Mechanical Engineering - ME 2013 GATE Paper (Practice Test)

Choose the grammatically INCORRECT sentence:

What will be the maximum sum of 44, 42, 40, ... ?

Q. No. 6 – 10 Carry Two Marks Each

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is

Find the sum of the expression

The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is

After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history.

Which one of the following assertions is best supported by the above information?

Q. No. 11 – 35 Carry One Mark Each

The partial differential equation  is a

The eigen values of symmetric matrix are all

Match the CORRECT pairs:

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from E₁ to E₂ along the length of the rod, the normal stress developed at the section-SS is

The threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is

A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1m, the magnitude of the absolute acceleration of the block at location A in m/s² is

For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the pressure drop Δp over a length L and the wall shear stress τ_w are related by

The pressure, dry bulb temperature, and relative humidity of air in a room are 1bar, 30ºC and 70% respectively. If the saturated steam pressure at 30ºC is 4.25kPa, the specific humidity of the room air in kg water vapour/kg dry air is

Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The  conductivity of the wall is given by k = k₀ + bT ; where k₀ and b are positive constants and T is temperature.

As x increases, the temperature gradient (dT / dx) will

In a rolling process, the state of stress of the material undergoing deformation is

Match the CORRECT pairs.

A metric thread of pitch 2mm and thread angle 60º is inspected for its pitch diameter using 3-wire method. The diameter of the best size wire in mm is

Customers arrive at a ticket counter at a rate of 50 per hour and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in minutes is:

In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material removal rate in mm³/s is 

A cube shaped casting solidifies in 5 minutes. The solidification time in minutes for a cube of the same material, which is 8 times heavier than the original casting will be

For a ductile material, toughness is a measure of

In order to have maximum power from a Pelton turbine, the bucket speed must be

Consider one-dimensional steady state heat conduction along x-axis (0 < x < L) , through a plane wall with the boundary surfaces (x = 0 and x = L) maintained at temperatures 0ºC and 100ºC. Heat is generated uniformly throughout the wall. 

Choose the CORRECT statement.

A cylinder contains 5m³ of ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is

A long thin walled cylindrical shell, closed at both ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is

If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is

A planar closed kinematic chain is formed with rigid links PQ = 2.0m, QR = 3.0m, RS = 2.5m and SP = 2.7m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-rocker) mechanism is

Let X be a nominal variable with mean 1 and variance 4. The probability P (X < 0) is

Choose the CORRECT set of functions, which are linearly dependent.

Q. No. 26 – 55 Carry Two Marks Each

Q. The following surface integral is to be evaluated over a sphere for the given steady velocity vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.

Where S is the sphere, x² + y² + z² = 1 and n is the outward unit normal vector to the sphere. The value of the surface integral is

The function f(t) satisfies the differential equation  and the auxiliary conditions, 
 The Laplace transform of f(t) is given by

Ram and Shyam shared a secret and promised to each other that it would remain between them. Ram expressed himself in one of the following ways as given in the choices below. Identify the correct way as per standard English

Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is 20mm with uniform velocity of 2 m/s. Acceleration due to gravity is 9.81 m/s². Assuming steady, inviscid flow, constant atmospheric pressure everywhere and neglecting curvature and surface tension effects, the diameter is mm of the stream 0.5m below the tap is approximately

A steel ball of diameter 60 mm is initially in thermal equilibrium at 1030°C in a furnace. It is suddenly removed from the furnace and cooled in ambient air at 30°C , with convective heat transfer coefficient h = 20 W/m²K. The thermophysical properties of steel are: density ρ = 7800 kg /m³ , conductivity
  and specific heat c = 600 J/kgK. The time required in seconds to cool the steel ball in air from 1030°C to 430°C is

A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation of speed is not to exceed ±2%, the mass moment of inertia of the flywheel in kg − m² is

A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20, respectively. Gears Q and R are mounted on the same shaft as shown in the figure below. The diameter of the gear Q is twice that of the gear R. If the module of the gear R is 2 mm, the center distance in mm between gears P and S is 

A pin jointed uniform rigid rod of weight W and Length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is

Two cutting tools are being compared for a machining operation. The tool life equations are:

Where V is the cutting speed in m/min and T is the tool life in min. The carbide toll will provide higher tool life if the cutting speed in m/min exceeds

In a CAD package, mirror image of a 2D point P(5, 10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterlockwise with the X-axis. The coordinates of the transformed point will be

A linear programming problem is shown below:

It has

Cylindrical pins of  diameter are electroplated in a shop. Thickness of  the plating is 2.0 30 micron + . Neglecting gage tolerances, the size of the GO gage in mm to inspect the plated components is  

During the electrochemical machining (ECM) of iron (atomic weight = 56, valency  =2) at current of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titanium (atomic weight = 48, valency=3) is machined by the ECM process at the current of 2000 A with 90% current efficiency, the expected material removal rate in gm/s will be

A single degree of freedom system having mass 1 kg and stiffness 10kN/m initially at rest is subjected to an impulse force of magnitude 5 kN for 10⁻⁴ seconds. The amplitude in mm of the resulting free vibration is

A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the area of cross-section in mm² of the bar for a factor of safety of 2 is

A simply supported beam of length L is subjected to a varying distributed load

, where the distance x is measured from the left support. The magnitude of the vertical force in N at the left support is

Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of 400 K and 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is, the net radiation heat exchange rate in kW/m² between the two plates is

A hinged gate of length 5 m, inclined at 30° with the horizontal and with water mass on its left, is shown in figure below. Density of water is 1000 kg/m² . The minimum mass of the gate in kg per unit width (perpendicular to the plane of paper), required to keep it closed is

The pressure, temperature and velocity of air flowing in a pipe are 5 bar, 500 K and 50 m/s, respectively. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of the air stream is

The probability that a student knows the correct answer to a multiple choice question is 2/3 . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student known the correct answer is

The solution to the differential equation   where k is a constant, subjected to the boundary conditions u(0)=0 and u(L)=U, is

The value of the definite integral 

Common Data Questions: 58 & 59

A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details:

Width of the plate w = 200 mm, thickness of the plate t = 5 mm, number of rivets n = 3, diameter of the rivet d_r = 10mm, diameter of the rivet hole d_h = 11mm, allowable tensile stress of the plate σ_p = 200MPa, allowable shear stress of the rivet σ_s = 100 MPa and allowable bearing stress of the σ_c = 150 MPa 48.

Q. If the rivets are to be designed to avoid crushing failure, the maximum permissible load P in kN is

Common Data Questions: 58 & 59

A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details:

Width of the plate w = 200 mm, thickness of the plate t = 5 mm, number of rivets n = 3, diameter of the rivet d_r = 10mm, diameter of the rivet hole d_h = 11mm, allowable tensile stress of the plate σ_p = 200MPa, allowable shear stress of the rivet σ_s = 100 MPa and allowable bearing stress of the σ_c = 150 MPa 48.

Q. If the plates are to be designed to avoid tearing failure, the maximum permissible load P in kN is

Common Data Questions: 60 & 61

Water (specific heat, cp = 4.18 kJ / kgK ) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C . The pipe, of diameter 50 mm and length 3m, is subjected to a wall heat flux

Q. If , where x is in m and in the direction of flow (x=0 at the inlet), the bulk mean temperature of the water leaving the pipe in °C is

Common Data Questions: 60 & 61

Water (specific heat, cp = 4.18 kJ / kgK ) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C . The pipe, of diameter 50 mm and length 3m, is subjected to a wall heat flux

Q. If = 5000, and the convection heat transfer coefficient at the pipe outlet is 1000W /m²K , the temperature in °C at the inner surface of the pipe at the outlet is

Linked Answer Questions: Q.62 to Q.65 Carry Two Marks Each

Statement for Linked Answer Questions: 62 & 63

In orthogonal turning of a bar of 100 mm diameter with a feed of 0.25 mm/rev, depth of cut of 4 mm and cutting velocity of 90 m/min, it is observed that the main (tangential) cutting force is perpendicular to the friction force acting at the chip-tool interface. The main (tangential) cutting force is 1500 N.

Q. The orthogonal rake angle of the cutting tool in degree is

Linked Answer Questions: Q.62 to Q.65 Carry Two Marks Each

Statement for Linked Answer Questions: 62 & 63

In orthogonal turning of a bar of 100 mm diameter with a feed of 0.25 mm/rev, depth of cut of 4 mm and cutting velocity of 90 m/min, it is observed that the main (tangential) cutting force is perpendicular to the friction force acting at the chip-tool interface. The main (tangential) cutting force is 1500 N.

Q. The normal force acting at the chip-tool interface in N is

Statement for Linked Answer Questions: 64 & 65

In a simple Brayton cycle, the pressure ration is 8 and temperatures at the entrance of compressor and turbine are 300 K and 1400 K, respectively. Both compressor and gas turbine have isentropic efficiencies equal to 0.8. For the gas, assume a constant value of p c (specific heat at constant pressure) equal to 1 kJ/kgK and ratio of specific heats as 1.4. Neglect changes in kinetic and potential energies.

Q. The power required by the compressor in kW/kg of gas flow rate is

Statement for Linked Answer Questions: 64 & 65

In a simple Brayton cycle, the pressure ration is 8 and temperatures at the entrance of compressor and turbine are 300 K and 1400 K, respectively. Both compressor and gas turbine have isentropic efficiencies equal to 0.8. For the gas, assume a constant value of p c (specific heat at constant pressure) equal to 1 kJ/kgK and ratio of specific heats as 1.4. Neglect changes in kinetic and potential energies.

Q. The thermal efficiency of the cycle in percentage (%) is