NO NEGATIVE MARKINGS. SECTIONS A
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1 Application No. Department of Materials Science & Engineering, IIT Kanpur **********: Written Examination: ******* Examination: ********* Duration: 1 hour Maximum Marks: 60 Please read these instructions carefully Please fill in your Application No. in the space provided in the top right corner; DO NOT write your name on this sheet. Any unauthorized materials, such as books, papers, documents and electronic devices with communication and/or storage capabilities are not permitted into the examination hall. Mobile phones brought into the examination hall must be switched off at ALL times. DO NOT turn over the question paper placed on your desk until instructed to do so at the time of commencement of the examination. You are not allowed to communicate by word of mouth or otherwise with another candidate. Please raise your hand if you wish to communicate with an invigilator. Unless granted permission by an invigilator, you are not allowed to leave your seat. Once you have entered the examination hall, you will not be allowed to leave the hall until the end of examination. DO NOT continue to write after the examination has ended. You are to remain seated quietly while your answer scripts are being collected and counted. Type of Examination Closed Book: No reference materials, in whatever format, are allowed. Calculators are allowed in the examination. However, memory should be cleared prior to examination. A candidate who is suspected of cheating in the examination is liable to disciplinary action including expulsion from the examination hall. Paper Structure The question paper consists of a total of 12 PAGES (including this page). The question paper consists of FOUR SECTIONS, viz. A, B, C and D. All sections carry equal marks and there are NO NEGATIVE MARKINGS. SECTIONS A and B are COMPULSORY while candidate has an option to CHOOSE EITHER SECTION C or D. You can use the back side of all the pages for the rough work. For Examiner s purpose only Section A (Aptitude and Mathematics) B (Fundamentals of Metallurgical and Materials Engineering) C (Electronic Properties of Materials) D (Mechanical Properties of Materials) Points TOTAL
2 Section A (Aptitude and Mathematics) Q (2 marks each) 1. A piece of wood 5 feet long is cut into three smaller pieces. How long is the longest of the three pieces? Statement (1): One piece is 2 feet 7 inches long. Statement (2): One piece is 7 inches longer than another piece and the remaining piece is 5 inches long. (A) One can get the answer from statement (1) alone but not from statement (2) alone (B) One can get the answer from statement (2) alone but not from statement (1) alone (C) One can get the answer from statements (1) and (2) together, although neither statement by itself suffices (D) Statement (1) alone suffices and statement (2) alone suffices 2. One alloy contains silver and copper in the ratio 5:1 and the other contains silver and copper in the ratio 7:2. What weights of the two alloys must be mixed together to get 5 kg alloy containing 80% silver? (a) 0.5 kg and 4.5 kg (b) 1.0 kg and 4.0 kg (c) 2.0 kg and 3.0 kg (d) 3.5 kg and 1.5 kg 3. Find the statement that must be true according to the given information: Rahul is twelve years old. For three years, he has been asking his parents for a dog. His parents have told him that they believe a dog would not be happy in an apartment, but they have given him permission to have a bird. Rahul has not yet decided what kind of bird he would like to have. (A) Rahul's parents like birds more than they like dogs. (B) Rahul does not like birds. (C) Rahul and his parents live in an apartment. (D) Rahul and his parents would like to move. 4. Find out the wrong number in the given sequence of numbers (odd man out). 396, 462, 572, 427, 671, 264 (A) 396 (B) 427 (C) 264 (D) None of the Above
3 5. The limit is equal to (a) (b) 1/2 (c) 0 (d) -1/2 6. Solve the differential equation: d 3 y/dx 3 =0, given that y(x)=3 at x=0, dy/dx=4 at x=1 and d 2 y/dx 2 =6 at x=2 7. Find the projection of the vector on the vector 8. Find divergence of vector at the point (1,-1,1)
4 9. We have to make a rectangular sheet (negligible thickness) of fixed area 16 cm 2. What should be the value of x and y so that the rectangle has the smallest diagonal. (Hint: you have to minimize the length of the diagonal of a rectangle of fixed area). 10. Plot in range
5 Q (1 Mark each) SECTION B (Fundamentals of Metallurgical and Materials Engineering) Gas Constant, R = J K -1 mol The equilibrium fraction of pro-eutectoid ferrite in an eutectoid steel is: 12. The miller indices for the third peak in a powder X-ray diffraction pattern of a pure BCC metal would be 13. The equilibrium fraction of vacancies in Al at 900K is:. ( Enthalpy of formation of vacancies in Al is 68 kj/mol) 14. Among the following which method increases both the strength as well as ductility in materials: (A) precipitation hardening (B) annealing (C) solute addition (D) grain refinement 15. As compared to the engineering stress-strain curve the true stress strain curve is (A) above and to the left (B) below and to the right (C) crosses the engineering curve (D) none of the above 16. If a three-component non-reactive system exists in three-phase equilibrium and if pressure is not allowed to vary, how many independent variables are still available to change the state of the system without disturbing the equilibrium? a. 0 b. 1 c. 2 d Packing factor of a diamond crystal is: 18. The radii of cation (A) and anion (X) are nm and nm respectively. The expected coordination of the structure is: 19. The possible slip directions for slip on a (111) plane in a fcc metal are:,, and. 20. The theoretical density of iron at room temperature is: kg.m -3. (Given the lattice parameter to be nm and the atomic weight to be 56)
6 21. A well annealed metal block of 100 mm thickness has to be rolled down to 20mm thickness by rolling and annealing cycles. The metal can be reduced maximum by 20% at a time and annealing fully recovers the ductility of the metal. What is the minimum number of annealing cycles the metal block has to pass through? a. 2 b. 3 c. 7 d Fractography is usually carried out in a Scanning Electron Microscope because of its a. large depth of focus b. large depth of field c. high resolution d. low optical aberration 23. Which one of the following surfaces is expected to have the least surface energy in an FCC crystal? a. {110} b. {111} c. {100} d. {112} 24. A researcher measured self-diffusivity of Cu over various temperatures. The plot of lnd versus 1/T is a straight line with a slope of K and an intercept on Y-axis of What s the self-diffusivity of Cu at 400 o C? (a) ~2x10-16 m 2 /s (b) ~4x10-12 m 2 /s (c) ~3x10-24 m 2 /s (d) cannot be determined from given data 25. Number of tetrahedral voids in a unit cell of a FCC pure metal is: a. 2 b. 4 c. 6 d A Carnot engine operates between two thermal reservoirs having temperatures of 20 C and 400 C. What s the maximum possible thermal efficiency of the engine? a. 56.5% b. 95% c. 46.3% d. 100%
7 27. Which one of the following statements is correct about Entropy? a. Entropy of a closed system can never decrease b. Entropy of an isolated system can never decrease c. Entropy of an isolated system can never increase d. Entropy of a closed system can never increase 28. The equilibrium partial pressure of oxygen for the oxidation of one mole of solid iron to solid Fe3O4 is atm at 800 C. What is the standard Gibbs free energy change of the reaction? a kJ b. -45kJ c kJ d. 45kJ 29. A very commonly used etchant for plain carbon steel is: a. Kroll s reagent b. Nital c. Aqua Regia d. HF 30. List any four signals generated upon interaction of electron beam and sample in an electron microscope a. b. c. d.
8 SECTION C (Electronic Properties of Materials) Q : Multiple type questions (1 Mark each) 31. Phonon is a. a positive charge carrier (b) an exciton (c) a lattice wave (d) an antimatter particle 32. If a defect free semiconductor shows optical absorption only when the wavelength of incident photons is 0, then the bandgap of this semiconductor should be a. 0 /hc (b) 2hc/ 0 (c) hc/ 0 (d) hc When placed in an external magnetic field the magnetic dipoles in a diamagnetic material are aligned as a. Parallel to the direction of external magnetic field lines. b. Anti-parallel to the direction of external magnetic field lines. c. 50% of all the dipoles are parallel to, and remaining are antiparallel to the external field. d. None of the above. 34. The transmitted intensity of a monochromatic radiation from a material of thickness 1 cm is 50% of the incident intensity. What is the absorption coefficient of this material? a. 1 cm -1 (b) 0.5 cm -1 (c) 0.7 cm -1 (d) 0.25 cm For a semiconductor having n electrons and p holes per unit volume, which of the following relations is correct, provided that the symbol n i represents the intrinsic charge carrier concentration in all of the following expressions. 2 (a) n.p= n i (b) n.p= n (1/2) 2 3 i (c) n/p= n i (d) n.p= n i Q State True or False (1 Mark each) 36. Light hole occupies the portion of E-k diagram which has lower curvature compared to that for the heavy hole. 37. Ferroelectric hysteresis loop is a consequence of domain reorientation. 38. A multiferroic material which couples ferroelectricity and ferromagnetism is also a pyroelectric. 39. Indirect band-gap semiconductors are generally better LEDs than direct band gap. 40. Fermi level in an intrinsic semiconductor is always in the middle of the bandgap. Q : Fill in the blanks (1 Marks each) 41. What is the average energy of electrons according to free electron theory (QM)at T =0K? 42. Density of states g(e) varies with energy (E) as 43. The shape of Fermi energy surface in free electron theory is a
9 44. A rectangular silicon semiconductor bar of length 12 cm and cross-section 1 5 mm is uniformly doped with n-type with concentration N d = cm 3. Assuming all donors are ionized, calculate the room temperature current flow if contacts are made on the two ends of the bar and 10V is applied to the bar (μ n = 1350 cm 2 V -1 s -1, μ p = 480 cm 2 V -1 s -1 ) (4 Marks) 45. Show that the minimum conductivity of a semiconductor sample occurs when n = ni ( p / n ) (3 Marks).
10 SECTION D (Mechanical Properties of Materials) Q : Fill in the blanks (4 X 1 marks) 46. As temperature increases, the Young s modulus of a metal (increases /decreases /remains constant) 47. The rank of a stress tensor is 48. Fine grained metals will show more creep resistance than coarse grained metals (True/False) 49. The total number of slip systems for BCC crystal is Q : Multiple Option Questions (More than one choice might be correct) (3 X 2 marks) 50. Factors that can promote brittle-cleavage type fracture are (a) Triaxial state of stress (b) Low temperature (c) A high strain rate (d) High temperature (e) None of the above 51. Striations are observed in a fractograph for a sample tested in (a) Uniaxial tension (b) Torsion (c) Impact (d) Creep (e) Fatigue 52. Which of these are characteristics of screw dislocation (a) is parallel to dislocation line (b) is perpendicular to the dislocation line (c) Dislocation line is parallel to direction of dislocation line movement (d) is parallel to direction of dislocation line movement (e) It is a planar defect Q : Provide solutions to the following problems: 53. The yield stress of AISI 1020 steel with a grain size of 200 μm is 200 MPa. Estimate the yield stress for a grain size of 10 μm if the Hall-Petch constant k = 0.8 MN/m 3/2 (3 marks)
11 54. A steel with yield stress of 300 MPa is tested under a state of stress whereσ y = σ x /2,σ z = 0 and shear stresses as zero. Given, σ x andσ y are > 0 (+ve). Whatare the stress values (σ x,σ y,σ z )at which yielding occurs according to Tresca criteria? (4 marks)
12 55. A single crystal of copper is deformed in tension. The loading axis is [112]. Rank the following slip systems in terms of activation (means which slip system will activate first and second). Given: critical resolved shear stress value is 50 MPa. (3 marks)
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