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GATE ME 2020 Set 1

All 65 solved GATE ME 2020 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Questions

65

Paper marks

100

Question formats

2

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 22Medium 34Hard 9

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    He is known for his unscrupulous ways. He always sheds ______ tears to deceive people.
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    Question

    Jofra Archer, the England fast bowler, is ______ than accurate.
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    Question

    Select the word that fits the analogy:
    Build : Building :: Grow : ______
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    Question

    I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.
    What does the phrase “having said that” mean in the given text?
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    Question

    Define [x][x] as the greatest integer less than or equal to xx, for each x∈(−∞,∞)x \in (-\infty, \infty). If y=[x]y = [x], then area under yy for x∈[1,4]x \in [1,4] is ______.
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    Question

    Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.
    Based on the above paragraph, which of the following is correct about crowd funding?
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    Question

    P,Q,RP, Q, R and SS are to be uniquely coded using α\alpha and β\beta. If PP is coded as αα\alpha\alpha and QQ as αβ\alpha\beta, then RR and SS, respectively, can be coded as ______.
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    Question

    The sum of the first nn terms in the sequence 8,88,888,8888,…8, 88, 888, 8888, \dots is ______.
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    Question

    Select the graph that schematically represents BOTH y=xmy = x^m and y=x1/my = x^{1/m} properly in the interval 0≤x≤10 \leq x \leq 1, for integer values of mm, where m>1m > 1.
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    Question

    The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is ______.
    Bar graph showing the number of students appeared and passed for schools P, Q, R, and S
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Mechanical Engineering

55
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    Question

    Multiplication of real valued square matrices of same dimension is
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    Question

    The value of lim⁡x→1(1−e−c(1−x)1−xe−c(1−x))\lim_{x \to 1} \left( \frac{1 - e^{-c(1-x)}}{1 - x e^{-c(1-x)}} \right) is
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    Question

    The Laplace transform of a function f(t)f(t) is L(f)=1s2+ω2\mathcal{L}(f) = \frac{1}{s^2 + \omega^2}. Then, f(t)f(t) is
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    Question

    Which of the following function f(z)f(z), of the complex variable zz, is NOT analytic at all the points of the complex plane?
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    Question

    The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load P>0P > 0 with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are
    A truss structure with joints A through H. Joint A is a pin support. Joint E is a roller support on a 45-degree inclined surface. A vertical downward load P is applied at joint C. All horizontal and vertical members are 1m long.
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    Question

    A single-degree-of-freedom oscillator is subjected to harmonic excitation F(t)=F0cos⁡(ωt)F(t) = F_0 \cos(\omega t) as shown in the figure.
    A mass-spring-damper system (SDOF) with mass m, spring constant k, and damping coefficient c, subjected to an external force F(t).
    The non-zero value of ω\omega, for which the amplitude of the force transmitted to the ground will be F0F_0, is
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    Question

    The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa10\text{ MPa}. If one unit on the σ−τ\sigma - \tau plane is 1 MPa1\text{ MPa}, the Mohr's circle representation of the state-of-stress is given by
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    Question

    A four bar mechanism is shown below.
    A four-bar mechanism with link lengths 600 mm, 300 mm, 400 mm and unknown link PQ.
    For the mechanism to be a crank-rocker mechanism, the length of the link PQPQ can be
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    Question

    A helical gear with 20∘20^\circ pressure angle and 30∘30^\circ helix angle mounted at the mid-span of a shaft that is supported between two bearings at the ends. The nature of the stresses induced in the shaft is
    1. A.
      normal stress due to bending only
    2. B.
      normal stress due to bending in one plane and axial loading; shear stress due to torsion
    3. C.
      normal stress due to bending in two planes and axial loading; shear stress due to torsion
    4. D.
      normal stress due to bending in two planes; shear stress due to torsion

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    Question

    The crystal structure of γ\gamma iron (austenite phase) is
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    Question

    Match the following.
    Heat treatment processEffect
    P: Tempering1. Strengthening
    Q: Quenching2. Toughening
    R: Annealing3. Hardening
    S: Normalizing4. Softening
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    Question

    The base of a brass bracket needs rough grinding. For this purpose, the most suitable grinding wheel grade specification is
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    Question

    In the Critical Path Method (CPM), the cost-time slope of an activity is given by
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    Question

    Froude number is the ratio of
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    Question

    Match the following non-dimensional numbers with the corresponding definitions:
    Non-dimensional numberDefinition
    P Reynolds number1 Buoyancy forceViscous force\frac{\text{Buoyancy force}}{\text{Viscous force}}
    Q Grashof number2 Momentum diffusivityThermal diffusivity\frac{\text{Momentum diffusivity}}{\text{Thermal diffusivity}}
    R Nusselt number3 Inertia forceViscous force\frac{\text{Inertia force}}{\text{Viscous force}}
    S Prandtl number4 Convective heat transferConduction heat transfer\frac{\text{Convective heat transfer}}{\text{Conduction heat transfer}}
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    Question

    The velocity field of an incompressible flow in a Cartesian system is represented byV⃗=2(x2−y2)i^+vj^+3k^\vec{V} = 2(x^2 - y^2)\hat{i} + v\hat{j} + 3\hat{k}Which one of the following expressions for vv is valid?
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    Question

    For an ideal gas, the value of the Joule-Thomson coefficient is
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    Question

    For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature (TT) versus specific entropy (ss) diagram. CpC_p is the specific heat at constant pressure and CvC_v is the specific heat at constant volume. The ratio of the slopes of the constant pressure and constant volume lines at the point of intersection is
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    Question

    For three vectors A⃗=2j^−3k^\vec{A} = 2\hat{j} - 3\hat{k}, B⃗=−2i^+k^\vec{B} = -2\hat{i} + \hat{k} and C⃗=3i^−j^\vec{C} = 3\hat{i} - \hat{j}, where i^\hat{i}, j^\hat{j} and k^\hat{k} are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of (A⃗⋅(B⃗×C⃗)+6)(\vec{A} \cdot (\vec{B} \times \vec{C}) + 6) is ______.
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    Question

    A flywheel is attached to an engine to keep its rotational speed between 100 rad/s100\text{ rad/s} and 110 rad/s110\text{ rad/s}. If the energy fluctuation in the flywheel between these two speeds is 1.05 kJ1.05\text{ kJ} then the moment of inertia of the flywheel is ______ kg.m2\text{kg.m}^2 (round off to 2 decimal places).
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    Question

    A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of 10 grams10\text{ grams}, attached to four points on the 100 mm100\text{ mm} radius circle shown in the figure.
    A balanced rigid disc with four identical point masses A, B, C, and D attached at 90-degree intervals on a circle of radius r = 100 mm
    The rotor is driven by a motor at uniform angular speed of 10 rad/s10\text{ rad/s}. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is ______ N\text{N} (round off to 2 decimal places).
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    Question

    A sheet metal with a stock hardness of 250 HRC250\text{ HRC} has to be sheared using a punch and a die having a clearance of 1 mm1\text{ mm} between them. If the stock hardness of the sheet metal increases to 400 HRC400\text{ HRC}, the clearance between the punch and the die should be ______ mm\text{mm}.
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    Question

    A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is ______ (round off to 2 decimal places).
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    Question

    The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of 6 in a two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the inlet temperature of the first stage, before its entry to the second stage. Air enters the compressor at 300 K300\text{ K} and 100 kPa100\text{ kPa}. If the properties of gas are constant, the intercooling pressure for minimum compressor work is ______ kPa\text{kPa} (round off to 2 decimal places).

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    Question

    In a concentric tube counter-flow heat exchanger, hot oil enters at 102∘C102^\circ C and leaves at 65∘C65^\circ C. Cold water enters at 25∘C25^\circ C and leaves at 42∘C42^\circ C. The log mean temperature difference (LMTD) is ________ ∘C^\circ C (round off to one decimal place).
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    Question

    The evaluation of the definite integral ∫11.4x∣x∣ dx\int_{1}^{1.4} x|x| \, dx by using Simpson's 1/3rd (one-third) rule with step size h=0.6h = 0.6 yields
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    Question

    A vector field is defined asf⃗(x,y,z)=x(x2+y2+z2)3/2i^+y(x2+y2+z2)3/2j^+z(x2+y2+z2)3/2k^\vec{f}(x, y, z) = \frac{x}{(x^2 + y^2 + z^2)^{3/2}} \hat{i} + \frac{y}{(x^2 + y^2 + z^2)^{3/2}} \hat{j} + \frac{z}{(x^2 + y^2 + z^2)^{3/2}} \hat{k}where, i^,j^,k^\hat{i}, \hat{j}, \hat{k} are unit vectors along the axes of a right-handed rectangular /Cartesian coordinate system. The surface integral ∬f⃗⋅dS⃗\iint \vec{f} \cdot d\vec{S} (where dS⃗d\vec{S} is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the center, and internal and external radii of 11 and 22, respectively, is
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    Question

    Bars of square and circular cross-section with 0.5 m0.5\text{ m} length are made of a material with shear strength of 20 MPa20\text{ MPa}. The square bar cross-section dimension is 4 cm×4 cm4\text{ cm} \times 4\text{ cm} and the cylindrical bar cross-section diameter is 4 cm4\text{ cm}. The specimens are loaded as shown in the figure.
    Four loading cases: Tensile load, Compressive load, Torsional load, and Bending load
    Which specimen(s) will fail due to the applied load as per maximum shear stress theory?
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    Question

    The 2 kg2\text{ kg} block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness 5 N/m5\text{ N/m}.
    Top view of a block on a horizontal surface attached to an elastic cord of length 0.5 m, given an initial velocity v = 1.5 m/s
    The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity vv of 1.5 m/s1.5\text{ m/s} perpendicular to the cord. The magnitude of velocity in m/s\text{m/s} of the block at the instant the cord is stretched by 0.4 m0.4\text{ m} is
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    Question

    The truss shown in the figure has four members of length ll and flexural rigidity EIEI, and one member of length l2l\sqrt{2} and flexural rigidity 4EI4EI. The truss is loaded by a pair of forces of magnitude PP, as shown in the figure.
    Square truss with a diagonal member, loaded by forces P at opposite corners along the diagonal
    The smallest value of PP, at which any of the truss members will buckle is
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    Question

    A rigid mass-less rod of length LL is connected to a disc (pulley) of mass mm and radius r=L/4r = L/4 through a friction-less revolute joint. The other end of that rod is attached to a wall through a friction-less hinge. A spring of stiffness 2k2k is attached to the rod at its mid-span. An inextensible rope passes over half the disc periphery and is securely tied to a spring of stiffness kk at point C as shown in the figure. There is no slip between the rope and the pulley. The system is in static equilibrium in the configuration shown in the figure and the rope is always taut.
    A diagram showing a horizontal massless rod hinged at one end to a wall. A spring of stiffness 2k is attached at the mid-span (L/2). At the other end (L), a disc of mass m and radius r=L/4 is attached via a revolute joint. An inextensible rope is fixed to the wall, passes over the top of the disc, and is connected to a spring of stiffness k at point C.
    Neglecting the influence of gravity, the natural frequency of the system for small amplitude vibration is
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    Question

    A strip of thickness 40 mm40\text{ mm} is to be rolled to a thickness of 20 mm20\text{ mm} using a two-high mill having rolls of diameter 200 mm200\text{ mm}. Coefficient of friction and arc length in mm, respectively are
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    Question

    For an assembly line, the production rate was 4 pieces per hour4\text{ pieces per hour} and the average processing time was 60 minutes60\text{ minutes}. The WIP inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by 30 percent30\text{ percent}. As a result of this change in the processing time, the WIP inventory
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    Question

    A small metal bead (radius 0.5 mm), initially at 100∘C100^\circ\text{C}, when placed in a stream of fluid at 20∘C20^\circ\text{C}, attains a temperature of 28∘C28^\circ\text{C} in 4.35 seconds. The density and specific heat of the metal are 8500 kg/m38500 \text{ kg/m}^3 and 400 J/kg.K400 \text{ J/kg.K}, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in W/m2.K\text{W/m}^2\text{.K}) between the metal bead and the fluid stream is
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    Question

    Consider two exponentially distributed random variables XX and YY, both having a mean of 0.50. Let Z=X+YZ = X + Y and rr be the correlation coefficient between XX and YY. If the variance of ZZ equals 0, then the value of rr is ________ (round off to 2 decimal places).
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    An analytic function of a complex variable z=x+iyz = x + iy (i=−1i = \sqrt{-1}) is defined as f(z)=x2−y2+iψ(x,y),f(z) = x^2 - y^2 + i \psi(x, y), where ψ(x,y)\psi(x, y) is a real function. The value of the imaginary part of f(z)f(z) at z=(1+i)z = (1 + i) is ________ (round off to 2 decimal places).
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    Question

    In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm250\text{ mm} and 50 mm50\text{ mm}, respectively. An axial force F1F_1 is needed to transmit a torque by a new clutch. However, to transmit the same torque, one needs an axial force F2F_2 when the clutch wears out. If contact pressure remains uniform during operation of a new clutch, and the coefficient of friction does not change, then the ratio F1/F2F_1/F_2 is ________ (round off to 2 decimal places).
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    Question

    A cam with a translating flat-face follower is desired to have the follower motiony(θ)=4[2πθ−θ2],0≤θ≤2π.y(\theta) = 4 [ 2\pi\theta - \theta^2 ], \quad 0 \leq \theta \leq 2\pi.Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than 40 mm40\text{ mm} anywhere. The minimum permissible base circle radius is ________ mm\text{mm} (round off to one decimal place).
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    Question

    A rectangular steel bar of length 500 mm500\text{ mm}, width 100 mm100\text{ mm}, and thickness 15 mm15\text{ mm} is cantilevered to a 200 mm200\text{ mm} steel channel using 4 bolts, as shown.
    Diagram showing a steel bar bolted to a channel with dimensions and a force F=10kN applied at the tip
    For an external load of 10 kN10\text{ kN} applied at the tip of the steel bar, the resultant shear load on the bolt at B, is ________ kN\text{kN} (round off to one decimal place).
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    Question

    The barrier shown between two water tanks of unit width (1 m1 \text{ m}) into the plane of the screen is modeled as a cantilever.
    Barrier between two water tanks
    Taking the density of water as 1000 kg/m31000 \text{ kg/m}^3, and the acceleration due to gravity as 10 m/s210 \text{ m/s}^2, the maximum absolute bending moment developed in the cantilever is ___________ kN⋅m\text{kN}\cdot\text{m} (round off to the nearest integer).
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    Question

    The magnitude of reaction force at joint CC of the hinge-beam shown in the figure is ___________ kN\text{kN} (round off to 2 decimal places).
    Hinge-beam with loads
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    Question

    A slot of 25 mm×25 mm25 \text{ mm} \times 25 \text{ mm} is to be milled in a workpiece of 300 mm300 \text{ mm} length using a side and face milling cutter of diameter 100 mm100 \text{ mm}, width 25 mm25 \text{ mm} and having 20 teeth.
    For a depth of cut 5 mm5 \text{ mm}, feed per tooth 0.1 mm0.1 \text{ mm}, cutting speed 35 m/min35 \text{ m/min} and approach and over travel distance of 5 mm5 \text{ mm} each, the time required for milling the slot is ___________ minutes (round off to one decimal place).
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    Question

    The following data applies to basic shaft system:
    tolerance for hole = 0.002 mm0.002\text{ mm},
    tolerance for shaft = 0.001 mm0.001\text{ mm},
    allowance = 0.003 mm0.003\text{ mm},
    basic size = 50 mm50\text{ mm}.
    The maximum hole size is ______ mm (round off to 3 decimal places).
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    A steel part with surface area of 125 cm2125\text{ cm}^2 is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation:I=12+0.2tI = 12 + 0.2twhere, I=current (A)I = \text{current (A)} and t=time (minutes)t = \text{time (minutes)}. The part is submerged in the plating solution for a duration of 20 minutes20\text{ minutes} for plating purpose. Assuming the cathode efficiency of chromium to be 15%15\% and the plating constant of chromium acid sulphate to be 2.50×10−2 mm3/A⋅s2.50 \times 10^{-2}\text{ mm}^3/\text{A}\cdot\text{s}, the resulting coating thickness on the part surface is ______ μm\mu\text{m} (round off to one decimal place).
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    In a turning process using orthogonal tool geometry, a chip length of 100 mm100\text{ mm} is obtained for an uncut chip length of 250 mm250\text{ mm}.
    The cutting conditions are: cutting speed =30 m/min= 30\text{ m/min}, rake angle =20∘= 20^\circ.
    The shear plane angle is ______ degrees (round off to one decimal place).
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    The thickness of a steel plate with material strength coefficient of 210 MPa, has to be reduced from 20 mm to 15 mm in a single pass in a two-high rolling mill with a roll radius of 450 mm and rolling velocity of 28 m/min. If the plate has a width of 200 mm and its strain hardening exponent, nn is 0.25, the rolling force required for the operation is ________ kN (round off to 2 decimal places).
    Note: Average Flow Stress=Material Strength Coefficient×(True Strain)n(1+n)Average\ Flow\ Stress = Material\ Strength\ Coefficient \times \frac{(True\ Strain)^n}{(1+n)}
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    Two business owners Shveta and Ashok run their businesses in two different states. Each of them, independent of the other, produces two products A and B, sells them at Rs. 2,000 per kg and Rs. 3,000 per kg, respectively, and uses Linear Programming to determine the optimal quantity of A and B to maximize their respective daily revenue. Their constraints are as follows: i) for each business owner, the production process is such that the daily production of A has to be at least as much as B, and the upper limit for production of B is 10 kg per day, and ii) the respective state regulations restrict Shveta's production of A to less than 20 kg per day, and Ashok's production of A to less than 15 kg per day. The demand of both A and B in both the states is very high and everything produced is sold.
    The absolute value of the difference in daily (optimal) revenue of Shveta and Ashok is ___________ thousand Rupees (round off to 2 decimal places).
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    Consider two cases as below.
    Case 1: A company buys 1000 pieces per year of a certain part from vendor 'X'. The changeover time is 2 hours and the price is Rs. 10 per piece. The holding cost rate per part is 10% per year.
    Case 2: For the same part, another vendor 'Y' offers a design where the changeover time is 6 minutes, with a price of Rs. 5 per piece, and a holding cost rate per part of 100% per year. The order size is 800 pieces per year from 'X' and 200 pieces per year from 'Y'.
    Assume the cost of downtime as Rs. 200 per hour. The percentage reduction in the annual cost for Case 2, as compared to Case 1 is ________ (round off to 2 decimal places).
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    Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter DD. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: V=−C(r2−D24)V = -C \left(r^2 - \frac{D^2}{4}\right) m/s, where CC is a constant. The rate of kinetic energy (in J/s) at the control surface A-B, as shown in the figure, is proportional to DnD^n. The value of nn is ______.
    Velocity profile in a circular pipe with control volume A-B
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    Air discharges steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in figure.
    Air jet from a nozzle hitting a vertical plate
    The inlet and outlet areas of the nozzle are 0.1 m20.1\text{ m}^2 and 0.02 m20.02\text{ m}^2, respectively. Take air density as constant and equal to 1.2 kg/m31.2\text{ kg/m}^3. If the inlet gauge pressure of air is 0.36 kPa0.36\text{ kPa}, the gauge pressure at point O on the plate is ______ kPa (round off to two decimal places).
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    Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K310\text{ K}. The pressure ratio of the compressor is 66. Specific heat at constant pressure for air is 1005 J/kg.K1005\text{ J/kg.K} and ratio of specific heats at constant pressure and constant volume is 1.41.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 8585 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ______ kJ/kg (round off to nearest integer).
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    One kg of air, initially at a temperature of 127∘C127^\circ\text{C}, expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is 287 J/kg.K287\text{ J/kg.K}, the magnitude of work transfer is __________ kJ (round off to 2 decimal places).
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    For an ideal Rankine cycle operating between pressures of 30 bar30\text{ bar} and 0.04 bar0.04\text{ bar}, the work output from the turbine is 903 kJ/kg903\text{ kJ/kg} and the work input to the feed pump is 3 kJ/kg3\text{ kJ/kg}. The specific steam consumption is __________ kg/kW.h (round off to 2 decimal places).
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    For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in figure.
    Outlet blade velocity diagram for a Kaplan turbine showing flow velocity $C_f$, blade velocity $C_b$, relative velocity $C_r$, and outlet angle $\beta$
    The diameter at this section is 3 m3\text{ m}. The hub and tip diameters of the blade are 2 m2\text{ m} and 4 m4\text{ m}, respectively. The water volume flow rate is 100 m3/s100\text{ m}^3/\text{s}. The rotational speed of the turbine is 300 rpm300\text{ rpm}. The blade outlet angle β\beta is __________ degrees (round off to one decimal place).
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    The indicated power developed by an engine with compression ratio of 8, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition is 10 kW. The ratio of specific heats at constant pressure and constant volume is 1.4. The mechanical efficiency of the engine is 80 percent.
    The brake power output of the engine is ______ kW (round off to one decimal place).
    Your answer

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