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QuestionLikes!Dislikes!Answers!
1)Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is (gate 2018 mechanical engineering)

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2)In a linearly hardening plastic material, the true stress beyond initial yielding (gate 2018 Mechanical engineering)

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3)A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure. (Gate 2018 Mechnanical engineering)

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4)The rank of the matrix (Gate 2018 Mechnanical engineering)

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5)According to the Mean Value Theorem, for a continuous function f x( ) in the interval [ , ], a b there exists a value  in this interval such that ( ) b a f x dx (Gate 2018 Mechanical engineering)

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6)F z( ) is a function of the complex variable z x iy   given by (Gate 2018 Mechanical engineering)

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7)If  1 and  3 are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is (Gate 2018 Mechanical Engineering)

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8)The equation of motion for a spring-mass system excited by a harmonic force is (Gate 2018 Mechanical engineering)

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9)For an Oldham coupling used between two shafts, which among the following statements are correct? (Gate 2018 Mechanical engineering)

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10)For a two-dimensional incompressible flow field given by u  Axi ˆ  y ˆ j  , where A  0 , which one of the following statements is FALSE? (Gate 2018 Mechanical engineering)

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11)Which one of the following statements is correct for a superheated vapour? (Gate 2018 Mechanical engineering)

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12)The type of weld represented by the shaded region in the figure is (Gate 2018 Mechanical engineering)

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13)Using the Taylor’s tool life equation with exponent n  0.5, if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is (Gate 2018 Mechanical engineering )

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14)A grinding ratio of 200 implies that the (Gate 2018 Mechanical engineering)

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15)Interpolator in a CNC machine (Gate 2018 Mechanical engineering)

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16)The time series forecasting method that gives equal weightage to each of the m most recent observations is (Gate 2018 Mechanical engineering)

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17)The number of atoms per unit cell and the number of slip systems, respectively, for a face- centered cubic (FCC) crystal are (Gate 2018 Mechanical engineering)

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18)A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is(Gate 2018 Mechanical engineering)

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19) (Gate 2018 Mechanical engineering)A steel column of rectangular section (15 mm × 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is ____

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20)A four bar mechanism is made up of links of length 100, 200, 300 and 350 mm. If the 350 mm link is fixed, the number of links that can rotate fully is __________. (Gate 2018 Mechanical engineering)

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21)If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____(Gate 2018 Mechanical engineering)

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22)A flat plate of width L = 1 m is pushed down with a velocity U = 0.01 m/s towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figure.(Gate 2018 Mechanical engineering)

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23)(Gate 2018 Mechanical engineering)An ideal gas undergoes a process from state 1 ( T1 = 300 K, 1 p = 100 kPa) to state 2 ( T2 = 600 K, 2 p = 500 kPa). The specific heats of the ideal gas are : cp = 1 kJ/kg-K and cv = 0.7 kJ/kg-K. The change in specific entropy of the ideal gas from state 1 to state 2 (in kJ/kg-K) is ___________

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24)(Gate 2018 Mechanical engineering)For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is _______ (correct to two decimal places).

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25)The height (in mm) for a 125 mm sine bar to measure a taper of 27 ̊32 on a flat work piece is _______ (correct to three decimal places). (Gate 2018 Mechanical engineering)

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26)(Gate 2018 Mechanical engineering) Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations 1, 2, respectively. Consider Y = X1 – X2; μ1 = μ2 =1, 1 = 1, 2 = 2. Then, (A) Y is normally distributed with mean 0 and variance 1 (B) Y is normally distributed with mean 0 and variance 5 (C) Y has mean 0 and variance 5, but is NOT normally distributed (D) Y has mean 0 and variance 1, but is NOT normally distributed

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27)The value of the integral (Gate 2018 Mechanical engineering)

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28)A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t  0. It loses 20% of its impact velocity after each collision with the ground. (Gate 2018 Mechanical engineering)

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29)(Gate 2018 Mechanical engineering)An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is

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30)A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of  30  as shown in the figure.(Gate 2018 Mechanical engineering)

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31)A self-aligning ball bearing has a basic dynamic load rating (C10, for 106 revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in 106 revolutions) is (Gate 2018 Mechanical Engineering)

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32)A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance X (in m) where the jet strikes the floor is (Gate 2018 Mechanical engineering)

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33)In a Lagrangian system, the position of a fluid particle in a flow is described as x = xoe −kt and y = yoe kt where t is the time while xo, yo, and k are constants. The flow is (Gate 2018 Mechanical engineering)

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34)The maximum reduction in cross-sectional area per pass ( R ) of a cold wire drawing process is ( 1) 1 , n R e    where n represents the strain hardening coefficient. For the case of a perfectly plastic material, R is (Gate 2018 Mechanical engineering)

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35)The percentage scrap in a sheet metal blanking operation of a continuous strip of sheet metal as shown in the figure is _______ (Gate 2018 Mechanical engineering)

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36)An explicit forward Euler method is used to numerically integrate the differential equation dy y dt  using a time step of 0.1. (Gate 2018 Mechanical engineering)

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37)F s( ) is the Laplace transform of the function 2 ( ) 2 t f t t e  F(1) is ________ (Gate 2018 Mechanical engineering).

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38)A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) (Gate 2018 Mechanical engineering) in the beam is __________

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39)A machine of mass m = 200 kg is supported on two mounts, each of stiffness k = 10 kN/m. The machine is subjected to an external force (in N) F(t) = 50 cos 5t. Assuming only vertical translatory motion, the magnitude of the dynamic force (in N) transmitted from each mount to the ground is ______ (Gate 2018 Mechanical engineering)

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40)A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45o and a force of 40 N is acting towards the left on the slider. The length of the crank is 30 mm and the connecting rod is 70 mm. (Gate 2018 Mechanical engineering)

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41)A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles. (Gate 2018 Mechanical engineering)

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42)A solid block of 2.0 kg mass slides steadily at a velocity V along a vertical wall as shown in the figure below. A thin oil film of thickness h = 0.15 mm provides lubrication between the block and the wall. (Gate 2018 Mechanical engineering)

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43)A tank of volume 0.05 m3 contains a mixture of saturated water and saturated steam at 200C. The mass of the liquid present is 8 kg. The entropy (in kJ/kg K) of the mixture is ___________ (Gate 2018 Mechanical engineering)

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44)Steam flows through a nozzle at a mass flow rate of m   0.1 kg/s with a heat loss of 5 kW. The enthalpies at inlet and exit are 2500 kJ/kg and 2350 kJ/kg, respectively. (Gate 2018 Mechanical engineering)

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45)An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air: p c = 1.005 kJ/kg K, v c = 0.718 kJ/kg K, R = 0.287 kJ/kg K. The maximum temperature (in K) of the cycle is (Gate 2018 Mechanical engineering)

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46)A plane slab of thickness L and thermal conductivity k is heated with a fluid on one side (P), and the other side (Q) is maintained at a constant temperature, TQ of 25C, as shown in the figure. (Gate 2018 Mechanical engineering)

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47)(Gate 2018 Mechanical engineering)An orthogonal cutting operation is being carried out in which uncut thickness is 0.010 mm, cutting speed is 130 m/min, rake angle is 15 and width of cut is 6 mm. It is observed that the chip thickness is 0.015 mm, the cutting force is 60 N and the thrust force is 25 N. The ratio of friction energy to total energy is __________

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48)A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is (Gate 2018 Mechanical engineering)

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49)The minimum value of 3x + 5y such that: 3x + 5y ≤ 15 4x + 9y ≤ 8 13x + 2y ≤ 2 x ≥ 0, y ≥ 0 is (Gate 2018 Mechanical engineering)

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50)Processing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is (Gate 2018 Mechnanical engineering)

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51)The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. (Gate 2018 Mechanical engineering)

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52)Block P of mass 2 kg slides down the surface and has a speed 20 m/s at the lowest point, Q, where the local radius of curvature is 2 m as shown in the figure. (Gate 2018 Mechanical engineering)

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53)An electrochemical machining (ECM) is to be used to cut a through hole into a 12 mm thick aluminum plate. The hole has a rectangular cross-section, 10 mm × 30 mm. The ECM operation will be accomplished in 2 minutes, with efficiency of 90%. Assuming specific removal rate for aluminum as 3.44 × 10-2 mm3 /(A s), the current (in A) required is __________ (Gate 2018 Mechanical engineering).

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54)The Fourier cosine series for an even function f x( ) is given by (Gate 2018 Mechanical engineering)

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55)The divergence of the vector field u e  y i y j x ˆ  cos ˆ  sin  is (Gate 2018 Mechanical engineering)

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56)Consider a function u which depends on position x and time t. The partial differential equation (Gate 2018 Mechanical engineering)

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57)If y is the solution of the differential equation 0 3 3  x  dx dy y , y0 1 , the value of y1 is (Gate 2018 Mechanical engineeering)

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58)The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned slender column with bending stiffness EI and length L is (Gate 2018 Mechanical engineering)

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59)A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is (Gate 2018 Mechanical engineering)

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60)In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS true? (Gate 2018 Mechanical engineering)

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61)For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy (s) from state 1 to 2? (Gate 2018 Mechanical engineering)

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62)Match the following products with the suitable manufacturing process (Gate 2018 Mechanical engineering)

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63)Metal removal in electric discharge machining takes place through (Gate 2018 Mechanical engineering)

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65)Fatigue life of a material for a fully reversed loading condition is estimated from (Gate 2018 Mechanical engineering)

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66)Let z be a complex variable. For a counter-clockwise integration around a unit circle C , centred at origin, (Gate 2018 Mechanical engineering)

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67)For a position vector r x y z    i j k the norm of the vector can be defined as 2 2 2 r x y z    . Given a function   ln r , its gradient  is (Gate 2018 Mechanical engineering)

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68)In a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180 m/s2 . If the instantaneous acceleration of point Q is zero, the acceleration (in m/s2 ) of point R is (Gate 2018 Mechanical engineering)

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69)A rigid rod of length 1 m is resting at an angle 45o   as shown in the figure. The end P is dragged with a velocity of U  5 m/s to the right. At the instant shown, the magnitude of the velocity V (in m/s) of point Q as it moves along the wall without losing contact is (Gate 2018 Mechanical engieering)

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70)A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment T = 150 Nm is applied at a distance of 100 mm from end P. The torsional reactions (TP, TQ) in Nm at the ends P and Q respectively are (Gate 2018 Mechanical engineering)

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71)In a cam-follower, the follower rises by h as the cam rotates by  (radians) at constant angular velocity  (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period. Assuming that the magnitudes of the acceleration and deceleration are same, the maximum velocity of the follower is (gate 2018 Mechanical engineerinf)

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72)Air flows at the rate of 1.5 m3 /s through a horizontal pipe with a gradually reducing cross- section as shown in the figure. The two cross-sections of the pipe have diameters of 400 mm and 200 mm. (Gate 2018 Mechanical engineering)

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73)Given the ordinary differential equation (Gate 2018 Mechanical engineering)

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74)The true stress (in MPa) versus true strain relationship for a metal is given by (Gate 2018 Mechanical engineering)

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75)A steel wire is drawn from an initial diameter (di) of 10 mm to a final diameter (df) of 7.5 mm. The half cone angle () of the die is 5 and the coefficient of friction () between the die and the wire is 0.1. (Gate 2018 Mechanical engineering)

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76)The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node 1 to node 6 is _______. (Gate 2018 Mechanical engineering)

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77)A circular hole of 25 mm diameter and depth of 20 mm is machined by EDM process. The material removal rate (in mm3 /min) is expressed as (Gate 2018 Mechanical engineering)

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