# Recent questions tagged gate2013

Velocity of an object fired directly in upward direction is given by V = 80 – 32 t, where t (time) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec? (1, 3/2) (½, 1) (½, 3/2) (1, 3)
All professors are researchers Some scientists are professors Which of the given conclusions is logically valid and is inferred from the above arguments: All scientists are researchers All professors are scientists Some researchers are scientists No conclusion follows
Following table gives data on tourists from different countries visiting India in the year 2011 ... the one third of the total number of tourists who visited India in 2011? USA and Japan USA and Australia England and France Japan and Australia
If $|-2x+9| = 3$ then the possible value of $|-X|-X^2$ would be: 30 -30 -42 42
In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponents from the combined lot is found defective, what is the probability that it was manufactured by M2? 0.35 0.45 0.5 0.4
The Headmaster ______ to speak to you. Which of the following options is incorrect to complete the above sentence? is wanting. wants want was wanting
Mahatma Gandhi was known for his humility as he played an important role in humiliating exit of British from India. he worked for humanitarian causes. he displayed modesty in his interactions. he was a fine human being.
Select the pair that best expresses a relationship similar to that expressed in the pair: water:pipe:: cart: road electricity: wire sea: beach music: instrument
Consider the following transfer function G${_p}$(s) = $\frac{5}{(2s+1)^4}$ (Note: The unit of the processor time constant is in seconds.) The crossover frequency (in rad/s) of the process is 20 0.1 0.5 0.05
For the computation of Ziegler-Nichols settings, the ultimate period (in s/cycle) and the ultimate gain are $\pi$ and 0.8, respectively 4$\pi$ and 0.8, respectively 4$\pi$ and 1.25, respectively $\pi$ and 1.25, respectively
If 3 $\le$ X $\le$ 5 and 8 $\le$ Y $\le$ 11 then which of the following options is TRUE? $\frac{3}{5}$ $\le$ $\frac{X}{Y}$ $\le$ $\frac{8}{5}$ $\frac{3}{11}$ $\le$ $\frac{X}{Y}$ $\le$ $\frac{5}{8}$ $\frac{3}{11}$ $\le$ $\frac{X}{Y}$ $\le$ $\frac{8}{5}$ $\frac{3}{5}$ $\le$ $\frac{X}{Y}$ $\le$ $\frac{8}{11}$
$\frac{Allengineering students }{I}$ $\frac{should learn mechanics}{II}$, $\frac{mathematics and}{III}$ $\frac{how to do computation}{IV}$ Which of the above underlined parts of the sentence is not appropriate? I II III IV
The vapor liquid equilibrium relation for an ideal binary system is given by y*${_A}$ = $\frac{\alpha{_A}{_B}x{_A}}{1 + ({\alpha}{_A}{_B} - 1)x{_A}}$ Here x${_A}$ and y*${_A}$ ... $\frac{0.5}{(\sqrt{{\alpha}_{AB}+1)}}$ $\frac{0.75}{(\sqrt{{\alpha}_{AB}+1})}$
The vapor liquid equilibrium relation for an ideal binary system is given by y*${_A}$ = $\frac{\alpha{_A}{_B}x{_A}}{1 + ({\alpha}{_A}{_B} - 1)x{_A}}$ Here x${_A}$ and y*${_A}$ are the mole fractions of species A in the liquid and vapor, respectively. The relative ... a final liquid mole fraction of 0.25. If $\alpha{_A}{_B}$ is 2.5, the fraction of the feed vaporized is 0.08 0.20 0.67 0.74
Liquid reactant A decomposes as follows A $\rightarrow$ R r${_R}$= k${_1}$C$^{2}${_A}$k${_1}$= 0.5m$^{3}$/mol-s A$\rightarrow$S r${_S} $= k${_2}$C${_A}$k${_2}$= 1 s$^{-1}$What is the % conversion of A, to the nearest integer, so that the concentration of S in the exit stream is 11.8 mol/m$^{3}$?$\_\_\_ \_\_\_\_$0 votes 0 answers Liquid reactant A decomposes as follows A$\rightarrow$R r${_R} $= k${_1}$C$^{2}${_A}$ k${_1}$ = 0.5m$^{3}$/mol-s A $\rightarrow$ S r${_S}$= k${_2}$C${_A}$ k${_2}$ = 1 s$^{-1}$ An aqueous feed of composition C${_AO}$ = 30 mol/m$^{3}$, C${_RO}$ = 2 mol/m$^{3}$, C${_SO}$ = 1 mol/m$^{3}$, enters a CSTR in which the above reactions occur. Assume isothermal and steady state conditions.
A fraction $f$ of the feed is bypassed and mixed with the permeate to obtain treated water having a fluoride concentration of 1 mg/L. Here also the flow rate of the reject stream is 60% of the flow rate entering the reverse osmosis unit (after the bypass). The value of $f$, up to 2 digits after the decimal point, is $\_\_\_\_\_\_\_$
A reverse osmosis unit treats feed water (F) containing fluoride and its output consists of a permeate stream (P) and a reject stream (R). Let C${_F}$, C${_p}$, and C${_R}$ denote the fluoride concentrations in the feed, permeate, and reject streams, respectively. Under steady state conditions, ... 1mg/L. The value of C${_R}$ in mg/L, up to one digit after the decimal point, is $\_\_\_\_\_\_\_$
A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N$^{1.3}$. The selling price per compressor is Rs1000. The number of compressors to br manufactured, to the nearest integer, in order to maximize the daily profit is $\_\_\_\_\_\_\_$
Match the reactant-product combination in Group 1 with the unit process in Group 2 Group 1 Group 2 (P) propylene – butanol (1) pyrolysis (Q) cumene – phenol (2) Dehydrogenation (R) butane – butadiene (3) Hydroformylation (S) ethylene dichloride – viny chloride (4) Peroxidation P-3, Q-2, R-4, S-1 P-2, Q-4,R-3, S-1 P-1, Q-3, R-2, S-4 P-3, Q-4, R-2, S-1
Identify which of the following statements are FALSE. (P) Oils with an oleic radical (1 double bond) are more suitable than oils with a linolenic radical (3 double bonds) as film forming vehicles for paints (Q) Production of synthesis gas from coal and stream is an ... ammonia, the main intermediate product formed is ammonium bicarbonate P and Q only R and S only Q and R only P and S only
The gas phase decomposition of azomethane to give ethane and nitrogen takes place according to the following sequence of elementary reactions. (CH${_3}){_2}$N${_2}$ + (CH${_3}){_2}$N${_2}$ $\rightarrow ^{K_1}$ (CH${_3}){_2}$N${_2}$ + [(CH${_3}){_2}$ ... respect to azomethane in the rate expression for the formation of ethane, in the limit of high concentrations of a azomethane, is $\_\_\_\_\_\_$
The purchase cost of a heat exchanger of 20 m$^{2}$ area was Rs 500000 in 2006. What will be the estimated cost (in Rs to the nearest integer) of a similar heat exchanger of 50 m$^{2}$ area in the year 2013? Assume the six-tenths factor rule for scaling and the cost index for 2006 as 430.2. The projected cost index for the year 2013is 512.6. $\_\_\_\_\_\_\_\_$
A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is $\_\_\_\_\_\_\_$
A unit gain 2$^{nd}$ order underdamped process has a period of oscillation 1 second and decay ratio 0.25. The transfer function of the process is $\frac{1}{0.024s^2 + 0.067s+1}$ $\frac{1}{0.067s^2 + 0.024s+1}$ $\frac{1}{0.021s^2 + 0.1176s+1}$ $\frac{1}{0.1176s^2 + 0.021s+1}$
A control value, with a turndown ratio of 50, follows equal percentage characteristics. The flow rate of a liquid through the value at 40% stem positions is 1 m$^{3}$/h. What will be the flow rate in m$^{3}$/h at 50% stem positions, if the pressure drop across the value remains unchanged? (Up to 2 digits after the decimal point.) $\_\_\_\_\_\_\_$
In the elutriation leg of a commercial crystallizer containing a mixture of coarse and very fine crystals of the same material, a liquid is pumped vertically upward. The liquid velocity is adjusted such that it is slightly lower than the terminal velocity of the ... will be carried upward and the crystals will settle the coarse crystals will be carried upward and the very fine crystals will settle
A crosscurrent cascade of N ideal stages is used to treat a feed stream of molar flow rate E. The feed stream contains a solute which is to be recovered by a pure solvent having a molar flow rate S. The solvent is divided equally between these N stages. The linear equilibrium curve relating the mole fraction x and y* of ... $^{N}$ [1+($\frac {NE}{mS}$)]$^{N}$ [1+($\frac {mE}{NS}$)]$^{N}$
In a double pipe counter-current heat exchanger, the temperature profiles shown in the figure were observed. During operation, due to fouling inside the pipe, the heat transfer rate reduces to half of the original value. Assuming that the flow rates and the physical properties of the fluids do not change, the LMTD (in ${_o}$C) in the new situations is 0 20 40 indeterminate
100 ton/h of a rock feed, of which 80% passed through a mesh size of 2.54 mm, were reduced in size such that 80% of the crushed product passed through a mesh size of 1.27 mm. The power consumption was 100 kW. If 100 ton/h of the same material is similarly crushed from a mesh size of ... size of 2.54 mm, the power consumption (in kW, to the nearest integer) using Bond's law, is $\_\_\_\_\_\_\_\_$
Calculate the heat required (in kJ, up to 1 digit after the decimal point) to raise the temperature of 1 mole of a solid material from 100 $^{o}$C to 1000 $^{o}$C. The specific heat (C${_p}$) of the material (in J/mol-K) is expressed as C${_p}$ = 20 + 0.005T, where T is in K. Assume no phase change. $\_\_\_\_\_\_\_$
The vapor-liquid equilibrium curve of a binary mixture A-B,may be approximated by a linear equation over a narrow range of liquid mole fractions (0.2 < x${_A}$ < 0.3) as follows y*${_A}$ = 1.325x${_A}$ + 0.121 Here y*${_A}$ is the mole fraction of A in ... equation, the number of moles of the residue left behind in the distillation unit, up to 2 digits after the decimal point, is $\_\_\_\_\_$
A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient k${_c}$ has been calculated as 1 mm/s using the correlation Sh = 0.025 Re$^{0.6}$ Sc$^{0.33}$ If the velocity ... , what is the new value of k${_c}$ in mm/s, up to 2 digits after the decimal point? $\_\_\_\_\_\_\_$
The solution of the differential equation $\frac{d^2y}{dx^2}$ – $\frac{dy}{dx}$ + 0.25y = 0, given y = 0 at x = 0 and $\frac{dy}{dx}$ = 1 at x = 0 is xe$^{0.5x}$ – xe$^{-0.5x}$ 0.5xe$^{x}$ – 0.5xe$^{-x}$ xe$^{0.5x}$ -xe$^{0.5x}$
In a process occurring in a closed system F, the heat transferred from F to the surroundings E is 600 J. If the temperature of E is 300 K and that of F is in the range 380 - 400 K, the entropy changes of the surroundings (${\Delta}S{_E}$) and systems (${\Delta}S{_F}$ ... ${\Delta}S{_E}$ = 2, ${\Delta}S{_F}$ < -2 ${\Delta}S{_E}$ = 2, ${\Delta}S{_F}$ > -2
For the function f(z) = $\frac{1}{(2-z)(z+2)}$ the residue at z = 2 is $\_\_\_\_\_$
The solution of the differential equation $\frac{dy}{dx}$ – y$^{2}$ = 0, given y=1 at x=0 is $\frac{1}{1+x}$ $\frac{1}{1-x}$ $\frac{1}{(1-x)^2}$ $\frac{x^3}{3}$+1
The value of the integral ${\scriptstyle \int^{0.5} _{0.1}}$ e$^{-x^3}$dx evaluated by Simpson’s rule using 4 subintervals (up to 3 digits after the decimal point) is $\_\_\_\_\_\_$
A binary liquid mixture is in equilibrium with its vapor at a temperature T = 300 K. The liquid mole fraction x${_1}$ of species 1 is 0.4 and the molar excess Gibbs free energy is 200 J/mol. The value of the universal gas constant is 8.314 J/mol-K, and ${\gamma}{_1}$ denotes the liquid- ... ${\gamma}{_2}$), up to 2 digits after the decimal point, is $\_\_\_\_\_\_$
Water (density 1000 kg/m$^{3}$) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship the diameters of the nozzle at location 1 and 2 is D${_1}$ = 4 D${_2}$.The average velocity of the stream at location 2 is 16 m/s and the ... 1 and location 2 is 10000 Pa. Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1 is $\_\_\_\_\_$