Mechanical Engineering - ME 2014 GATE Paper (Practice Test) - Mechanical Engineering

The next term in the series 81, 54, 36, 24 … is ________

(Important - Enter only the numerical value in the answer) 

In which of the following options will the expression P < M be definitely true?

Q. No. 6 – 10 Carry Two Marks Each

Q. Find the next term in the sequence: 7G, 11K, 13M, ___

The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The correct conclusions from this information are:

(i) Butterflies are birds
(ii) There are more tigers in this forest than red ants
(iii) All reptiles in this forest are either snakes or crocodiles
(iv) Elephants are the largest mammals in this forest

A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in km per hour.

(Important - Enter only the numerical value in the answer) 

A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw material expenses increased by 30% and all other expenses increased by 20%. If the company registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air purifier sold?

(Important - Enter only the numerical value in the answer) 

A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch
is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.
The probability that the current batch is accepted is _________

(Important - Enter only the numerical value in the answer) 

Q. No. 11 – 35 Carry One Mark Each
1. Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a = 0 , b = 0 with respective eigen vectors  . If a = b then x₁y₁ + x₂y₂ + x₂y₂ equals

If a function is continuous at a point,

Divergence of the vector field at (1, -1, 1) is

A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______

(Important - Enter only the numerical value in the answer)

The definite integral  is evaluated using Trapezoidal rule with a step size of 1. The correct answer is ________

(Important - Enter only the numerical value in the answer) 

A rotating steel shaft is supported at the ends. It is subjected to a point load at the centre. The maximum bending stress developed is 100 MPa. If the yield, ultimate and corrected endurance strength of the shaft material is 300 MPa, 500 MPa and 200 MPa, respectively, then the factor of safety for the shaft is _______

(Important - Enter only the numerical value in the answer) 

Two solid circular shafts of radii R1 and R2 are subjected to same torque. The maximum shear stresses developed in the two shafts are τ₁ and τ₂ . If R1 / R2=2, then τ₂ / τ₁ is _______

(Important - Enter only the numerical value in the answer) 

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is

A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m₂ of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is

Which one of following is NOT correct?

Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with Gear 3. Gear 3 and Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of teeth on Gears 2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is

Consider a long cylindrical tube of inner and outer radii, r_i and r_o , respectively, length, L and thermal conductivity, k. Its inner and outer surfaces are maintained at T_i and T₀, respectively ( T_i > T_O ). Assuming one-dimensional steady state heat conduction in the radial direction, the thermal resistance in the wall of the tube is

Which one of the following pairs of equations describes an irreversible heat engine?

Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct pair of statements.
I. The fluid is well-mixed
II. The fluid is unmixed
III. Re_D < 2300
IV. Re_D > 2300

For a gas turbine power plant, identify the correct pair of statements. 

P. Smaller in size compared to steam power plant for same power output

Q. Starts quickly compared to steam power plant

R. Works on the principle of Rankine cycle

S. Good compatibility with solid fuel

A source at a temperature of 500 K provides 1000 kJ of heat. The temperature of environment is 27^OC. The maximum useful work (in kJ) that can be obtained from the heat source is_______

(Important - Enter only the numerical value in the answer) 

A sample of moist air at a total pressure of 85 KPa has a dry bulb temperature of 30°C (saturation vapour pressure of water = 4.24 KPa). If the air sample has a relative humidity of 65%, the absolute humidity (in gram) of water vapour per kg of dry air is _______

(Important - Enter only the numerical value in the answer) 

The process utilizing mainly thermal energy for removing material is

The actual sales of a product in different months of a particular year are given below:

The forecast of the sales, using the 4-month moving average method, for the month of February is _______

(Important - Enter only the numerical value in the answer) 

A straight turning operation is carried out using a single point cutting tool on an AISI 1020 steel rod. The feed is 0.2 mm/rev and the depth of cut is 0.5 mm. The tool has a side cutting edge angle of 60°. The uncut chip thickness (in mm) is _______

(Important - Enter only the numerical value in the answer) 

A minimal spanning tree in network flow models involves

A path forms a loop or cycle if it connects a node itself. A spanning tree links all the nodes of network with no loops allowed.

Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work interaction, because

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table.

The hot tearing in a metal casting is due to

Q. No. 36 – 65 Carry Two Marks Each

Q. An analytic function of a complex variable z = x + iy is expressed as f(z) = w(x, y) + iv(x, y), where. If u(x, y) = x² – y², then expression for v(x, y) in terms of x, y and a general constant c would be

Consider two solutions x(t) = x₁t and x(t) and x(t) = x₂(t) of the differential equation

A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

The real root of the equation 5x − 2cosx −1 = 0 (up to two decimal accuracy) is _______

(Important - Enter only the numerical value in the answer) 

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is 0.2. The dimensions shown in the figure are in mm. The braking torque (in N.m) for the brake shoe is _______

(Important - Enter only the numerical value in the answer) 

A body of mass (M) 10 kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is 0.5. The body slides down the plane and attains a velocity of 20 m/s. The distance travelled (in meter) by the body along the plane is _______

(Important - Enter only the numerical value in the answer) 

Consider a simply supported beam of length, 50h, with a rectangular cross-section of depth, h, and width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is

The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1 kg, stiffness 100 N/m and viscous damping coefficient of 25 N.s/m is _______

An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the centre of mass is v, the kinetic energy of the disc is

A force P is applied at a distance x from the end of the beam as shown in the figure. What would be the value of x so that the displacement at ‘A’ is equal to zero?

Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by t, lying in the interval 0 to 2π, is associated with the maximum translation of the follower during one full rotation of the cam rotating about the center at (x, y) = (0, 0) ?

A four-wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in 10 s, the braking torque (in N.m) on each wheel is _______

(Important - Enter only the numerical value in the answer) 

A slider-crank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter clockwise. For the given configuration, the speed (in m/s) of the slider is _______

(Important - Enter only the numerical value in the answer) 

Consider an objective function Z(x₁ ,x₂) = 3x₁ + 9x₂ and the constraints
x₁ + x₂ < 8,

x₁ + 2x₂ < 4,

x₁ >  x₂ > 0,

The maximum value of the objective function is _______

A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10 cos(25t) N. At the steady state, the vibration amplitude of the mass is 40 mm. The damping coefficient (c, in N.s/m) of the dashpot is _______ 

A certain amount of an ideal gas is initially at a pressure P₁ and temperature T1. First, it undergoes a constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constant volume process 2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume of the ideal gas is

An amount of 100 kW of heat is transferred through a wall in steady state. One side of the wall is maintained at 127^OC and the other side at 27^OC. The entropy generated (in W/K) due to the heat transfer through the wall is _______

(Important - Enter only the numerical value in the answer) 

A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry and exit. At the exit of the siphon, the velocity of water is

Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness (l). The conductivity of one section is k and that of the other is 2k. The left face of the wall is at 600 K and the right face is at 300 K. The interface temperature Ti (in K) of the composite wall is _______

A fluid of dynamic viscosity 2 × 10^-5 kg/m.s and density 1 kg/m³ flows with an average velocity of 1 m/s through a long duct of rectangular (25 mm × 15 mm) cross-section. Assuming laminar flow, the pressure drop (in Pa) in the fully developed region per meter length of the duct is _______

(Important - Enter only the numerical value in the answer) 

At the inlet of an axial impulse turbine rotor, the blade linear speed is 25 m/s, the magnitude of absolute velocity is 100 m/s and the angle between them is 25°. The relative velocity and the axial component of velocity remain the same between the inlet and outlet of the blades. The blade inlet and outlet velocity triangles are shown in the figure. Assuming no losses, the specific work (in J/kg) is _______

(Important - Enter only the numerical value in the answer) 

A solid sphere of radius r₁ = 20 mm is placed concentrically inside a hollow sphere of radius r₂ = 30 mm as shown in the figure. 

The view factor F21 for radiation heat transfer is

A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at 19 liter/s is heated from 10^OC to 38^OC. Shell side water at 25 liter/s is entering at 46^OC. Assume constant properties of water, density is 1000 kg/m³ and specific heat is 4186 J/kg K. The LMTD (in ^OC) is ________

(Important - Enter only the numerical value in the answer) 

A diesel engine has a compression ratio of 17 and cut-off take place at 10% of the stroke. Assuming ratio of specific heats (g ) as 1.4, the air-standard efficiency (in percent) is_______

(Important - Enter only the numerical value in the answer) 

Consider the given project network, where numbers along various activities represent the normal time. The free float on activity 4-6 and the project duration, respectively, are

A manufacturer can produce 12000 bearings per day. The manufacturer received an order of 8000 bearings per day from a customer. The cost of holding a bearing in stock is Rs.0.20 per month. Setup cost per production run is Rs.500. Assuming 300 working days in a year, the frequency of production run should be

A cylindrical blind riser with diameter d and height h, is placed on the top of the mold cavity of a closed type sand mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio h/d is

The diameter of a recessed ring was measured by using two spherical balls of diameter d₂ =60 mm and d₁ = 40 mm as shown in the figure.

The distance H₂ = 35.55 mm and H₁ = 20.55 mm. The diameter (D, in mm) of the ring gauge is _______

Which pair of following statements is correct for orthogonal cutting using a single-point cutting tool?

P. Reduction in friction angle increases cutting force
Q. Reduction in friction angle decreases cutting force
R. Reduction in friction angle increases chip thickness
S. Reduction in friction angle decreases chip thickness

For spot welding of two steel sheets (base metal) each of 3 mm thickness, welding current of 10000 A is applied for 0.2s. The heat dissipated to the base metal is 1000 J. Assuming that the heat required for melting 1 mm³ volume of steel is 20 J and interfacial contact resistance between sheets is 0.000 2? , the volume (in mm³) of weld nugget is _______

(Important - Enter only the numerical value in the answer)