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GATE ME 2017 Set 1

All 65 solved GATE ME 2017 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 27Medium 35Hard 3

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    He was one of my best ______ and I felt his loss ______.
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    As the two speakers became increasingly agitated, the debate became ________.
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    Question

    A right-angled cone (with base radius 5 cm5\text{ cm} and height 12 cm12\text{ cm}), as shown in the figure below, is rolled on the ground keeping the point PP fixed until the point QQ (at the base of the cone, as shown) touches the ground again.
    A right-angled cone with base radius $5\text{ cm}$ and height $12\text{ cm}$ rolling on the ground with apex $P$ fixed
    By what angle (in radians) about PP does the cone travel?
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    Question

    In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000, 8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is
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    Question

    PP, QQ, and RR talk about SS’s car collection. PP states that SS has at least 3 cars. QQ believes that SS has less than 3 cars. RR indicates that to his knowledge, SS has at least one car. Only one of PP, QQ and RR is right. The number of cars owned by SS is
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    Question

    “Here, throughout the early 1820s, Stuart continued to fight his losing battle to allow his sepoys to wear their caste-marks and their own choice of facial hair on parade, being again reprimanded by the commander-in-chief. His retort that ‘A stronger instance than this of European prejudice with relation to this country has never come under my observations’ had no effect on his superiors.”
    According to this paragraph, which of the statements below is most accurate?
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    Question

    What is the sum of the missing digits in the subtraction problem below?
    A subtraction problem with missing digits represented by underscores
    5 _ _ _ _−4 8 _ 8 91 1 1 1\begin{array}{r} 5 \text{ } \_ \text{ } \_ \text{ } \_ \text{ } \_ \\ - 4 \text{ } 8 \text{ } \_ \text{ } 8 \text{ } 9 \\ \hline 1 \text{ } 1 \text{ } 1 \text{ } 1 \end{array}
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    Question

    Let S1S_1 be the plane figure consisting of the points (x,y)(x, y) given by the inequalities ∣x−1∣≤2|x - 1| \leq 2 and ∣y+2∣≤3|y + 2| \leq 3. Let S2S_2 be the plane figure given by the inequalities x−y≥−2x - y \geq -2, y≥1y \geq 1, and x≤3x \leq 3. Let SS be the union of S1S_1 and S2S_2. The area of SS is
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    Question

    Two very famous sportsmen Mark and Steve happened to be brothers, and played for country K. Mark teased James, an opponent from country E, "There is no way you are good enough to play for your country." James replied, "Maybe not, but at least I am the best player in my own family."
    Which one of the following can be inferred from this conversation?
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    Question

    The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of 0.8 (in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in 1 litre of milk is plotted as a function of time, at two different temperatures, 25 ∘C25\text{ }^\circ\text{C} and 37 ∘C37\text{ }^\circ\text{C}.
    Graph showing population density of lactobacillus vs time at 25°C and 37°C
    Consider the following statements based on the data shown above:
    i. The growth in bacterial population stops earlier at 37 ∘C37\text{ }^\circ\text{C} as compared to 25 ∘C25\text{ }^\circ\text{C}
    ii. The time taken for curd formation at 25 ∘C25\text{ }^\circ\text{C} is twice the time taken at 37 ∘C37\text{ }^\circ\text{C}Which one of the following options is correct?
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Mechanical Engineering

55
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    Question

    The product of eigenvalues of the matrix PP isP=[2014−3302−1]P = \begin{bmatrix} 2 & 0 & 1 \\ 4 & -3 & 3 \\ 0 & 2 & -1 \end{bmatrix}
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    Question

    The value of lim⁡x→0x3−sin⁡(x)x\lim_{x \to 0} \frac{x^3 - \sin(x)}{x} is
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    Question

    Consider the following partial differential equation for u(x,y)u(x, y) with the constant c>1c > 1:∂u∂y+c∂u∂x=0\frac{\partial u}{\partial y} + c \frac{\partial u}{\partial x} = 0Solution of this equation is
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    Question

    The differential equation d2ydx2+16y=0\frac{d^2y}{dx^2} + 16y = 0 for y(x)y(x) with the two boundary conditions dydx∣x=0=1\left. \frac{dy}{dx} \right|_{x=0} = 1 and dydx∣x=π2=−1\left. \frac{dy}{dx} \right|_{x=\frac{\pi}{2}} = -1 has
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    Question

    A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _______
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    Question

    For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?
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    Question

    Consider the two-dimensional velocity field given by V⃗=(5+a1x+b1y)i^+(4+a2x+b2y)j^\vec{V} = (5 + a_1x + b_1y)\hat{i} + (4 + a_2x + b_2y)\hat{j}, where a1,b1,a2a_1, b_1, a_2 and b2b_2 are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?
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    Question

    Water (density = 1000 kg/m31000 \text{ kg/m}^3) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of 1 kg/s1 \text{ kg/s}. If the pressure drop across the pipe is 100 kPa100 \text{ kPa}, the minimum power required to pump the water across the pipe, in watts, is ________.
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    Which one of the following is NOT a rotating machine?
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    Question

    Saturated steam at 100∘C100^\circ\text{C} condenses on the outside of a tube. Cold fluid enters the tube at 20∘C20^\circ\text{C} and exits at 50∘C50^\circ\text{C}. The value of the Log Mean Temperature Difference (LMTD) is ________ ∘C^\circ\text{C}.
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    Question

    The molar specific heat at constant volume of an ideal gas is equal to 2.52.5 times the universal gas constant (8.314 J/mol⋅K8.314\text{ J/mol}\cdot\text{K}). When the temperature increases by 100 K100\text{ K}, the change in molar specific enthalpy is ________ J/mol\text{J/mol}.
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    Question

    A heat pump absorbs 10 kW10\text{ kW} of heat from outside environment at 250 K250\text{ K} while absorbing 15 kW15\text{ kW} of work. It delivers the heat to a room that must be kept warm at 300 K300\text{ K}. The Coefficient of Performance (COP) of the heat pump is ________.
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    The Poisson's ratio for a perfectly incompressible linear elastic material is
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    Question

    A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t)=t2,θ(t)=tr(t) = t^2, \theta(t) = t, where tt is time. The kinetic energy of the particle at time t=2t = 2 is
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    Question

    A motor driving a solid circular steel shaft transmits 40 kW40\text{ kW} of power at 500 rpm500\text{ rpm}. If the diameter of the shaft is 40 mm40\text{ mm}, the maximum shear stress in the shaft is ______ MPa.
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    Question

    Consider a beam with circular cross-section of diameter dd. The ratio of the second moment of area about the neutral axis to the section modulus of the area is
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    Question

    The following figure shows the velocity-time plot for a particle traveling along a straight line. The distance covered by the particle from t=0t = 0 to t=5t = 5 s is ______ m.
    velocity-time plot for a particle
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    Question

    The damping ratio for a viscously damped spring mass system, governed by the relationship md2xdt2+cdxdt+kx=F(t)m \frac{d^2x}{dt^2} + c \frac{dx}{dt} + kx = F(t), is given by
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    Question

    Consider the schematic of a riveted lap joint subjected to tensile load FF, as shown below. Let dd be the diameter of the rivets, and SfS_f be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of the plates? Assume the plates to be identical.
    Schematic of a riveted lap joint showing top and side views
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    Question

    Cylindrical pins of diameter 15±0.02015^{\pm 0.020} mm are being produced on a machine. Statistical quality control tests show a mean of 14.99514.995 mm and standard deviation of 0.0040.004 mm. The process capability index CpC_p is
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    Question

    In a metal forming operation when the material has just started yielding, the principal stresses are σ1=+180 MPa\sigma_1 = +180 \text{ MPa}, σ2=−100 MPa\sigma_2 = -100 \text{ MPa}, σ3=0\sigma_3 = 0. Following von Mises' criterion, the yield stress is ________ MPa.
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    Question

    Match the processes with their characteristics.
    ProcessCharacteristics
    P: Electrical Discharge Machining1. No residual stress
    Q: Ultrasonic machining2. Machining of electrically conductive materials
    R: Chemical machining3. Machining of glass
    S: Ion Beam Machining4. Nano-machining
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    In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sectional area of the weld bead will
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    Metric thread of 0.80.8 mm pitch is to be cut on a lathe. Pitch of the lead screw is 1.51.5 mm. If the spindle rotates at 15001500 rpm, the speed of rotation of the lead screw (rpm) will be
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    In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers to
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    Question

    Consider the matrix P=[12012010−12012]P = \begin{bmatrix} \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ 0 & 1 & 0 \\ \frac{-1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \end{bmatrix}.
    Which one of the following statements about PP is INCORRECT?
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    For the vector V⃗=2yzi^+3xzj^+4xyk^\vec{V} = 2yz \hat{i} + 3xz \hat{j} + 4xy \hat{k}, the value of ∇⋅(∇×V⃗)\nabla \cdot (\nabla \times \vec{V}) is ____________.
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    A parametric curve defined by x=cos⁡(πu2),y=sin⁡(πu2)x = \cos\left(\frac{\pi u}{2}\right), y = \sin\left(\frac{\pi u}{2}\right) in the range 0≤u≤10 \leq u \leq 1 is rotated about the X-axis by 360 degrees. Area of the surface generated is
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    Question

    P(0,3)P(0, 3), Q(0.5,4)Q(0.5, 4), and R(1,5)R(1, 5) are three points on the curve defined by f(x)f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson’s rule within limits x=0x = 0 and x=1x = 1 for the curve. The difference between the two results will be
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    The velocity profile inside the boundary layer for flow over a flat plate is given as uU∞=sin⁡(πy2δ)\frac{u}{U_\infty} = \sin\left(\frac{\pi y}{2\delta}\right), where U∞U_\infty is the free stream velocity and δ\delta is the local boundary layer thickness. If δ∗\delta^* is the local displacement thickness, the value of δ∗δ\frac{\delta^*}{\delta} is
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    Consider steady flow of an incompressible fluid through two long and straight pipes of diameters d1d_1 and d2d_2 arranged in series. Both pipes are of equal length and the flow is turbulent in both pipes. The friction factor for turbulent flow though pipes is of the form, f=K(Re)−nf = K(Re)^{-n}, where KK and nn are known positive constants and ReRe is the Reynolds number. Neglecting minor losses, the ratio of the frictional pressure drop in pipe 1 to that in pipe 2, (ΔP1ΔP2)(\frac{\Delta P_1}{\Delta P_2}), is given by
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    For a steady flow, the velocity field is V⃗=(−x2+3y)i^+(2xy)j^\vec{V} = (-x^2 + 3y)\hat{i} + (2xy)\hat{j}. The magnitude of the acceleration of a particle at (1,−1)(1, -1) is
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    One kg of an ideal gas (gas constant, R=400 J/kg⋅KR = 400\text{ J/kg}\cdot\text{K}; specific heat at constant volume, cv=1000 J/kg⋅Kc_v = 1000\text{ J/kg}\cdot\text{K}) at 1 bar, and 300 K is contained in a sealed rigid cylinder. During an adiabatic process, 100 kJ of work is done on the system by a stirrer. The increase in entropy of the system is ______ J/K.
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    The pressure ratio across a gas turbine (for air, specific heat at constant pressure, cp=1040c_p = 1040 J/kg·K and ratio of specific heats, γ=1.4\gamma = 1.4) is 10. If the inlet temperature to the turbine is 1200 K and the isentropic efficiency is 0.9, the gas temperature at turbine exit is ______ K.
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    Moist air is treated as an ideal gas mixture of water vapor and dry air (molecular weight of air = 28.84 and molecular weight of water = 18). At a location, the total pressure is 100 kPa, the temperature is 30∘C30^\circ\text{C} and the relative humidity is 55%. Given that the saturation pressure of water at 30∘C30^\circ\text{C} is 4246 Pa, the mass of water vapor per kg of dry air is ______ grams.
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    Air contains 79% N2N_2 and 21% O2O_2 on a molar basis. Methane (CH4CH_4) is burned with 50% excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of N2N_2 in the products is ______.
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    Two black surfaces, AB and BC, of lengths 5 m5\text{ m} and 6 m6\text{ m}, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor F12=0.5F_{12} = 0.5, T1=800 KT_1 = 800\text{ K}, T2=600 KT_2 = 600\text{ K}, Tsurrounding=300 KT_{\text{surrounding}} = 300\text{ K} and Stefan Boltzmann constant, σ=5.67×10−8 W/(m2K4)\sigma = 5.67 \times 10^{-8}\text{ W}/(\text{m}^2\text{K}^4), the heat transfer rate from Surface 2 to the surrounding environment is ________ kW.
    Diagram showing two black surfaces AB and BC and the surrounding environment

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    Question

    Heat is generated uniformly in a long solid cylindrical rod (diameter =10 mm= 10\text{ mm}) at the rate of 4×107 W/m34 \times 10^7\text{ W}/\text{m}^3. The thermal conductivity of the rod material is 25 W/m⋅K25\text{ W}/\text{m}\cdot\text{K}. Under steady state conditions, the temperature difference between the centre and the surface of the rod is ________ ∘C^\circ\text{C}.
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    An initially stress-free massless elastic beam of length LL and circular cross-section with diameter dd (d≪Ld \ll L) is held fixed between two walls as shown. The beam material has Young's modulus EE and coefficient of thermal expansion α\alpha.
    Massless elastic beam fixed between two walls
    If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to
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    A point mass of 100 kg100\text{ kg} is dropped onto a massless elastic bar (cross-sectional area =100 mm2= 100\text{ mm}^2, length =1 m= 1\text{ m}, Young's modulus =100 GPa= 100\text{ GPa}) from a height HH of 10 mm10\text{ mm} as shown (Figure is not to scale). If g=10 m/s2g = 10\text{ m/s}^2, the maximum compression of the elastic bar is _____ mm.
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    Two disks A and B with identical mass (mm) and radius (RR) are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the center of disk A to the velocity of the center of disk B is
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    A rectangular region in a solid is in a state of plane strain. The (x,y)(x, y) coordinates of the corners of the undeformed rectangle are given by P(0,0)P(0, 0), Q(4,0)Q(4, 0), R(4,3)R(4, 3), S(0,3)S(0, 3). The rectangle is subjected to uniform strains, ϵxx=0.001\epsilon_{xx} = 0.001, ϵyy=0.002\epsilon_{yy} = 0.002, γxy=0.003\gamma_{xy} = 0.003. The deformed length of the elongated diagonal, upto three decimal places, is ________ units.
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    A machine element has an ultimate strength (σu\sigma_u) of 600 N/mm2600\text{ N/mm}^2, and endurance limit (σen\sigma_{en}) of 250 N/mm2250\text{ N/mm}^2. The fatigue curve for the element on a log-log plot is shown below. If the element is to be designed for a finite life of 1000010000 cycles, the maximum amplitude of a completely reversed operating stress is ______ N/mm2\text{N/mm}^2.
    Log-log plot of failure stress vs number of cycles showing points A at (10^3, 0.8*sigma_u) and B at (10^6, sigma_en)
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    Question

    A horizontal bar, fixed at one end (x=0x = 0), has a length of 1 m1\text{ m}, and cross-sectional area of 100 mm2100\text{ mm}^2. Its elastic modulus varies along its length as given by E(x)=100e−x GPaE(x) = 100 e^{-x}\text{ GPa}, where xx is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN10\text{ kN} is applied at the free end (x=1x = 1). The axial displacement of the free end is ______ mm.
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    Question

    In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100 rpm100\ rpm. Let the number of teeth on the sun, planet and outer gears be 5050, 2525, and 100100, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is ______.
    Diagram of an epicyclic gear train with sun gear, planet gear, outer ring gear, and carrier arm
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    Question

    A thin uniform rigid bar of length LL and mass MM is hinged at point O, located at a distance of L3\frac{L}{3} from one of its ends. The bar is further supported using springs, each of stiffness kk, located at the two ends. A particle of mass m=M4m = \frac{M}{4} is fixed at one end of the bar, as shown in the figure. For small rotations of the bar about O, the natural frequency of the system is
    A rigid bar of length L hinged at O (L/3 from left end) with springs of stiffness k at both ends and a mass m at the right end.
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    Question

    For an inline slider-crank mechanism, the lengths of the crank and connecting rod are 33 m and 44 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 11 m/s, the magnitude of angular velocity (upto 33 decimal points accuracy) of the crank is ________ radian/s.
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    Question

    A 1010 mm deep cylindrical cup with diameter of 1515 mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto 22 decimal points accuracy) of the blank is ________ mm.
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    Question

    Circular arc on a part profile is being machined on a vertical CNC milling machine. CNC part program using metric units with absolute dimensions is listed below:
    N60 G01 X 30 Y 55 Z -5 F50
N70 G02 X 50 Y 35 R 20
N80 G01 Z 5
    The coordinates of the centre of the circular arc are:
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    Question

    Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is 20 μm20\ \mu\text{m}, the central line average surface roughness RaR_a (in μm\mu\text{m}) is
    Triangular surface roughness profile
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    Question

    Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is ________.
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    Question

    Following data refers to the jobs (P, Q, R, S) which have arrived at a machine for scheduling. The shortest possible average flow time is ________ days.
    JobProcessing Time (days)
    P15
    Q9
    R22
    S12
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    Question

    A block of length 200 mm200\text{ mm} is machined by a slab milling cutter 34 mm34\text{ mm} in diameter. The depth of cut and table feed are set at 2 mm2\text{ mm} and 18 mm/minute18\text{ mm/minute}, respectively. Considering the approach and the over travel of the cutter to be same, the minimum estimated machining time per pass is ________ minutes.
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    A sprue in a sand mould has a top diameter of 20 mm20\text{ mm} and height of 200 mm200\text{ mm}. The velocity of the molten metal at the entry of the sprue is 0.5 m/s0.5\text{ m/s}. Assume acceleration due to gravity as 9.8 m/s29.8\text{ m/s}^2 and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.
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    Question

    Two cutting tools with tool life equations given below are being compared:
    Tool 1: VT0.1=150VT^{0.1} = 150
    Tool 2: VT0.3=300VT^{0.3} = 300
    where VV is cutting speed in m/minute and TT is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ______ m/minute.
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