GATE CH exam:gate PYQs & Answers — Page 62

Questions 611–620 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 62 of 65

For the initial value problem

the value of

, is __________.

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The Laplace transform of a function is

The initial and final values, respectively, of the function are

Your answerChoose one option.

0 and 1

1 and

and 1

and 0

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Match the problem type in Group-1 with the numerical method in Group-2.

Group-1 P) System of linear algebraic equations Q) Non-linear algebraic equations R) Ordinary differential equation S) Numerical integration

Group-2 I) Newton-Raphson II) Gauss-Seidel III) Simpson’s rule IV) Runge-Kutta

Choose the correct set of combinations.

Your answerChoose one option.

P-II, Q-I, R-III, S-IV

P-I, Q-II, R-IV, S-III

P-IV, Q-III, R-II, S-I

P-II, Q-I, R-IV, S-III

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A box has 6 red balls and 4 white balls. A ball is picked at random and replaced in the box, after which a second ball is picked. The probability of both the balls being red, rounded to 2 decimal places, is ________.

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An aqueous salt-solution enters a crystallizer operating at steady state at 25°C. The feed temperature is 90°C and the salt concentration in the feed is 40 weight %. The salt crystallizes as a pentahydrate. The crystals and the mother liquor leave the crystallizer. The molecular weight of the anhydrous salt is 135. The solubility of the salt at 25°C is 20 weight %. The feed flowrate required for a production rate of 100 kg/s of the hydrated salt, rounded to the nearest integer, is ________ kg/s.

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Reaction A → B is carried out in a reactor operating at steady state and 1 mol/s of pure A at 425°C enters the reactor. The outlet stream leaves the reactor at 325°C. The heat input to the reactor is 17 kW. The heat of reaction at the reference temperature of 25°C is 30 kJ/mol. The specific heat capacities (in kJ/mol.K) of A and B are 0.1 and 0.15, respectively. The molar flowrate of B leaving the reactor, rounded to 2 decimal places, is __________ mol/s.

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The pressure of a liquid is increased isothermally. The molar volume of the liquid decreases from

m³/mol to

m³/mol during this process. The isothermal compressibility of the liquid is

Pa⁻¹, which can be assumed to be independent of pressure. The change in the molar Gibbs free energy of the liquid, rounded to nearest integer, is ______ J/mol.

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A sparingly soluble gas (solute) is in equilibrium with a solvent at 10 bar. The mole fraction of the solute in the gas phase is 0.01. At the operating temperature and pressure, the fugacity coefficient of the solute in the gas phase and the Henry’s law constant are 0.92 and 1000 bar, respectively. Assume that the liquid phase obeys Henry’s law. The MOLE PERCENTAGE of the solute in the liquid phase, rounded to 2 decimal places, is ______.

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The vapour pressure of a pure substance at a temperature

is 30 bar. The actual and ideal gas values of

for the saturated vapour at this temperature

and 30 bar are 7.0 and 7.7, respectively. Here,

is the molar Gibbs free energy and

is the universal gas constant. The fugacity of the saturated liquid at these conditions, rounded to 1 decimal place, is ________ bar.

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Oil is being delivered at a steady flowrate through a circular pipe of radius

m and length 10 m. The pressure drop across the pipe is 500 Pa. The shear stress at the pipe wall, rounded to 2 decimal places, is __________ Pa.

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GATE CH exam:gate PYQs

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35