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GATE (Graduate Aptitude Test in Engineering) Mechanical Engineering is an online examination conducted to get admission in M-Tech (Masters in Technology), ME (Master of Engineering ) and PhD at IITs (Indian Institutes of Technology), NITs (National Institutes of Technology), IIITs (Indian Institutes of Information Technology) and other universities in India. GATE exam is jointly conducted by IIT Bombay, IIT Delhi, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT Madras, IIT Roorkee and Indian Institute for Science, Bangalore (IISC Bangalore). The exam is divided into two different parts General Aptitude (GA) and Candidate’s Selected Subject (Core Subjects). GATE Mechanical Engineering online mock tests help candidates in preparing for the GATE exam. By attempting GATE online mock tests candidates get familiar with the pattern of actual question paper. BrPaper provides all GATE question papers completely free. Here you can practice free online mock tests of complete exam exam of GATE Mechanical Engineering. We advise candidates to solve the online GATE Mechanical Engineering mock tests to get good marks in the exam. Start practicing Mechanical GATE 2019 Mock tests here online for free

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Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 1:

Once the team of analysts identify the problem, we _________ in a better position to comment on the issue Which one of the following choices CANNOT fill the given blank?

A	will be	B	were to be
C	are going to be	D	might be

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 2:

A final examination is the _________ of a series of evaluations that a student has to go through.

A	culmination	B	consultation
C	consultation	D	insinuation

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 3:

If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = ____.

A	JDE	B	JED
C	JDC	D	JCD

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 4:

The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

A	6	B	7
C	8	D	9.5

All of these

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 5:

Are there enough seats here? There are ________ people here than I expected.

A	many	B	most
C	least	D	more

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 6:

Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ___.

A	37.50	B	35.70
C	25.00	D	10.00

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 7:

Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is ____.

A	13.50	B	14.50
C	15.50	D	16.50

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 8:

While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and in Manhattan penthouses with clinking ice cubes. This was, till an eminent Caribbean writer gave the writers in the once-colonised countries the confidence to see the shabby lives around them as worthy of being “told”. The writer of this passage is surprised by the creative writing assignments of his students, because _____________.

A	Some of the students had written stories set in foreign places
B	None of the students had written stories set in India
C	None of the students had written about ice cubes and cowboys
D	Some of the students had written about ice cubes and cowboys

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 9:

Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?

Type	Month
Type	January	February	March	April
Pool	170	320	215	190
Mini	110	220	180	70
Prime	75	180	120	90

A	16.24	B	23.97
C	25.86	D	38.74

Category: GATE Mechanical Engineering 2019 set 2 General Aptitude

Question 10:

X is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, X is almost forcing its customers towards its loyalty membership. If its loyalty membership continues to grow at its current rate, within the next eight years more households will be watching X than cable television. Which one of the following statements can be inferred from the above paragraph?

A	Most households that subscribe to X’s loyalty membership discontinue watching cable television
B	Non-members prefer to watch cable television
C	Cable television operators don’t subscribe to X’s loyalty membership
D	The X is cancelling accounts of non-members

Category: GATE Mechanical Engineering 2019 set 2

Question 11:

In matrix equation

[A] \{X\} = \{R\}

[A] = [\begin{matrix} 4 & 8 & 4 \\ 8 & 16 & - 4 \\ 4 & - 4 & 15 \end{matrix}], \{X\} = \{\begin{matrix} 2 \\ 1 \\ 4 \end{matrix}\} a n d \{R\} = \{\begin{matrix} 32 \\ 16 \\ 64 \end{matrix}\}

One of the eigenvalues of matrix

[A]

A	4	B	8
C	15	D	16

Category: GATE Mechanical Engineering 2019 set 2

Question 12:

The directional derivative of the function

f (x, y) = x^{2} + y^{2}

along a line directed from (0,0) to (1,1), evaluated at the point x=1, y=1 is

A	$\sqrt{2}$	B	2
C	$2 \sqrt{2}$	D	$4 \sqrt{2}$

Category: GATE Mechanical Engineering 2019 set 2

Question 13:

The differential equation

\frac{d y}{d x} + 4 y = 5

is valid in the domain

0 \leq x \leq 1

with y(0)=2.25. The solution of the differential equation is

A	$y = e^{- 4 x} + 5$	B	$y = e^{- 4 x} + 1.25$
C	$y = e^{4 x} + 5$	D	$y = e^{4 x} + 1.25$

Category: GATE Mechanical Engineering 2019 set 2

Question 14:

An analytic function

f (z)

of complex variable z= x + i y may be written as f(z)=u(x, y)+iv(x, y). Then, u(x, y) and v(x, y) must satisfy

A	$\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} a n d \frac{\partial u}{\partial y} = \frac{\partial v}{\partial x}$	B	$\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} a n d \frac{\partial u}{\partial y} = - \frac{\partial v}{\partial x}$
C	$\frac{\partial u}{\partial x} = - \frac{\partial v}{\partial y} a n d \frac{\partial u}{\partial y} = \frac{\partial v}{\partial x}$	D	$\frac{\partial u}{\partial x} = - \frac{\partial v}{\partial y} a n d \frac{\partial u}{\partial y} = - \frac{\partial v}{\partial x}$

Category: GATE Mechanical Engineering 2019 set 2

Question 15:

A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of points P and R are

V_{p}

and

V_{R}

, in the x and y directions, respectively. The magnitude of the angular velocity of the body is

A	$2 V_{R}$	B	$2 V_{p}$
C	$V_{R} / \sqrt{3}$	D	$V_{p} / \sqrt{3}$

Category: GATE Mechanical Engineering 2019 set 2

Question 16:

Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensilestress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young’s modulus E = 200 MPa and Poisson’s ratio ν = 0.3 are given. The principal strains in the plane of the sheet are

A	(0.35, −0.15)	B	(0.5, 0.0)
C	(0.5, −0.15)	D	(0.5, −0.5)

Category: GATE Mechanical Engineering 2019 set 2

Question 17:

A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is

A	$\frac{πD}{T}$	B	$\frac{T}{D}$
C	$\frac{D}{T}$	D	$\frac{2 πD}{T}$

Category: GATE Mechanical Engineering 2019 set 2

Question 18:

Endurance limit of a beam subjected to pure bending decreases with

A	decrease in the surface roughness and decrease in the size of the beam
B	increase in the surface roughness and decrease in the size of the beam
C	increase in the surface roughness and increase in the size of the beam
D	decrease in the surface roughness and increase in the size of the beam

Category: GATE Mechanical Engineering 2019 set 2

Question 19:

A two-dimensional incompressible frictionless flow field is given by

\vec{u} = x \hat{i} - y \hat{j} .

If ρ is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as

A	$ρ (x \hat{i} + y \hat{j})$	B	$- ρ (x \hat{i} + y \hat{j})$
C	$ρ (x \hat{i} - y \hat{j})$	D	$- ρ (x^{2} \hat{i} + y^{2} \hat{j})$

Category: GATE Mechanical Engineering 2019 set 2

Question 20:

Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4 m. The view factor

F_{12}

A	0.0625	B	0.25
C	0.5	D	1.0

Category: GATE Mechanical Engineering 2019 set 2

Question 21:

One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is

A	Linear	B	Quadratic
C	Logarithmic	D	Exponential

Category: GATE Mechanical Engineering 2019 set 2

Question 22:

For a simple compressible system, v s p and T are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell’s relations,

{(\frac{\partial v}{\partial s})}_{p}

is equal to

A	${(\frac{\partial s}{\partial T})}_{p}$	B	${(\frac{\partial p}{\partial v})}_{T}$
C	$- {(\frac{\partial T}{\partial v})}_{p}$	D	${(\frac{\partial T}{\partial p})}_{s}$

Category: GATE Mechanical Engineering 2019 set 2

Question 23:

Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet?

A	Increasing the boiler pressure.
B	Decreasing the boiler pressure.
C	Increasing the turbine inlet temperature.
D	Decreasing the condenser pressure.

Category: GATE Mechanical Engineering 2019 set 2

Question 24:

Hardenability of steel is a measure of

A	the ability to harden when it is cold worked
B	the maximum hardness that can be obtained when it is austenitized and then quenched
C	the depth to which required hardening is obtained when it is austenitized and then quenched
D	the ability to retain its hardness when it is heated to elevated temperatures

Category: GATE Mechanical Engineering 2019 set 2

Question 25:

The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in

A	viscosity	B	surface tension
C	freezing range	D	degree of superheat

Category: GATE Mechanical Engineering 2019 set 2

Question 26:

The cold forming process in which a hardened tool is pressed against a workpiece (when there is relative motion between the tool and the workpiece) to produce a roughened surface with a regular pattern is

A	Roll forming	B	Strip rolling
C	Knurling	D	Chamfering

Category: GATE Mechanical Engineering 2019 set 2

Question 27:

The most common limit gage used for inspecting the hole diameter is

A	Snap gage	B	Ring gage
C	Plug gage	D	Master gage

Category: GATE Mechanical Engineering 2019 set 2

Question 28:

The transformation matrix for mirroring a point in x - y plane about the line y = x is given by

A	$[\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}]$	B	$[\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}]$
C	$[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$	D	$[\begin{matrix} 0 & - 1 \\ - 1 & 0 \end{matrix}]$

Category: GATE Mechanical Engineering 2019 set 2

Question 29:

If x is the mean of data 3, x, 2 and 4, then the mode is____

3 to 3

3 to 4

2 to 3

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 30:

The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A, then the magnitude of the force produced in member CD is ______ N.

0 to -0

-1 to 0

0 to 0

Category: GATE Mechanical Engineering 2019 set 2

Question 31:

The state of stress at a point in a component is represented by a Mohr’s circle of radius 100 MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane atthe same point is ______ MPa.

70 to 77

79 to 81

56 to 73

none of these

Category: GATE Mechanical Engineering 2019 set 2

Question 32:

A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ______ MPa.

49 to 51

Category: GATE Mechanical Engineering 2019 set 2

Question 33:

Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number

R e_{D}

= 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is ______.

500 to 600

500 to 500

600 to 600

none of these

Category: GATE Mechanical Engineering 2019 set 2

Question 34:

A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings, and the properties of the surrounding fluid, are constant. The relationship between the average Nusselt and Rayleigh numbers is given as

N u = K R a^{1 / 4}

where K is a constant. The length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is

h_{1}

and that for the second plate is

h_{2}

, the value of the ratio

h_{1} / h_{2}

is _____.

2 to 2

0 to 2

2 to 0

none of these

Category: GATE Mechanical Engineering 2019 set 2

Question 35:

In an electrical discharge machining process, the breakdown voltage across inter electrode gap (IEG) is 200 V and the capacitance of the RC circuit is 50 µF. The energy (in J) released per spark across the IEG is____

-1 to 1

0 to 1

1 to 1

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 36:

Given a vector

\vec{u} = \frac{1}{3} (- y^{3} \hat{i} + x^{3} \hat{j} + z^{3} \hat{k})

and

\hat{n}

as the unit normal vector to the surface of the hemisphere

(x^{2} + y^{2} + z^{2} = 1; z \geq 0),

the value of integral

\int (\nabla \times \vec{u})

•

\hat{n}

dS evaluated on the curved surface of the hemisphere S is

A	$- \frac{π}{2}$	B	$\frac{π}{3}$
C	$\frac{π}{2}$	D	$π$

Category: GATE Mechanical Engineering 2019 set 2

Question 37:

A differential equation is given as

x^{2} \frac{d^{2} y}{d x^{2}} - 2 x \frac{d y}{d x} + 2 y = 4

. The solution of the differential equation in terms of arbitrary constants

C_{1} a n d C_{2}

A	$y = C_{1} x^{2} + C_{2} x + 2$	B	$y = \frac{C_{1}}{x^{2}} + C_{2} x + 2$
C	$y = C_{1} x^{2} + C_{2} x + 4$	D	$y = \frac{C_{1}}{x^{2}} + C_{2} x + 4$

Category: GATE Mechanical Engineering 2019 set 2

Question 38:

The derivative of f(x) = cos(x) can be estimated using the approximation f'(x) =

\frac{f (x + h) - f (x - h)}{2 h}

. The percentage error is calculated as

(\frac{E x a c t v a l u e - A p p r o x i m a t e v a l u e}{E x a c t v a l u e}) x 100 .

The percentage error in the derivative of f (x) at x=

π

/6 radian, choosing h =0.1 radian, is

A	$< 0.1 %$	B	>0.1 % and <1 %
C	> 1 % and < 5 %	D	> 5 %

Category: GATE Mechanical Engineering 2019 set 2

Question 39:

A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value(s) of m is/are

A	1 kg only	B	6 kg only
C	1 kg, 6 kg	D	1 kg, 9 kg

Category: GATE Mechanical Engineering 2019 set 2

Question 40:

Consider two concentric circular cylinders of different materials M and N in contact with each other at 𝑟 = 𝑏, as shown below. The interface at 𝑟 = 𝑏 is frictionless. The composite cylinder system is subjected to internal pressure

P L e t (u_{r}^{m}, u_{θ}^{M}) a n d (σ_{r r}^{M}, σ_{θ θ}^{M})

denote the radial and tangential displacement and stress components, respectively, in material M. Similarly,

(u_{r}^{N}, u_{θ}^{N}) a n d (σ_{r r}^{N}, σ_{θ θ}^{N})

denote the radial and tangential displacement and stress components, respectively, in material N. The boundary conditions that need to be satisfied at the frictionless interface between the two cylinders are:

A	$u_{r}^{M} = u_{r}^{N} a n d σ_{r r}^{M} = σ_{r r}^{N} o n l y$
B	$u_{r}^{M} = u_{r}^{N} a n d σ_{r r}^{M} a n d σ_{θ θ}^{M} = σ_{θ θ}^{N}$
C	$u_{θ}^{M} = u_{θ}^{N} a n d σ_{θ θ}^{M} = σ_{θ θ}^{N} o n l y$
D	$σ_{r r}^{M} = σ_{r r}^{N} a n d σ_{θ θ}^{M} = σ_{θ θ}^{N} o n l y$

Category: GATE Mechanical Engineering 2019 set 2

Question 41:

A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young’s modulus E, and area moment of inertia I, the magnitude of the maximum deflection is

A	$\frac{q L^{4}}{15 E I}$	B	$\frac{q L^{4}}{30 E I}$
C	$\frac{q L^{4}}{10 E I}$	D	$\frac{q L^{4}}{60 E I}$

Category: GATE Mechanical Engineering 2019 set 2

Question 42:

A slender uniform rigid bar of mass 𝑚 is hinged at O and supported by two springs, with stiffnesses 3𝑘 and 𝑘, and a damper with damping coefficient 𝑐, as shown in the figure. For the system to be critically damped, the ratio 𝑐/

\sqrt{k m}

should be.

A	2	B	4
C	$2 \sqrt{7}$	D	$4 \sqrt{7}$

Category: GATE Mechanical Engineering 2019 set 2

Question 43:

The figure shows a heat engine (HE) working between two reservoirs. The amount of heat

(Q_{2})

rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output (W) of the heat engine. If temperatures,

T_{1} > T_{3} > T_{2},

then the relation between the efficiency (η) of the heat engine and the coefficient of performance (COP) of the heat pump is

A	COP=η	B	COP=1+η
C	COP= $η^{- 1}$	D	COP= $η^{- 1} - 1$

Category: GATE Mechanical Engineering 2019 set 2

Question 44:

The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in weight percent) at 1250 °C, respectively, will be

A	77.8% and 22.2%	B	22.2% and 77.8%
C	68.0% and 32.0%	D	32.0% and 68.0%

Category: GATE Mechanical Engineering 2019 set 2

Question 45:

The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship “X < Y, Z” means that X is predecessor of activities Y and Z. The time to complete the activities along the critical path is ______ weeks.

Activity	Duration (Weeks)	Precedence Relationship
A	5	A<B,C,D
B	7	B<E,F,G
C	10	C<I
D	6	D<G
E	3	E<H
F	9	F<I
G	7	G<I
H	4	H<I
I	2	----

A	17	B	21
C	23	D	25

Category: GATE Mechanical Engineering 2019 set 2

Question 46:

The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity 𝜔, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where the crank is parallel to x-axis, is given by

A	- $ω^{2} r$	B	$2 ω^{2} r$
C	$ω^{2} r$	D	$- 2 ω^{2} r$

Category: GATE Mechanical Engineering 2019 set 2

Question 47:

A horizontal cantilever beam of circular cross-section, length 1.0 m and flexural rigidity

E I = 200 N \cdot m^{2}

is subjected to an applied moment

M_{A} = 1.0 N \cdot m

at the free ends as shown in the figure. The magnitude of the vertical deflection of the free end is_______ off to one decimal place).

2.4 to 2.6

2.3 to 2.9

2.7 to 2.8

none of these

Category: GATE Mechanical Engineering 2019 set 2

Question 48:

Two masses A and B having mass

m_{a}

and

m_{b}

, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses

m_{a}

and

m_{b}

are

r_{a}

and

r_{b}

, respectively. The angle between lines OA and OB is 90°. If

m_{a} = 10 k g, m_{b} = 20 k g, r_{a} = 200 m m a n d r_{b} = 400 m m,

then the balance mass to be placed at a radius of 200 mm is ______ kg (round off to two decimal places).

41.00 to 42.50

41.50 to 42.00

41.00 to 42.00

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 49:

A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed

ω_{2}

. Length of different links are:

O_{2} O_{4} = O_{2} A = L, A B = O_{4} B = \sqrt{2} L .

The magnitude of the angular speed of the output link 4 is

ω_{4}

at the instant when link 2 makes an angle of 90º with

O_{2} O_{4}

as shown. The ratio

\frac{ω_{4}}{ω_{2}}

is ______ (round off to two decimal places).

0.77 to 0.70

0.78 to 0.80

0.68 to 0.84

0.76 to 0.80

Category: GATE Mechanical Engineering 2019 set 2

Question 50:

The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts will be defective is ______ (round off to two decimal places).

0.16 to 0.18

0.15 to 0.17

0.16 to 0.17

0.14 to 0.18

Category: GATE Mechanical Engineering 2019 set 2

Question 51:

A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular speed 𝜔, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical axis at

ω_{p} = ω / 10

in the clockwise direction when viewed from above. Let

R_{p}

and

R_{Q}

(positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming

ω^{2} r = 300 m / s^{2} a n d g = 10 m / s^{2},

the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is _______

3 to -3

-3 to 3

3 to 3

-3 to -3

Category: GATE Mechanical Engineering 2019 set 2

Question 52:

Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates

Q_{B} / Q_{A}

is______ (round off to two decimal places).

0.38 to 0.52

0.48 to 0.52

0.58 to 0.62

0.46 to 0.52

Category: GATE Mechanical Engineering 2019 set 2

Question 53:

The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1 with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same amount of power needed to overcome the aerodynamic drag, the speed of the car with the windows and roof open (round off to two decimal places), is ________ km/h (The density of air and the frontal area may be assumed to be constant).

21.90 to 22.20

22.20 to 22.90

21.00 to 22.00

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 54:

Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor

F_{I J}

is defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the values of

F_{L M} a n d F_{N R}

are 0.8 and 0.4, respectively. The value of

F_{P Q}

(round off to one decimal place) is ______.

6.0 to 6.6

0.6 to 0.0

0.6 to 0.6

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 55:

Water flowing at the rate of 1 kg/s through a system is heated using an electric heater such that the specific enthalpy of the water increases by 2.50 kJ/kg and the specific entropy increases by 0.007 kJ/kg·K. The power input to the electric heater is 2.50 kW. There is no other work or heat interaction between the system and the surroundings. Assuming an ambient temperature of 300 K, the irreversibility rate of the system is ______ kW (round off to two decimal places).

2.05 to 2.15

1.05 to 2.50

2.00 to 2.10

2.50 to 2.50

Category: GATE Mechanical Engineering 2019 set 2

Question 56:

An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is ______ kg/s (round off to two decimal places).

8.20 to 8.20

8.00 to 8.00

8.00 to 8.20

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 57:

An air standard Otto cycle has thermal efficiency of 0.5 and the mean effective pressure of the cycle is 1000 kPa. For air, assume specific heat ratio γ = 1.4 and specific gas constant R = 0.287 kJ/kg·K. If the pressure and temperature at the beginning of the compression stroke are 100 kPa and 300 K, respectively, then the specific net work output of the cycle is ______ kJ/kg (round off to two decimal places).

705.50 to 715.00

705.00 to 715.50

705.50 to 715.50

705.00 to 715.00

Category: GATE Mechanical Engineering 2019 set 2

Question 58:

The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is 9.81

m / s^{2}

. The time (in s, round off to two decimal places) to fill up the mold cavity (of size 40 cm 30 x cm x 15 cm) is____

28.80 to 29.80

28.80 to 29.00

27.00 to 28.00

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 59:

A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of 20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input per unit length of the weld will be ______ kJ/mm (round off to one decimal place).

0.26 to 1.26

0.7 to 1.26

0.7 to 0.26

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 60:

The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ______ mm (round off to two decimal places).

1.24 to 1.26

0.24 to 1.26

1.24 to 1.24

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 61:

A through hole is drilled in an aluminum alloy plate of 15 mm thickness with a drill bit of diameter 10 mm, at a feed of 0.25 mm/rev and a spindle speed of 1200 rpm. If the specific energy required for cutting this material is 0.7 N·m/

m m^{3}

, the power required for drilling is ______ W (round off to two decimal places).

274.50 to 276.00

274.00 to 276.50

274.00 to 276.00

274.50 to 276.50

Category: GATE Mechanical Engineering 2019 set 2

Question 62:

In an orthogonal machining with a single point cutting tool of rake angle 10°, the uncut chip thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchant’s first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool interface is ______ (round off to two decimal places).

1.72 to 1.76

0.84 to 0.76

0.72 to 1.76

0.72 to .76

Category: GATE Mechanical Engineering 2019 set 2

Question 63:

The annual demand of valves per year in a company is 10,000 units. The current order quantity is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs. 400 per order. If the current order quantity is changed to Economic Order Quantity, then the saving in the total cost of inventory per year will be Rs. ______ (round off to two decimal places).

941.50 to 946.00

941.00 to 946.00

941.50 to 946.50

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 64:

Hot and cold fluids enter a parallel flow double tube heat exchanger at 100 °C and 15 °C, respectively. The heat capacity rates of hot and cold fluids are

C_{h}

= 2000 W/K and

C_{c}

= 1200 W/K, respectively. If the outlet temperature of the cold fluid is 45 °C, the log mean temperature difference (LMTD) of the heat exchanger is _________ K (round off to two decimal places).

56.00 to 58.50

57.50 to 58.50

57.00 to 58.00

None of these

Category: GATE Mechanical Engineering 2019 set 2

Question 65:

A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500 mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in the figure. The drum is rotating anti-clockwise. The braking torque on the drum is ______ N·m (round off to two decimal places).

17.00 to 22.00

19.00 to 21.00

20.00 to 21.00

19.00 to 19.00

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Answered & Marked for Review (will be considered for evaluation)

Question 1:

Once the team of analysts identify the problem, we _________ in a better position to comment on the issue Which one of the following choices CANNOT fill the given blank?

A	will be	B	were to be
C	are going to be	D	might be

Correct Answer : B

Question 2:

A final examination is the _________ of a series of evaluations that a student has to go through.

A	culmination	B	consultation
C	consultation	D	insinuation

Correct Answer : A

Question 3:

If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = ____.

A	JDE	B	JED
C	JDC	D	JCD

Correct Answer : B

Question 4:

The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

A	6	B	7
C	8	D	9.5

Correct Answer : All of these

Question 5:

Are there enough seats here? There are ________ people here than I expected.

A	many	B	most
C	least	D	more

Correct Answer : D

Question 6:

Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ___.

A	37.50	B	35.70
C	25.00	D	10.00

Correct Answer : A

Question 7:

A	13.50	B	14.50
C	15.50	D	16.50

Correct Answer : B

Question 8:

A	Some of the students had written stories set in foreign places
B	None of the students had written stories set in India
C	None of the students had written about ice cubes and cowboys
D	Some of the students had written about ice cubes and cowboys

Correct Answer : B

Question 9:

Type	Month
Type	January	February	March	April
Pool	170	320	215	190
Mini	110	220	180	70
Prime	75	180	120	90

A	16.24	B	23.97
C	25.86	D	38.74

Correct Answer : B

Question 10:

A	Most households that subscribe to X’s loyalty membership discontinue watching cable television
B	Non-members prefer to watch cable television
C	Cable television operators don’t subscribe to X’s loyalty membership
D	The X is cancelling accounts of non-members

Correct Answer : A

Question 11:

In matrix equation

[A] \{X\} = \{R\}

[A] = [\begin{matrix} 4 & 8 & 4 \\ 8 & 16 & - 4 \\ 4 & - 4 & 15 \end{matrix}], \{X\} = \{\begin{matrix} 2 \\ 1 \\ 4 \end{matrix}\} a n d \{R\} = \{\begin{matrix} 32 \\ 16 \\ 64 \end{matrix}\}

One of the eigenvalues of matrix

[A]

A	4	B	8
C	15	D	16

Correct Answer : D

Question 12:

The directional derivative of the function

f (x, y) = x^{2} + y^{2}

along a line directed from (0,0) to (1,1), evaluated at the point x=1, y=1 is

A	$\sqrt{2}$	B	2
C	$2 \sqrt{2}$	D	$4 \sqrt{2}$

Correct Answer : C

Question 13:

The differential equation

\frac{d y}{d x} + 4 y = 5

is valid in the domain

0 \leq x \leq 1

with y(0)=2.25. The solution of the differential equation is

A	$y = e^{- 4 x} + 5$	B	$y = e^{- 4 x} + 1.25$
C	$y = e^{4 x} + 5$	D	$y = e^{4 x} + 1.25$

Correct Answer : B

Question 14:

An analytic function

f (z)

of complex variable z= x + i y may be written as f(z)=u(x, y)+iv(x, y). Then, u(x, y) and v(x, y) must satisfy

A	$\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} a n d \frac{\partial u}{\partial y} = \frac{\partial v}{\partial x}$	B	$\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} a n d \frac{\partial u}{\partial y} = - \frac{\partial v}{\partial x}$
C	$\frac{\partial u}{\partial x} = - \frac{\partial v}{\partial y} a n d \frac{\partial u}{\partial y} = \frac{\partial v}{\partial x}$	D	$\frac{\partial u}{\partial x} = - \frac{\partial v}{\partial y} a n d \frac{\partial u}{\partial y} = - \frac{\partial v}{\partial x}$

Correct Answer : B

Question 15:

V_{p}

and

V_{R}

, in the x and y directions, respectively. The magnitude of the angular velocity of the body is

A	$2 V_{R}$	B	$2 V_{p}$
C	$V_{R} / \sqrt{3}$	D	$V_{p} / \sqrt{3}$

Correct Answer : A

Question 16:

A	(0.35, −0.15)	B	(0.5, 0.0)
C	(0.5, −0.15)	D	(0.5, −0.5)

Correct Answer : C

Question 17:

A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is

A	$\frac{πD}{T}$	B	$\frac{T}{D}$
C	$\frac{D}{T}$	D	$\frac{2 πD}{T}$

Correct Answer : C

Question 18:

Endurance limit of a beam subjected to pure bending decreases with

A	decrease in the surface roughness and decrease in the size of the beam
B	increase in the surface roughness and decrease in the size of the beam
C	increase in the surface roughness and increase in the size of the beam
D	decrease in the surface roughness and increase in the size of the beam

Correct Answer : C

Question 19:

A two-dimensional incompressible frictionless flow field is given by

\vec{u} = x \hat{i} - y \hat{j} .

If ρ is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as

A	$ρ (x \hat{i} + y \hat{j})$	B	$- ρ (x \hat{i} + y \hat{j})$
C	$ρ (x \hat{i} - y \hat{j})$	D	$- ρ (x^{2} \hat{i} + y^{2} \hat{j})$

Correct Answer : B

Question 20:

Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4 m. The view factor

F_{12}

A	0.0625	B	0.25
C	0.5	D	1.0

Correct Answer : D

Question 21:

A	Linear	B	Quadratic
C	Logarithmic	D	Exponential

Correct Answer : C

Question 22:

For a simple compressible system, v s p and T are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell’s relations,

{(\frac{\partial v}{\partial s})}_{p}

is equal to

A	${(\frac{\partial s}{\partial T})}_{p}$	B	${(\frac{\partial p}{\partial v})}_{T}$
C	$- {(\frac{\partial T}{\partial v})}_{p}$	D	${(\frac{\partial T}{\partial p})}_{s}$

Correct Answer : D

Question 23:

Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet?

A	Increasing the boiler pressure.
B	Decreasing the boiler pressure.
C	Increasing the turbine inlet temperature.
D	Decreasing the condenser pressure.

Correct Answer : C

Question 24:

Hardenability of steel is a measure of

A	the ability to harden when it is cold worked
B	the maximum hardness that can be obtained when it is austenitized and then quenched
C	the depth to which required hardening is obtained when it is austenitized and then quenched
D	the ability to retain its hardness when it is heated to elevated temperatures

Correct Answer : C

Question 25:

The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in

A	viscosity	B	surface tension
C	freezing range	D	degree of superheat

Correct Answer : D

Question 26:

A	Roll forming	B	Strip rolling
C	Knurling	D	Chamfering

Correct Answer : C

Question 27:

The most common limit gage used for inspecting the hole diameter is

A	Snap gage	B	Ring gage
C	Plug gage	D	Master gage

Correct Answer : C

Question 28:

The transformation matrix for mirroring a point in x - y plane about the line y = x is given by

A	$[\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}]$	B	$[\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}]$
C	$[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$	D	$[\begin{matrix} 0 & - 1 \\ - 1 & 0 \end{matrix}]$

Correct Answer : C

Question 29:

If x is the mean of data 3, x, 2 and 4, then the mode is____

Correct Answer : 3 to 3

Question 30:

The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A, then the magnitude of the force produced in member CD is ______ N.

Correct Answer : 0 to 0

Question 31:

Correct Answer : 79 to 81

Question 32:

Correct Answer : 49 to 51

Question 33:

Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number

R e_{D}

= 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is ______.

Correct Answer : 500 to 500

Question 34:

N u = K R a^{1 / 4}

where K is a constant. The length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is

h_{1}

and that for the second plate is

h_{2}

, the value of the ratio

h_{1} / h_{2}

is _____.

Correct Answer : 2 to 2

Question 35:

Correct Answer : 1 to 1

Question 36:

Given a vector

\vec{u} = \frac{1}{3} (- y^{3} \hat{i} + x^{3} \hat{j} + z^{3} \hat{k})

and

\hat{n}

as the unit normal vector to the surface of the hemisphere

(x^{2} + y^{2} + z^{2} = 1; z \geq 0),

the value of integral

\int (\nabla \times \vec{u})

•

\hat{n}

dS evaluated on the curved surface of the hemisphere S is

A	$- \frac{π}{2}$	B	$\frac{π}{3}$
C	$\frac{π}{2}$	D	$π$

Correct Answer : C

Question 37:

A differential equation is given as

x^{2} \frac{d^{2} y}{d x^{2}} - 2 x \frac{d y}{d x} + 2 y = 4

. The solution of the differential equation in terms of arbitrary constants

C_{1} a n d C_{2}

A	$y = C_{1} x^{2} + C_{2} x + 2$	B	$y = \frac{C_{1}}{x^{2}} + C_{2} x + 2$
C	$y = C_{1} x^{2} + C_{2} x + 4$	D	$y = \frac{C_{1}}{x^{2}} + C_{2} x + 4$

Correct Answer : A

Question 38:

The derivative of f(x) = cos(x) can be estimated using the approximation f'(x) =

\frac{f (x + h) - f (x - h)}{2 h}

. The percentage error is calculated as

(\frac{E x a c t v a l u e - A p p r o x i m a t e v a l u e}{E x a c t v a l u e}) x 100 .

The percentage error in the derivative of f (x) at x=

π

/6 radian, choosing h =0.1 radian, is

A	$< 0.1 %$	B	>0.1 % and <1 %
C	> 1 % and < 5 %	D	> 5 %

Correct Answer : B

Question 39:

A	1 kg only	B	6 kg only
C	1 kg, 6 kg	D	1 kg, 9 kg

Correct Answer : D

Question 40:

P L e t (u_{r}^{m}, u_{θ}^{M}) a n d (σ_{r r}^{M}, σ_{θ θ}^{M})

denote the radial and tangential displacement and stress components, respectively, in material M. Similarly,

(u_{r}^{N}, u_{θ}^{N}) a n d (σ_{r r}^{N}, σ_{θ θ}^{N})

A	$u_{r}^{M} = u_{r}^{N} a n d σ_{r r}^{M} = σ_{r r}^{N} o n l y$
B	$u_{r}^{M} = u_{r}^{N} a n d σ_{r r}^{M} a n d σ_{θ θ}^{M} = σ_{θ θ}^{N}$
C	$u_{θ}^{M} = u_{θ}^{N} a n d σ_{θ θ}^{M} = σ_{θ θ}^{N} o n l y$
D	$σ_{r r}^{M} = σ_{r r}^{N} a n d σ_{θ θ}^{M} = σ_{θ θ}^{N} o n l y$

Correct Answer : A

Question 41:

A	$\frac{q L^{4}}{15 E I}$	B	$\frac{q L^{4}}{30 E I}$
C	$\frac{q L^{4}}{10 E I}$	D	$\frac{q L^{4}}{60 E I}$

Correct Answer : B

Question 42:

\sqrt{k m}

should be.

A	2	B	4
C	$2 \sqrt{7}$	D	$4 \sqrt{7}$

Correct Answer : D

Question 43:

The figure shows a heat engine (HE) working between two reservoirs. The amount of heat

(Q_{2})

rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output (W) of the heat engine. If temperatures,

T_{1} > T_{3} > T_{2},

then the relation between the efficiency (η) of the heat engine and the coefficient of performance (COP) of the heat pump is

A	COP=η	B	COP=1+η
C	COP= $η^{- 1}$	D	COP= $η^{- 1} - 1$

Correct Answer : C

Question 44:

A	77.8% and 22.2%	B	22.2% and 77.8%
C	68.0% and 32.0%	D	32.0% and 68.0%

Correct Answer : B

Question 45:

Activity	Duration (Weeks)	Precedence Relationship
A	5	A<B,C,D
B	7	B<E,F,G
C	10	C<I
D	6	D<G
E	3	E<H
F	9	F<I
G	7	G<I
H	4	H<I
I	2	----

A	17	B	21
C	23	D	25

Correct Answer : C

Question 46:

The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity 𝜔, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where the crank is parallel to x-axis, is given by

A	- $ω^{2} r$	B	$2 ω^{2} r$
C	$ω^{2} r$	D	$- 2 ω^{2} r$

Correct Answer : C

Question 47:

A horizontal cantilever beam of circular cross-section, length 1.0 m and flexural rigidity

E I = 200 N \cdot m^{2}

is subjected to an applied moment

M_{A} = 1.0 N \cdot m

at the free ends as shown in the figure. The magnitude of the vertical deflection of the free end is_______ off to one decimal place).

Correct Answer : 2.4 to 2.6

Question 48:

Two masses A and B having mass

m_{a}

and

m_{b}

m_{a}

and

m_{b}

are

r_{a}

and

r_{b}

, respectively. The angle between lines OA and OB is 90°. If

m_{a} = 10 k g, m_{b} = 20 k g, r_{a} = 200 m m a n d r_{b} = 400 m m,

then the balance mass to be placed at a radius of 200 mm is ______ kg (round off to two decimal places).

Correct Answer : 41.00 to 42.00

Question 49:

A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed

ω_{2}

. Length of different links are:

O_{2} O_{4} = O_{2} A = L, A B = O_{4} B = \sqrt{2} L .

The magnitude of the angular speed of the output link 4 is

ω_{4}

at the instant when link 2 makes an angle of 90º with

O_{2} O_{4}

as shown. The ratio

\frac{ω_{4}}{ω_{2}}

is ______ (round off to two decimal places).

Correct Answer : 0.78 to 0.80

Question 50:

Correct Answer : 0.16 to 0.18

Question 51:

ω_{p} = ω / 10

in the clockwise direction when viewed from above. Let

R_{p}

and

R_{Q}

(positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming

ω^{2} r = 300 m / s^{2} a n d g = 10 m / s^{2},

the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is _______

Correct Answer : -3 to -3

Question 52:

Q_{B} / Q_{A}

is______ (round off to two decimal places).

Correct Answer : 0.48 to 0.52

Question 53:

Correct Answer : 21.90 to 22.20

Question 54:

Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor

F_{I J}

is defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the values of

F_{L M} a n d F_{N R}

are 0.8 and 0.4, respectively. The value of

F_{P Q}

(round off to one decimal place) is ______.

Correct Answer : 0.6 to 0.6

Question 55:

Correct Answer : 2.05 to 2.15

Question 56:

Correct Answer : 8.00 to 8.20

Question 57:

Correct Answer : 705.00 to 715.00

Question 58:

The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is 9.81

m / s^{2}

. The time (in s, round off to two decimal places) to fill up the mold cavity (of size 40 cm 30 x cm x 15 cm) is____

Correct Answer : 28.80 to 29.00

Question 59:

Correct Answer : 0.7 to 1.26

Question 60:

Correct Answer : 1.24 to 1.26

Question 61:

m m^{3}

, the power required for drilling is ______ W (round off to two decimal places).

Correct Answer : 274.00 to 276.00

Question 62:

Correct Answer : 0.72 to .76

Question 63:

Correct Answer : 941.00 to 946.00

Question 64:

Hot and cold fluids enter a parallel flow double tube heat exchanger at 100 °C and 15 °C, respectively. The heat capacity rates of hot and cold fluids are

C_{h}

= 2000 W/K and

C_{c}

= 1200 W/K, respectively. If the outlet temperature of the cold fluid is 45 °C, the log mean temperature difference (LMTD) of the heat exchanger is _________ K (round off to two decimal places).

Correct Answer : 57.00 to 58.00

Question 65:

Correct Answer : 19.00 to 21.00

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