# GATE Mechanical Engineering sample paper

**Related:** GATE Mechanical Engineering (ME) Syllabus

**Q. No. 1 – Q. No. 25 Carry One Mark Each**

**Question 1: **

The divergence of the vector field 3xz + 2xy – yz2 at a point (1,1,1 ) is equal to

(a) 7

(b) 4

**(c) 3**

(d) 0

**Question 2: **

If three coins are tossed simultaneously, the probability of getting at least one head

(a) 1/8

(b) 3/8

(c) 1/2

**(d) 7/8**

**Question 3: **

If a closed system is undergoing an irreversible process, the entropy of the system

(a) Must increase

(b) Always remains constant

(c) Must decrease

**(d) Can increase, decrease or remain constant**

**Question 4: **

A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015 m. It expands quasi-statically at constant temperature to a final volume of 0.030 m. The work output (in kJ) during this process will be

**(a) 8.32**

(b) 12.00

(c) 554.67

(d) 8320.00

**Question 5: **

In an ideal vapour compression refrigeration cycle, the specific enthalpy of refrigerant (in kJ/kg) at the following states is given as:

Inlet of condenser: 283

Exit of condenser: 116

Exit of evaporator: 232

The COP of this cycle is

**(a) 2.27**

(b) 2.75

(c) 3.27

(d) 3.75

**Question 6: **

If the principal stresses in a plane stress problem, are 1 = 100MPa, 2 = 40MPa , the magnitude of the maximum shear stress (in MPa) will be

(a) 60

(b) 50

**(c) 30**

(d) 20

**Question 7: **

A simple quick return mechanism is shown in the figure. The forward to return ratio of the quick return mechanism is 2 : 1. If the radius of the crank O1P is 125 mm, then the distance ‘d’ (in mm) between the crank centre to lever pivot centre point should be

(a) 144.3

(b) 216.5

(c) 240.0

**(d) 250.0**

**Question 8: **

The rotor shaft of a large electric motor supported between short bearings at both deflection of 1.8mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at both the ends, the likely critical speed (in rpm) of the shaft is

(a) 350

**(b) 705**

(c) 2810

(d) 4430

**Question 9: **

Friction at the tool-chip interface can be reduced by

(a) decreasing the rake angle

(b) increasing the depth of cut

(c) decreasing the cutting speed

**(d) increasing the cutting speed**

**Question 10: **

Which of the following forecasting methods takes a fraction of forecast error into account for the next period forecast?

(a) simple average method

(b) moving average method

(c) weighted moving average method

**(d) exponential smoothening method**

**Question 11: **

The Blasius equation,

is a

(a) Second order nonlinear ordinary differential equation

**(b) Third order nonlinear ordinary differential equation**

(c) Third order linear ordinary differential equation

(d) Mixed order nonlinear ordinary differential equation

**Question 12: **

There are two points P and Q on a planar rigid body. The relative velocity between the two points

(a) should always be along PQ

(b) Can be oriented along any direction

**(c) should always be perpendicular to PQ**

(d) should be along QP when the body undergoes pure translation

**Question 13: **

Which of the following statements is INCORRECT?

**(a) Grashof’s rule states that for a planar crank-rocker four bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.**

(b) Inversions of a mechanism are created by fixing different links one at a time.

(c) Geneva mechanism is an intermittent motion device

(d) Gruebler’s criterion assumes mobility of a planar mechanism to be one.

**Question 14: **

Tooth interference in an external involute spur gear pair can be reduced by

(a) decreasing center distance between gear pair

(b) decreasing module

(c) decreasing pressure angle

**(d) increasing number of gear teeth**

**Question 15: **

The maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is 6ms. The mean velocity (in ms) of the flow is

(a) 2

(b) 3

**(c) 4**

(d) 5

**Question 16: **

A turbo-charged four-stroke direct injection diesel engine has a displacement volume of 0.0259m (25.9litres). The engine has an output of 950kW at 2200rpm. The mean effective pressure in MPa is closest to

**(a) 2**

(b) 1

(c) 0.2

(d) 0.1

**Question 17: **

One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is

(a) equal to entropy change of the reservoir

(b) equal to entropy change of water

(c) equal to zero

**(d) always positive**

**Question 18: **

A hydraulic turbine develops 1000kW power for a head of 40m. If the head is reduced to 20m, the power developed (in kW) is

(a) 177

**(b) 354**

(c) 500

(d) 707

**Question 19: **

The material property which depends only on the basic crystal structure is

(a) fatigue strength

(b) work hardening

**(c) fracture strength**

(d) elastic constant

**Question 20: **

In a gating system, the ratio 1 : 2 : 4 represents

**(a) sprue base area: runner area: ingate area**

(b) pouring basin area: ingate area: runner area

(c) sprue base area: ingate area: casting area

(d) runner area: ingate area: casting area

**Question 21: **

In a CNC program block, N002 G02 G91 X40 Z40…, G02 AND G91 refer to

(a) circular interpolation in counterclockwise direction and incremental dimension

(b) circular interpolation in counterclockwise direction and absolute dimension

**(c) circular interpolation in clockwise direction and incremental dimension**

(d) circular interpolation in clockwise direction and absolute dimension

**Question 22: **

The demand and forecast for February are 12000 and 10275, respectively. Using single exponential smoothening method (smoothening coefficient = 0.25), forecast for the month of March is

(a) 431

(b) 9587

**(c) 10706**

(d) 11000

**Question 23: **

Simplex method of solving linear programming problem uses

(a) all the points in the feasible region

**(b) only the corner points of the feasible region**

(c) intermediate points within the infeasible region

(d) only the interior points in the feasible region

**Question 24: **

The maximum possible draft in cold rolling of sheet increases with the

**(a) Increase in coefficient of friction**

(b) Decrease in coefficient of friction

(c) Decrease in roll radius

(d) Increase in roll velocity

**Question 25: **

The operation in which oil is permeated into the pores of a powder metallurgy product is known as

(a) Mixing

(b) Sintering

**(c) Impregnation**

(d) Infiltration

**Q. No. 26 – 51 Carry Two Marks Each**

**Question 26: **

A torque *T *is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for *d *to produce an angular twist at the free end is

(a) | (b) | (c) | (d) |

**Ans. (b) **

**Question 27: **

Figure shows the schematic for the measurement of velocity of air (density = 1.2 kg/m) through a constant–area duct using a pitot tube and a water-tube manometer. The differential head of water (density = 1000 kg/m ) in the two columns of the manometer is 10mm. Take acceleration due to gravity as 2 9.8m/ s . The velocity of air in m/s is

(a) 6.4

(b) 9.0

**(c) 12.8**

(d) 25.6

**Question 28: **

The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are 2800kJ/kg and 1800kJ/kg respectively. Neglecting pump work, the specific steam consumption in kg/kW-hour is

**(a) 3.60**

(b) 0.36

(c) 0.06

(d) 0.01

**Question 29: **

For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. the length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD in rad/s is

(a) 3

(b) 3/2

(c) 1

(d) 2/3

**Question 30: **

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

(a) 1/32

(b) 13/32

(c) 16/32

**(d) 31/32**

**Question 31: **

A mass of 1kg is attached to two identical springs each with stiffness k = 20kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to

**(a) 32**

(b) 23

(c) 16

(d) 11

**Question 32: **

The shear strength of a sheet metal is 300MPa. The blanking force required to produce a blank of 100mm diameter from a 1.5 mm thick sheet is close to

(a) 45 kN

(b) 70 kN

**(c) 141 kN**

(d) 3500 kN

**Question 33: **

The crank radius of a single–cylinder I. C. engine is 60mm and the diameter of the cylinder is 80mm. The swept volume of the cylinder in cm is

(a) 48

(b) 96

(c) 302

**(d) 603**

**Question 34: **

An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar, has minimum and maximum temperatures of 300K and 1500K. The ratio of specific heats of the working fluid is 1.4. The approximate final temperatures in Kelvin at the end of the compression and expansion processes are respectively

**(a) 500 and 900**

(b) 900 and 500

(c) 500 and 500

(d) 900 and 900

**Question 35: **

A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is

(a) | (b) | (c) | (d) |

**Ans. (c) **

**Question 36: **

A 1 kg block is resting on a surface with coefficient of friction µ = 0.1. A force of 0.8N is applied to the block as shown in figure. The friction force is

(a) 0

**(b) 0.8N**

(c) 0.98N

(d) 1.2N

**Question 37: **

A single–point cutting tool with 12 rake angle is used to machine a steel work–piece. The depth of cut, i.e. uncut thickness is 0.81mm. The chip thickness under orthogonal machining condition is 1.8mm. The shear angle is approximately

(a) 22

**(b) 26**

(c) 56

(d) 76

**Question 38: **

Match the following non-traditional machining processes with the corresponding material removal mechanisms :

**Machining process Mechanism of material removal**

P. Chemical machining 1. Erosion

Q. Electro-chemical machining 2. Corrosive reaction

R. Electro – discharge machining 3. Ion displacement

S. Ultrasonic machining 4. Fusion and vaporization

**(a) P – 2, Q – 3, R – 4, S – 1**

(b) P – 2, Q – 4, R – 3, S – 1

(c) P – 3, Q – 2, R – 4, S – 1

(d) P – 2, Q – 3, R – 1, S – 4

**Question 39: **

A cubic casting of 50mm side undergoes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No. riser is used.

Assume uniform cooling in all directions. The side of the cube after solidification and contraction is

**(a) 48.32mm**

(b) 49.90mm

(c) 49.94mm

(d) 49.96mm

**Question 40: **

In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid, flowing at 1kg/s with Cp = 4kJ/kgK, enters the heat exchanger at 102°C while the cold fluid has an inlet temperature of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1kW/mK and the corresponding heat transfer surface area is 5m. Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: 2 = 1 – exp (-2NTU) . The exit temperature (in °C) for the cold fluid is

(a) 45

**(b) 55**

(c) 65

(d) 75

**Question 41: **

In an air-standard Otto cycle, the compression ratio is 10. The condition at the beginning of the compression process is 100kPa and 27°C. Heat added at constant volume is 1500kJ/kg, while 700kJ/kg of heat is rejected during the other constant volume process in the cycle. Specific gas constant for air = 0.287 kJ/kgK. The mean effective pressure (in kPa) of the cycle is

(a) 103

(b) 310

(c) 515

**(d) 1032**

**Question 42: **

An irreversible heat engine extracts heat from a high temperature source at a rate of 100kW and rejects heat to a sink at a rate of 50kW. The entire work output of the heat engine is used to drive a reversible heat pump operating between a set of independent isothermal heat reservoirs at 17°C and 75°C. The rate (in kW) at which the heat pump delivers heat to its high temperature sink is

(a) 50

(b) 250

**(c) 300**

(d) 360

**Question 43: **

Water at 25°C is flowing through a 1.0km long G.I pipe of 200mm diameter at the rate of 0.07m3/s. If value of Darcy friction factor for this pipe is 0.02 and density of water is 1000kg/m, the pumping power (in kW) required to maintain the flow is

(a) 1.8

**(b) 17.4**

(c) 20.5

(d) 41.0

**Question 44: **

A solid shaft of diameter, d and length L is fixed at both the ends. A torque, T is applied at a distance, L/4 from the left end as shown in the figure given below

The maximum shear stress in the shaft is

(a) | (b) | (c) | (d) |

**Ans. (b) **

**Question 45: **

An automotive engine weighing 240kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16MN/m while the stiffness of each rear spring is 32MN/m. The engine speed (in rpm), at which resonance is likely to occur, is

(a) 6040

**(b) 3020**

(c) 1424

(d) 955

**Question 46: **

A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of 2L/3 from the hinge so that the rod swings to the right. The reaction at the hinge is

(a) -P

**(b) 0**

(c) P/3

(d) 2P/3

**Question 47: **

Match the approaches given below to perform stated kinematics / dynamics analysis of machine.

Analysis |
Approach |

P. Continuous relative rotation | 1. D’ Alembert principle |

Q. velocity and acceleration | 2. Grubler’s criterion |

R. Mobility | 3. Grashoff’s law |

S. dynamic-static analysis | 4. Kennedy’s theorem |

(a) P-1,Q-2,R-3,S-4

**(b) P-3,Q-4,R-2,S-1**

(c) P-2,Q-3,R-4,S-1

(d) P-4,Q-2,R-1,S-3

**Common Data Questions: 48 & 49**

In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150kPa and 350K. The temperature at station Q is 300K.

The following are the properties and relations pertaining to air:

Specific heat at constant pressure, Cp = 1.005kJ /kgK;

Specific heat at constant volume, Cv = 0.718kJ /kgK;

Characteristic gas constant, R = 0.287kJ /kgK

Enthalpy, ho = c T

Internal energy, uv = c T

**Question 48: **

If the air has to flow from station P to station Q, the maximum possible value of pressure in kPa at station Q is close to

(a) 50

**(b) 87**

(c) 128

(d) 150

**Question 49: **

If the pressure at station Q is 50kPa, the change in entropy (SQ -SP) in kJ/kgK is

(a) -0.155

(b) 0

**(c) 0.160**

(d) 0.355

**Common Data Questions: 50 & 51**

Radiative heat transfer is intended between the inner surfaces of two very large isothermal parallel metal plates. While the upper plate (designated as plate 1) is a black surface and is the warmer one being maintained at 727ºC, the lower plate (plate 2) is a diffuse and gray surface with an emissivity of 0.7 and is kept at 227ºC. Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as 5.67×10 W/mK

**Question 50: **

The irradiation (in kW/m) for the upper plate (plate 1) is

**(a) 2.5**

(b) 3.6

(c) 17.0

(d) 19.5

**Question 51: **

If plate 1 is also a diffuse and gray surface with an emissivity value of 0.8, the net radiation heat exchange (in kW/m) between plate 1 and plate 2 is

(a) 17.0

(b) 19.0

(c) 23.0

**(d) 31.7**

*Linked Answer Questions: Q.52 to Q.55 Carry Two Marks Each*

In a machining experiment, tool life was found to vary with the cutting speed in the following manner:

Cutting speed (m/min) |
Tool life (minutes) |

60 |
81 |

90 |
36 |

**Question 52: **

The exponent (n) and constant (k) of the Taylor’s tool life equation are

**(a) n = 0.5 and k = 540**

(b) n = 1 and k = 4860

(c) n = -1 and k = 0.74

(d) n = −0.5 and k = 1.155

**Question 53: **

What is the percentage increase in tool life when the cutting speed is halved?

(a) 50%

(b) 200%

**(c) 300%**

(d) 400%

**Statement for Linked Answer Questions: 54 & 55**

The temperature and pressure of air in a large reservoir are 400K and 3 bar respectively. A converging–diverging nozzle of exit area 0.005m is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287kJ/kgK and 1.4 respectively.

**Question 54: **

The density of air in kg / m at the nozzle exit is

(a) 0.560

(b) 0.600

**(c) 0.727**

(d) 0.800

**Question 55: **

The mass flow rate of air through the nozzle in kg/s is

(a) 1.30

(b) 1.77

(c) 1.85

**(d) 2.06**

**Q. No. 56 – 60 Carry One Mark Each**

**Question 56: **

Which of the following options is the closest in the meaning to the word below:

**Inexplicable**

**(a) Incomprehensible**

(b) Indelible

(c) Inextricable

(d) Infallible

**Question 57: **

Choose the word from the options given below that is most nearly opposite in meaning to the given word: **Amalgamate**

(a) Merge

**(b) Split**

(c) Collect

(d) Separate

**Question 58: **

Choose the most appropriate word from the options given below to complete the following sentence.

**If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or**_____________.

(a) Hyperbolic

**(b) Restrained**

(c) Argumentative

(d) Indifferent

**Question 59: **

If in a certain language, 943 is coded as BED and 12448 is coded as SWEET, how is 492311 coded in that language ?

(a) EDSWBS

(b) TSWBDD

(c) DSWTEE

**(d) EBWDSS**

**Question 60: **

Choose the most appropriate word(s) from the options given below to complete the following sentence.

**I contemplated________Singapore for my vacation but decided against it.**

(a) To visit

(b) having to visit

**(c) visiting**

(d) for a visit

*Q. No. 61 – 65 Carry Two Marks Each*

**Question 61: **

Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting.

Based on the above passage which topic would not be included in a unit on bereavement?

(a) how to write a letter of condolence

(b) what emotional stages are passed through in the healing process

**(c) what the leading causes of death are**

(d) how to give support to a grieving friend

**Question 62: **

The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?

**(a) 5**

(b) 4

(c) 7

(d) 6

**Question 63: **

A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time.

How much spirit is now left in the container?

(a) 7.58 litres

(b) 7.84 litres

(c) 7 litres

**(d) 7.29 litres**

**Question 64: **

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?

(a) 4

(b) 5

**(c) 6**

(d) 7

**Question 65: **

P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below

A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

(a) P

(b) Q

(c) R

**(d) S**