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GATE ME 2016 Set 1

All 65 solved GATE ME 2016 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 26Medium 36Hard 3

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Which of the following is CORRECT with respect to grammar and usage?
    Mount Everest is ____________.
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    Question

    The policeman asked the victim of a theft, “What did you ____________?”
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    Question

    Despite the new medicine’s ____________ in treating diabetes, it is not ____________widely.
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    Question

    In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples?
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    Question

    Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?
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    Question

    A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?
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    Question

    In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong.
    Which of the following inference(s) is/are logically valid and can be inferred from the above passage?
    (i) His friends were always asking him to help them.
    (ii) He felt that when in need of help, his friends would let him down.
    (iii) He was sure that his friends would help him when in need.
    (iv) His friends did not help him last week.
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    Question

    Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.
    Which one of the following statements must be TRUE based on the above?
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    Question

    If q−a=1rq^{-a} = \frac{1}{r} and r−b=1sr^{-b} = \frac{1}{s} and s−c=1qs^{-c} = \frac{1}{q}, the value of abcabc is ________.
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    Question

    P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?
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Mechanical Engineering (ME)

55
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    Question

    The solution to the system of equations[12−43]{xy}={2−30}\begin{bmatrix} 1 & 2 \\ -4 & 3 \\ \end{bmatrix} \begin{Bmatrix} x \\ y \\ \end{Bmatrix} = \begin{Bmatrix} 2 \\ -30 \\ \end{Bmatrix}is
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    Question

    If f(t)f(t) is a function defined for all t≥0t \geq 0, its Laplace transform F(s)F(s) is defined as
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    Question

    f(z)=u(x,y)+iv(x,y)f(z) = u(x, y) + i v(x, y) is an analytic function of complex variable z=x+iyz = x + iy where i=−1i = \sqrt{-1}. If u(x,y)=2xyu(x, y) = 2xy, then v(x,y)v(x, y) may be expressed as
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    Question

    Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is μ\mu. The standard deviation for this distribution is given by
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    Question

    Solve the equation x=10cos⁡(x)x = 10 \cos(x) using the Newton-Raphson method. The initial guess is x=π/4x = \pi/4. The value of the predicted root after the first iteration, up to second decimal, is ________
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    Question

    A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force FF such that the string makes an angle of 30∘30^\circ with the vertical. The magnitude of force FF (in N) is __________
    A rigid ball of weight 100 N suspended by a string making an angle of 30 degrees with the vertical, pulled by a horizontal force F
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    Question

    A point mass MM is released from rest and slides down a spherical bowl (of radius RR) from a height HH as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is
    A point mass M sliding down a spherical bowl of radius R from height H
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    Question

    The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that r3>r1r_3 > r_1 and r4>r2r_4 > r_2, and that the areas of the cross-sections are the same. J1J_1 and J2J_2 are the torsional rigidities of the bars on the left and right, respectively. The ratio J2/J1J_2/J_1 is
    Cross sections of two hollow bars with radii r1, r2 and r3, r4
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    Question

    A cantilever beam having square cross-section of side aa is subjected to an end load. If aa is increased by 19%, the tip deflection decreases approximately by
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    Question

    A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car. The combined moment of inertia of the rotating masses is 10 kg-m2^2. The magnitude of the gyroscopic moment (in N-m) is __________
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    Question

    A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm.
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    Question

    The spring constant of a helical compression spring DOES NOT depend on
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    Question

    The instantaneous stream-wise velocity of a turbulent flow is given as follows:u(x,y,z,t)=uˉ(x,y,z)+u′(x,y,z,t)u(x, y, z, t) = \bar{u}(x, y, z) + u'(x, y, z, t)The time-average of the fluctuating velocity u′(x,y,z,t)u'(x, y, z, t) is
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    Question

    For a floating body, buoyant force acts at the
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    Question

    A plastic sleeve of outer radius r0=1 mmr_0 = 1\text{ mm} covers a wire (radius r=0.5 mmr = 0.5\text{ mm}) carrying electric current. Thermal conductivity of the plastic is 0.15 W/m-K0.15\text{ W/m-K}. The heat transfer coefficient on the outer surface of the sleeve exposed to air is 25 W/m2-K25\text{ W/m}^2\text{-K}. Due to the addition of the plastic cover, the heat transfer from the wire to the ambient will
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    Question

    Which of the following statements are TRUE with respect to heat and work?
    (i) They are boundary phenomena
    (ii) They are exact differentials
    (iii) They are path functions
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    Question

    Propane (C3H8C_3H_8) is burned in an oxygen atmosphere with 10% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, the volume percentage of CO in the products is __________
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    Question

    Consider two hydraulic turbines having identical specific speed and effective head at the inlet. If the speed ratio (N1/N2N_1/N_2) of the two turbines is 2, then the respective power ratio (P1/P2P_1/P_2) is _____________
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    Question

    The INCORRECT statement about regeneration in vapor power cycle is that
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    Question

    The "Jominy test” is used to find
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    Question

    Under optimal conditions of the process the temperatures experienced by a copper work piece in fusion welding, brazing and soldering are such that
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    Question

    The part of a gating system which regulates the rate of pouring of molten metal is
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    Question

    The non-traditional machining process that essentially requires vacuum is
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    Question

    In an orthogonal cutting process the tool used has rake angle of zero degree. The measured cutting force and thrust force are 500 N and 250 N, respectively. The coefficient of friction between the tool and the chip is _________
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    Question

    Match the following:
    Column 1Column 2
    P. Feeler gaugeI. Radius of an object
    Q. Fillet gaugeII. Diameter within limits by comparison
    R. Snap gaugeIII. Clearance or gap between components
    S. Cylindrical plug gaugeIV. Inside diameter of straight hole
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    Question

    Consider the function f(x)=2x3−3x2f(x) = 2x^3 - 3x^2 in the domain [−1,2][-1, 2]. The global minimum of f(x)f(x) is ____________
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    If y=f(x)y = f(x) satisfies the boundary value problem y′′+9y=0y'' + 9y = 0, y(0)=0y(0) = 0, y(π/2)=2y(\pi/2) = \sqrt{2}, then y(π/4)y(\pi/4) is ________
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    The value of the integral ∫−∞∞sin⁡xx2+2x+2dx\int_{-\infty}^{\infty} \frac{\sin x}{x^2 + 2x + 2} dx evaluated using contour integration and the residue theorem is
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    Question

    Gauss-Seidel method is used to solve the following equations (as per the given order):
    x1+2x2+3x3=5x_1 + 2x_2 + 3x_3 = 5
    2x1+3x2+x3=12x_1 + 3x_2 + x_3 = 1
    3x1+2x2+x3=33x_1 + 2x_2 + x_3 = 3
    Assuming initial guess as x1=x2=x3=0x_1 = x_2 = x_3 = 0, the value of x3x_3 after the first iteration is ________
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    Question

    A block of mass mm rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is 0.25. The string can withstand a maximum force of 20 N. The maximum value of the mass (mm) for which the string will not break and the block will be in static equilibrium is ____________ kg.
    Take cos⁡θ=0.8\cos \theta = 0.8 and sin⁡θ=0.6\sin \theta = 0.6.
    Acceleration due to gravity g=10 m/s2g = 10 \text{ m/s}^2
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    Question

    A two-member truss PQRPQR is supporting a load WW. The axial forces in members PQPQ and QRQR are respectively
    A two-member truss PQR with a vertical load W at joint Q. Member PQ is horizontal with length L. Member QR is inclined at an angle such that the angle at R is 60 degrees and the angle at Q between PQ and QR is 30 degrees.
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    Question

    A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections ABAB and BCBC are 3E3E and EE, respectively.
    A horizontal bar fixed at A, with a force P acting leftwards at B and a force F acting rightwards at C. Lengths AB = L and BC = L.

    For the deflection at CC to be zero, the ratio P/FP/F is ____________
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    Question

    The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in mm4mm^4) of this cross-section about its base is ____________
    A square cross-section of 10mm x 10mm with two semi-circular cutouts of radius R=4mm on the left and right sides, centered at a height of 5mm from the base. All dimensions are in mm.
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    Question

    A simply-supported beam of length 3L3L is subjected to the loading shown in the figure.
    Simply-supported beam with two point loads
    It is given that P=1P = 1 N, L=1L = 1 m and Young’s modulus E=200E = 200 GPa. The cross-section is a square with dimension 10 mm×10 mm10 \text{ mm} \times 10 \text{ mm}. The bending stress (in Pa) at the point A located at the top surface of the beam at a distance of 1.5L1.5L from the left end is _____________
    (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)
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    Question

    A slider crank mechanism with crank radius 200 mm200 \text{ mm} and connecting rod length 800 mm800 \text{ mm} is shown. The crank is rotating at 600 rpm600 \text{ rpm} in the counterclockwise direction. In the configuration shown, the crank makes an angle of 90∘90^\circ with the sliding direction of the slider, and a force of 5 kN5 \text{ kN} is acting on the slider. Neglecting the inertia forces, the turning moment on the crank (in kN-m) is __________
    Slider crank mechanism diagram
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    In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The number of teeth on gear 2, 3, and 4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4 rotates with an angular velocity of 100 rpm100\text{ rpm} in the counterclockwise direction, the angular speed of arm 5 (in rpm) is
    epicyclic gear train with sun gear 2, planet gear 3 on arm 5, and ring gear 4
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    Question

    A solid disc with radius aa is connected to a spring at a point dd above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is MM and the spring constant is KK. The polar moment of inertia for the disc about its centre is J=Ma2/2J = Ma^2/2.
    A solid disc with radius a and mass M rolling on the ground, connected to a spring with constant K at a point d above its center.
    The natural frequency of this system in rad/s is given by
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    Question

    The principal stresses at a point inside a solid object are σ1=100 MPa\sigma_1 = 100\text{ MPa}, σ2=100 MPa\sigma_2 = 100\text{ MPa} and σ3=0 MPa\sigma_3 = 0\text{ MPa}. The yield strength of the material is 200 MPa200\text{ MPa}. The factor of safety calculated using Tresca (maximum shear stress) theory is nTn_T and the factor of safety calculated using von Mises (maximum distortional energy) theory is nVn_V. Which one of the following relations is TRUE?
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    Question

    An inverted U-tube manometer is used to measure the pressure difference between two pipes A and B, as shown in the figure. Pipe A is carrying oil (specific gravity = 0.8) and pipe B is carrying water. The densities of air and water are 1.16 kg/m31.16\text{ kg/m}^3 and 1000 kg/m31000\text{ kg/m}^3, respectively. The pressure difference between pipes A and B is __________ kPa.
    Acceleration due to gravity g = 10 m/s2^2.
    Inverted U-tube manometer diagram connecting pipes A and B with oil, air, and water columns
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    Question

    Oil (kinematic viscosity, νoil=1.0×10−5 m2/s\nu_{oil} = 1.0 \times 10^{-5} \text{ m}^2/\text{s}) flows through a pipe of 0.5 m0.5 \text{ m} diameter with a velocity of 10 m/s10 \text{ m/s}. Water (kinematic viscosity, νw=0.89×10−6 m2/s\nu_w = 0.89 \times 10^{-6} \text{ m}^2/\text{s}) is flowing through a model pipe of diameter 20 mm20 \text{ mm}. For satisfying the dynamic similarity, the velocity of water (in m/s) is __________
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    A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is UoU_o. The velocity profile at the inlet a−ba-b is uniform, while that at a downstream location c−dc-d is given by u=Uo[2(yδ)−(yδ)2]u = U_o \left[ 2 \left( \frac{y}{\delta} \right) - \left( \frac{y}{\delta} \right)^2 \right].
    Boundary layer flow over a flat plate showing inlet section a-b and downstream section c-d with velocity profiles
    The ratio of the mass flow rate, m˙bd\dot{m}_{bd}, leaving through the horizontal section b−db-d to that entering through the vertical section a−ba-b is ___________
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    Question

    A steel ball of 10 mm10 \text{ mm} diameter at 1000 K1000 \text{ K} is required to be cooled to 350 K350 \text{ K} by immersing it in a water environment at 300 K300 \text{ K}. The convective heat transfer coefficient is 1000 W/m2-K1000 \text{ W/m}^2\text{-K}. Thermal conductivity of steel is 40 W/m-K40 \text{ W/m-K}. The time constant for the cooling process τ\tau is 16 s16 \text{ s}. The time required (in s) to reach the final temperature is __________
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    Question

    An infinitely long furnace of 0.5 m×0.4 m0.5\text{ m} \times 0.4\text{ m} cross-section is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature T1=T3=927∘CT_1 = T_3 = 927^\circ\text{C} while the side walls are at temperature T2=T4=527∘CT_2 = T_4 = 527^\circ\text{C}. The view factor, F1−2F_{1-2} is 0.260.26. The net radiation heat loss or gain on side 1 is_________ W/m.
    Stefan-Boltzmann constant =5.67×10−8 W/m2-K4= 5.67 \times 10^{-8}\text{ W/m}^2\text{-K}^4
    Cross-section of a rectangular furnace with sides labeled 1 to 4 and their respective temperatures
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    Question

    A fluid (Prandtl number, Pr=1Pr = 1) at 500 K500\text{ K} flows over a flat plate of 1.5 m1.5\text{ m} length, maintained at 300 K300\text{ K}. The velocity of the fluid is 10 m/s10\text{ m/s}. Assuming kinematic viscosity, ν=30×10−6 m2/s\nu = 30 \times 10^{-6}\text{ m}^2\text{/s}, the thermal boundary layer thickness (in mm) at 0.5 m0.5\text{ m} from the leading edge is __________
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    For water at 25∘C25^\circ\text{C}, dps/dTs=0.189 kPa/Kdp_s/dT_s = 0.189\text{ kPa/K} (psp_s is the saturation pressure in kPa and TsT_s is the saturation temperature in K) and the specific volume of dry saturated vapour is 43.38 m3/kg43.38\text{ m}^3\text{/kg}. Assume that the specific volume of liquid is negligible in comparison with that of vapour. Using the Clausius-Clapeyron equation, an estimate of the enthalpy of evaporation of water at 25∘C25^\circ\text{C} (in kJ/kg) is __________
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    An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript 1) and at the end (subscript 2) of the process with usual notation are: p1=100 kPap_1 = 100 \text{ kPa}, V1=0.2 m3V_1 = 0.2 \text{ m}^3 and p2=200 kPap_2 = 200 \text{ kPa}, V2=0.1 m3V_2 = 0.1 \text{ m}^3 and the gas constant, R=0.275 kJ/kg-KR = 0.275 \text{ kJ/kg-K}. The magnitude of the work required for the process (in kJ) is ________
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    In a steam power plant operating on an ideal Rankine cycle, superheated steam enters the turbine at 3 MPa and 350 ∘^\circ C. The condenser pressure is 75 kPa. The thermal efficiency of the cycle is ________ percent.
    Given data:
    For saturated liquid, at P=75 kPaP = 75 \text{ kPa}, hf≅384.39 kJ/kgh_f \cong 384.39 \text{ kJ/kg}, vf≅0.001037 m3/kgv_f \cong 0.001037 \text{ m}^3/\text{kg}, sf=1.213 kJ/kg-Ks_f = 1.213 \text{ kJ/kg-K}
    At 75 kPa, hfg=2278.6 kJ/kgh_{fg} = 2278.6 \text{ kJ/kg}, sfg=6.2434 kJ/kg-Ks_{fg} = 6.2434 \text{ kJ/kg-K}
    At P=3 MPaP = 3 \text{ MPa} and T=350 ∘CT = 350 \text{ }^\circ\text{C} (superheated steam), h≅3115.3 kJ/kgh \cong 3115.3 \text{ kJ/kg}, s≅6.7428 kJ/kg-Ks \cong 6.7428 \text{ kJ/kg-K}
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    A hypothetical engineering stress-strain curve shown in the figure has three straight lines PQ, QR, RS with coordinates P(0,0), Q(0.2,100), R(0.6,140) and S(0.8,130). 'Q' is the yield point, 'R' is the UTS point and 'S' the fracture point.
    Engineering stress-strain curve with points P, Q, R, S
    The toughness of the material (in MJ/m3^3) is __________
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    Heat is removed from a molten metal of mass 22 kg at a constant rate of 1010 kW till it is completely solidified. The cooling curve is shown in the figure.
    Temperature (K) vs Time (s) cooling curve for a molten metal
    Assuming uniform temperature throughout the volume of the metal during solidification, the latent heat of fusion of the metal (in kJ/kg) is
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    The tool life equation for HSS tool is VT0.14f0.7d0.4=ConstantVT^{0.14} f^{0.7} d^{0.4} = \text{Constant}. The tool life (TT) of 30 min is obtained using the following cutting conditions:
    V=45 m/minV = 45 \text{ m/min}, f=0.35 mmf = 0.35 \text{ mm}, d=2.0 mmd = 2.0 \text{ mm}
    If speed (VV), feed (ff) and depth of cut (dd) are increased individually by 25%, the tool life (in min) is
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    A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) is
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    A 300300 mm thick slab is being cold rolled using roll of 600600 mm diameter. If the coefficient of friction is 0.080.08, the maximum possible reduction (in mm) is __________
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    The figure below represents a triangle PQRPQR with initial coordinates of the vertices as P(1,3)P(1,3), Q(4,5)Q(4,5) and R(5,3.5)R(5,3.5). The triangle is rotated in the X−YX-Y plane about the vertex PP by angle θ\theta in clockwise direction. If sin⁡θ=0.6\sin \theta = 0.6 and cos⁡θ=0.8\cos \theta = 0.8, the new coordinates of the vertex QQ are
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    The annual demand for an item is 10,00010,000 units. The unit cost is Rs. 100100 and inventory carrying charges are 14.4%14.4\% of the unit cost per annum. The cost of one procurement is Rs. 20002000. The time between two consecutive orders to meet the above demand is _______ month(s).
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    Maximize Z=15X1+20X2Z = 15X_1 + 20X_2
    subject to12X1+4X2≥3612X_1 + 4X_2 \geq 3612X1−6X2≤2412X_1 - 6X_2 \leq 24X1,X2≥0X_1, X_2 \geq 0The above linear programming problem has
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