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GATE ME 2016 Set 3

All 65 solved GATE ME 2016 Set 3 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

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Difficulty mixEasy 34Medium 30Hard 1

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Based on the given statements, select the appropriate option with respect to grammar and usage.
    Statements
    (i) The height of Mr. X is 6 feet.
    (ii) The height of Mr. Y is 5 feet.
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    Question

    The students ___________ the teacher on teachers’ day for twenty years of dedicated teaching.
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    Question

    After India’s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket till then, decided to concentrate only on cricket. And the rest is history.
    What does the underlined phrase mean in this context?
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    Question

    Given (9 inches)1/2=(0.25 yards)1/2(9 \text{ inches})^{1/2} = (0.25 \text{ yards})^{1/2}, which one of the following statements is TRUE?
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    Question

    S,M,ES, M, E and FF are working in shifts in a team to finish a project. MM works with twice the efficiency of others but for half as many days as EE worked. SS and MM have 6 hour shifts in a day, whereas EE and FF have 12 hours shifts. What is the ratio of contribution of MM to contribution of EE in the project?
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    Question

    The Venn diagram shows the preference of the student population for leisure activities.
    Venn diagram showing student preferences for reading books, watching TV, and playing sports
    From the data given, the number of students who like to read books or play sports is ______.
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    Question

    Social science disciplines were in existence in an amorphous form until the colonial period when they were institutionalized. In varying degrees, they were intended to further the colonial interest. In the time of globalization and the economic rise of postcolonial countries like India, conventional ways of knowledge production have become obsolete.
    Which of the following can be logically inferred from the above statements?
    (i) Social science disciplines have become obsolete.
    (ii) Social science disciplines had a pre-colonial origin.
    (iii) Social science disciplines always promote colonialism.
    (iv) Social science must maintain disciplinary boundaries.
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    Question

    Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without number markings seemed to show 1:30. What is the actual current time shown by the clock?
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    Question

    M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?
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    Question

    A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
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Mechanical Engineering (ME)

55
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    Question

    A real square matrix AA is called skew-symmetric if
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    Question

    Ltx→0log⁡e(1+4x)e3x−1\text{Lt}_{x \to 0} \frac{\log_e (1+4x)}{e^{3x}-1} is equal to
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    Question

    Solutions of Laplace’s equation having continuous second-order partial derivatives are called
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    Question

    The area (in percentage) under standard normal distribution curve of random variable ZZ within limits from −3-3 to +3+3 is __________
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    Question

    The root of the function f(x)=x3+x−1f(x) = x^3+x-1 obtained after first iteration on application of Newton-Raphson scheme using an initial guess of x0=1x_0=1 is
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    Question

    A force FF is acting on a bent bar which is clamped at one end as shown in the figure.
    A bent bar clamped at its base with a force F applied at its free end at an angle of 60 degrees to the horizontal.
    The CORRECT free body diagram is
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    Question

    The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity I1I_1, while the circular cross-section has flexural rigidity I2I_2. Both sections have the same cross-sectional area. The ratio I1/I2I_1/I_2 is
    Square and circular cross-sections
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    Question

    The state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b).
    Stress elements in two coordinate systems
    The components (τxx,τyy,τxy)(\tau_{xx}, \tau_{yy}, \tau_{xy}) are given by
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    Question

    A rigid link PQPQ is undergoing plane motion as shown in the figure (VPV_P and VQV_Q are non-zero). VQPV_{QP} is the relative velocity of point QQ with respect to point PP.
    Rigid link PQ with velocity vectors
    Which one of the following is TRUE?
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    Question

    The number of degrees of freedom in a planar mechanism having nn links and jj simple hinge joints is
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    Question

    The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g=10 m/s2g = 10 \text{ m/s}^2. The natural frequency of this spring-mass system (in rad/s) is_____________
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    Question

    Which of the bearings given below SHOULD NOT be subjected to a thrust load?
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    Question

    A channel of width 450 mm450\text{ mm} branches into two sub-channels having width 300 mm300\text{ mm} and 200 mm200\text{ mm} as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is 0.9 m3/s0.9\text{ m}^3/\text{s} and the velocity in the sub-channel of width 200 mm200\text{ mm} is 3 m/s3\text{ m}/\text{s}, the velocity in the sub-channel of width 300 mm300\text{ mm} is _____________ m/s.
    Assume both inlet and outlet to be at the same elevation.
    diagram of branching channels showing main channel of width 450 mm and flow rate 0.9 m³/s branching into two sub-channels of widths 300 mm and 200 mm, with the 200 mm channel having a velocity of 3 m/s
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    Question

    For a certain two-dimensional incompressible flow, velocity field is given by 2xyi^−y2j^2xy \hat{i} - y^2 \hat{j}. The streamlines for this flow are given by the family of curves
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    Question

    Steady one-dimensional heat conduction takes place across the faces 1 and 3 of a composite slab consisting of slabs A and B in perfect contact as shown in the figure, where kA,kBk_A, k_B denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature T2T_2 (in ∘C^\circ\text{C}) is __________
    diagram of composite slab with slab A (width 0.1 m, kA = 20 W/m.K) and slab B (width 0.3 m, kB = 100 W/m.K). Face 1 is at T1 = 130°C and face 3 is at T3 = 30°C. Interface is face 2.
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    Question

    Grashof number signifies the ratio of
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    Question

    The INCORRECT statement about the characteristics of critical point of a pure substance is that
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    Question

    For a heat exchanger, ΔTmax\Delta T_{max} is the maximum temperature difference and ΔTmin\Delta T_{min} is the minimum temperature difference between the two fluids. LMTD is the log mean temperature difference. CminC_{min} and CmaxC_{max} are the minimum and the maximum heat capacity rates. The maximum possible heat transfer (QmaxQ_{max}) between the two fluids is
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    Question

    The blade and fluid velocities for an axial turbine are as shown in the figure.
    axial turbine blade velocity diagram
    The magnitude of absolute velocity at entry is 300 m/s300 \text{ m/s} at an angle of 65∘65^\circ to the axial direction, while the magnitude of the absolute velocity at exit is 150 m/s150 \text{ m/s}. The exit velocity vector has a component in the downward direction. Given that the axial (horizontal) velocity is the same at entry and exit, the specific work (in kJ/kg) is__________
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    Question

    Engineering strain of a mild steel sample is recorded as 0.100%0.100\%. The true strain is
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    Question

    Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminum. The shape of the cavity is a cylinder with 15 mm15\text{ mm} diameter. The size of the moulds are such that the outside temperature of the moulds do not increase appreciably beyond the atmospheric temperature during solidification. The sequence of solidification in the mould from the fastest to slowest is
    (Thermal conductivities of steel, copper and aluminum are 60.560.5, 401401 and 237 W/m-K237\text{ W/m-K}, respectively.
    Specific heats of steel, copper and aluminum are 434434, 385385 and 903 J/kg-K903\text{ J/kg-K}, respectively.
    Densities of steel, copper and aluminum are 78547854, 89338933 and 2700 kg/m32700\text{ kg/m}^3, respectively.)
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    Question

    In a wire-cut EDM process the necessary conditions that have to be met for making a successful cut are that
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    Question

    Internal gears are manufactured by
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    Question

    Match the following part programming codes with their respective functions
    Part Programming CodesFunctions
    P. G01I. Spindle stop
    Q. G03II. Spindle rotation, clockwise
    R. M03III. Circular interpolation, anticlockwise
    S. M05IV. Linear interpolation
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    Question

    In PERT chart, the activity time distribution is
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    Question

    The number of linearly independent eigenvectors of matrix A=[210020003]A = \begin{bmatrix} 2 & 1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix} is _________
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    Question

    The value of the line integral ∮CF⃗⋅r⃗′ds\oint_C \vec{F} \cdot \vec{r}' ds, where CC is a circle of radius 4π\frac{4}{\sqrt{\pi}} units is ________
    Here, F⃗(x,y)=yi^+2xj^\vec{F}(x, y) = y \hat{i} + 2x \hat{j} and r⃗′\vec{r}' is the UNIT tangent vector on the curve CC at an arc length ss from a reference point on the curve. i^\hat{i} and j^\hat{j} are the basis vectors in the x−yx-y Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.
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    Question

    lim⁡x→∞x2+x−1−x\lim_{x \to \infty} \sqrt{x^2 + x - 1} - x is
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    Question

    Three cards were drawn from a pack of 52 cards. The probability that they are a king, a queen, and a jack is
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    Question

    An inextensible massless string goes over a frictionless pulley. Two weights of 100100 N and 200200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is __________
    A pulley system with two weights of 100 N and 200 N attached to the ends of a string.
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    Question

    A circular disc of radius 100100 mm and mass 11 kg, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed vv of the disc when it reaches position B is _________ m/s.
    A circular disc rolling down a curved path from height 30 meters
    Acceleration due to gravity g=10g = 10 m/s2^2.
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    Question

    A rigid rod (AB) of length L=2L = \sqrt{2} m is undergoing translational as well as rotational motion in the xx-yy plane (see the figure). The point A has the velocity V1=i^+2j^V_1 = \hat{i} + 2\hat{j} m/s. The end B is constrained to move only along the xx direction.
    A rigid rod AB with velocity vectors at ends A and B
    The magnitude of the velocity V2V_2 (in m/s) at the end B is __________
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    Question

    A square plate of dimension L×LL \times L is subjected to a uniform pressure load p=250p = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E=200E = 200 GPa.
    A square plate under uniform pressure p on all four edges
    The deformed shape is a square of dimension L−2δL - 2\delta. If L=2L = 2 m and δ=0.001\delta = 0.001 m, the Poisson’s ratio of the plate material is __________
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    Question

    Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, θS\theta_S is the twist and τS\tau_S is the maximum shear stress in the solid shaft, whereas θH\theta_H is the twist and τH\tau_H is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?
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    Question

    A beam of length LL is carrying a uniformly distributed load ww per unit length. The flexural rigidity of the beam is EIEI. The reaction at the simple support at the right end is
    A propped cantilever beam of length L with a uniformly distributed load w and a simple support at the right end
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    Question

    Two masses mm are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses m1m_1 is attached to the opposite sides of the shaft in the vertical plane as shown in figure.
    diagram of rotating shaft with masses
    Consider m=1 kg,e=50 mm,e1=20 mm,b=0.3 m,a=2 mm = 1\text{ kg}, e = 50\text{ mm}, e_1 = 20\text{ mm}, b = 0.3\text{ m}, a = 2\text{ m} and a1=2.5 ma_1 = 2.5\text{ m}. For the system to be dynamically balanced, m1m_1 should be ________ kg.
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    Question

    A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of 3km\sqrt{\frac{3k}{m}}, the ratio of the amplitude of steady state response to the static deflection of the spring is __________
    A single degree of freedom spring-mass system with a spring of stiffness k and a mass m, subjected to a harmonic force F sin(wt).
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    Question

    A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is 25 mm225\text{ mm}^2. A torque T=200 N-mT = 200\text{ N-m} is acting on the joint. Neglecting friction due to clamping force, maximum shear stress in a bolt is ______ MPa.
    Bolted joint diagram showing four bolts on a 100 mm diameter circle and an applied torque T.
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    Question

    Consider a fully developed steady laminar flow of an incompressible fluid with viscosity μ\mu through a circular pipe of radius RR. Given that the velocity at a radial location of R/2R/2 from the centerline of the pipe is U1U_1, the shear stress at the wall is KμU1/RK\mu U_1/R, where KK is __________
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    Question

    The water jet exiting from a stationary tank through a circular opening of diameter 300 mm300\text{ mm} impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ kN.
    Density of water is 1000 kg/m31000\text{ kg/m}^3.
    Acceleration due to gravity g=10 m/s2g = 10\text{ m/s}^2.
    A stationary tank with water at a height of 6.2 m above a circular opening of diameter 300 mm. A water jet exits the opening and hits a stationary rigid wall.
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    Question

    For a two-dimensional flow, the velocity field is u⃗=xx2+y2i^+yx2+y2j^\vec{u} = \frac{x}{x^2 + y^2} \hat{i} + \frac{y}{x^2 + y^2} \hat{j}, where i^\hat{i} and j^\hat{j} are the basis vectors in the x−yx-y Cartesian coordinate system. Identify the CORRECT statements from below.
    (1) The flow is incompressible.
    (2) The flow is unsteady.
    (3) y-component of acceleration, ay=−y(x2+y2)2a_y = \frac{-y}{(x^2 + y^2)^2}
    (4) x-component of acceleration, ax=−(x+y)(x2+y2)2a_x = \frac{-(x + y)}{(x^2 + y^2)^2}
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    Question

    Two large parallel plates having a gap of 10 mm in between them are maintained at temperatures T1=1000 KT_1 = 1000\text{ K} and T2=400 KT_2 = 400\text{ K}. Given emissivity values, ϵ1=0.5,ϵ2=0.25\epsilon_1 = 0.5, \epsilon_2 = 0.25 and Stefan-Boltzmann constant σ=5.67×10−8 W/m2-K4\sigma = 5.67 \times 10^{-8}\text{ W/m}^2\text{-K}^4, the heat transfer between the plates (in kW/m2^2) is __________
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    Question

    A cylindrical steel rod, 0.01 m0.01\text{ m} in diameter and 0.2 m0.2\text{ m} in length is first heated to 750 ∘C750\text{ }^\circ\text{C} and then immersed in a water bath at 100 ∘C100\text{ }^\circ\text{C}. The heat transfer coefficient is 250 W/m2-K250\text{ W/m}^2\text{-K}. The density, specific heat and thermal conductivity of steel are ρ=7801 kg/m3\rho = 7801\text{ kg/m}^3, c=473 J/kg-Kc = 473\text{ J/kg-K}, and k=43 W/m-Kk = 43\text{ W/m-K}, respectively. The time required for the rod to reach 300 ∘C300\text{ }^\circ\text{C} is ________ seconds.
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    Question

    Steam at an initial enthalpy of 100 kJ/kg100\text{ kJ/kg} and inlet velocity of 100 m/s100\text{ m/s}, enters an insulated horizontal nozzle. It leaves the nozzle at 200 m/s200\text{ m/s}. The exit enthalpy (in kJ/kg) is __________
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    Question

    In a mixture of dry air and water vapor at a total pressure of 750 mm of Hg750\text{ mm of Hg}, the partial pressure of water vapor is 20 mm of Hg20\text{ mm of Hg}. The humidity ratio of the air in grams of water vapor per kg of dry air (gw/kgdag_w/kg_{da}) is __________
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    Question

    In a 3-stage air compressor, the inlet pressure is p1p_1, discharge pressure is p4p_4 and the intermediate pressures are p2p_2 and p3p_3 (p2<p3p_2 < p_3). The total pressure ratio of the compressor is 10 and the pressure ratios of the stages are equal. If p1=100p_1 = 100 kPa, the value of the pressure p3p_3 (in kPa) is __________
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    In the vapour compression cycle shown in the figure, the evaporating and condensing temperatures are 260 K and 310 K, respectively. The compressor takes in liquid-vapour mixture (state 1) and isentropically compresses it to a dry saturated vapour condition (state 2). The specific heat of the liquid refrigerant is 4.8 kJ/kg-K and may be treated as constant. The enthalpy of evaporation for the refrigerant at 310 K is 1054 kJ/kg.
    The difference between the enthalpies at state points 1 and 0 (in kJ/kg) is ____________
    T-s diagram of a vapour compression cycle showing states 0, 1, 2, 3, and 4
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    Spot welding of two steel sheets each 2 mm thick is carried out successfully by passing 4 kA of current for 0.2 seconds through the electrodes. The resulting weld nugget formed between the sheets is 5 mm in diameter. Assuming cylindrical shape for the nugget, the thickness of the nugget is________mm.
    PropertyValue
    Latent heat of fusion for steel1400 kJ/kg
    Effective resistance of the weld joint200 μΩ\mu\Omega
    Density of steel8000 kg/m3^3
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    For an orthogonal cutting operation, tool material is HSS, rake angle is 22∘22^\circ, chip thickness is 0.8 mm0.8\text{ mm}, speed is 48 m/min48\text{ m/min} and feed is 0.4 mm/rev0.4\text{ mm/rev}. The shear plane angle (in degrees) is
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    Question

    In a sheet metal of 22 mm thickness a hole of 1010 mm diameter needs to be punched. The yield strength in tension of the sheet material is 100100 MPa and its ultimate shear strength is 8080 MPa. The force required to punch the hole (in kN) is __________
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    In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor’s exponent is 0.250.25. If the cutting speed is reduced by 50%50\% then the tool life changes by ______ times.
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    Two optically flat plates of glass are kept at a small angle θ\theta as shown in the figure. Monochromatic light is incident vertically.
    Two glass plates forming a small angle theta with monochromatic light incident vertically
    If the wavelength of light used to get a fringe spacing of 1 mm is 450 nm, the wavelength of light (in nm) to get a fringe spacing of 1.5 mm is _________
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    A point P(1,3,−5)P (1, 3, -5) is translated by 2i^+3j^−4k^2\hat{i} + 3\hat{j} - 4\hat{k} and then rotated counter clockwise by 90∘90^\circ about the zz-axis. The new position of the point is
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    Question

    The demand for a two-wheeler was 900900 units and 10301030 units in April 2015 and May 2015, respectively. The forecast for the month of April 2015 was 850850 units. Considering a smoothing constant of 0.60.6, the forecast for the month of June 2015 is
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    A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts I and II are Rs. 40 and Rs. 100, respectively. The maximum profit per week of the firm is Rs._________
    Type of machineMachining time required for the machine part (minutes) IMachining time required for the machine part (minutes) IIMaximum machining time available per week (minutes)
    Turning Center1266000
    Milling Center4104000
    Grinding Machine231800
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