gate-2016 mechanical set-1 full solution

GATEMENTOREDUSERVICES PVT.LTD.

erycMechanical GATEMENTOReryc

SET - 1GATE 2016 MECHANICAL

DETAILED SOLUTION & ANSWER KEY

GATE 2016 General Aptitude - GA Set-1

1/2

Q. 1 – Q. 5 carry one mark each.

Q.1 Which of the following is CORRECT with respect to grammar and usage? Mount Everest is ____________.

(A) the highest peak in the world (B) highest peak in the world (C) one of highest peak in the world (D) one of the highest peak in the world

Q.2 The policeman asked the victim of a theft, “What did you ?”

(A) loose (B) lose (C) loss (D) louse Q.3 Despite the new medicine’s ______________ in treating diabetes, it is not ______________widely.

(A) effectiveness --- prescribed (B) availability --- used (C) prescription --- available (D) acceptance --- proscribed

Q.4 In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of

the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples?

(A) 2029198 (B) 2467482 (C) 2789080 (D) 3577422 Q.5 Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away

from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?

(A) 3.00 (B) 4.99 (C) 6.02 (D) 7.01

Q. 6 – Q. 10 carry two marks each.

Q.6 A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.

However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

(A) 15 (B) 33 (C) 35 (D) 37

GATEMENTOR

GATE 2016 General Aptitude - GA Set-1

2/2

Q.7 In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong. Which of the following inference(s) is/are logically valid and can be inferred from the above passage?

(i) His friends were always asking him to help them.

(ii) He felt that when in need of help, his friends would let him down.

(iii) He was sure that his friends would help him when in need.

(iv) His friends did not help him last week.

(A) (i) and (ii) (B) (iii) and (iv) (C) (iii) only (D) (iv) only Q.8 Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra

and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be TRUE based on the above?

(A) When Shiva plays chess with Leela and Pavithra, he often loses. (B) Leela is the oldest of the three. (C) Shiva is a better chess player than Pavithra. (D) Pavithra is the youngest of the three.

Q.9 If 𝑞𝑞−𝑎𝑎 = 1

𝑟𝑟 and 𝑟𝑟−𝑏𝑏 = 1

𝑠𝑠 and 𝑠𝑠−𝑐𝑐 = 1

𝑞𝑞 , the value of abc is .

(A) (𝑟𝑟𝑞𝑞𝑠𝑠)−1 (B) 0 (C) 1 (D) r+q+s

END OF THE QUESTION PAPER

Q.10 P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

(A) 10:11 (B) 11:10 (C) 20:21 (D) 21:20

GATEMENTOR

GATE 2016 SET-1 Mechanical Engineering (ME)

ME (Set-1) 1/11

Q. 1 – Q. 25 carry one mark each.

Q.1 The solution to the system of equations

2 5−4 3

𝑥𝑦 =

2−30

is

(A) 6, 2 (B) −6, 2 (C) −6,−2 (D) 6, −2

Q.2 If 𝑓 𝑡 is a function defined for all t ≥ 0, its Laplace transform F(s) is defined as

(A) 𝑒𝑠𝑡∞

0 𝑓 𝑡 d𝑡 (B) 𝑒−𝑠𝑡∞

0 𝑓 𝑡 d𝑡

(C) 𝑒𝑖𝑠𝑡∞

0 𝑓 𝑡 d𝑡 (D) 𝑒−𝑖𝑠𝑡∞

0 𝑓 𝑡 d𝑡

Q.3 𝑓 𝑧 = 𝑢 𝑥, 𝑦 + 𝑖 𝑣 𝑥, 𝑦 is an analytic function of complex variable 𝑧 = 𝑥 + 𝑖 𝑦 where

𝑖 = −1. If 𝑢 𝑥, 𝑦 = 2 𝑥𝑦, then 𝑣 𝑥, 𝑦 may be expressed as

(A) − 𝑥2 + 𝑦2 + constant (B) 𝑥2 − 𝑦2 + constant

(C) 𝑥2 + 𝑦2 + constant (D) − 𝑥2 + 𝑦2 + constant

Q.4 Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is µ.

The standard deviation for this distribution is given by

(A) 𝜇 (B) 𝜇2 (C) µ (D) 1/𝜇

Q.5 Solve the equation 𝑥 = 10 cos(𝑥) using the Newton-Raphson method. The initial guess is

𝑥 = 𝜋/4. The value of the predicted root after the first iteration, up to second decimal, is ________

Q.6 A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a

horizontal force F such that the string makes an angle of 30 with the vertical. The magnitude of

force F (in N) is __________

30

F

100 N

GATEMENTOR


ME (Set-1) 2/11

Q.7 A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height

H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the

mass at the bottom of the bowl is

(A) 𝑔𝐻 (B) 2𝑔𝑅 (C) 2𝑔𝐻 (D) 0

Q.8 The cross sections of two hollow bars made of the same material are concentric circles as shown in

the figure. It is given that 𝑟3 > 𝑟1 and 𝑟4 > 𝑟2, and that the areas of the cross-sections are the same.

J1 and J2 are the torsional rigidities of the bars on the left and right, respectively. The ratio J2/J1 is

(A) > 1 (B) < 0.5 (C) =1 (D) between 0.5 and 1

Q.9 A cantilever beam having square cross-section of side a is subjected to an end load. If a is increased

by 19%, the tip deflection decreases approximately by

(A) 19% (B) 29% (C) 41% (D) 50%

Q.10 A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating

masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from

the front of the car. The combined moment of inertia of the rotating masses is 10 kg-m2. The

magnitude of the gyroscopic moment (in N-m) is __________

Q.11 A single degree of freedom spring mass system with viscous damping has a spring constant of

10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor

(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm.

Q.12 The spring constant of a helical compression spring DOES NOT depend on

(A) coil diameter

(B) material strength

(C) number of active turns

(D) wire diameter

H

RM

GATEMENTOR


ME (Set-1) 3/11

Q.13 The instantaneous stream-wise velocity of a turbulent flow is given as follows:

),,,(),,(),,,( tzyxuzyxutzyxu

The time-average of the fluctuating velocity ),,,( tzyxu is

(A) 𝑢′/2 (B) − 𝑢 /2 (C) zero (D) 𝑢 /2

Q.14 For a floating body, buoyant force acts at the

(A) centroid of the floating body

(B) center of gravity of the body

(C) centroid of the fluid vertically below the body

(D) centroid of the displaced fluid

Q.15 A plastic sleeve of outer radius r0 = 1 mm covers a wire (radius r = 0.5 mm) carrying electric

current. Thermal conductivity of the plastic is 0.15 W/m-K. The heat transfer coefficient on the

outer surface of the sleeve exposed to air is 25 W/m2-K. Due to the addition of the plastic cover, the

heat transfer from the wire to the ambient will

(A) increase

(B) remain the same

(C) decrease

(D) be zero

Q.16 Which of the following statements are TRUE with respect to heat and work?

(i) They are boundary phenomena

(ii) They are exact differentials

(iii) They are path functions

(A) both (i) and (ii) (B) both (i) and (iii) (C) both (ii) and (iii) (D) only (iii)

Q.17 Propane (C3H8) is burned in an oxygen atmosphere with 10% deficit oxygen with respect to the

stoichiometric requirement. Assuming no hydrocarbons in the products, the volume percentage of

CO in the products is __________

Q.18 Consider two hydraulic turbines having identical specific speed and effective head at the inlet. If

the speed ratio (N1/N2) of the two turbines is 2, then the respective power ratio (P1/P2)

is _____________

Q.19 The INCORRECT statement about regeneration in vapor power cycle is that

(A) it increases the irreversibility by adding the liquid with higher energy content to the steam

generator

(B) heat is exchanged between the expanding fluid in the turbine and the compressed fluid before

heat addition

(C) the principle is similar to the principle of Stirling gas cycle

(D) it is practically implemented by providing feed water heaters

GATEMENTOR


ME (Set-1) 4/11

Q.20 The “Jominy test” is used to find

(A) Young’s modulus (B) hardenability

(C) yield strength (D) thermal conductivity

Q.21 Under optimal conditions of the process the temperatures experienced by a copper work piece in

fusion welding, brazing and soldering are such that

(A) Twelding > Tsoldering> Tbrazing (B) Tsoldering > Twelding > Tbrazing

(C) Tbrazing >Twelding > Tsoldering (D) Twelding > Tbrazing > Tsoldering

Q.22 The part of a gating system which regulates the rate of pouring of molten metal is

(A) pouring basin (B) runner (C) choke (D) ingate

Q.23 The non-traditional machining process that essentially requires vacuum is

(A) electron beam machining (B) electro chemical machining

(C) electro chemical discharge machining (D) electro discharge machining

Q.24 In an orthogonal cutting process the tool used has rake angle of zero degree. The measured cutting

force and thrust force are 500 N and 250 N, respectively. The coefficient of friction between the

tool and the chip is _________

Q.25 Match the following:

P. Feeler gauge I. Radius of an object

Q. Fillet gauge II. Diameter within limits by comparison

R. Snap gauge III. Clearance or gap between components

S. Cylindrical plug gauge IV. Inside diameter of straight hole

(A) P–III, Q–I, R–II, S–IV (B) P–III, Q–II, R–I, S–IV

(C) P–IV, Q–II, R–I, S–III (D) P–IV, Q–I, R–II, S–III

Q. 26 – Q. 55 carry two marks each.

Q.26 Consider the function 𝑓 𝑥 = 2𝑥3 − 3𝑥2 in the domain [−1, 2]. The global minimum of 𝑓(𝑥)

is ____________

Q.27 If 𝑦 = 𝑓(𝑥) satisfies the boundary value problem 𝑦′′ + 9 𝑦 = 0, 𝑦 0 = 0, 𝑦 𝜋/2 = 2, then

𝑦 𝜋/4 is ________

GATEMENTOR


ME (Set-1) 5/11

Q.28 The value of the integral

sin𝑥

𝑥2 + 2𝑥 + 2d𝑥

∞

−∞

evaluated using contour integration and the residue theorem is

(A) –𝜋 sin(1)/e (B) −𝜋 cos(1)/e (C) sin(1)/e (D) cos(1)/e

Q.29 Gauss-Seidel method is used to solve the following equations (as per the given order):

𝑥1 + 2𝑥2 + 3𝑥3 = 5

2𝑥1 + 3𝑥2 + 𝑥3 = 1

3𝑥1 + 2𝑥2 + 𝑥3 = 3

Assuming initial guess as 𝑥1 = 𝑥2 = 𝑥3 = 0, the value of 𝑥3 after the first iteration is __________

Q.30 A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the

figure. The coefficient of static friction between the plane and the block is 0.25. The string can

withstand a maximum force of 20 N. The maximum value of the mass (m) for which the string will

not break and the block will be in static equilibrium is ____________ kg.

Take cosand sin

Acceleration due to gravity g = 10 m/s2

Q.31 A two-member truss PQR is supporting a load W. The axial forces in members PQ and QR are

respectively

(A) 2𝑊 tensile and 3𝑊 compressive

(B) 3𝑊 tensile and 2𝑊 compressive

(C) 3𝑊 compressive and 2𝑊 tensile

(D) 2𝑊 compressive and 3𝑊 tensile

W

30

L P Q

R

60

GATEMENTOR


ME (Set-1) 6/11

Q.32 A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The

Young’s moduli for the sections AB and BC are 3E and E, respectively.

For the deflection at C to be zero, the ratio P/F is ____________

Q.33 The figure shows cross-section of a beam subjected to bending. The area moment of inertia

(in mm4) of this cross-section about its base is __________

Q.34 A simply-supported beam of length 3L is subjected to the loading shown in the figure.

It is given that P = 1 N, L = 1 m and Young’s modulus E = 200 GPa. The cross-section is a square

with dimension 10 mm × 10 mm. The bending stress (in Pa) at the point A located at the top surface

of the beam at a distance of 1.5L from the left end is _____________

(Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

Q.35 A slider crank mechanism with crank radius 200 mm and connecting rod length 800 mm is shown.

The crank is rotating at 600 rpm in the counterclockwise direction. In the configuration shown, the

crank makes an angle of 90 with the sliding direction of the slider, and a force of 5 kN is acting on

the slider. Neglecting the inertia forces, the turning moment on the crank (in kN-m) is __________

P P

L L L

A

All dimensions are in mm

5 kN

800 mm 200 mm

90

10

R4 8

R4

10

10

GATEMENTOR


ME (Set-1) 7/11

Q.36 In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The

number of teeth on gear 2, 3, and 4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4

rotates with an angular velocity of 100 rpm in the counterclockwise direction, the angular speed of

arm 5 (in rpm) is

(A) 166.7 counterclockwise (B) 166.7 clockwise

(C) 62.5 counterclockwise (D) 62.5 clockwise

Q.37 A solid disc with radius a is connected to a spring at a point d above the center of the disc. The

other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the

ground. The mass of the disc is M and the spring constant is K. The polar moment of inertia for the

disc about its centre is J = 𝑀𝑎2/2.

The natural frequency of this system in rad/s is given by

(A) 2 𝐾 (𝑎+𝑑)2

3 𝑀 𝑎2 (B) 2 𝐾

3 𝑀 (C)

2 𝐾 (𝑎+𝑑)2

𝑀 𝑎2 (D) 𝐾 (𝑎+𝑑)2

𝑀 𝑎2

Q.38 The principal stresses at a point inside a solid object are 1 = 100 MPa, 2 = 100 MPa and 3 = 0

MPa. The yield strength of the material is 200 MPa. The factor of safety calculated using Tresca

(maximum shear stress) theory is nT and the factor of safety calculated using von Mises (maximum

distortional energy) theory is nV. Which one of the following relations is TRUE?

(A) nT = ( 3/2)nV

(B) nT = ( 3)nV

(C) nT = nV

(D) nV = ( 3)nT

KM, J

ad

5

2 3

4

GATEMENTOR


ME (Set-1) 8/11

Q.39 An inverted U-tube manometer is used to measure the pressure difference between two pipes A and

B, as shown in the figure. Pipe A is carrying oil (specific gravity = 0.8) and pipe B is carrying

water. The densities of air and water are 1.16 kg/m3

and 1000 kg/m3, respectively. The pressure

difference between pipes A and B is __________kPa.

Acceleration due to gravity g = 10 m/s2.

Q.40 Oil (kinematic viscosity, ν𝑜𝑖𝑙 = 1.0 × 10−5 m2/s) flows through a pipe of 0.5 m diameter with a

velocity of 10 m/s. Water (kinematic viscosity, ν𝑤 = 0.89 × 10−6 m2/s) is flowing through a model

pipe of diameter 20 mm. For satisfying the dynamic similarity, the velocity of water (in m/s)

is __________

Q.41 A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream

velocity of the fluid is Uo.. The velocity profile at the inlet a-b is uniform, while that at a

downstream location c-d is given by 𝑢 = 𝑈𝑜 2 𝑦

−

𝑦

2 .

The ratio of the mass flow rate, 𝑚 𝑏𝑑 , leaving through the horizontal section b-d to that entering

through the vertical section a-b is ___________

Q.42 A steel ball of 10 mm diameter at 1000 K is required to be cooled to 350 K by immersing it in a

water environment at 300 K. The convective heat transfer coefficient is 1000 W/m2-K. Thermal

conductivity of steel is 40 W/m-K. The time constant for the cooling process 𝜏 is 16 s. The time

required (in s) to reach the final temperature is __________

a

b

c

d

Uo

Uo

y

GATEMENTOR


ME (Set-1) 9/11

Q.43 An infinitely long furnace of 0.5 m × 0. 4 m cross-section is shown in the figure below. Consider

all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature

T1 = T3 = 927 oC while the side walls are at temperature T2 = T4 = 527

oC. The view factor, F1-2 is

0.26. The net radiation heat loss or gain on side 1 is_________ W/m.

Stefan-Boltzmann constant = 5.67 × 10−8 W/m2-K

4

Q.44 A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at

300 K. The velocity of the fluid is 10 m/s. Assuming kinematic viscosity, ν = 30 × 10−6 m2/s, the

thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is __________

Q.45 For water at 25 C, d𝑝s/d𝑇s = 0.189 kPa/K (𝑝s is the saturation pressure in kPa and 𝑇s is the

saturation temperature in K) and the specific volume of dry saturated vapour is 43.38 m3/kg.

Assume that the specific volume of liquid is negligible in comparison with that of vapour. Using

the Clausius-Clapeyron equation, an estimate of the enthalpy of evaporation of water at 25 C

(in kJ/kg) is __________

Q.46 An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The

conditions at the start (subscript 1) and at the end (subscript 2) of the process with usual notation

are: 𝑝1 = 100 kPa, 𝑉1 = 0.2 m3 and 𝑝2 = 200 kPa, 𝑉2 = 0.1 m

3 and the gas constant,

R = 0.275 kJ/kg-K. The magnitude of the work required for the process (in kJ) is ________

Q.47 In a steam power plant operating on an ideal Rankine cycle, superheated steam enters the turbine at

3 MPa and 350 oC. The condenser pressure is 75 kPa. The thermal efficiency of the cycle is

________ percent.

Given data:

For saturated liquid, at P = 75 kPa, 39.384fh kJ/kg, 001037.0fv m3/kg, sf = 1.213 kJ/kg-K

At 75 kPa, hfg = 2278.6 kJ/kg, sfg = 6.2434 kJ/kg-K

At P = 3 MPa and T = 350 oC (superheated steam), 3.3115h kJ/kg, 7428.6s kJ/kg-K

GATEMENTOR


ME (Set-1) 10/11

Q.48 A hypothetical engineering stress-strain curve shown in the figure has three straight lines PQ, QR,

RS with coordinates P(0,0), Q(0.2,100), R(0.6,140) and S(0.8,130). 'Q' is the yield point, 'R' is the

UTS point and 'S' the fracture point.

The toughness of the material (in MJ/m

3) is __________

Q.49 Heat is removed from a molten metal of mass 2 kg at a constant rate of 10 kW till it is completely

solidified. The cooling curve is shown in the figure.

Assuming uniform temperature throughout the volume of the metal during solidification, the latent

heat of fusion of the metal (in kJ/kg) is __________

Q.50 The tool life equation for HSS tool is 𝑉𝑇0.14𝑓0.7𝑑0.4 = Constant. The tool life (T) of 30 min is

obtained using the following cutting conditions:

V = 45 m/min, f = 0.35 mm, d = 2.0 mm

If speed (V), feed (f) and depth of cut (d) are increased individually by 25%, the tool life (in min) is

(A) 0.15 (B) 1.06 (C) 22. 50 (D) 30.0

Q.51 A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus

method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as

cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm)

is

(A) 150 (B) 200 (C) 100 (D) 125

Q.52 A 300 mm thick slab is being cold rolled using roll of 600 mm diameter. If the coefficient of

friction is 0.08, the maximum possible reduction (in mm) is __________

(0.2, 100)

(0.6, 140)(0.8, 130)

0

20

40

60

80

100

120

140

160

0 0.2 0.4 0.6 0.8 1En

gg. S

tres

s (M

Pa)

Engg. Strain (%)

P

Q

RS

(0, 0)

(0s, 1023K)

(10s, 873K)(20s, 873K)

(30s, 600K)500

600

700

800

900

1000

1100

0 10 20 30 40

Tem

per

atu

re (

K)

Time (s)

GATEMENTOR


ME (Set-1) 11/11

Q.53 The figure below represents a triangle PQR with initial coordinates of the vertices as P(1,3),

Q(4,5) and R(5,3.5). The triangle is rotated in the X-Y plane about the vertex P by angle in

clockwise direction. If sin = 0.6 and cos = 0.8, the new coordinates of the vertex Q are

(A) (4.6, 2.8) (B) (3.2, 4.6) (C) (7.9, 5.5) (D) (5.5, 7.9)

Q.54 The annual demand for an item is 10,000 units. The unit cost is Rs. 100 and inventory carrying

charges are 14.4% of the unit cost per annum. The cost of one procurement is Rs. 2000. The time

between two consecutive orders to meet the above demand is _______ month(s).

Q.55 Maximize Z=15X1 + 20X2

subject to

12X1 + 4X2 ≥ 36

12X1 − 6X2 ≤ 24

X1, X2 ≥ 0

The above linear programming problem has

(A) infeasible solution (B) unbounded solution

(C) alternative optimum solutions (D) degenerate solution

END OF THE QUESTION PAPER

GATEMENTOR

GATE MECHANICAL BOOKS

L ag

e din

ok Bo

Se

tors

aAvilab

le

A Al

tl

Availab

le

At

GATE MECHANICAL BOOKS

GATE – 2016

Set - 1

GATEMENTOREDUSERVICES PVT. LTD., A-213, STREET-27, SMRITI NAGAR, BHILAI–490020 CONTACT - 0788-6499334/4062366, www.gatementor.co.in | 1

ANSWER KEYS

Set 1 - Aptitude section

1 A 2 B 3 A 4 A 5 C

6 C 7 B 8 D 9 C 10 C

Set 1 - technical section

1 D 12 B 23 A 34 0 45 2443.248

2 B 13 C 24 0.5 35 1 46 15

3 A 14 D 25 A 36 C 47 26.017

4 A 15 A 26 -5 37 A 48 0.85

5 1.56 16 B 27 -1 38 C 49 50

6 57.735 17 14.28 28 A 39 2.2or-2.2 50 B

7 C 18 0.25 29 1.55 40 22.25 51 D

8 A 19 C 30 5 41 0.3333 52 1.92

9 D 20 B 31 B 42 42.22 53 A

10 200 21 D 32 4 43 24530.69 54 2

11 20 22 C 33 21439.056 44 6.124 55 B

GATE – 2016

Set - 1

GATEMENTOREDUSERVICES PVT. LTD., A-213, STREET-27, SMRITI NAGAR, BHILAI–490020 CONTACT - 0788-6499334, www.gatementor.co.in | 1

APTITUDE/ENGLISH 1.(A)

2.(B)

3.(A)

4.(A)

Number of apples x

Number of oranges y

5692000x y

Unripe fruits

0.15 x y

853800

Ripe fruits

0.85 x y

4838200

Unripe Number of apples

0.45 833800

384210

Ripe number of applies

1 0.66 4838200

1644988

Number of applies

384210 1644988x

2029198x

5.(C)

Only possible answer is C which is between 5

km and 7 km.

6.(C)

Probability of infected but

Not diseased 0.5 0.7

0.35

35%

7.(B)

8. (D) order of age

Shiva

Leela

Pavithra

9.(C)

1 1 1 1 1 1, ,

a b cr s qq r s

, ,

ln ln ,b ln ln ,c ln ln

ln ln ln,b ,c

ln ln ln

1

a b cq r r s s q

a q r r s s q

r s qa

q r s

abc

10.(C)

1

25 12 / per25

dayQ days hr day

1

50 12 /50

R days hr day per day

Work by 1

51225

Q

Work by 1

7 1850

R

60

60 2025 27 18 7 18 21

50

Q

R

TECHNICAL SECTION

1.(D)

2 5 2x y …(i)

4 3 90x y …(ii)

Solving (i) and (ii),

6 2x y

2.(B)

0

stL F t e f t dt

3.(A)

For analytic function

,u v u v

y x x y

2 ?u xy v

u v

x y

2v

yy

2u y F x …(i)

'u

F xx

GATE – 2016

Set - 1


'v

F xy

2 'x F x

2 constantF x x

From (i) 2 2 constantv y x

4.(A)

For poission distribution

Mean variance

Standard deviation

5. (1.5641)

10cosF x x x

' 1 10sinF x x

1

'

n

n n

n

F xx x

F x

0

1 0' o

F xx x

F x

4ox

10cos4 4

oF x

' 1 10sin4

oF x

6.2856oF x

' 8.07106oF x

from equation (i)

1

6.2856

4 8.07106x

1 1.5641x

6.(57.73)

600F

100N

900

1200

Sine – rule

100

sin150 sin120

F

57.73F N

7. (C)

Now energy balance

1 2PE KE

1 2

1

2mgH mv

2v gH

8. (A)

2 1

2 2 2 2

4 3 2 1

A A

r r r r

4 4

4 32

4 412 1

32

32

r rJ

Jr r

2 2 2 2

4 3 4 32

2 2 2 21 2 1 2 1

r r r rJ

J r r r r

2 2

4 32

2 21 2 1

r rJ

J r r

3 1 4 2

2 2 2 2

4 3 2 1

2 2

4 3

2 2

2 1

2

1

1

1

and r r r r

r r r r

r r

r r

J

J

9. (D)

Deflection3

3

Pl

EI

4

2 1 1

4 4

1 2 2

1

1.19

I a

I a

2

1

0.4986

Percentage change in deflection

2 1 2

1 1

100 1 100 50.14

2 10.4986

So

1 decreased by 50%

GATE – 2016

Set - 1


10.(200)

Gyroscopic couple “c”

. pC I

20 2

100 10p

V

r

100 / secrad

210 /I Kg m

210 100 200

10pC I Nm

11. (20)

Steady state amplitude,

2 221 2

staticm

XX

r r

3

1000.01 ,

10 10static

FX m

K

0.25

1 for resonance r

2 22

0.01

1 1 2 0.25 1mX

20mX mm

12.(B)

4

3

.

8

G dK

D N

4

3

1

1

k d

kD

kN

13.(C)

Fluctuation

Vavg

constu xyz

1

zeroT

o

u xyzt

time

14.(D)

Centroid of the displaced fluid is also known as

centre of buoyancy.

15.(A)

0.156

0.25c

kr mm

h

Q

rc

r

1or mm

Since 0 cr r

So increasing r will increase the heat Q for upto

6mm radius.

16.(B)

Work and heat are path function and are inexact

differential and boundary phenomena .

17.(14.28%)

For complete combustion of fuel

(stoichiometric):-

3 8 2 2 25 3 4C H O CO H O

But here 10% deficit of 2O than

3 8 2 2 2

92 4

2C H O CO H O CO

So % of CO in exhaust will be

1100 14.28%

7

18.(0.25)

Specific speed

1

5

24

, 2S

NN PN

NH

Now

1 2

1 2

S SN N

H H

1 1 2 2N P N P

2 2

1 1 2 2N P N P

2

1 2

2 1

P N

P N

1

2

1

4

P

P

GATE – 2016

Set - 1


19.(C)

Principle is not similar to the principle of

Stirling gas cycle, Regeneration is constant

pressure in vapor power cycle but constant

volume in stirling cycle.

20.(B)

Jominy test is used for finding hardenability of

test material such as ability up to how much

depth hardness can be achieved.

21.(D)

Twelding > Tbrazing > Tsoldering

22.(C)

The part of a gating system which regulates the

rate of pouring of molten metal is choke area

(minimum area).

23.(A)

Vacuum is required in Electron beam machining

operation to have non dispersive medium for

electron propagation.

24.(0.5)

tan 0.5T

c

F

F

25.(A)

26.(-5)

3 22 3F x x x

1,2x

2' 6 6F x x x

' 0 0 1F x x x

At

0 0 0x F

1, 1 1x F

Now at 1 5 minimumF

2 4 maximumF

Hence minimum value of F x is -5 in

1,2x

27.(-1)

" 9 0, 0 0 23

y y y y

2 9 0D y

A.E.,

2 9 0m

3m i

Now

1 2cos3 sin3y C x C x

1 2' 3 sin3 3 cos3y C x C x

From equation (i)

0 0y

10 C

From equation (i)

22

y

2

32 sin

2C

2 2C

Putting value of 1 2 and in equation (i)C C

2 sin3y x …(ii)

From equation (ii),

14

y

28.(A)

sin 1

e

29.(1.55)

Highest coefficient should be taken for

calculation of x1, x2, x3

1 2 32 3 5x x x …(i)

1 2 32 3 1x x x …(ii)

1 2 33 2 3x x x …(iii)

Largest coefficient of 1x in the above equation

is 3 which is in equation (iii) then from

equation (iii),

1 2 31 0 0

13 2

3x x x

1 1

13 2 0 0 1

3x

In the left equation Largest coefficient of 2x in

the above equation is 3 which is in equation

(ii) then from equation (ii),

2 1 31 1 0

11 2

3x x x

GATE – 2016

Set - 1


2 1

1 21 2 1 0

3 3x

Only left equation is equation (i), then

3 1 21 1 1

15 2

3x x x

3 1

1 2 145 1 2 1.55

3 3 9x

30.(5)

co sm g

20N

s inm g

co s

m g

m g

cos 0.8

sin 0.6

110 cos m 10sin 20

4m

5m kg

31.(B)

3060

TPQ

TRQ w

270

sin30 sin 60 sin90

PQ RQT TW

From above equation we get ,

3 tensilePQT W

2 compressiveRQT W

32.(4)

A B FP

C

Force in AB,

ABF F P

Force in BC,

BCF F

0 givenc

0AB BC

0AB BC

PL PL

AE AE

0

3

F P L FL

A E AE

4.P F

4P

F

33.(21439.05)

Parallel axis theorem

20

8

10

10

X’ x'

x x

34 410 20

8 6465.63 64

xxI mm

M.O.I of inertia about base,

2

' ' ' ' 10x x x xI I A

22

' '

4

' '

6465.6 10 20 8 104

21439.05

x x

x x

I

I mm

34.(0)

3

P

l l lPP

3

PA

3

3 2 2A

P lM l P

2 2A

Pl PlM

0AM

Moment At A = 0, stress is also = 0

GATE – 2016

Set - 1


35.(1)

5KN

800mm

90

5KN

5000 0.2tF r (Turning moment)

1000

1

Nm

KNm

36.(C)

Taking and -vecw ve ccw

23

5

4

T2=60T3=20

100=T4

Condition Arm 5

Gear 2

Gear 3 Gear 4

Arm Fix

Gear 2 +1rev

0 1 60

20

3

203

100

0.6

Into x

0 x 3x

0.6x

Add y

y x y

3x y

0.6x y

2 0N

0x y …(i)

4 100 . .N C CW

4 100N

0.6 100x y

…(ii)

Solving equation (i) and (ii)

62.5, 62.5x y

Speed of arm

5N y

5 62.5N

5 62.5 . .N C CW

37. (A)

k a d

a d I

a

d

c

22 2 23

2 2o c

maI I mr m a ma

Now

0oI K a d a d

223

02

ma K a d

2

23

2

eq

n

eq

K K a d

mma

2

2

2

3n

k a d

ma

38.(C)

1 100MPa

2 100MPa

3 0

200ytS MPa

Maximum shear stress,

max

100 050

2Mpa

fos by TrescaT

Fos by MDEv

Now by Tresca theory

max

2002

2 2 50

yt

T

S

max

2. . .

ytS

F O S

Now by MDE

2 3 2 2 2

1 2 1 2

2002

100 100 100

yt

T

S

Therefore,

T v

GATE – 2016

Set - 1


39. (–2.2 or 2.2)

Pressured left

Column = Pre. At right column

0.08 0.2 0.38airA oil water BP g g g P

2.2 2.2OrA B B AP P KPa P P KPa

40. (22.25)

5 21 10 /oil m s 0.5 10 /m V m s

6 20.89 10 /water m s 0.02d m

Satisfy the dynamic similarities

1 2 5 6

10 0.5 0.2Re Re

10 0.89 10

V

22.15 / sV m

41.(0.33)

Mass out flux tb Vo

b (displacement thickness) Vo

2

01 2o

y yb dy V

3 3b Vo b Vo

3

b vomass bd

bmass ab Vo

0

3 0.33ratio of

VoAm bd

m ab A V

42.(42.22)

10 1000 350d mm To K T K

2300 1000 /T K h w m K

*40 / 16secK w mk

x

o

T Te

T T

ln16o

T T

T T

42.22sec

43.(24530.7)

T3

1200k

800k800k

T4

0.5

0.4T2(527)0C

12 0.26F

Now

4 4

1 2 12 1 1 2Q F A T T

1 2 12265.34 /Q w m

Due to symmetry,

1 2 1 4Q Q

Total heat transfer,

1 1 2 1 4 1 22 24530.68 /Q Q Q Q w m

44.(6.12)

Pr=1 T =500 k

10m/S

1.5m

300k=TS

6 2300 10 /v m s

0.5x m

3.V.Re 166.66 10

L Vx

v

56.12

Reh

xmm

1

3

6.12h

T mm

pr

45.(2443)

343.38 / 298gv m kg T k

0.189dPs Kpa

dTs k

Clausius equation

.

fg

s fg

hdPs

dT TsV

0.189298 43.38

fgh

2443 /fgh kj kg

GATE – 2016

Set - 1


46.(15)

P

V

1

2

100 KPa

200 KPa

0.2m30.1m3

Area under curve is =15 kj

47. (26)

h1

h4

h3 h2

75KPa

3MPa350

1 3115.3 /h KJ kg

3 384.39 /h KJ kg

4 3 fh h v dp

4 387.42 /h KJ kg

1 2 6.7428 1.213 6.2434S S x

0.8856x

2 2402 /

net

add

h KJ kg

Q

Or 1 2 4 3

1 4

h h h h

h h

0.26 26%

48.(.85)

Area under the stress – strain diagram is

toughness:-

21 10.2 10 100 100 140

2 2

2 210.4 10 140 130 0.2 10

2

30.85 /MJ m

49.(50)

2 10 10 / secmass kg Q kw kJ

Time for phase change = 10 sec

. 10 10 at the time of phase changemass L H

. 50 /L H KJ kg

50.(B)

0.14 0.7 0.4VT F d C

1 1 130min 2.0 45 / minT d mm V m

1 0.35f mm

Now 25% increase individually

2 256.25 / min 0.4375V m f mm

2 2.5d mm

Now

0.14 0.7 0.4 0.14 0.7 0.4

1 1 1 1 2 2 2 2VT F d V T F d

2 1.055minT

51.(D)

200mm

100mmPart

2

22 2

V R H

A RH R

.25

2 2

V R H

A H R

&R er

R

VM

A

Hb

Riser

2

2

4

5

4

D HD

DH D

Modulus method

castingRiserM c M

c is ratio of solidification time of riser to casting.

As c is not given it can be assumed 1

1 255

D

125D mm

GATE – 2016

Set - 1


52.(1.92)

22

max 0.08 03 1.92H R mm

53.(A)

33.690(4,3)

2

(4,5)Q

(1,3)P

Q(4.6,2.8)

36.873.18 3 .6x

0 .2y

1 3

l

1 3

l

Rotation by ,

sin 0.6 36.87

Refer above figure,

sin3.18 0.213

cos3.18 3.613

yy

xx

Coordinate of point Q,

1 3.6,3 0.2

4.6,2.8

Q

Q

54.(2)

10,000D per year

100 0.144 100 14.4cC perunit C

2000oC per order

2 2 10,000 2000

14.4

O

c

D CEOQ

C

1666.66EOQ unit

No. of order = 6 per year

Month total in year = 12

Time between two order 12

26

month

55.(B)

1 2maxz 15 20x x

Subjected to

9 Unbounded Solution

432

-4

1 112 4 36x x …(i)

1 212 6 24x x …(ii)

1 2 0x x

Since there is no limit in maximum value of Z,

therefore solution is unbounded.

SELECTIONs IN PSU (MECHANICAL)SELECTIONs IN PSU (MECHANICAL)

AND MANY MORE......

GateMentorprovide a systematic coaching to GATE aspirants in Mechanical Stream. With just a few students in beginning we have grown to a premium institution with more and more students selecting us as their success partner every year. Our methodology and the subject knowledge has been our core strength. The results of our students every year is a proof of this fact. Our students are placed in every IIT and PSU in the country.The different programs provided by us for GATE and Public sector exams preparation, have been carefully designed and developed over the years. The course material and various offline/online tests provided by us are proven to be helpful to the students.From a modest beginning in 2008, GateMentor, has now grown into a fully integrated coaching institute. Every year GateMentor students achieved under 100 rank (AIR) in GATE examination. Almost every student crack Gate exam from our coaching centre. We are now in the Eight year of our existence. Almost twenty five batches of students have passed out with successful placement in the technical world and other organizations by clearing GATE exam.

was started by Mr. Arvind Rai, an alumnus of IIT Kharagpur, to

About GATEMENTORAbout GATEMENTOR

OfficeOffice

Plot No. A-213, Street No.-27Smriti Nagar, BhilaiPhone : 0788-6499334

Website

Email [email protected]

www.gatementor.co.in

erycMechanical

GATEMENTOR

eryc

GateMentor CentresGateMentor CentresBHILAI RAIPUR

0788-6499334 0771-6003456

gate-2016 mechanical set-1 full solution

Documents