________
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D etermine the correctness or otherwise of the following Assertion [a] and the Reason [r]. [a]: The reaction temperature and rate of agitation during polymerization of polyethylene terephthalate have an important effect on molecular weight of the polymer produced. [r]: Polymerization of polyester by melt polycondensation is a predominantly diffusion controlled process.
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T echniques used to determine the glass transition temperature of textile fibres are P. X-ray diffraction (XRD) Q. Differential scanning calorimetry (DSC) R. Thermogravimetric analysis (TGA) S. Dynamic mechanical analysis (DMA)
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D etermine the correctness or otherwise of the following Assertion [a] and the Reason [r]. [a]: In a carding machine, carding type of wire point configuration is used between cylinder and doffer. [r]: Carding type of wire point configuration gives the best fibre transfer without disturbing the fibre alignment.
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D etermine the correctness or otherwise of the following Assertion [a] and the Reason [r]. [a]: As the concentration of a surfactant in water increases, the surface tension of water initially decreases and then becomes constant. [r]: After reaching the Critical Micelle Concentration, additional surfactant molecules do not further reduce the surface tension.
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S tarting from the initial point 𝑥0 = 10, if the sequence {𝑥𝑛} is generated using Newton Raphson method to compute the root of the equation 𝑥4 − 600 = 0, then 𝑥2 , accurate to two decimal places, is equal to _____________
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I f the density of 100% crystalline polyethylene is 1000 kgm-3 and that of 100% amorphous polyethylene is 865 kgm-3, then the mass fractional crystallinity of a polyethylene fibre with density 970 kgm-3, accurate to two decimal places, is ___________
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n winding zone of ring spinning, the permissible minimum angle of lead is 30. For a ring of 40 mm diameter, the minimum diameter (in mm) of bobbin required is _________
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A n eight head comber is running at 400 nips/min. The lap fed is 60 kilotex and noil extracted is 20%. If the feed/nip is 7 mm, then with machine utilization of 80%, the production rate (in kg/h), accurate to one decimal place, is ____________
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A shuttle loom having 1.75 m reed width is running at 180 rpm. The shuttle enters and leaves the shed at 120 and 240 angular positions of crankshaft, respectively. If length of the shuttle is 0.25 m, then the mean velocity (in m/s) of the shuttle within the shed is ___________
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T he diameter and length of torsion rod used in a projectile loom are increased by 5% and 20%, respectively. If the torque required to twist the rod increases by X%, then the value of X, accurate to two decimal places, is _____________
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I n a vibroscope, a cotton fibre of 25 mm length is clamped at one end, led over a knifeedge support, tensioned by a weight of 350 mg, and is inclined to vibrate at a fundamental resonant frequency of 2.6 kHz. The linear density of the fibre (in tex), accurate to two decimal places, is ____________
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T he theoretical limit coefficient of variation (Vr in %) of the weight per unit length of cotton sliver is 𝑉𝑟 = 106/√𝑁, where N is the average number of fibres present in the crosssection of the sliver. To derive this expression, the coefficient of variation (in %) of the fibre weight per unit length, accurate to two decimal places, is considered as ______________
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T he bending length of a nonwoven fabric in machine direction is two times the bending length in cross-machine direction. The ratio of flexural rigidities of this fabric in machine direction to cross-machine direction is ______________
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A crease resist (CR) agent is applied by padding on a fabric of 1 m width and 200 g/m2 areal density. The concentration of CR agent in the pad bath is 100 gpl and the fabric speed is 50 m/min. The expression is 110% and the specific gravity of the pad liquor is 1.1. In order to maintain the bath concentration, the rate (in kg/min) at which the CR agent needs to be added to the bath, accurate to one decimal place, is_______________
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I n an electrochemical machining of aluminium with plane parallel electrodes, the current density is 70 A/cm2. Cross-sectional area of each electrode is 3 cm2. The current efficiency (i.e., the fraction of current used for dissolution of metal) is 80%. Gram atomic weight, valency and density of aluminium are 27 gram, 3 and 2700 kg/m3, respectively. Take Faraday’s constant as 96500 Coulomb. The volumetric material removal rate (in mm3/min) is ______
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A cylindrical workpiece is turned at a feed of 0.1 mm/rev with a perfectly sharp tool. In ASA system, the side and end cutting edge angles are 15° and 5°, respectively, as shown in the figure. The peak-to-valley roughness (in μm, up to one decimal place) of the machined surface is ______
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A 10 mm thick plate is rolled to 7 mm thickness in a rolling mill using 1000 mm diameter rigid rolls. The neutral point is located at an angle of 0.3 times the bite angle from the exit. The thickness (in mm, up to two decimal places) of the plate at the neutral point is ______
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T he breakeven point of a manufacturing company is 50000 units. The fixed cost is Rs. 200000 and the variable cost per unit is Rs. 20. The selling price per unit (in Rs.) of the product at this breakeven point is ______
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In a work sampling study of a worker, the information available are as follows: total time of study: 30 hour, number of items produced: 320, total number of observations: 1000, number of observations when worker is found working: 850 and average performance rating: 105%. Company policy is to give allowance of 10% of total time on the job. The standard time (in minute per item, up to one decimal place) for manufacturing the item is ______
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L ength, width and thickness of a plate are 400 mm, 400 mm and 30 mm, respectively. For the material of the plate, Young’s modulus of elasticity is 70 GPa, yield stress is 80 MPa and Poisson’s ratio is 0.33. When the plate is subjected to a longitudinal tensile stress of 70 MPa, the increase in the volume (in mm3) of the plate is ______
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I f 2 2 2( ) u x y and v axy represent the x- and y-components of the two-dimensional velocity field of an incompressible flow, the value of the constant a is ______
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A cylindrical wooden block of length 50 cm is floating in water in such a way that its axis is vertical. The densities of wood and water are 800 kg/m3 and 1000 kg/m3, respectively. The submerged depth, i.e., depth of immersion (in cm) of the cylinder is _______
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What is the area of the shaded part of the circle? O is the center of the circle. The radius of the circle is 4. x is 60. (GMAT-MATHS)
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If I and J are straight lines, Then find y. x = 100 z = 80 (GMAT-MATHS)
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Did the price of a bushel of soybeans increase during every week of 1980? The price of a bushel of soybeans was $2 on January 1, 1980. The price of a bushel of soybeans was $4 on January 1, 1981. (GMAT-MATHS)
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The high temperature magnetic susceptibility of solids having ions with magnetic moments can be described by 𝜒∝1𝑇+𝜃 with 𝑇 as absolute temperature and 𝜃 as constant. The three behaviors i.e. paramagnetic, ferromagnetic and anti-ferromagnetic are described, respectively, by
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For nucleus 164Er, a 𝐽𝜋=2+ state is at 90 keV. Assuming 164Er to be a rigid rotor, the energy of its 4+ state is ________ keV (up to one decimal place)
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If 𝑋 is the dimensionality of a free electron gas, the energy (𝐸) dependence of density of states is given by 𝐸12𝑋−𝑌, where 𝑌 is ________.
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A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places)
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A light beam of intensity 𝐼0 is falling normally on a surface. The surface absorbs 20% of the intensity and the rest is reflected. The radiation pressure on the surface is given by 𝑋𝐼0𝑐⁄, where X is ________ (up to one decimal place). Here 𝑐 is the speed of light.
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A quarter wave plate introduces a path difference of 𝜆/4 between the two components of polarization parallel and perpendicular to the optic axis. An electromagnetic wave with 𝐸⃗ =(𝑥̂+𝑦̂) 𝐸0 𝑒𝑖(𝑘𝑧−𝜔𝑡) is incident normally on a quarter wave plate which has its optic axis making an angle 135° with the 𝑥-axis as shown.
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The quantum effects in an ideal gas become important below a certain temperature 𝑇𝑄 when de Broglie wavelength corresponding to the root mean square thermal speed becomes equal to the inter-atomic separation. For such a gas of atoms of mass 2×10−26 kg and number density 6.4×1025 m–3, 𝑇𝑄= __________ ×10−3 K (up to one decimal place). (𝑘𝐵=1.38×10−23 J/K, ℎ=6.6×10−34 J-s)
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An atom in its singlet state is subjected to a magnetic field. The Zeeman splitting of its 650 nm spectral line is 0.03 nm. The magnitude of the field is ________ Tesla (up to two decimal places). ( 𝑒=1.60×10−19 C, 𝑚𝑒=9.11×10−31 kg, 𝑐=3.0×108 ms–1)
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