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1)The expenditure on the project _____ as follows: equipment Rs.20 lakhs, salaries Rs.12 lakhs, and contingency Rs.3 lakhs.
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2)The search engine’s business model ___________ around the fulcrum of trust.
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3)Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 km/h and the speed of the second car is 60 km/h. The number of hours it takes for the distance between the two cars to be 20 km is ___.
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4)Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs 150 more. The cost of the gift was Rs. ____.
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5)A court is to a judge as _____________ is to a teacher.
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6)The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:
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7)In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of ___________.
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8)“A recent High Court judgement has sought to dispel the idea of begging as a disease — which leads to its stigmatization and criminalization — and to regard it as a symptom. The underlying disease is the failure of the state to protect citizens who fall through the social security net.”
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9)In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is _____.
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10)Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests.
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11)A system of n homogeneous linear equations containing n unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is
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12)The value of the expression x x x tan lim 2 is
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13)Consider a rigid, perfectly insulated, container partitioned into two unequal parts by a thin membrane (see figure). One part contains one mole of an ideal gas at pressure Pi and temperature Ti while the other part is evacuated. The membrane ruptures, the gas fills the entire volume and the equilibrium pressure is Pf = Pi⁄4. If Cp (molar specific heat capacity at constant pressure), Cv (molar specific heat capacity at constant volume) and R (universal gas constant) have the same units as molar entropy, the change in molar entropy (Sf − Si) is
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14)For a single component system, vapor (subscript g) and liquid (subscript f) coexist in mechanical, thermal and phase equilibrium when
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15)For a binary nonideal A-B mixture exhibiting a minimum boiling azeotrope, the activity coefficients, γi (i = A, B), must satisfy
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16)For a fully-developed turbulent hydrodynamic boundary layer for flow past a flat plate, the thickness of the boundary layer increases with distance x from the leading edge of the plate, along the free-stream flow direction, as
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17)Consider a cylinder (diameter D and length D ), a sphere (diameter D ) and a cube (side length D ). Which of the following statements concerning the sphericity ( ) of the above objects is true:
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18)Prandtl number signifies the ratio of
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19)Pool boiling equipment operating above ambient temperature is usually designed to operate
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20)The desired liquid-phase reaction D + E k1 → F rF = k1 CD 2 CE 0.3 is accompanied by an undesired side reaction D + E k2 → G rG = k2 CD 0.4 CE 1.5
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21)For a first order reaction in a porous spherical catalyst pellet, diffusional effects are most likely to lower the observed rate of reaction for
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22)A thermocouple senses temperature based on the
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23)The correct expression for the Colburn j-factor for mass transfer that relates Sherwood number (Sh), Reynolds number (Re) and Schmidt number (Sc) is
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24)In the drying of non-dissolving solids at constant drying conditions, the internal movement of moisture in the solid has a dominant effect on the drying rate during
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25)Three distillation schemes for separating an equimolar, constant relative volatility ABC mixture into nearly pure components are shown. The usual simplifying assumptions such as constant molal overflow, negligible heat loss, ideal trays are valid. All the schemes are designed for minimum total reboiler duty. Given that the relative volatilities are in the ratio : : A B C 8:2:1, the correct option that arranges the optimally-designed schemes in ascending order of total reboiler duty is
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26)Consider the two countercurrent heat exchanger designs for heating a cold stream from tin to tout , as shown in figure. The hot process stream is available at Tin . The inlet stream conditions and overall heat transfer coefficients are identical in both the designs. The heat transfer area in Design I and Design II are respectively AHX I and AHX
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27)Producer gas is obtained by
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28)In Kraft process, the essential chemical reagents used in the digester are
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29)The most common catalyst used for oxidation of o-xylene to phthalic anhydride is
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30)In petroleum refining operations, the process used for converting paraffins and naphthenes to aromatics is
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31)The combination that correctly matches the polymer in Group-1 with the polymerization reaction type in Group-2 is
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32)The product of the eigenvalues of the matrix 2 3 0 7 is __________________ (rounded off to one decimal place).
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33)For a hydraulic lift with dimensions shown in figure, assuming g 10 m/s 2 , the maximum diameter Dleft (in m) that lifts a vehicle of mass 1000 kg using a force of 100 N is _____________ (rounded off to two decimal places).
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34)The liquid flow rate through an equal percentage control valve, when fully open, is 150 gal/min and the corresponding pressure drop is 50 psi. If the specific gravity of the liquid is 0.8, then the valve coefficient, ∁V, in gal/(min psi0.5) is _________ (rounded off to two decimal places).
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35)Consider a sealed rigid bottle containing CO2 and H2O at 10 bar and ambient temperature. Assume that the gas phase in the bottle is pure CO2 and follows the ideal gas law. The liquid phase in the bottle contains CO2 dissolved in H2O and is an ideal solution. The Henry’s constant at the system pressure and temperature is HCO2 = 1000 bar. The equilibrium mole fraction of CO2 dissolved in H2O is ________ (rounded off to three decimal places).
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36)The solution of the ordinary differential equation 3 1 dy y dx
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37)The value of the complex number 1/2 i (where i 1 ) is
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38)An incompressible Newtonian fluid flows in a pipe of diameter D1 at volumetric flow rate Q . Fluid with same properties flows in another pipe of diameter 2 1 D D / 2 at the same flow rate Q . The transition length required for achieving fully-developed flow is 1 l for the tube of diameter D1 , while it is 2 l for the tube of diameter D2 . Assuming steady laminar flow in both cases, the ratio 1 2 l l is:
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39)A disk turbine is used to stir a liquid in a baffled tank. To design the agitator, experiments are performed in a lab-scale model with a turbine diameter of 0.05 m and a turbine impeller speed of 600 rpm. The liquid viscosity is 0.001 Pa s while the liquid density is 1000 kg/m 3 . The actual application has a turbine diameter of 0.5 m, an impeller speed of 600 rpm, a liquid viscosity of 0.1 Pa s and a liquid density of 1000 kg/m 3 . The effect of gravity is negligible. If the power required in the lab-scale model is P1 and the estimated power for the actual application is P2 , then the ratio P 2/P1 is
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40)Consider two non-interacting tanks-in-series as shown in figure. Water enters TANK 1 at q cm3 /s and drains down to TANK 2 by gravity at a rate 1 k h (cm3 /s). Similarly, water drains from TANK 2 by gravity at a rate of 2 k h (cm3 /s) where 1 h and 2 h represent levels of TANK 1 and TANK 2, respectively (see figure). Drain valve constant k 4 cm2.5/s and cross- sectional areas of the two tanks are A A 1 2 28 cm2
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41)Choose the option that correctly matches the step response curves on the left with the appropriate transfer functions on the right. The step input change occurs at time t =0.
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42)100 kg of a feed containing 50 wt.% of a solute C is contacted with 80 kg of a solvent containing 0.5 wt.% of C in a mixer-settler unit. From this operation, the resultant extract and raffinate phases contain 40 wt.% and 20 wt.% of C, respectively. If E and R denote the mass of the extract and raffinate phases, respectively, the ratio E/R is
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43)The combination that correctly matches the process in Group-1 with the entries in Group-2 is
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44)If x y, and z are directions in a Cartesian coordinate system and i , j and k are the respective unit vectors, the directional derivative of the function 2 u x y z x yz ( , , ) 3 at the point (2,0, 4) in the direction i j k 2 6 is _____________ (rounded off to two decimal places).
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45)Two unbiased dice are thrown. Each dice can show any number between 1 and 6. The probability that the sum of the outcomes of the two dice is divisible by 4 is________ (rounded off to two decimal places).
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46)The Newton-Raphson method is used to determine the root of the equation ( ) x f x e x . If the initial guess for the root is 0, the estimate of the root after two iterations is ______ (rounded off to three decimal places).
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47)Carbon monoxide (CO) reacts with hydrogen sulphide (H2S) at a constant temperature of 800 K and a constant pressure of 2 bar as: CO + H2S ⇋ COS + H2 The Gibbs free energy of the reaction ∆g°rxn = 22972.3 J/mol and universal gas constant R=8.314 J/(mol K). Both the reactants and products can be assumed to be ideal gases. If initially only 4 mol of H2S and 1 mol of CO are present, the extent of the reaction (in mol) at equilibrium is _________ (rounded off to two decimal places).
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48)For a given binary system at constant temperature and pressure, the molar volume (in m3 /mol) is given by: 30 20 15 7 x x x x x x A B A B A B , where A x and B x are the mole fractions of components A and B, respectively. The volume change of mixing mix (in m3 /mol) at A x = 0.5 is __________ (rounded off to one decimal place).
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49)A fractionator recovers 95 mol % n-propane as the distillate from an equimolar mixture of n-propane and n-butane. The condensate is a saturated liquid at 55 °C. The Antoine equation is of the form, T C B P A sat in K ln in bar , and the constants are provided below: A B C n-propane 9.1058 1872.46 −25.16 n-butane 9.0580 2154.90 −34.42 Assuming Raoult’s law, the condenser pressure (in bar) is ________________ (rounded off to one decimal place).
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50)A centrifugal pump is used to pump water (density 1000 kg/m 3 ) from an inlet pressure of 5 10 Pa to an exit pressure of 5 2 10 Pa. The exit is at an elevation of 10 m above the pump. The average velocity of the fluid is 10 m/s. The cross-sectional area of the pipes at the pump inlet and outlet is 3 10 m 2 and acceleration due to gravity is g 10 m/s 2 . Neglecting losses in the system, the power (in Watts) delivered by the pump is ________ (rounded off to the nearest integer).
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51)A solid sphere of radius 1 cm and initial temperature of 25 °C is exposed to a gas stream at 100 °C. For the solid sphere, the density is 104 kg/m3 and the specific heat capacity is 500 J/(kg K). The density of the gas is 0.6 kg/m3 and its specific heat capacity is 103 J/(kg K). The solid sphere is approximated as a lumped system (Biot number ≪ 1) and all specific heats are constant. If the heat transfer coefficient between the solid and gas is 50 W/(m2 K), the time (in seconds) needed for the sphere to reach 95 °C is _____________ (rounded off to the nearest integer)
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52)Stream A with specific heat capacity CPA = 2000 J/(kg K) is cooled from 90 °C to 45 °Cin a concentric double pipe counter current heat exchanger having a heat transfer area of 8 m2 . The cold stream B of specific heat capacity CPB = 1000 J/(kg K) enters the exchanger at a flow rate 1 kg/s and 40 °C. The overall heat transfer coefficient U 250 W/(m2 K). Assume that the mean driving force is based on the arithmetic mean temperature difference, that is, , , , , 2 2 A in A out B in B out AMTD T T T T T where Ti in, and Ti out , refer to the temperature of the i th stream (i = A, B) at the inlet and exit, respectively. The mass flow rate of stream A (in kg/s), is _______________ (rounded off to two decimal places).
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53)A 20 cm diameter cylindrical solid pellet of a nuclear fuel with density 6000 kg/m3 and conductivity of 300 W/(m K) generates heat by nuclear fission at a spatially uniform rate of 104 W/kg. The heat from the fuel pellet is transferred to the surrounding coolant by convection such that the pellet wall temperature remains constant at 300 °C. Neglecting the axial and azimuthal dependence, the maximum temperature (in °C) in the pellet at steady state is ________________ (rounded off to the nearest integer).
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54)The elementary, irreversible, liquid-phase, parallel reactions, 2A → D and 2A → U, take place in an isothermal non-ideal reactor. The C-curve measured in a tracer experiment is shown in the figure, where C t() is the concentration of the tracer in g/m3 at the reactor exit at time t (in min).
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55)A first-order irreversible liquid phase reaction A → B k = 0.1 min−1 is carried out under isothermal, steady state conditions in the following reactor arrangement comprising an ideal CSTR (Continuous-Stirred Tank Reactor) and two ideal PFRs (Plug Flow Reactors). From the information in the figure, the volume of the CSTR (in Liters) is ___________ (rounded off to the nearest integer).
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56)The elementary liquid-phase irreversible reactions 1 1 k k 1 2 = 0.4 min = 0.1 min A B C take place in an isothermal ideal CSTR (Continuous-Stirred Tank Reactor). Pure A is fed to the reactor at a concentration of 2 mol/Liter. For the residence time that maximizes the exit concentration of B, the percentage yield of B, defined as net formation rate of B 100 consumption rate of A , is ___________ (rounded off to the nearest integer).
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57)The elementary irreversible gas-phase reaction A → B + C is carried out adiabatically in an ideal CSTR (Continuous-Stirred Tank Reactor) operating at 10 atm. Pure A enters the CSTR at a flow rate of 10 mol/s and a temperature of 450 K. Assume A, B and C to be ideal gases. The specific heat capacity at constant pressure ( CPi ) and heat of formation 0 ( ) Hi , of component i (i = A, B, C), are:
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58)For the closed loop system shown in figure, the phase margin (in degrees) is ___________ (rounded off to one decimal place).
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59)Two spherical camphor particles of radii 20 cm and 5 cm, far away from each other, are undergoing sublimation in a stream of air. The mass transfer coefficient is proportional to 1 ( ) r t , where r t is the radius of the sphere at time t. Assume that the partial pressure of camphor far away from the surface of the particle is zero. Also, assume quasi-steady state, identical ambient conditions, and negligible heat effects. If 1 t and 2 t are the times required for complete sublimation of the 20 cm and 5 cm camphor particles, respectively, the ratio 1 2 t t is _____________ (rounded off to one decimal place).
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60)A countercurrent absorption tower is designed to remove 95% of component A from an incoming binary gas mixture using pure solvent B. The mole ratio of A in the inlet gas is 0.02. The carrier gas flow rate is 50 kmol/h. The equilibrium relation is given by Y = 2X, where Y and X are the mole ratios of A in the gas and liquid phases, respectively. If the tower is operated at twice the minimum solvent flow rate, the mole ratio of A in the exit liquid stream is _______________ (rounded off to three decimal places).
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61)A binary mixture with components A and B is to be separated in a distillation column to obtain 95 mol% A as the top product. The binary mixture has a constant relative volatility αAB = 2. The column feed is a saturated liquid containing 50 mol% A. Under the usual simplifying assumptions such as constant molal overflow, negligible heat loss, ideal trays, the minimum reflux ratio for this separation is ___________________ (rounded off to one decimal place).
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62)Consider the reactor-separator-recycle process operating under steady state conditions as shown in the figure. The reactor is an ideal Continuous-Stirred Tank Reactor (CSTR), where the reaction A + B → C occurs. Assume that there is no impurity in the product and recycle streams. Other relevant information are provided in the figure. The mole fraction of B (xB) in the reactor that minimizes the recycle rate is__________________ (rounded off to two decimal places).
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63)Consider two competing equipment A and B. For a compound interest rate of 10% per annum, in order for equipment B to be the economically cheaper option, its minimum life (in years) is ________ (rounded off to the next higher integer).
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64)A taxi-car is bought for Rs 10 lakhs. Its salvage value is zero. The expected yearly income after paying all expenses and applicable taxes is Rs 3 lakhs. The compound interest rate is 9% per annum. The discounted payback period (in years), is _________________ (rounded off to the next higher integer).
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