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GATE ME 2017 Set 2

All 65 solved GATE ME 2017 Set 2 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 29Medium 32Hard 4

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    The ways in which this game can be played __________ potentially infinite.
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    Question

    If you choose plan P, you will have to ________ plan Q, as these two are mutually ________.
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    Question

    If aa and bb are integers and a−ba - b is even, which of the following must always be even?
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    Question

    A couple has 2 children. The probability that both children are boys if the older one is a boy is
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    Question

    P looks at Q while Q looks at R. P is married, R is not. The number of pairs of people in which a married person is looking at an unmarried person is
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    Question

    "If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters."
    Which of the following is closest in meaning to 'cleaving'?
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    Question

    XX bullocks and YY tractors take 8 days to plough a field. If we halve the number of bullocks and double the number of tractors, it takes 5 days to plough the same field. How many days will it take XX bullocks alone to plough the field?
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    Question

    There are 4 women P,Q,R,SP, Q, R, S and 5 men V,W,X,Y,ZV, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. PP is not to be paired with ZZ, and YY must necessarily be paired with someone. In how many ways can 4 such pairs be formed?
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    Question

    All people in a certain island are either 'Knights' or 'Knaves' and each person knows every other person's identity. Knights NEVER lie, and knaves ALWAYS lie.
    P says "Both of us are knights". Q says "None of us are knaves".
    Which one of the following can be logically inferred from the above?
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    Question

    In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 1010 °C) and a month in summer (average temperature 3030 °C).
    Graph showing pollutant concentration over days for winter and summer

    Consider the following statements based on the data shown above:
    i. Over the given months, the difference between the maximum and the minimum pollutant concentrations is the same in both winter and summer.
    ii. There are at least four days in the summer month such that the pollutant concentrations on those days are within 11 ppm of the pollutant concentrations on the corresponding days in the winter month.
    Which one of the following options is correct?
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Mechanical Engineering

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    Question

    Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ________
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    Question

    The divergence of the vector −yi+xj-y\mathbf{i} + x\mathbf{j} is ________
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    Question

    The determinant of a 2×22 \times 2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is ________
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    Question

    A sample of 15 data is as follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is
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    Question

    The Laplace transform of tette^t is
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    Question

    A mass mm is attached to two identical springs having spring constant kk as shown in the figure. The natural frequency ω\omega of this single degree of freedom system is
    A mass m suspended by two parallel springs each with spring constant k
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    Question

    The state of stress at a point is σx=σy=σz=τxz=τzx=τyz=τzy=0\sigma_x = \sigma_y = \sigma_z = \tau_{xz} = \tau_{zx} = \tau_{yz} = \tau_{zy} = 0 and τxy=τyx=50\tau_{xy} = \tau_{yx} = 50 MPa. The maximum normal stress (in MPa) at that point is ________
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    Question

    For a loaded cantilever beam of uniform cross-section, the bending moment (in N⋅mm\text{N}\cdot\text{mm}) along the length is M(x)=5x2+10xM(x) = 5x^2 + 10x, where xx is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mmx = 10 \text{ mm} is ________
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    Question

    A cantilever beam of length LL and flexural modulus EIEI is subjected to a point load PP at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is
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    Question

    A steel bar is held by two fixed supports as shown in the figure and is subjected to an increase of temperature ΔT=100 ∘C\Delta T=100\ ^\circ\text{C}. If the coefficient of thermal expansion and Young's modulus of elasticity of steel are 11×10−6 /∘C11\times10^{-6}\ /^\circ\text{C} and 200 GPa200\ \text{GPa}, respectively, the magnitude of thermal stress (in MPa) induced in the bar is ________
    A steel bar fixed between two rigid supports
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    Question

    A machine component made of a ductile material is subjected to a variable loading with σmin⁡=−50 MPa\sigma_{\min} = -50\ \text{MPa} and σmax⁡=50 MPa\sigma_{\max} = 50\ \text{MPa}. If the corrected endurance limit and the yield strength for the material are σe′=100 MPa\sigma_e' = 100\ \text{MPa} and σy=300 MPa\sigma_y = 300\ \text{MPa}, respectively, the factor of safety is ________
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    Question

    In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100 mm100\ \text{mm} and 160 mm160\ \text{mm}, respectively. The crank is rotating with an angular velocity of 10 radian/s10\ \text{radian/s} counter-clockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is ________
    Slider-crank mechanism with crank OB vertical and connecting rod BC
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    Question

    Which one of the following statements is TRUE?
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    Question

    A mass mm of a perfect gas at pressure p1p_1 and volume V1V_1 undergoes an isothermal process. The final pressure is p2p_2 and volume is V2V_2. The work done on the system is considered positive. If RR is the gas constant and TT is the temperature, then the work done in the process is
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    Question

    If a mass of moist air contained in a closed metallic vessel is heated, then its
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    Question

    For the stability of a floating body the
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    Question

    Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is denoted by τw\tau_w. The axial positions x1x_1 and x2x_2 on the plate are measured from the leading edge in the direction of flow. If x2>x1x_2 > x_1, then
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    Question

    The heat loss from a fin is 6 W6\text{ W}. The effectiveness and efficiency of the fin are 33 and 0.750.75, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is ___________
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    Question

    The emissive power of a blackbody is PP. If its absolute temperature is doubled, the emissive power becomes
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    Question

    Which one of the following statements is TRUE for the ultrasonic machining (USM) process?
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    Question

    The crystal structure of aluminium is
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    Question

    Given the atomic weight of FeFe is 56 and that of CC is 12, the weight percentage of carbon in cementite (Fe3CFe_3C) is ________
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    Question

    For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?
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    Question

    The standard deviation of linear dimensions P and Q are 3 μm3\ \mu m and 4 μm4\ \mu m, respectively. When assembled, the standard deviation (in μm\mu m) of the resulting linear dimension (P+Q) is ___________
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    Question

    It is desired to make a product having T-shaped cross-section from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?
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    Question

    The surface integral ∬SF⋅n dS\iint_S \mathbf{F} \cdot \mathbf{n} \, dS over the surface SS of the sphere x2+y2+z2=9x^2 + y^2 + z^2 = 9, where F=(x+y)i+(x+z)j+(y+z)k\mathbf{F} = (x+y)\mathbf{i} + (x+z)\mathbf{j} + (y+z)\mathbf{k} and n\mathbf{n} is the unit outward surface normal, yields _________
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    Question

    Consider the differential equation 3y′′(x)+27y(x)=03y''(x) + 27y(x) = 0 with initial conditions y(0)=0y(0) = 0 and y′(0)=2000y'(0) = 2000. The value of yy at x=1x = 1 is ________
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    Question

    Consider the matrix A=[50707080]A = \begin{bmatrix} 50 & 70 \\ 70 & 80 \end{bmatrix} whose eigenvectors corresponding to eigenvalues λ1\lambda_1 and λ2\lambda_2 are x1=[70λ1−50]x_1 = \begin{bmatrix} 70 \\ \lambda_1 - 50 \end{bmatrix} and x2=[λ2−8070]x_2 = \begin{bmatrix} \lambda_2 - 80 \\ 70 \end{bmatrix}, respectively. The value of x1Tx2x_1^T x_2 is ________.
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    If f(z)=(x2+ay2)+ibxyf(z) = (x^2 + ay^2) + ibxy is a complex analytic function of z=x+iyz = x + iy, where i=−1i = \sqrt{-1}, then
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    Question

    Block 2 slides outward on link 1 at a uniform velocity of 6 m/s6\text{ m/s} as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s20\text{ radian/s} counterclockwise. The magnitude of the total acceleration (in m/s2\text{m/s}^2) of point P of the block with respect to fixed point O is __________
    A diagram showing a block (2) sliding on a link (1). Link 1 is rotating about point O with angular velocity $20\text{ rad/s}$. Block 2 is at a distance of $100\text{ mm}$ from O and sliding at $6\text{ m/s}$.
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    Question

    The radius of gyration of a compound pendulum about the point of suspension is 100 mm100\text{ mm}. The distance between the point of suspension and the centre of mass is 250 mm250\text{ mm}. Considering the acceleration due to gravity as 9.81 m/s29.81\text{ m/s}^2, the natural frequency (in radian/s) of the compound pendulum is ________
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    Question

    A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is rotating at 400 rpm. The speed (in rpm) of the gear S is ________
    A compound gear train diagram showing gear P meshing with gear Q, which is on the same shaft as gear R, and gear R meshing with gear S.
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    Question

    A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa24\text{ MPa}. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is ________
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    Question

    Three masses are connected to a rotating shaft supported on bearings A and B as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For m1=10 kgm_1 = 10\text{ kg}, m2=5 kgm_2 = 5\text{ kg} and m3=2.5 kgm_3 = 2.5\text{ kg} and for a shaft angular speed of 1000 radian/s1000\text{ radian/s}, the magnitude of the bearing reaction (in N) at location B is
    Two views of a rotating shaft with three masses $m_1, m_2, m_3$ at different radii and angles
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    Question

    A steel plate, connected to a fixed channel using three identical bolts AA, BB and CC, carries a load of 6 kN6\text{ kN} as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt CC is
    Steel plate with three bolts A, B, C and a 6 kN load
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    Question

    A single-plate clutch has a friction disc with inner and outer radii of 20 mm20\text{ mm} and 40 mm40\text{ mm}, respectively. The friction lining in the disc is made in such a way that the coefficient of friction μ\mu varies radially as μ=0.01r\mu = 0.01r, where rr is in mm. The clutch needs to transmit a friction torque of 18.85 kN⋅mm18.85\text{ kN}\cdot\text{mm}. As per uniform pressure theory, the pressure (in MPa) on the disc is __________.
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    Question

    The principal stresses at a point in a critical section of a machine component are σ1=60\sigma_1 = 60 MPa, σ2=5\sigma_2 = 5 MPa and σ3=−40\sigma_3 = -40 MPa. For the material of the component, the tensile yield strength is σy=200\sigma_y = 200 MPa. According to the maximum shear stress theory, the factor of safety is
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    Question

    The rod PQ of length L=2L = \sqrt{2} m, and uniformly distributed mass of M=10M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g=10g = 10 m/s2^2. The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML2/12)(ML^2/12). At this instant, the magnitude of angular acceleration (in radian/s2^2) of the rod is
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    Question

    The arrangement shown in the figure measures the velocity VV of a gas of density 11 kg/m3^3 flowing through a pipe. The acceleration due to gravity is 9.819.81 m/s2^2. If the manometric fluid is water (density 10001000 kg/m3^3) and the velocity VV is 2020 m/s, the differential head hh (in mm) between the two arms of the manometer is
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    A 60 mm-diameter water jet strikes a plate containing a hole of 40 mm diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is deflected vertically. The density of water is 1000 kg/m31000 \text{ kg/m}^3. If velocities are as indicated in the figure, the magnitude of horizontal force (in N) required to hold the plate is ___________
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    Question

    For the laminar flow of water over a sphere, the drag coefficient CFC_F is defined as CF=F/(ρU2D2)C_F = F / (\rho U^2 D^2), where FF is the drag force, ρ\rho is the fluid density, UU is the fluid velocity and DD is the diameter of the sphere. The density of water is 1000 kg/m31000 \text{ kg/m}^3. When the diameter of the sphere is 100 mm and the fluid velocity is 2 m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200 mm under dynamically similar conditions, the drag force (in N) on this sphere is ___________
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    Question

    In the Rankine cycle for a steam power plant the turbine entry and exit enthalpies are 2803 kJ/kg2803 \text{ kJ/kg} and 1800 kJ/kg1800 \text{ kJ/kg}, respectively. The enthalpies of water at pump entry and exit are 121 kJ/kg121 \text{ kJ/kg} and 124 kJ/kg124 \text{ kJ/kg}, respectively. The specific steam consumption (in kg/kW.h) of the cycle is ___________
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    Question

    A calorically perfect gas (specific heat at constant pressure 1000 J/kg⋅K1000\text{ J/kg}\cdot\text{K}) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are 1100 K1100\text{ K} and 400 K400\text{ K}, respectively. The power produced is 4.6 MW4.6\text{ MW} and heat escapes at the rate of 300 kJ/s300\text{ kJ/s} through the turbine casing. The mass flow rate of the gas (in kg/s\text{kg/s}) through the turbine is
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    Question

    One kg of an ideal gas (gas constant R=287 J/kg⋅KR = 287\text{ J/kg}\cdot\text{K}) undergoes an irreversible process from state-1 (1 bar1\text{ bar}, 300 K300\text{ K}) to state-2 (2 bar2\text{ bar}, 300 K300\text{ K}). The change in specific entropy (s2−s1s_2 - s_1) of the gas (in J/kg⋅K\text{J/kg}\cdot\text{K}) in the process is __________
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    Question

    The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m32.87\text{ m}^3 and 300 K300\text{ K}, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5 bar0.5\text{ bar}. If the gas constant of air is R=287 J/kg⋅KR = 287\text{ J/kg}\cdot\text{K} and the atmospheric pressure is 1 bar1\text{ bar}, the mass of air (in kg) in the vessel is
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    Question

    In a counter-flow heat exchanger, water is heated at the rate of 1.5 kg/s1.5\text{ kg/s} from 40∘C40^\circ\text{C} to 80∘C80^\circ\text{C} by an oil entering at 120∘C120^\circ\text{C} and leaving at 60∘C60^\circ\text{C}. The specific heats of water and oil are 4.2 kJ/kg⋅K4.2\text{ kJ/kg}\cdot\text{K} and 2 kJ/kg⋅K2\text{ kJ/kg}\cdot\text{K}, respectively. The overall heat transfer coefficient is 400 W/m2⋅K400\text{ W/m}^2\cdot\text{K}. The required heat transfer surface area (in m2\text{m}^2) is
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    Question

    A metal ball of diameter 60 mm60\text{ mm} is initially at 220∘C220^\circ\text{C}. The ball is suddenly cooled by an air jet of 20∘C20^\circ\text{C}. The heat transfer coefficient is 200 W/m2⋅K200\text{ W/m}^2\cdot\text{K}. The specific heat, thermal conductivity and density of the metal ball are 400 J/kg⋅K400\text{ J/kg}\cdot\text{K}, 400 W/m⋅K400\text{ W/m}\cdot\text{K} and 9000 kg/m39000\text{ kg/m}^3, respectively. The ball temperature (in ∘C^\circ\text{C}) after 9090 seconds will be approximately
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    Question

    A product made in two factories, P and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:
    FactoryDestination RDestination S
    P107
    Q34
    Factory P produces 7 units and factory Q produces 9 units of the product. Each destination requires 8 units. If the north-west corner method provides the total transportation cost as XX (in Rupees) and the optimized (minimum) total transportation cost is YY (in Rupees), then (X−Y)(X-Y), in Rupees, is
    1. A.
      0
    2. B.
      15
    3. C.
      35
    4. D.
      105

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    Question

    A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table:
    ActivityImmediate predecessorDuration (days)
    A-4
    BA3
    CA7
    DB14
    EC4
    FD, E9
    The minimum project completion time (in days) is ____________.
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    Question

    A rod of length 20 mm20\text{ mm} is stretched to make a rod of length 40 mm40\text{ mm}. Subsequently, it is compressed to make a rod of final length 10 mm10\text{ mm}. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is
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    Question

    Maximize Z=5x1+3x2Z = 5x_1 + 3x_2,
    subject to
    x1+2x2≤10x_1 + 2x_2 \leq 10,
    x1−x2≤8x_1 - x_2 \leq 8,
    x1,x2≥0x_1, x_2 \geq 0.
    In the starting Simplex tableau, x1x_1 and x2x_2 are non-basic variables and the value of ZZ is zero. The value of ZZ in the next Simplex tableau is ____________.
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    Question

    A strip of 120 mm width and 8 mm thickness is rolled between two 300 mm-diameter rolls to get a strip of 120 mm width and 7.2 mm thickness. The speed of the strip at the exit is 30 m/min. There is no front or back tension. Assuming uniform roll pressure of 200 MPa in the roll bite and 100% mechanical efficiency, the minimum total power (in kW) required to drive the two rolls is ___________
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    Question

    A cylindrical pin of 25+0.000+0.02025^{+0.020}_{+0.000} mm diameter is electroplated. Plating thickness is 2.0±0.0052.0\pm0.005 mm. Neglecting the gauge tolerance, the diameter (in mm, up to 33 decimal points accuracy) of the GO ring gauge to inspect the plated pin is
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    Question

    During the turning of a 2020 mm-diameter steel bar at a spindle speed of 400400 rpm, a tool life of 2020 minute is obtained. When the same bar is turned at 200200 rpm, the tool life becomes 6060 minute. Assume that Taylor's tool life equation is valid. When the bar is turned at 300300 rpm, the tool life (in minute) is approximately
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    Question

    In an orthogonal machining with a tool of 9∘9^\circ orthogonal rake angle, the uncut chip thickness is 0.20.2 mm. The chip thickness fluctuates between 0.250.25 mm and 0.40.4 mm. The ratio of the maximum shear angle to the minimum shear angle during machining is __________
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