Previous Year Questions

Chemistry

a. A water sample contains the following impurities: Mg(HCO₃)₂ = 73 mg/L (formula weight 146 amu) MgCl₂ = 180 mg/L (formula weight 95 amu) CaSO₄ = 68 mg/L (form…

Chemistry

a. Define corrosion and explain the difference between dry and wet corrosion. (3 marks) b. What is differential aeration corrosion? Illustrate with a diagram. (…

Chemical Process Principles

How will you differentiate unit processes from unit operations in chemical industries? Explain heat transfer operations and fluid flow operations in detail

Engineering Thermodynamics

a. Define the following terms: system, boundary, equilibrium, saturation temperature, and pure substance. (5 marks) b. Define the zeroth and the first law of th…

Mathematics

a. Test the function f(x) for continuity at the point x = 0, given f(x) = x(1/x),\ x 0, and f(0) = 0 at x = 0. (3 marks) b. Examine for continuity and different…

Engineering Thermodynamics

The water in a large lake is to be used to generate electricity by the installation of a hydraulic turbine-generator at a location where the depth of the water…

Chemical Process Principles

a.Convert a heat transfer coefficient of 175 Btu/h·ft²·°F into W/m²·°C. (2 marks) b.What is the weight of one litre of propane at standard conditions? (2 marks)

Mathematics

a. Verify Rolle's theorem in the case of function f(x) = 2x3 + x2 - 4x - 2. (4 marks) b. If x2a2+u + y2b2+u + z2c2+u = 1, then prove that ux2 + uy2 + uz2 = 2(x…

Chemical Process Principles

a. An aqueous solution contains 18% ethyl alcohol by volume. Express the composition in weight % and mole %. The densities of ethyl alcohol and water are 790 kg…

Mathematics

a. If y1 = r1, y2 = r12, y3 = r123, …, yn-1 = r12n-2n-1 and yn = r12n-1, then find the value of (y1, y2, , yn)(r, 1, 2, , n-1). (5 marks) b. Discuss the maximum…

Engineering Thermodynamics

a. A mass of 5 kg of saturated water vapour at 100 kPa is heated at constant pressure until the temperature reaches 200 °C. Calculate the work done by the steam…

Chemical Process Principles

When heated to 100 °C and 720 mm Hg, 19.2 g of N₂O₄ gas occupies 11450 cc. Assuming the ideal gas law applies, calculate the percentage dissociation of N₂O₄ to…

Engineering Thermodynamics

Complete this table for H₂O: array|c|c|c|c|c| T,\ C & P,\ kPa & h,\ kJ/kg & x & Phase description \\ & 200 & & 0.7 & \\ 140 & & 1800 & & \\ & 950 & & 0.0 & \\ 8…

Chemical Process Principles

A furnace is designed to burn coke at 200 lb/h. The coke is 91.1% C and 8.9% ash. The grate efficiency is such that 90% of the carbon charged is burnt. Air is s…

Chemical Process Principles

How many types of unit operations are used in chemical industries? Describe the mechanical operations in detail.

Mathematics

a. State and prove Rolle's mean value theorem. (3 marks) b. Show that v-u1+v2 < -1v - -1u < v-u1+u2. (2 marks)

Chemical Process Principles

a. Convert the heat transfer coefficient of value 250 Btu/h·ft²·°F into W/m²·°C. (2 marks) b. How many grams of liquid butane will be formed by liquefaction of…

Mathematics

a. Using – approach, show that (x,y)(0,0) xy\,x2-y2x2+y2 = 0. (2 marks) b. Check for the continuity of the following functions: (3 marks) (i) f(x,y) = cases 2x2…

Chemical Process Principles

Natural gas has the following composition: CH₄: 91%, C₂H₆: 5% and N₂: 4%. This gas is piped from the well at 80 °F and 80 psi. Calculate the following: (a) Part…

Mathematics

a. Prove that the function f(x,y) = |xy| is not differentiable at origin. Do its partial derivatives exist at origin? Justify. (3 marks) b. Show that the functi…

Mathematics

a. Expand -1yx in the neighborhood of (1,1) by Taylor's theorem. Hence compute f(1.1, 0.9). (2 marks) b. If u = -1x3+y3x+y, then show that x u x + y u y = 2u an…

Chemical Process Principles

A solvent recovery system delivers a gas saturated with benzene vapour which analyzes on a benzene-free basis as follows: CO: 11%, O₂: 7% and N₂: 82%. This gas…

Mathematics

a. (i) Evaluate r3\,dr\,d over the area bounded between the circles r = 2 and r = 4. (ii) Find the area enclosed by the pair of curves y = 2 - x and y2 = 2(2 -…

Chemical Process Principles

A spent dye sample obtained from a soap-making unit contains 7.6% glycerol and 9.3% salt. It is concentrated at a rate of 5000 kg/h in a double effect evaporato…

Chemistry

a. Discuss shapes and geometries of the following molecules on the basis of Valence Bond theory: (i) HClO₃ (ii) SO₃ (1+1 marks) b. Comment on the significance o…

Chemical Process Principles

How many types of unit operations are used in chemical industries? Describe the mass transfer operations in detail.

Engineering Thermodynamics

a. Does the specific internal energy of superheated water at 250 °C decrease or increase with an increase in pressure? (1 mark) b. Separate the list P, V, ρ, T,…

Mathematics

a. State and prove Lagrange's Mean Value theorem. Discuss the geometrical interpretation of it. (2 marks) b. Using Cauchy Mean Value theorem, show that 2e x2-1x…

Engineering Thermodynamics

A hydraulic piston/cylinder (Figure 1 in the original paper) has a cylinder diameter D = 0.1 m with a piston and rod mass of 25 kg. The rod has a diameter of 0.…

Chemical Process Principles

The flow rate of water through a pipe is reported as 20 cubic feet per minute. Taking density of water as 1 g/cm³, calculate the mass flow rate in kg/s.

Chemistry

a. Dolomite and lime stone mining in the basins of the Indravati river is widely known in the Orissan district of Koraput. A number of families are residing alo…

Mathematics

a. Define ε–δ definition of continuity of a function of two variables f : D R2 R. Using ε–δ definition, discuss the continuity of the function f(x,y) = cases x2…

Engineering Thermodynamics

Fill out the following table for substance water: array|c|c|c|c|c| & P\ [kPa] & T\ [C] & v\ [m3/kg] & x \\ a. & 500 & & 0.20 & \\ b. & 1400 & 200 & & \\ array

Chemical Process Principles

How many molecules are present in 791 g K₂CO₃?

Mathematics

a. Show that for the function f(x,y) = cases y(x2-y2)x2+y2, & if (x,y) (0,0) \\ 0, & if (x,y) = (0,0) cases, fxy(0,0) fyx(0,0). (2 marks) b. If u = -1x1/3+y1/3x…

Chemical Process Principles

Natural gas is piped from the well at 300 K and 400 kPa. The gas is found to contain 93.0% methane, 4.5% ethane and the rest nitrogen. Calculate the following:…

Mathematics

a. If xyz - u = 0, x2 + y2 + z2 - v = 0, and x + y + z - w = 0, find (x,y,z)(u,v,w). (2 marks) b. Obtain a quadratic Taylor's series approximation to the functi…

Engineering Thermodynamics

Draw and explain a P-T diagram for a pure substance including all points, lines and regions.

Chemical Process Principles

A liquid mixture containing 65 mol % benzene and 35 mol % toluene is subjected to flash vaporization at 363 K and 101.3 kPa. The vapour pressure of benzene at t…

Mathematics

The temperature T at any point (x,y,z) in space is given by T(x,y,z) = kxyz2, where k is a positive constant. Find the highest temperature on the surface of the…

Engineering Thermodynamics

Consider two tanks, A and B, connected by a valve (figure in the original paper). Each has a volume of 200 L, and tank A has R-134a at 25 °C, 10% liquid and 90%…