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Download GATE GATE ME Question Paper With Solutions

Download GATE (Graduate Aptitude Test in Engineering) GATE ME Question Paper With Solutions

This post was last modified on 18 December 2019

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GATE Previous Last 10 Years 2010-2020 Question Papers With Solutions And Answer Keys

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General Aptitude

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A final examination is the _______ of a series of evaluations that a student has to go through.
1. desperation
2. insinuation
3. consultation
4. culmination
Ans: option (D)

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

Meaning of culmination is the highest or climactic point of something, especially as attained after a long time.

Hence, it is the most appropriate word.

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If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = ________.
1. JDC
2. JCD
3. JDE
4. JED
Ans: option (D)

Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P

Hence, IDC will be written as JED

I + 1 = J, D + 1 = E, C + 1 = D

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Are there enough seats here? There are _______ people here than I expected.
1. many
2. most
3. more
4. least
Ans: option (C)

Sol: Comparison is made here between the number of people and number of seats, hence, more is the most appropriate word
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?
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1. might be
2. are going to be
3. will be
4. were to be
Ans: option (C)
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Sol: Future is being discussed here, hence will be is the most appropriate phrase.
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?
1. 7
2. 6
3. 8
4. 9.5
Ans: option (A)

Sol: XYZ = 192 and Z = 4

So, XY = 48
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P = (X + Y) / 2

For finding the minimum possible of P, X + Y should be minimum

Now, the possible values of X and Y are as follows

X Y

48 1
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24 2

16 3

12 4

8 6

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice -versa
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So minimum value of P = (8 + 6) / 2 = 7
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?
1. Most households that subscribe to X’s loyalty membership discontinue watching cable television
2. Non-members prefer to watch cable television
3. The X is cancelling accounts of non-members
4. Cable television operators don’t subscribe to X’s loyalty membership
Ans: option (A)

Sol: option A is the most appropriate solution
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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 ____________.
1. 35.70
2. 10.00
3. 37.50
4. 25.00
Ans: option (C)

Sol: Let the GDP in 2015 = x

Then, the GDP in 2016 will be = 1.1x

So, fiscal deficit in 2015 = 0.04 x = 0.04x
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And the fiscal deficit in 2016 = 0.05 x 1.1x = 0.055x

Increase in fiscal deficit = 0.055x – 0.04x = 0.015x

So, the percentage increase in fiscal deficit = (0.015 / 0.04) × 100 = 37.5%
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 _________.
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1. 16.50
2. 14.50
3. 15.50
4. 13.50
Ans: option (B)
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Sol: 1 hour work of P = 1/6

1 hour work of Q = 1/9

1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)

Tank filled when P and R works initially for 4 hours = 4 * ((1/6) – (1/12)) = 1/3

Tank filled by when Q and R works for another 6 hours = 6 * ((1/9) – (1/12)) = 1/6
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Total tank filled in these 10 hours = (1/3) + (1/6) = 0.5

So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in 9 hours)

Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours
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 Manhattam 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".
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The writer of this passage is surprised by the creative writing assignments of his students, because
1. Some of the students had written about ice cubes and cowboys
2. None of the students had written about ice cubes and cowboys
3. Some of the students had written stories set in foreign places
4. None of the students had written stories set in India
Ans: option (C)

Sol: option C is the most appropriate solution
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?

Month Type January February March April

Pool 170 320 215 190

Mini 110 220 180 70

Prime 75 180 120 90
1. 38.74
2. 23.97
3. 25.86
4. 16.24
Ans: option (B)

Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
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Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580

Revenue contributed by Prime = 75 + 180 + 120 +90 = 465

Total revenue of Mola = 895 + 580 + 465 = 1940

So, the percentage share = (465 / 1940) × 100 = 23.97%

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MECHANICAL ENGINEERING

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.

Ans: 50

Sol: Tensile stress

s = E * y = 100 x 10³ * (1 / (1000 * 2)) = 50 MPa
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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 ______.

Ans: 1

Sol:

E = 0.5 * Capacitance * voltage²
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E = 0.5 * 50 * 10^-6 * 200² = 1 J
If x is the mean of data 3, x, 2 and 4, then the mode is ________.

Ans: 3

Sol: x = (3+x+2+4) / 4
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4x = 3+x+2+4

4x - x = 3+2+4 = 9

x = 3

Mode is 3. (Maximum repeated value)

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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
1. Strip rolling
2. Knurling
3. Roll forming
4. Chamfering
Ans: option (B)

Sol: We provide special pattern to prevent the relative motion between contact surface. This special pattern is known as Knurling.
Endurance limit of a beam subjected to pure bending eases with
1. increase in the surface roughness and increase in the size of the beam
2. decrease in the surface roughness and decrease in the size of the beam
3. decrease in the surface roughness and increase in the size of the beam
4. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)

Sol: Formula for endurance limit
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se = Ka x K_b X K_c XK_d X s'

Where

Ka - Surface factor

Ka - Size factor

Kc - load factor
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Ka - Temperature factor

s' – Endurance Strength

Form above formula it is clear that the Endurance limit increases with increase in size, surface, load, temp and endurance strength.
In matrix equation [A] {X} = {R},
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[A] = [[4, 8, 4], [8, 16, -4], [4, -4, 15]]

{X} = [[2], [1], [4]] and {R} = [[32], [16], [64]].

One of the eigenvalues of matrix [A] is
1. 4
2. 15
3. 8
4. 16
Ans: option (D)

Sol: [A] {X} = {R}.

We know AX = ?X; Where ? – Eigen Value
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[A] {X} = [[4, 8, 4], [8, 16, -4], [4, -4, 15]] * [[2], [1], [4]] = [[32], [16], [64]]

Hence, ? = 16
Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number Re_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 _______.

Ans: 500
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Sol: Reynold's Number

Re = (? * V_av * D) / µ

Where:

? - Fluid Density

V_av – Average velocity
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D – Dimeter of Pipe

µ – Dynamic viscosity of Fluid

Re = (?V_avD) / (µ * A_pipe) * A_pipe

From above expiration, Reynold's Number is independent of flow profile. Hence, Reynold's Number for parabolic flow profile is 500.

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For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell's relations, (?p/?T)_v is equal to
1. (?s/?v)_T
2. (?v/?s)_T
3. (?s/?v)_p
4. - (?v/?s)_p
Ans: option (C)

Sol: From mathematical relation expiration

dx = Mdy + Ndz

(?M/?z)_y = (?N/?y)_z

From Maxwell relation
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dh = Tds + Vdp

(?T/?p)_s = (?v/?s)_p
Hardenability of steel is a measure of
1. the ability to harden when it is cold worked
2. the maximum hardness that can be obtained when it is austenitized and then quenched
3. the ability to retain its hardness when it is heated to elevated temperatures
4. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)

Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.
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The directional derivative of the function f(x, y) = x² + y² along a line directed from (0, 0) to (1, 1), evaluated at the point x = 1, y = 1 is
1. 2
2. v2
3. 4/v2
4. 2v2
Ans: option (D)

Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e. we have to calculate value of derivative of function in the direction of given line vector

?f = î(?f/?x) + j(?f/?y)

?f = 2î + 2j
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Now, calculating the value of ?f in (î+ j) / v2

D.D of given function is (2î + 2j) * ((î+ j) / v2) = 2v2
A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
1. 2pD / T
2. D / T
3. pD / T
4. T / D
Ans: option (C)

Sol: circular pitch = pD / T
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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
1. V_R/v3
2. V_p/v3
3. 2V_R
4. 2V_p
Ans: option (C)

Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the possible motion is translation and angular motion. we know that the angular motion of the object is always defined as the motion about the point. Hence, first we have to find a point parallel to both velocity V_p and V_R.

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? = (V_p - V_R) / (v3 / 2)

? = 2V_R
Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4 m. The view factor F₁₂ is
1. 0.25
2. 0.0625
3. 1.0
4. 0.5
Ans: option (C)

Sol: F₁₂ = 1
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The transformation matrix for mirroring a point in x – y plane about the line y = x is given by
1. [[1, 0], [0, -1]]
2. [[0, 1], [1, 0]]
3. [[1, 0], [0, 1]]
4. [[1, 0], [0, 1]]
Ans: option (C)

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

[[0, 1], [1, 0]]

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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 at the same point is ___________ MPa.

Ans: 80

Sol:

R=100

t = v(100² - 60²) = 80 MPa
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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
1. Quadratic
2. Exponential
3. Logarithmic
4. Linear
Ans: option (C)

Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.

If there is

A(x) = A₀ + A_cx
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d/dx(-k*A(x)*dT/dx) = 0

d/dx(-kA*dT/dx) = 0

-k(A₀ + A_cx) * dT/dx = C

dT = -C dx / (k(A₀ + A_cx))

T₂ - T₁ = -C/K * ln(A_cx + A₀) / A₀
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An analytic function f(z) of complex variable z = x + iy may be written as f(z) = u(x, y) + iv(x, y). Then, u(x, y) and v(x, y) must satisfy
1. ?u/?x = ?v/?y and ?u/?y = ?v/?x
2. ?u/?x = ?v/?y and ?u/?y = -?v/?x
3. ?u/?x = -?v/?y and ?u/?y = ?v/?x
4. ?u/?x = -?v/?y and ?u/?y = -?v/?x
Ans: option (C)

Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

?u/?x = ?v/?y

?u/?y = -?v/?x
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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 Nu = K Ra^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 h₁ and that for the second plate is h₂, the value of the ratio h₁/h₂ is ________.

Ans: 2

Sol: Nu = K (Ra)^1/4
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We know that Ra = GrPr

Nu = K (GrPr)^1/4

hL / a = K (gß?TL³ / v² * Pr)^1/4

h ? L^-1/4

h ? L^-3/4
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h₁ / h₂ = (L₂ / L₁)^1/4 = (16L / L)^1/4

h₁ / h₂ = 2
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?
1. Decreasing the condenser pressure.
2. Increasing the boiler pressure.
3. Decreasing the boiler pressure.
4. Increasing the turbine inlet temperature.
Ans: option (D)

Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet.
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Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress 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 v = 0.3 are given. The principal strains in the plane of the sheet are
1. (0.5, 0.0)
2. (0.35, -0.15)
3. (0.5, -0.5)
4. (0.5, -0.15)
Ans: option (D)

Sol:

e₁ = (s₁/E) - µ(s₂/E)

e₂ = (s₂/E) - µ(s₁/E)
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s₁ = 100 MPa

s₂ = 0

e₁ = 100 / 200 = 0.5

e₂ = -0.3 * 100 / 200 = -0.15

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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 _________ ?.

Ans: 0

Sol:

The momentum about the point A must be zero, because there is no deformation of any truss.
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Hence, F_CD = 0 [F_CD is not passing through the point A]
The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in
1. freezing range
2. surface tension
3. degree of superheat
4. viscosity
Ans: option (C)

Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

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The most common limit gage used for use respecting the hole diameter is
1. Ring gage
2. Snap gage
3. Plug gage
4. Master gage
Ans: option (C)

Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.
The differential equation dy/dx + 4y = 5 is valid in the domain 0 = x = 1 with y(0) = 2.25. The solution of the differential equation is
1. y = e^-4x + 1.25
2. y = e^4x + 5
3. y = e^4x + 1.25
4. y = e^-4x + 5
Ans: option (A)

Sol: The given equation is.
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dy/dx + 4y = 5

If Integration factor = e^?4dx = e^4x

? y × IF = ? 5 × IF dx + C

? y * e^4x = ? 5 * e^4x dx + C

? y * e^4x = 5 * (e^4x / 4) + C
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Now for at x=0, y = 2.25

? 2.25 = 5/4 + C....(1)

? C = 1

?Using the value of C in equ (1)

y * e^4x = 5 * (e^4x / 4) + 1
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y = (5/4) + e^-4x

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This post was last modified on 18 December 2019