ACE Engineering Academy. Hyderabad Delhi Bhopal Pune Bhubaneswar Bengaluru Lucknow Patna Chennai Vijayawada Visakhapatnam Tirupati

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2 : : GATE_06_Forenoon Session -5 carry one mark each GENERAL APTITUDE 0. If I were you, I that laptop, It s much too expensive. (A) won t buy (B) shan t buy (C) wouldn t buy (D) would buy Ans: (C) In if clause (type) were is in the past tense so the so main clause should be in the conditional clause (past tense). Therefore C is the best answer 0. He turned a deaf ear to my request. What does the underlined phrasal verb mean? (A) ignored (B) appreciated (C) twisted (D) returned Ans: (A) turned a deaf ear means ignored 03. Choose the most appropriate set of words from the options given below to complete the following sentence. is a will, is a way. (A) Wear, there, their (B) Were, their, there (C) Where, there, there (D) Where, their, their Ans: (C) Where there is a will there is a way. It is a quotation 04. (x% of y) + (y% of x) is equivalent to. (A) % of xy (B) % of (xy/00) (C) xy % of 00 (D) 00 % of xy Ans: (A)

3 (x% of y) + (y% of x) = x y y x xy xy 00 xy 00 = % of xy : 3 : GATE_06_Forenoon Session 05. The sum of the digits of a two digit number is. If the new number formed by reversing the digits is greater than the original number by 54, find the original number. (A) 39 (B) 57 (C) 66 (D) 93 Ans: (A) The new number formed by reversing the digits is greater than the original number is possible in options A and B only. Options A : Sum of two digits in the number = = After reversing the two digits number = 93 The difference between the new number formed and original number = = 54 option A is correct. Option B : original number = 57 After reversing, the number is formed = 75 The difference between these two numbers = = 8 It is not.

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5 : 5 : GATE_06_Forenoon Session 06-0 Carry two marks each 06. Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to year. Yearwise annual rates of interest offered by these companies are shown by the line graph provided below P Q If the amounts invested in the companies, P and Q, in 006 are in the ratio 8:9, then the amounts received after one year as interests from companies P and Q would be in the ratio: (A) :3 (B) 3:4 (C) 6:7 (D) 4:3 Ans: (D) The amounts invested in the companies of, P and Q in 006 = 8 : 9 The rate of interest of company P in 006 = 6% The rate of interest of company Q in 006 = 4% The amounts received after one year by P and Q companies in 006 year P Q 6% of 8 : 4% of : : Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the availability of evidence today. Which of the following can be logically inferred from the above sentences?

6 : 6 : GATE_06_Forenoon Session Ans: (A) Emperors who do not leave significant sculpted evidence are completely forgotten. (B) Ashoka produced stone carved edicts to ensure that later historians will respect him. (C) Statues of kings are a reminder of their greatness. (D) A king s greatness, as we know him today, is interpreted by historians. (D) Today, historians correlate greatness of a king at his time with the availability of evidence. This statement leads to the best inference i.e. option D 08 Fact : Humans are mammals. Fact : Some humans are engineers. Fact 3: Engineers build houses. If the above statements are facts, which of the following can be logically inferred? I. All mammals build houses. II. Engineers are mammals. III. Some humans are not engineers. (A) II only. (B) III only. (C) I, II and III. (D) I only. Ans: (B) From given facts, the following venn diagram is possible. H = Humans M = Mammals E = Engineers BH = Build houses From above diagram, statement III is true. H M E BH 09. A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the lateral surface area of the pyramid? (A) x (B) 0.75 x (C) 0.50 x (D) 0.5 x

7 : 7 : GATE_06_Forenoon Session Ans: (D) Base perimeter of square pyramid = x = p x Slant height l Lateral surface area of pyramid Base perimeter (p) slant height (l) x x 4 p l x = 0.5x x x/4 x/4 x/ 0. Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages to be read by Ananth, twice that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace. (A) (B) (C) 3 (D) 4 Ans: (C) Ananth takes 6 hours to read a book Bharath takes 4 hours to read a book L.C.M = The number of pages read by Ananth and Bharath must be (or) multiple of only. If Ananth read number of pages in 6 hrs hr = 6 = pages If Bharath read number of pages in 4 hrs

8 : 8 : GATE_06_Forenoon Session hr = 4 = 3 pages hrs Option A Ananth Bharath Read pages Not read 0 pages Read 3 pages Not read 9 pages 0 : 9 it is not hrs Option B Read 4 pages Ananth Not read 8 pages Read 6 pages Bharath Not read 6 pages 8 : 6 4 : 3 it is not Options C 3 hrs Ananth Bharath Read 6 pages Not read 6 pages Read 9 pages Not read 3 pages : After 3 hours is the number of pages to be read by Ananth, twice that to be read by Bharath.

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10 : 0 : GATE_06_Forenoon Session 0 Q. 5 carry one mark each The eigenvalues of the matrix are 0 (A) i and i (B) and (C) 0 and (D) 0 and Ans: (A) + = 0; = + = i = i 0. The number of solutions of the simultaneous algebraic equations y = 3x + 3 and y = 3x+5 is (A) zero (B) (C) (D) infinite Ans: (A) y = 3x+5 & y = 3x+3 are parallel to each other No solution is zero solution x 03. At x = 0, the function is f (x) sin ( < x <, L >0) L (A) continuous and differentiable. (B) not continuous and not differentiable. (C) not continuous but differentiable. (D) continuous but not differentiable. Ans: (D) f x x sin L at x = 0 is having graph -L -L 0 L L It is continuous at x = 0 but not differential at x = 0

11 For the two functions f x, y x 3xy and : : GATE_06_Forenoon Session g x, y 3x y y which one of the following options is correct? (A) f x g x (B) f x g y (C) f g y x (D) f g y x Ans: (C) f g 6xy; 6xy y x f g y x 05. The function Z z is singular at z 4 f (A) z = (B) z = (C) z = i (D) z = i Ans: (D) To get singular points let z +4 = 0 z = 4 z = i 06. A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is (A) N (B) N (C) N (D) N Ans: (C) 07. A normal random variable X has the following probability density function f X x e 8 x 8 (A) 0 (B), x Then (C) f X x dx (D) e

12 : : GATE_06_Forenoon Session Ans: (B) e x x t dx dt dx = dt 0 e t dt t V t = V = e 0 V V dv t dt = dv dt dv V = e 0 V V 08. The elastic modulus of a rigid perfectly plastic solid is (A) 0 (B) (C)00 (D)infinity Ans: (A) Modulus is slope of curve (i.e zero) in elastic region Stress Strain 09. Consider the following statements: (P) Hardness is the resistance of a material to indentation. (Q) Elastic modulus is a measure of ductility. (R) Deflection depends on stiffness. (S) The total area under the stress-strain curve is a measure of resilience. Among the above statements, the correct ones are (A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.

13 : 3 : GATE_06_Forenoon Session Ans: (C) Hardness of a material will be measured by indentation technique. If a material undergo more strain (deflection) in elastic region means stiffness is low. 0. A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the weight of the beam. The correct Free Body Diagram of the beam is (A) (B) (C) (D) Ans: (B)

14 : 4 : GATE_06_Forenoon Session. Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 0 mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is 5 mm P (A) 5 (B) 0 (C) 40 (D) 45 Ans: (B) For the highest position the distance between the cam center and follower = (r+5) mm For the lowest position it is (r 5) mm So the distance between the two positions = (r+5) (r 5) = 0 mm. A vertical cylindrical tank of m diameter is filled with water up to a height of 5 m from its bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm area forms at the bottom of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due to gravity to be 0 m/s, the rate of leakage of water (in litre/min) through the hole from the tank to the atmosphere, under the given conditions, is Ans: (3) V g h 0 5 0m / s Q = AV = = 50 5 m 3 /sec = 0.05 liter/sec = = 3 lit/min

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16 : 6 : GATE_06_Forenoon Session 3. The figure below shows an air standard Diesel cycle in p-v diagram. The cut-off ratio is given by: 3 P 4 V (A) v v 3 (B) v v (C) v v 3 (D) v v 3 Ans: (C)

17 : 7 : GATE_06_Forenoon Session 4. The ratio of press force required to punch a square hole of 30 mm side in a mm thick aluminium sheet to that needed to punch a square hole of 60 mm side in a mm thick aluminium sheet is Ans: (0.5) F Ratio of force F max max 4x 4x t t u u x t x t Which one of the following is a natural polymer? (A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride Ans: (A) cellulose is made by C, H,O atoms can be extracted from trees. 6. In powder metallurgy, sintering of the component (A) increases density and reduces ductility (B) increases porosity and reduces density (C) increases density and reduces porosity (D) increases porosity and reduces brittleness Ans: (B) During sintering the solvent added at mixing stage will evaporate and produce porosity which comes the reduction in density of the component. 7. A single point right handed turning tool is used for straight turning. The feed is 0.5 mm/rev and the uncut chip thickness is found to be 0.5 mm. The inclination angle of the main cutting edge is 0 o. The back rake angle (in degrees) is Ans: (0 0 ) Turning operation, i = inclination angle = 0,

18 : 8 : GATE_06_Forenoon Session f = 0.5 mm/rev, t = 0.5 = f cos C s cos Cs C s = 0 f 0.5 = 90 C s = 90 0 = 90 tan b = sin tan i + cos tan = sin90 tan0 + cos 90 tan = = 0.76 b = tan (0.76) = 0 8. Consider the following statements. (P) Electrolyte is used in Electro-chemical machining. (Q) Electrolyte is used in Electrical discharge machining. (R) Abrasive-slurry is used in Ultrasonic machining. (S) Abrasive-slurry is used in Abrasive jet machining. Among the above statements, the correct ones are (A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only Ans: (A) In EDM, dielectric fluid is used. Hence Q is wrong. 9. Consider the following statements. (P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP). (Q) Production flow analysis helps in work cell formation. (R) Group technology takes input from choice of machining or cutting parameters. Among the above statements, the correct one(s) is (are) (A) P only (B) Q and R only (C) P and R only (D) Q only Ans: (B) CAPP will takes inputs from design but not from MRP. Hence P is wrong.

19 : 9 : GATE_06_Forenoon Session 0. The limits of a shaft designated as 00h5 are mm and mm. Similarly, the limits of a shaft designated as 00h8 are mm and mm. If a shaft is designated as 00h6, the fundamental deviation (in m) for the same is (A) (B) zero (C) (D) 4 Ans: (B) Fundamental deviation for shaft h is always zero irrespective of grade of tolerance.. The roughness profile of a surface is depicted below. Profile height centre-line of the profile m m X 5 mm The surface roughness parameter R a (in m) is. Ans: (0) R a h n The facility layout technique that uses relationship (REL) chart is (A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.

20 Ans: (D) ALDEP BASED ON REL REQUIREMENTS : 0 : GATE_06_Forenoon Session 3. For a random variable, X, let X be the sample average. The sample size is n. The mean and the standard deviation of X are µ and σ, respectively. The standard deviation of X is (A) n (B) (C ) (D) n n Ans: (D) Standard deviation, s n 4. ST and NT denote the standard time and the normal time, respectively, to complete a job. Allowance = LL ST, where 0 < LL<. Which one of the following relationships is correct? NT NT (A) ST (B) ST=NT(+LL) (C ) ST (D) ST=NT( LL) LL LL Ans: (A) RA = Relaxation allowance = LL ST ST = NT + RA ST = NT + LL ST ST ( LL) = NT NT ST LL 5. The throughput rate of a production system is 0 units per hour. The average flow time is 30 Ans: (C) minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is (A).5 (B) 9 (C) 0 (D).33 Average max.production min.production units

21 : : GATE_06_Forenoon Session Q. 6 Q. 55 carry two marks each The range of values of k for which the function f (x) k 4 x 6x 8x has a local maxima at point x = 0 is (A) k < or k > (B) k or k (C) < k < (D) k Ans: (A) f(x) = 3x 3 +8x +(k 4)x f(x) = 96 x + 36x + (k 4) f(0) = (k 4) < 0 k 4 < 0 k < (or) k > 7. lim 5x e x x 0 is equal to. Ans: (5) 5x 5x e e = Lt 5 5 x0 5x 5x 5x 5x e e = Lt 5 Lt 5 x0 5x x0 5x = 5 5 = 5 8. To solve the equation sinx = x by Newton-Raphson method, the initial guess was chosen to be x =.0. Consider x in radian only. The value of x (in radian) obtained after one iteration will be closest to (A) 8.0 (B).90 (C).099 (D).0

22 : : GATE_06_Forenoon Session Ans: (B) f(x) = sin x x f(x)(sin x x) h f(x) cos x = x = +h = = In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K) is given as c q T, where q is the heat input per unit length (in J/m) of weld, is the thermal diffusivity (in m /s) of the plate materials and C is a constant independent of process parameters and material types. Two welding cases are given below. Case I: V = 5 V, I = 00 A, v = 5 mm/s, k = 50 W/mK, = 3000 kg/m 3, C = 900 J/kg-K Case II: V = 5 V, I = 300 A, v = 0 mm/s, k = 50 W/mK, = 8000 kg/m 3, C = 450 J/kg-K Ans: (A) where, V is welding voltage, I is welding current, v is welding speed, and k, and C refer to the thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider that electrical energy is completely converted to thermal energy. All other conditions remain same. The ratio of the peak temperature in Case I to that in Case II is (A) 3 k C (B) (C) (D)

23 : 3 : GATE_06_Forenoon Session VI 5 00 q 60 3 r q T T q q A bar of rectangular cross-sectional area of 50 mm is pulled from both the sides by equal forces of 00 N as shown in the figure below. The shear stress (in MPa) alo ng the plane making an angle 45 0 with the axis, shown as a dashed line in the figure, is. 00 N 00 N 45 o Ans: () 00 / 50 max MPa 3. A m 0 mm 0 mm cantilever beam is subjected to a uniformly distributed load per unit length of 00 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point P is.

24 : 4 : GATE_06_Forenoon Session Point P 00 N/m m Ans: (300) M 00 50N m 3 M MPa(Tension) Z A thin-walled cylindrical pressure vessel of internal diameter m is designed to withstand an Ans: (5) internal pressure of 500 kpa (gauge). If the allowable normal s tress at any point within the cylindrical portion of the vessel is 00 MPa, the minimum thickness of the plate of the vessel (in mm) is. P = 500 kpa = 0.5 MPa h = 00 MPa,D = m h PD t t thickness, t = 5mm 33. An engine, connected with a flywheel, is designed to operate at an average angular speed of 800 rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to be 640 J. In order to keep the fluctuation of the angular speed within ±% of its average value, the moment of inertia (in kg-m ) of the flywheel should be.

25 : 5 : GATE_06_Forenoon Session Ans: (44.45) Given mean speed N = 800 rpm N rad / sec 60 Fluctuation of energy E = 640 J Fluctuation of speed = % Moment of inertia I =? We know E = I C s E 640 I = kg-m Cs N A m m square opening in a vertical wall is covered with a metallic plate of the same dimensions as shown in the figure below. Consider the acceleration due to gravity to be 0.0 m/s. The force (in kn) exerted by water on the plate is P atm water m m P atm vertical wall m m square plate vertical wall Ans: (0) F gah 0000 ( ) = 0 kn

26 : 6 : GATE_06_Forenoon Session 35. An ideal gas of mass m is contained in a rigid tank of volume V at a pressure P. During a reversible process its pressure reduces to P. Following statements are made regarding the process. (P) Heat is transferred from the gas. (Q) Work done by the gas is zero. (R) Entropy of the gas remains constant. (S) Entropy of the gas decreases. Among the above statements, the correct ones are (A) P and R only (B) P, Q and R only (C) Q and R only (D) P, Q and S only Ans: (D) At constant volume to decrease pressure, temperature has to be decreased. So heat has to be transferred from the gas. As the change in volume is zero, work done by the gas is zero. Entropy of the gas decrease as system is losing heat. 36. A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end of the fin is kept at a constant temperature t b. The fin loses heat by convection to the atmosphere which is at a temperature t a (t a < t b ). Four options of temperature profiles are shown. Identify the correct option. convection t b x atmosphere at t a x=l (A) (B) temperature t b t a 0 x L temperature t b t a 0 x L

27 : 7 : GATE_06_Forenoon Session (C) (D) Ans: (B) temperature t b t a 0 x L temperature t b t a 0 x L cosh m(l c x) cosh m L 0 c d 0, so angle of inclination of tangents for curve should increase with x dx 37. In a fully developed turbulent flow through a circular pipe, a head loss of h is observed. The diameter of the pipe is increased by 0% for the same flow rate and a head loss of h is noted. Assume friction factor for both the cases of pipe flow is the same. The ratio of (A) 0.34 (B) 0.6 (C) 0.87 (D).00 Ans: (B) flq For turbulent flow h.d h d 5 h d h.d 5 h h is closest to 38. Two cast iron blocks P and Q, each of 500 mm length, have the same cross-sectional area. Block P has rectangular cross-section of 00 mm 00 mm. Block Q is of square cross-section. Both P and Q were cast under the same conditions with all their surfaces enclosed within the mould. The solidification time of a casting is proportional to the square of the ratio of its volume to its surface area. The ratio of solidification time of the block P to that of the block Q is.

28 : 8 : GATE_06_Forenoon Session Ans: (0.906) L P = L Q = 500, Block P is rectangular = 0000 Block Q is square (Ac) P = (Ac) Q = x x M P mm V A s M Q V A s P Q M M P Q A 300 mm long copper wire of uniform cross-section is pulled in tension so that a maximum tensile stress of 70 MPa is developed within the wire. The entire deformation of the wire remains linearly elastic. The elastic modulus of copper is 00 GPa. The resultant elongation (in mm) is. Ans: (0.8 mm) Given l = 300 mm

29 : 9 : GATE_06_Forenoon Session max = 70 MPa E = 00 GPa max E l =800 3 m = 0.8mm 40. In a single-pass rolling operation, a 00 mm wide metallic strip is rolled from a thickness 0 mm to a thickness 6 mm. The roll radius is 00 mm and it rotates at 00 rpm. The roll-strip contact length is a function of roll radius and, initial and final thickness of the strip. If the average flow stress in plane strain of the strip material in the roll gap is 500 MPa, the roll separating force (in kn) is Ans: (598) b = 00 mm, H 0 = 0mm, H = 6mm, R = 00 mm, N = 00 rpm y = 500 MPa, Roll separating force 3 y L b L 4H L RH by assuming maximum reduction H R H 8 R.S.F = N kN

30 : 30 : GATE_06_Forenoon Session 4. Two solid cylinders of equal diameter have different heights. They are compressed plastically by a pair of rigid dies to create the same percentage reduction in their respective heights. Consider that the die-workpiece interface friction is negligible. The ratio of the final diameter of the shorter cylinder to that of the longer cylinder is Let d = d = d h = height of first cylinder h = height of second cylinder assume h < h let % reduction in height = 0% I st cylinder h h f h h 0 h f = 0. h 0 h f = h 0 0. h 0 = 0.9 h 0 A 0 h 0 = A f h f d 0 h 0 = d f h f d d f 0 h h 0 f d 0 h h 0 =.054 d 0 =.054 (d 0 ) II nd cylinder A 0 h 0 = A f h f d 0 h 0 = d f h f d d f 0 h h 0 f h 0 d0 =.054 (d 0 ) 0.9h 0

31 : 3 : GATE_06_Forenoon Session Ratio d 0 d 0 d 0 d 0 4. Two flat steel sheets, each of.5 mm thickness, are being resistance spot welded using a current of 6000 A and weld time of 0. s. The contact resistance at the interface between the two sheets is 00 and the specific energy to melt steel is J/m 3. A spherical melt pool of diameter 4 mm is formed at the interface due to the current flow. Consider that electrical energy is completely converted to thermal energy. The ratio of the heat used for melting to the total resistive heat generated is Ans: (0.37) t =.5 mm, I = 6000A, = 0.sec R = 00 Heat required, (H.R/m 3 )= 00 9 J/m 3 nugget diameter = d = 4mm (sphere ) Heat generated = I R = = 440 J Heat required = volume heat required/m 3 4 R = J H.R / m Heat required H.I Heat generated

32 : 3 : GATE_06_Forenoon Session 43. A cylindrical bar of 00 mm diameter is orthogonally straight turned with cutting velocity, feed and depth of cut of 0 m/min, 0.5 mm/rev and 4 mm, respectively. The specific cutting energy of the work material is 0 9 J/m 3. Neglect the contribution of feed force towards cutting power. The main or tangential cutting force (in N) is Ans: (000) Orthogonal cutting D = 00 mm, V c = 0 m/min, f = 0.5 mm/rev d = 4mm, Specific cutting energy (Sp.C.E) = 0 9 J/m 3 power Specific cutting energy F V f d V 0 C C C 6 J / m F C = Sp.C.E f d or Work done MRR 44. A 60 mm wide block of low carbon steel is face milled at a cutting speed of 0 m/min, feed of 0. mm/tooth and axial depth of cut of 4 mm. A schematic representation of the face milling process is shown below. The diameter of the cutter is 0 mm and it has cutting edges. The material removal rate (in mm 3 /s) is 0 mm 60 mm feed work piece + cutter schematic representation (top view)

33 : 33 : GATE_06_Forenoon Session Ans: (57.887) b = 60 mm, V = 0 m/min t = 0. mmtooth, d = 4 mm End mill cutter, D = 0 mm z = f m = f t z N = 0. 0 = rpm MRR = bdf m = = mm 3 /min = mm 3 /sec 45. In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing Ans: (680) with abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added to the water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of the focusing tube, abrasive particles and water come out with equal velocity. Consider that there is no air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) of the abrasive water jet at the end of the focusing tube is V w = 800 m/s m w = 3.4 kg/min m a = 0.6 kg/min m a v a m w v w m a m w V V = V 5 V = = = 680 m/sec

34 : 34 : GATE_06_Forenoon Session 46. A single axis CNC table is driven by a DC servo motor that is directly coupled to a lead screw of 5 mm pitch. The circular encoder attached to the lead screw generates 000 voltage pulses per revolution of the lead screw. The table moves at a constant speed of 6 m/min. The corresponding frequency (in khz) of the voltage pulses generated by the circular encoder is p = 5 mm 000 pulses rev of motor rev of lead screw Velocity of table = 6 m/min = 6000 mm/min = 00 mm/sec 000 pulses rev of lead screw 5 mm 5 pulse mm 000 BLU = mm Table speed = BLU Rate of Pulses Rate of pulses = = 0000 pulses/sec = 0000 Hz = 0 khz A helical gear with involute tooth profile has been machined with a disc-type form gear milling Ans: (69.8) cutter. The helical gear has 30 teeth and a helix angle of 30 o. The module of the gear milling cutter is. The pitch circle diameter (in mm) of the helical gear is m n = normal module = mm Pitch circle diameter, Z mn 30 d cos cos 30 = 69.8mm

35 : 35 : GATE_06_Forenoon Session 48. A quality control engineer has collected 5 samples, each of size 30. The numbers of defective items in the samples are given in the table below. Sample Number I II III IV V Number of defective items The upper three-sigma (3σ) control limit for the proportion of defective items in any sample is Ans: UCL = sumof defectives p samplesize number of samples Standard error of proportion p p p n Central line = p = 0. Upper control limit = p 3 p = = Lower control limit = p 3 p = = 0

36 : 36 : GATE_06_Forenoon Session 49. A job consists of two work elements, P and Q. Completion time (in minutes) of each work element was measured. A pilot study involved collecting a sample of 40 observations. The results of this pilot study are summarized in the table below. Work element Mean completion time (in minutes) Standard deviation (in minutes) P 0.50 Q 0.05 Ans: (96) For the main study, the minimum sample size for the sample mean time of any work element to be within 0. minutes of its true mean time with 95% confidence (corresponding standard normal value, Z 0.05 =.96 is Standard deviation = s = 0.5 minutes Error of study = h = 0. minutes Z 0.05 =.96 h Zs h = observations 0. Standard deviation = s = 0.05 minutes Error of study = h = 0. minutes Z 0.05 =.96 h Zs h = observations 0. Larger of the two values is 96. Hence study should be continued upto 96 observations.

37 : 37 : GATE_06_Forenoon Session 50. Consider a system with 0 identical components connected in series. The time to failure of each Ans: component is exponentially distributed with a failure rate of 0.0 per 500 days. The reliability of the system after 400 days of operation is R s = e -nt Failure rate, t = 400 days n = 0 in series R S e For a process, the quality loss coefficient is 5. The target value on the dimension to be attained through the process is 50 mm. If the maximum loss permissible (in monetary terms) is INR 80, the maximum allowable deviation (in mm) from the target is (A) 4 (B) 0 (C) 4 (D) 0 Ans: (C) R A 0 0 R = Quality loss coefficient A 0 = Economic consequence 0 = Functional limit or customer tolerance R = 5, A 0 = 80, A R 5

38 : 38 : GATE_06_Forenoon Session 5. Consider a network with nodes,, 3, 4, 5 and 6. The nodes are connected with directed arcs as shown in the table below. The respective costs (in INR) incurred while traversing the directed arcs are also mentioned. Directed arcs Cost (in INR) The second shortest path from node to node 6 (i.e. the path that has the second least total cost and does not use any part of the shortest path) has a total cost (in INR) of (A) 7 (B) 8 (C) 5 (D) 9 Ans: (C) Path Duration = = = = = = = = 5

39 : 39 : GATE_06_Forenoon Session 53. Five jobs need to be processed on a single machine. All the jobs are available for processing at time t = 0. Their respective processing times are given below. Jobs I II III IV V Processing times (in minutes) The average completion time (in minutes) of jobs as per the Shortest Processing Time rule is (A) 9.8 (B) 4. (C) 49.0 (D).0 Ans: (B) SPT RULE Job Time Completion time (c i ) II 4 4 III 7 V I 3 35 IV 4 49 C i = Mean completion Time C n 5 i 4. min 54. Transportation costs (in INR/unit) from factories to respective markets are given in the table below. The market requirements and factory capacities are also given. Using the North-West Corner method, the quantity (in units) to be transported from factory R to market II is Factory Requirements (in units) P Q R S I Market II III 4 30 Factory capacity(in units) (A) 30 (B) 0 (C) 0 (D) 0

40 : 40 : GATE_06_Forenoon Session Ans: (C) Supply = = 00 units Demand = = 00 units FACTORY P Q R S REQ I X X 50 II 4 X X 0 III X X Factory R to market II is 0 units. 55. In a given year, a restaurant earned INR 38,500 in revenues. In that year, total expenses incurred Ans: 8300 were INR 30,000 and the depreciation amount was INR 3,00. At 40% tax rate, the net cash flow (in INR) for that year was Amount (INR) Yearly revenue Total expenses Earning before taxes 8500 Tax 40% 3400 Earnings after taxes (EAT) 500 Depreciation 300 Net Cash flow = (EAT + Depreciation) 8300