- The inverse Laplace transform of is

- e-t/2 – e-t (B) 2e-t/2 – e-t

- e-t – 2e-t/2 (D) e-t – e-t/2

- The characteristic equation of a closed loop system using a proportional controller with gain Kc is

12 s3 + 19 s2 + 8 s + 1 + Kc = 0

At the onset of instability, the value of Kc is

- 35/3 (B) 10 (C) 25/3 (D) 20/3

- The block diagram for a control system is shown below :

For a unit step change in the set point, R(s), the steady state offset in the output Y(s) is

## (A) 0.2 (B) 0.3 (C) 0.4 (D) 0.5

- For a tank of cross-sectional area 100 cm2 and inlet flow rate (Qi in cm3/s), the outlet flow rate (Qo in cm3/s) is related to the liquid height (H in cm) as Qo = 3 ? H (see figure below).

Then the transfer function (overbar indicates deviation variables) of the process around the steady-state point, Qi,s = 18 cm3/s and Hs = 36 cm, is

## (A) (B)

## (C) (D)

- A column costs Rs. 5.0 lakhs and has a useful life of 10 years. Using the double declining balance depreciation method, the book value of the unit at the end of five years (in lakhs of Rs.) is

## (A) 1.21 (B) 1.31 (C) 1.64 (D) 2.05

- An equi-molar mixture of four hydrocarbons (1, 2, 3, 4) is to be separated into high purity individual components using a sequence of simple distillation columns (one overhead and one bottom stream). Four possible schemes are shown below.

Scheme R Scheme S

Using the Ki (+ yi*/xi) values given above, the optimal scheme is

## (A) P (B) Q (C) R (D) S

- Match the equipment in Group I to the internals in Group II.

## GROUP I GROUP II

- Centrifugal pump 1. Baffle
- Distillation column 2. Impeller
- Heat exchanger 3. Tray

- Volute

## (A) P-2, Q-1, R-4 (B) P-2, Q-4, R-3

## (C) P-1, Q-3, R-4 (D) P-4, Q-3, R-1

- Match the product in Group I with the name of the process in Group II.

## 1 GROUP I GROUP II

2 P. Sodium carbonate 1. Haber

3 Q. Ammonia 2. Solvay

4 R. Sulphuric acid 3. Fischer-Tropsch

- Contact

## (A) P-2, Q-1, R-4 (B) P-4, Q-1, R-2

## (C) P-3, Q-4, R-2 (D) P-2, Q-1, R-3

- Match the product in Group I to the raw material in Group II.

## 1 GROUP I GROUP II

2 P. Ethylene 1. Natural gas

3 Q. Methanol 2. Synthesis gas

4 R. Phthalic anhydride 3. Naphtha

- Naphthalene

## (A) P-1, Q-2, R-3 (B) P-2, Q-1, R-4

## (C) P-3, Q-1, R-4 (D) P-3, Q-2, R-4

- Match the unit process in Group I with the industry in Group II GROUP I GROUP II

- Steam cracking 1. Petroleum refining
- Hydrocracking 2. Petrochemicals
- Condensation 3. Polymers

4 Soaps and Detergents

## (A) P-1, Q-2, R-3 (B) P-2, Q-3, R-3

## (C) P-1, Q-2, R-4 (D) P-2, Q-1, R-3

Common Data Questions

Common Data for Questions 51 and 52 :

An ideal gas with molar heat capacity (where R = 8.314 J/mol.K) is compressed adiabatically from 1 bar and 300 K to pressure P2 in a closed system. The final temperature after compression is 600 K and the mechanical efficiency of compression is 50%.

- The work required for compression (in kJ/mol) is

## (A) 3.74 (B) 6.24 (C) 7.48 (D) 12.48

- The final pressure P2 (in bar) is

- 23/4 (B) 25/4 (C) 23/2 (D) 25/2

Common Data for Questions 53 and 54 :

A slab of thickness L with one side (x = 0) insulated and the other side (x = L) maintained at a constant temperature T0is shown below.

A uniformly distributed internal heat source produces heat in the slab at the rate of S W/m3. Assume the heat conduction to be steady and 1-D along the x-direction.

- The maximum temperature in the slab occurs at x equal to

- 0 (B) L/4 (C) L/2 (D) L

- The heat flux at x = L is

- 0 (B) S L/4 (C) S L/2 (D) S L

Common Data for Questions 53 and 54 :

A flash distillation drum (see figure below) is used to separate a methanol-water mixture. The mole fraction of methanol in the feed is 0.5, and the feed flow rate is 1000 kmol/hr. The feed is preheated in a heater with heat duty Qh and is subsequently flashed in the drum. The flash drum can be assumed to be an equilibrium stage, operating adiabatically. The equilibrium relation between the mole fractions of methanol in the vapor and liquid phases is y* = 4 x. The ratio of distillate to feed flow rate is 0.5.

- The mole fraction of methanol in the distillate is

## (A) 0.2 (B) 0.7 (C) 0.8 (D) 0.9

- If the enthalpy of the distillate with reference to the feed is 3000 kJ/kmol, and the enthalpy of the bottoms with reference to the feed is –1000 kJ/kmol, the heat duty of the preheater (Qh in kJ/hr) is

- –2×106 (B) –1×106 (C) 1×106 (D) 2×106

Linked Answer Questions :

Statement for Linked Answer Question 57 and 58 :

A free jet of water is emerging from a nozzle (diameter 75 mm) attached to a pipe (diameter 225 mm) as shown below.

The velocity of water at point A is 18 m/s. Neglect friction in the pipe and nozzle. Use g = 9.81 m/s2 and density of water = 1000 kg/m3.

- The velocity of water at the tip of the nozzle (in m/s) is

## (A) 13.4 (B) 18.0 (C) 23.2 (D) 27.1

- The gauge pressure (in kPa) at point B is

## (A) 80.0 (B) 100.0 (C) 239.3 (D) 367.6

Statement for Linked Answer Questions 59 and 60 :

The liquid-phase reaction AàB + C is conducted isothermally at 50°C in a continuous stirred tank reactor (CSTR). The inlet concentration of A is 8.0 gmol/liter. At a space time of 5 minutes, the concentration of A at the exit of CSTR is 4.0 gmol/liter. The kinetics of the reaction is

A plug flow reactor of the same volume is added in series after the existing CSTR.

- The rate constant (k) for this reaction at 50°C is

## (A) 0.2 (B) 0.2

## (C) 0.4 (D) 0.4

- The concentration of A (in gmol/liter) at the exit of the plug flow reactor is