Numerical Computation and Estimation - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2014 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2014

A factory has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes?

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2

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

Operators □, ◇ and → are defined by: a □ b = \frac{a-b}{a+b}; a ◇ b = \frac{a+b}{a-b}; a→b = ab.
Find the value of (66 □ 6) → (66 ◇ 6).

A

-2

B

-1

C

1

D

2

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3

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

Consider a linear ordinary differential equation: \(\frac{dy}{dx} + p(x)y = r(x)\). Functions \(p(x)\) and \(r(x)\) are defined and have a continuous first derivative. The integrating factor of this equation is non-zero. Multiplying this equation by its integrating factor converts this into a:

A

Homogeneous differential equation

B

Non-linear differential equation

C

Second order differential equation

D

Exact differential equation

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4

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

A complex-valued function, \(f(z)\), given below is analytic in domain D: \(f(z) = u(x,y) + iv(x,y) \quad z = x + iy\) Which of the following is NOT correct?

A

\(\frac{df}{dz} = \frac{\partial v}{\partial y} + i\frac{\partial u}{\partial y}\)

B

\(\frac{df}{dz} = \frac{\partial u}{\partial x} + i\frac{\partial v}{\partial x}\)

C

\(\frac{df}{dz} = \frac{\partial v}{\partial y} - i\frac{\partial u}{\partial y}\)

D

\(\frac{df}{dz} = \frac{\partial v}{\partial y} + i\frac{\partial v}{\partial x}\)

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5

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

For a pure liquid, the rate of change of vapour pressure with temperature is 0.1 bar/K in the temperature range of 300 to 350 K. If the boiling point of the liquid at 2 bar is 320 K, the temperature (in K) at which it will boil at 1 bar (up to one decimal place) is ________.

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6

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

For a gas phase cracking reaction \(A \rightarrow B + C\) at 300°C, the Gibbs free energy of the reaction at this temperature is \(\Delta G^o = -2750\) J/mol. The pressure is 1 bar and the gas phase can be assumed to be ideal. The universal gas constant R = 8.314 J/mol.K. The fractional molar conversion of A at equilibrium is:

A

0.44

B

0.50

C

0.64

D

0.80

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7

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

If v, u, s and g represent respectively the molar volume, molar internal energy, molar entropy and molar Gibbs free energy, then match the entries in the left and right columns below and choose the correct option. P. \(-(\partial u/\partial v)_s\) I. Temperature Q. \((\partial g/\partial P)_T\) II. Pressure R. \(-(\partial g/\partial T)_P\) III. v S. \((\partial u/\partial s)_v\) IV. s

A

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

B

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

C

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

D

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

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8

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

Two different liquids are flowing through different pipes of the same diameter. In the first pipe, the flow is laminar with centerline velocity, \(V_{max,1}\), whereas in the second pipe, the flow is turbulent. For turbulent flow, the average velocity is 0.82 times the centerline velocity, \(V_{max,2}\). For equal volumetric flow rates in both the pipes, the ratio \(V_{max,1}/V_{max,2}\) (up to two decimal places) is ________.

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9

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

A cylindrical packed bed of height 1 m is filled with equal sized spherical particles. The particles are nonporous and have a density of 1500 kg/m³. The void fraction of the bed is 0.45. The bed is fluidized using air (density 1 kg/m³). If the acceleration due to gravity is 9.8 m/s², the pressure drop (in Pa) across the bed at incipient fluidization (up to one decimal place) is ________.

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10

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

Two infinitely large parallel plates (I and II) are held at temperatures \(T_I\) and \(T_{II}\) (\(T_I > T_{II}\)) respectively, and placed at a distance 2d apart in vacuum. An infinitely large flat radiation shield (III) is placed in parallel in between I and II. The emissivities of all the plates are equal. The ratio of the steady state radiative heat fluxes with and without the shield is:

A

0.5

B

0.75

C

0.25

D

0

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11

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

For a binary mixture of components A and B, \(N_A\) and \(N_B\) denote the total molar fluxes of components A and B, respectively. \(J_A\) and \(J_B\) are the corresponding molar diffusive fluxes. Which of the following is true for equimolar counter-diffusion in the binary mixture?

A

\(N_A + N_B = 0\) and \(J_A + J_B \neq 0\)

B

\(N_A + N_B \neq 0\) and \(J_A + J_B = 0\)

C

\(N_A + N_B \neq 0\) and \(J_A + J_B \neq 0\)

D

\(N_A + N_B = 0\) and \(J_A + J_B = 0\)

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12

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

Benzene is removed from air by absorbing it in a non-volatile wash-oil at 100 kPa in a counter-current gas absorber. Gas flow rate is 100 mol/min , which includes 2 mol/min of benzene. The flow rate of wash-oil is 50 mol/min. Vapor pressure of benzene at the column conditions is 50 kPa. Benzene forms an ideal solution with the wash-oil and the column is operating at steady state. Gas phase can be assumed to follow ideal gas law. Neglect the change in molar flow rates of liquid and gas phases inside the column.
For this process, the value of the absorption factor (up to two decimal places) is ______________ .

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13

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

A spherical naphthalene ball of 2 mm diameter is subliming very slowly in stagnant air at 25°C. The change in the size of the ball during the sublimation can be neglected. The diffusivity of naphthalene in air at 25°C is \(1.1 \times 10^{-6} \text{ m}^2/s\).
The value of mass transfer coefficient is B \(\times 10^{-3}\) m/s, where B (up to one decimal place) is ______________ .

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14

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

For which reaction order, the half-life of the reactant is half of the full lifetime (time for 100 % conversion) of the reactant?

A

Zero order

B

Half order

C

First order

D

Second order

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15

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

The diameters of sand particles in a sample range from 50 to 150 microns. The number of particles of diameter \( x \) in the sample is proportional to \( \frac{1}{50+x} \). The average diameter, in microns, (up to one decimal place) is __________.

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16

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

A vector \( \boldsymbol{u} = -2 y \hat{i} + 2 x \hat{j} \), where \( \hat{i} \) and \( \hat{j} \) are unit vectors in \( x \) and \( y \) directions, respectively. Evaluate the line integral
\[ I = \oint_C \boldsymbol{u} \cdot d\boldsymbol{r} \]
where \( C \) is a closed loop formed by connecting points (1,1), (3,1), (3,2) and (1,2) in that order.
The value of \( I \) is __________.

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17

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

For complex variable \( z \), the value of the contour integral \[ \frac{1}{2\pi i} \oint_C \frac{e^{-2z}}{z(z-3)} dz \] along the clockwise contour \( C : |z| = 2 \) (up to two decimal places) is __________.

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18

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

The schematic diagram of a steady state process is shown below. The fresh feed (F) to the reactor consists of 96 mol% reactant A and 4 mol% inert I. The stoichiometry of the reaction is A → C. A part of the reactor effluent is recycled. The molar flow rate of the recycle stream is 0.3 F. The product stream P contains 50 mol% C. The percentage conversion of A in the reactor based on A entering the reactor at point 1 in the figure (up to one decimal place) is __________.

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19

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

An ideal gas is initially at a pressure of 0.1 MPa and a total volume of \( 2 \text{ m}^3 \). It is first compressed to 1 MPa by a reversible adiabatic process and then cooled at constant pressure to a final volume of \( 0.2 \text{ m}^3 \). The total work done (in kJ) on the gas for the entire process (up to one decimal place) is __________.
Data: R = 8.314 J/mol.K; heat capacity at constant pressure (\( C_p \)) = 2.5R

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20

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Chemical Engineering (CH) 2015

Given that molar residual Gibbs free energy, \( g^R \), and molar residual volume, \( v^R \), are related as \( \frac{g^R}{RT} = \int_0^P \left( \frac{v^R}{RT} \right) dP \), find \( g^R \) at T = 27°C and P = 0.2 MPa. The gas may be assumed to follow the virial equation of state, \( z = 1 + BP/RT \), where \( B = -10^{-4} \text{ m}^3/\text{mol} \) at the given conditions (R = 8.314 J/mol.K). The value of \( g^R \) in J/mol is:

A

0.008

B

-2.4

C

20

D

-20

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