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QUESTION: 1

**Q. 1 – Q. 5 carry one mark each.**

Choose the most appropriate alternative from the options given below to complete the following sentence:

Suresh’s dog is the one ––––––––– was hurt in the stampede.

Solution:

QUESTION: 2

The cost function for a product in a firm is given by 5q^{2}, where q is the amount of production. The firm can sell the product at a market price of Rs. 50 per unit. The number of units to be produced by the firm such that the profit is maximized is

Solution:

QUESTION: 3

Choose the most appropriate alternative from the options given below to complete the following sentence:

Despite several ––––––––– the mission succeeded in its attempt to resolve the conflict.

Solution:

QUESTION: 4

Which one of the following options is the closest in meaning to the word given below?

**Mitigate**

Solution:

QUESTION: 5

C hoose the grammatically **INCORRECT** sentence:

Solution:

QUESTION: 6

**Q. 6 - Q. 10 carry two marks each.**

**Q. **Given the sequence of terms, AD CG FK JP, the next term is

Solution:

Here 1st letter of each term in order are: A C F J

Now In alphabets, A and C have a difference of 1 alphabet, C and F have a difference of 2, and F and J have a difference of 3. Hence next term here should contain its 1st letter as an alphabet with a difference of 4 after J, i.e O.

Similarly, 2nd letter of each term in order are: D G K P

Now In alphabets, D and G have a difference of 2 alphabets, G and K have a difference of 3, and K and P have a difference of 4. Hence next term here should contain its 2nd letter as an alphabet with a difference of 5 after P, i.e V.

QUESTION: 7

**Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.**

Which one of the following is the best inference from the above advertisement?

Solution:

QUESTION: 8

A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x – 0.1x^{2} where y is the height of the arch in meters. The maximum possible height of the arch is

Solution:

y = 2x – 0.1x^{2}

dy/dx = 2 – 0.2x

So the value maximizes at 2 – 0.2x = 0

=> x = 10

=> y = 20 – 10 = 10 meters

QUESTION: 9

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.

The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

Solution:

QUESTION: 10

W hich of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list

Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list

R: Doubling each entry in a list doubles the mean of the list

S: Doubling each entry in a list leaves the standard deviation of the list unchanged

Solution:

QUESTION: 11

**Q. 11 – Q. 35 carry one mark each.**

Q. In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the

material removal rate

Solution:

QUESTION: 12

Match the following metal forming processes with their associated stresses in the workpiece.

Solution:

QUESTION: 13

In an interchangeable assembly, shafts of size mate with holes of size The maximum interference (in microns) in the assembly is

Solution:

QUESTION: 14

During normalizing process of steel, the specimen is heated

Solution:

QUESTION: 15

Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of length 500 m. The volumetric flow rate is 0.2 m^{3}/s. The head loss (in m) due to friction is (assume g = 9.81 m/s^{2})

Solution:

QUESTION: 16

For an opaque surface, the absorptivity (α), transmissivity (τ) and reflectivity (ρ) are related by the equation:

Solution:

QUESTION: 17

Steam enters an adiabatic turbine operating at steady state with an enthalpy of 3251.0 kJ/kg and leaves as a saturated mixture at 15 kPa with quality (dryness fraction) 0.9. The enthalpies of the saturated liquid and vapor at 15 kPa are h_{f} = 225.94 kJ/kg and h_{g} = 2598.3 kJ/kg respectively. The mass flow rate of steam is 10 kg/s. Kinetic and potential energy changes are negligible. The power output of the turbine in MW is

Solution:

QUESTION: 18

The following are the data for two crossed helical gears used for speed reduction:

Gear I : Pitch circle diameter in the plane of rotation 80 mm and helix angle 30º

Gear II : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5º

If the input speed is 1440 rpm, the output speed in rpm is

Solution:

QUESTION: 19

A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity ω and angular acceleration α. The magnitude of the acceleration of the point of contact on the disc is

Solution:

QUESTION: 20

A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

Solution:

QUESTION: 21

The area enclosed between the straight line y = x and the parabola y = x^{2} in the x-y plane is

Solution:

QUESTION: 22

Consider the function f (x) = |x| in the interval -1 __<__ x __<__ 1. At the point x = 0, f(x) is

Solution:

QUESTION: 23

Which one of the following is NOT a decision taken during the aggregate production planning stage?

Solution:

QUESTION: 24

Solution:

QUESTION: 25

A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm). The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is

Solution:

QUESTION: 26

A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies to a height of 25 mm. The percentage change in diameter is

Solution:

QUESTION: 27

The velocity triangles at the inlet and exit of the rotor of a turbomachine are shown. V denotes the absolute velocity of the fluid, W denotes the relative velocity of the fluid and U denotes the blade velocity. Subscripts 1 and 2 refer to inlet and outlet respectively. If V_{2} = W_{1} and V_{1} = W_{2}, then the degree of reaction is

Solution:

QUESTION: 28

W hich one of the following configurations has the highest fin effectiveness?

Solution:

QUESTION: 29

A n ideal gas of mass m and temperature T_{1} undergoes a reversible isothermal process from an initial pressure P_{1} to final pressure P_{2}. The heat loss during the process is Q. The entropy change ΔS of the gas is

Solution:

QUESTION: 30

In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is

**Note: **All dimensions are in mm.

Solution:

QUESTION: 31

A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is

Solution:

QUESTION: 32

A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of the beam cross section about the neutral axis is I and the Young’s modulus is E. The magnitude of the maximum deflection is

Solution:

QUESTION: 33

F or a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

Solution:

QUESTION: 34

At x = 0, the function f(x) = x^{3} + 1 has

Solution:

QUESTION: 35

F or the spherical surface x^{2} + y^{2} + z^{2} = 1, the unit outward normal vector at the point

Solution:

QUESTION: 36

**Q. 36 - Q. 65 carry two marks each.**

Q. The homogeneous state of stress for a metal part undergoing plastic deformation is

where the stress component values are in MPa. Using von Mises yield criterion, the value of estimated shear yield stress, in MPa is

Solution:

QUESTION: 37

Details pertaining to an orthogonal metal cutting process are given below.

The shear strain rate in s^{–1} during the process is

Solution:

QUESTION: 38

In a single pass drilling operation, a through hole of 15 mm diameter is to be drilled in a steel plate of 50 mm thickness. Drill spindle speed is 500 rpm, feed is 0.2 mm/rev and drill point angle is 118°. Assuming 2mm clearance at approach and exit, the total drill time (in seconds) is

Solution:

QUESTION: 39

C onsider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If D_{1} and D_{2} are the diameters of the inner and outer tubes respectively, then the view factor F_{22} is given by

Solution:

QUESTION: 40

A n incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be

Solution:

QUESTION: 41

A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature of air in the room are 100 kPa and 25°C respectively. Given that the saturation pressure for water at 25°C is 3.17 kPa, the relative humidity of the air in the room is

Solution:

QUESTION: 42

A fillet welded joint is subjected to transverse loading F as shown in the figure. Both legs of the fillets are of 10 mm size and the weld length is 30 mm. If the allowable shear stress of the weld is 94 MPa, considering the minimum throat area of the weld, the maximum allowable transverse load in kN is

Solution:

QUESTION: 43

A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is

Solution:

QUESTION: 44

T he state of stress at a point under plane stress condition is

σ_{xx} = 40 MPa, σ_{yy} = 100 MPa and τ_{xy} = 40 MPa.

The radius of the Mohr’s circle representing the given state of stress in MPa is

Solution:

QUESTION: 45

T he inverse Laplace transform of the function is given by

Solution:

QUESTION: 46

F or the matrix A = , ONE of the normalized eigen vectors is given as

Solution:

QUESTION: 47

Calculate the punch size in mm, for a circular blanking operation for which details are given below.

Solution:

QUESTION: 48

In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and thickness 8 mm undergoes 10 % reduction of thickness. The angle of bite in radians is

Solution:

QUESTION: 49

In a DC arc welding operation, the voltage-arc length characteristic was obtained as V_{arc} = 20 + 5l where the arc length l was varied between 5 mm and 7 mm. Here V_{arc} denotes the arc voltage in Volts. The arc current was varied from 400 A to 500 A. Assuming linear power source characteristic, the open circuit voltage and the short circuit current for the welding operation are

Solution:

QUESTION: 50

A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in h_{1}, h_{2} and h_{3} are negligible, the instantaneous discharge velocity is

Solution:

QUESTION: 51

W ater (C_{p} = 4.18 kJ/kg.K) at 80°C enters a counterflow heat exchanger with a mass flow rate of 0.5 kg/s. Air (C_{p} = 1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is

Solution:

QUESTION: 52

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by ΔT. If the thermal coefficient of the material is α, Young’s modulus is E and the Poisson’s ratio is α, the thermal stress developed in the cube due to heating is

Solution:

QUESTION: 53

A solid circular shaft needs to be designed to transmit a torque of 50 N.m. If the allowable shear stress of the material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design diameter in mm is

Solution:

QUESTION: 54

A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown in the figure, where the wrapping angle is 180°. If the coefficient of friction between the drum and then band is 0.25, the braking torque applied, in N.m is

Solution:

QUESTION: 55

A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is

Solution:

QUESTION: 56

C onsider the differential equation with the boundary conditions of

y (0) = 0 and y (1) =1. The complete solution of the differential equation is

Solution:

QUESTION: 57

x + 2y + z = 4

2x + y + 2z = 5

x - y + z = 1

The system of algebraic equations given above has

Solution:

QUESTION: 58

**Common Data for Questions 58 and 59:**

Two steel truss members, AC and BC, each having cross sectional area of 100 mm^{2}, are subjected to a horizontal force F as shown in figure. All the joints are hinged.

**Q.** If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is

Solution:

QUESTION: 59

**Common Data for Questions 58 and 59:**

Two steel truss members, AC and BC, each having cross sectional area of 100 mm^{2}, are subjected to a horizontal force F as shown in figure. All the joints are hinged.

**Q.** The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 MPa is

Solution:

QUESTION: 60

**Common Data for Questions 60 and 61:**

A refrigerator operates between 120 kPa and 800 kPa in an ideal vapor compression cycle with R-134a as the refrigerant. The refrigerant enters the compressor as saturated vapor and leaves the condenser as saturated liquid. The mass flow rate of the refrigerant is 0.2 kg/s. Properties for R-134a are as follows:

**Q.** The rate at which heat is extracted, in kJ/s from the refrigerated space is

Solution:

QUESTION: 61

**Common Data for Questions 60 and 61:**

A refrigerator operates between 120 kPa and 800 kPa in an ideal vapor compression cycle with R-134a as the refrigerant. The refrigerant enters the compressor as saturated vapor and leaves the condenser as saturated liquid. The mass flow rate of the refrigerant is 0.2 kg/s. Properties for R-134a are as follows:

**Q.** The power required for the compressor in kW is

Solution:

QUESTION: 62

**Statement for Linked Answer Questions 62 and 63:**

Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPa with a velocity of 180 m/s. The inlet area is 80 cm^{2}. The specific heat of air Cp is 1008 J/kg.K.

**Q. **The exit temperature of the air is

Solution:

QUESTION: 63

**Statement for Linked Answer Questions 62 and 63:**

Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPa with a velocity of 180 m/s. The inlet area is 80 cm^{2}. The specific heat of air Cp is 1008 J/kg.K.

**Q.** The exit area of the nozzle in cm^{2} is

Solution:

QUESTION: 64

**Statement for Linked Answer Questions 64 and 65:**

For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.

**Q. **The critical path for the project is

Solution:

QUESTION: 65

**Statement for Linked Answer Questions 64 and 65:**

For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.

**Q.** If the duration of activity f alone is changed from 9 to 10 days, then the

Solution:

### GATE Solved Paper (Mechanical)- 2012

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