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GATE ME 2018 Set 1

All 65 solved GATE ME 2018 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 29Medium 32Hard 4

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    “Going by the _______ that many hands make light work, the school _____ involved all the students in the task.”
    The words that best fill the blanks in the above sentence are
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    Question

    “Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”
    The word that best fills the blank in the above sentence is
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    Question

    Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?
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    Question

    A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2650\text{ m}^2 of area. What is the area of the original rectangle in square meters?
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    Question

    A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?
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    Question

    For integers a,ba, b and cc, what would be the minimum and maximum values respectively of a+b+ca + b + c if log⁡∣a∣+log⁡∣b∣+log⁡∣c∣=0\log |a| + \log |b| + \log |c| = 0?
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    Question

    Given that aa and bb are integers and a+a2b3a + a^2 b^3 is odd, which one of the following statements is correct?
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    Question

    From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?
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    Question

    Which of the following functions describe the graph shown in the below figure?
    A W-shaped graph on a coordinate plane with x-axis from -3 to 3 and y-axis from -3 to 3.
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    Question

    Consider the following three statements:
    (i) Some roses are red.
    (ii) All red flowers fade quickly.
    (iii) Some roses fade quickly.
    Which of the following statements can be logically inferred from the above statements?
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Mechanical Engineering (Set 1)

55
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    Question

    Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is
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    Question

    The rank of the matrix [−41−1−1−1−17−31]\begin{bmatrix} -4 & 1 & -1 \\ -1 & -1 & -1 \\ 7 & -3 & 1 \end{bmatrix} is
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    Question

    According to the Mean Value Theorem, for a continuous function f(x)f(x) in the interval [a,b][a, b], there exists a value ξ\xi in this interval such that ∫abf(x)dx=\int_{a}^{b} f(x) dx =
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    Question

    F(z) is a function of the complex variable z=x+iyz = x+iy given by F(z)=iz+kRe(z)+iIm(z).F(z) = i z + k Re(z) + i Im(z). For what value of kk will F(z)F(z) satisfy the Cauchy-Riemann equations?
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    Question

    A bar of uniform cross section and weighing 100 N100\text{ N} is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.
    A horizontal bar of length $L$ supported by two vertical strings S1 and S2. S1 is at the left end, and S2 is at the midpoint $L/2$.
    The tensions in the strings are
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    Question

    If σ1\sigma_1 and σ3\sigma_3 are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is
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    Question

    The equation of motion for a spring-mass system excited by a harmonic force isMx¨+Kx=Fcos⁡(ωt),M \ddot{x} + Kx = F \cos(\omega t),where MM is the mass, KK is the spring stiffness, FF is the force amplitude and ω\omega is the angular frequency of excitation. Resonance occurs when ω\omega is equal to
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    Question

    For an Oldham coupling used between two shafts, which among the following statements are correct?
    I. Torsional load is transferred along shaft axis.
    II. A velocity ratio of 1:2 between shafts is obtained without using gears.
    III. Bending load is transferred transverse to shaft axis.
    IV. Rotation is transferred along shaft axis.
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    Question

    For a two-dimensional incompressible flow field given by u⃗=A(xi^−yj^)\vec{u} = A(x\hat{i} - y\hat{j}), where A>0A > 0, which one of the following statements is FALSE?
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    Question

    Which one of the following statements is correct for a superheated vapour?
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    Question

    In a linearly hardening plastic material, the true stress beyond initial yielding
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    Question

    The type of weld represented by the shaded region in the figure is
    A diagram showing a vertical plate joined to a horizontal plate with a triangular shaded region at the corner.
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    Question

    Using the Taylor’s tool life equation with exponent n=0.5n = 0.5, if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is
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    Question

    A grinding ratio of 200 implies that the
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    Question

    Interpolator in a CNC machine
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    Question

    The time series forecasting method that gives equal weightage to each of the mm most recent observations is
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    Question

    The number of atoms per unit cell and the number of slip systems, respectively, for a face-centered cubic (FCC) crystal are
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    Question

    A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is
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    Question

    A steel column of rectangular section (15 mm×10 mm15\text{ mm} \times 10\text{ mm}) and length 1.5 m1.5\text{ m} is simply supported at both ends. Assuming modulus of elasticity, E=200 GPaE = 200\text{ GPa} for steel, the critical axial load (in kN) is ____ (correct to two decimal places).
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    Question

    A four bar mechanism is made up of links of length 100, 200, 300 and 350 mm. If the 350 mm link is fixed, the number of links that can rotate fully is __________.
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    Question

    If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).
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    Question

    A flat plate of width L=1 mL = 1\text{ m} is pushed down with a velocity U=0.01 m/sU = 0.01\text{ m/s} towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figure. Assume two-dimensional incompressible flow and that the plate remains parallel to the wall. The average velocity, uavgu_{avg} of the fluid (in m/s) draining out at the instant shown in the figure is _____________(correct to three decimal places).
    Diagram showing a plate of width L moving down with velocity U towards a wall, with fluid draining out at the sides with average velocity u_avg through a gap of height d=0.1m
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    Question

    An ideal gas undergoes a process from state 1 (T1=300 KT_1 = 300\text{ K}, p1=100 kPap_1 = 100\text{ kPa}) to state 2 (T2=600 KT_2 = 600\text{ K}, p2=500 kPap_2 = 500\text{ kPa}). The specific heats of the ideal gas are : cp=1 kJ/kg-Kc_p = 1\text{ kJ/kg-K} and cv=0.7 kJ/kg-Kc_v = 0.7\text{ kJ/kg-K}. The change in specific entropy of the ideal gas from state 1 to state 2 (in kJ/kg-K) is ___________(correct to two decimal places).
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    Question

    For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is _______ (correct to two decimal places).
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    Question

    The height (in mm) for a 125 mm sine bar to measure a taper of 27∘32′27^\circ 32' on a flat work piece is _______ (correct to three decimal places).
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    Question

    Let X1,X2X_1, X_2 be two independent normal random variables with means μ1,μ2\mu_1, \mu_2 and standard deviations σ1,σ2\sigma_1, \sigma_2, respectively. Consider Y=X1−X2Y = X_1 - X_2; μ1=μ2=1,σ1=1,σ2=2\mu_1 = \mu_2 = 1, \sigma_1 = 1, \sigma_2 = 2. Then,
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    Question

    The value of the integral∯Sr⃗⋅n⃗dS\oiint_S \vec{r} \cdot \vec{n} dSover the closed surface SS bounding a volume VV, where r⃗=xi^+yj^+zk^\vec{r} = x\hat{i} + y\hat{j} + z\hat{k} is the position vector and n⃗\vec{n} is the normal to the surface SS, is
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    Question

    A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t=0t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s2^2 and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of
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    Question

    The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress σy\sigma_y (in kPa) is
    State of stress diagram showing $\sigma_x = 100$ kPa, $\sigma_y$, and $\tau_{xy} = 50$ kPa
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    Question

    An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is
    Epicyclic gear train diagram with gears A, B, C, and D
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    Question

    A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of θ=30∘\theta = 30^\circ as shown in the figure.
    The glue used at the interface fails if
    Criterion 1: the maximum normal stress exceeds 2.5 MPa.
    Criterion 2: the maximum shear stress exceeds 1.5 MPa.
    Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface
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    Question

    A self-aligning ball bearing has a basic dynamic load rating (C10C_{10}, for 10610^6 revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in 10610^6 revolutions) is
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    Question

    A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance XX (in m) where the jet strikes the floor is
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    Question

    In a Lagrangian system, the position of a fluid particle in a flow is described as x=xoe−ktx = x_o e^{-kt} and y=yoekty = y_o e^{kt} where tt is the time while xox_o, yoy_o, and kk are constants. The flow is
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    Question

    The maximum reduction in cross-sectional area per pass (RR) of a cold wire drawing process isR=1−e−(n+1),R = 1 - e^{-(n+1)},where nn represents the strain hardening coefficient. For the case of a perfectly plastic material, RR is
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    Question

    The percentage scrap in a sheet metal blanking operation of a continuous strip of sheet metal as shown in the figure is
    Sheet metal blanking operation diagram
    _______ (correct to two decimal places).
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    Question

    An explicit forward Euler method is used to numerically integrate the differential equationdydt=y\frac{dy}{dt} = yusing a time step of 0.1. With the initial condition y(0)=1y(0) = 1, the value of y(1)y(1) computed by this method is ___________ (correct to two decimal places).
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    Question

    F(s)F(s) is the Laplace transform of the functionf(t)=2t2e−tf(t) = 2t^2 e^{-t}F(1)F(1) is ________ (correct to two decimal places).
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    Question

    A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).
    A simply supported beam of length 4 m with a uniformly distributed load of 10 kN/m.
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    Question

    A machine of mass m=200m = 200 kg is supported on two mounts, each of stiffness k=10k = 10 kN/m. The machine is subjected to an external force (in N) F(t)=50cos⁡5tF(t) = 50 \cos 5t. Assuming only vertical translatory motion, the magnitude of the dynamic force (in N) transmitted from each mount to the ground is ______ (correct to two decimal places).
    A machine of mass m supported by two springs of stiffness k on a rigid ground, with an external force F(t) acting vertically upwards.
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    Question

    A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45∘45^\circ and a force of 4040 N is acting towards the left on the slider. The length of the crank is 3030 mm and the connecting rod is 7070 mm. Ignoring the effect of gravity, friction and inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is _________ (correct to two decimal places).
    A slider crank mechanism with crank length 30 mm and connecting rod 70 mm. A force of 40 N acts on the slider towards the left.
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    Question

    A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles. The total flow rate QQ through the sprinkler is 11 litre/sec and the cross-sectional area of each exit nozzle is 11 cm2^2. Assuming equal flow rate through both arms and a frictionless hinge, the steady state angular speed of rotation (in rad/s) of the sprinkler is ______ (correct to two decimal places).
    A horizontal sprinkler with two arms of lengths 10 cm and 20 cm. Water is discharged at Q/2 from each nozzle.
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    Question

    A solid block of 2.0 kg mass slides steadily at a velocity VV along a vertical wall as shown in the figure below. A thin oil film of thickness h=0.15h = 0.15 mm provides lubrication between the block and the wall. The surface area of the face of the block in contact with the oil film is 0.04 m2^2. The velocity distribution within the oil film gap is linear as shown in the figure. Take dynamic viscosity of oil as 7×10−37 \times 10^{-3} Pa-s and acceleration due to gravity as 10 m/s2^2. Neglect weight of the oil. The terminal velocity VV (in m/s) of the block is _________ (correct to one decimal place).
    Diagram showing a block of mass m=2.0 kg sliding down a vertical wall with an oil film of thickness h=0.15mm and contact area A=0.04 m^2.
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    Question

    A tank of volume 0.05 m3^3 contains a mixture of saturated water and saturated steam at 200∘^{\circ} C. The mass of the liquid present is 8 kg. The entropy (in kJ/kg K) of the mixture is ___________ (correct to two decimal places).
    Property data for saturated steam and water are:
    At 200∘^{\circ} C, psat=1.5538p_{sat} = 1.5538 MPa
    PropertyValue
    vfv_f0.001157 m3^3/kg
    vgv_g0.12736 m3^3/kg
    sfgs_{fg}4.1014 kJ/kg K
    sfs_f2.3309 kJ/kg K
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    Question

    Steam flows through a nozzle at a mass flow rate of m˙=0.1\dot{m} = 0.1 kg/s with a heat loss of 5 kW. The enthalpies at inlet and exit are 2500 kJ/kg and 2350 kJ/kg, respectively. Assuming negligible velocity at inlet (C1≈0C_1 \approx 0), the velocity (C2C_2) of steam (in m/s) at the nozzle exit is __________ (correct to two decimal places).
    Schematic of a nozzle showing inlet state (h1, C1), mass flow rate m_dot, heat loss Q_dot, and exit state (h2, C2).
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    Question

    An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air: cp=1.005c_p = 1.005 kJ/kg K, cv=0.718c_v = 0.718 kJ/kg K, R=0.287R = 0.287 kJ/kg K. The maximum temperature (in K) of the cycle is _________ (correct to one decimal place).
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    Question

    A plane slab of thickness LL and thermal conductivity kk is heated with a fluid on one side (P), and the other side (Q) is maintained at a constant temperature, TQT_Q of 25°C, as shown in the figure. The fluid is at 45°C and the surface heat transfer coefficient, hh, is 10 W/m2^2 K. The steady state temperature, TPT_P, (in °C) of the side which is exposed to the fluid is _______ (correct to two decimal places).
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  48. Think it through. Then check your answer.

    Question

    The true stress (σ\sigma) - true strain (ϵ\epsilon) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of 500 MPa and strain of 0.5. Then from point A, there is unloading up to point B, i.e., to stress of 100 MPa. Given that the Young’s modulus E=200E = 200 GPa, the natural strain at point B (ϵB\epsilon_B) is _________ (correct to three decimal places).
    True stress vs true strain diagram showing loading to point A at 500 MPa and 0.5 strain, and unloading to point B at 100 MPa and $\epsilon_B$ strain.
    Your answer

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  49. Think it through. Then check your answer.

    Question

    An orthogonal cutting operation is being carried out in which uncut thickness is 0.0100.010 mm, cutting speed is 130130 m/min, rake angle is 15∘15^\circ and width of cut is 66 mm. It is observed that the chip thickness is 0.0150.015 mm, the cutting force is 6060 N and the thrust force is 2525 N. The ratio of friction energy to total energy is __________ (correct to two decimal places).
    Your answer

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  50. Think it through. Then check your answer.

    Question

    A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is _________________ (correct to two decimal places).
    Your answer

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  51. Think it through. Then check your answer.

    Question

    The minimum value of 3x+5y3x + 5y
    such that:
    3x+5y≤153x + 5y \leq 15
    4x+9y≤84x + 9y \leq 8
    13x+2y≤213x + 2y \leq 2
    x≥0,y≥0x \geq 0, y \geq 0
    is _______.
    Your answer

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  52. Think it through. Then check your answer.

    Question

    Processing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is ___________ (correct to two decimal places).
    JobProcessing time (days)Due date (days)
    A38
    B716
    C44
    D918
    E517
    F1319
    Your answer

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  53. Think it through. Then check your answer.

    Question

    The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at point X. A force F=100F = 100 N is applied at the free end of the lever as shown. Given that the coefficient of friction between the shoe and the drum is 0.3, the braking torque (in Nm ) applied on the drum is _______ (correct to two decimal places).
    Schematic of an external drum brake with a lever XYZ and a force F applied at Z
    (All dimensions are in mm)
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

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  54. Think it through. Then check your answer.

    Question

    Block P of mass 2 kg slides down the surface and has a speed 20 m/s at the lowest point, Q, where the local radius of curvature is 2 m as shown in the figure. Assuming g=10g = 10 m/s2^2, the normal force (in N) at Q is _______ (correct to two decimal places).
    Block P sliding down a curved surface to point Q
    Your answer

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    Question

    An electrochemical machining (ECM) is to be used to cut a through hole into a 12 mm12\text{ mm} thick aluminum plate. The hole has a rectangular cross-section, 10 mm×30 mm10\text{ mm} \times 30\text{ mm}. The ECM operation will be accomplished in 2 minutes2\text{ minutes}, with efficiency of 90%90\%. Assuming specific removal rate for aluminum as 3.44×10−2 mm3/(A s)3.44 \times 10^{-2}\text{ mm}^3/(A\text{ s}), the current (in A) required is __________ (correct to two decimal places).
    Your answer

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