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GATE ME 2016 Set 2

All 65 solved GATE ME 2016 Set 2 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Questions

65

Paper marks

100

Question formats

2

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 22Medium 34Hard 9

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    The volume of a sphere of diameter 1 unit is ________ than the volume of a cube of side 1 unit.
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    Question

    The unruly crowd demanded that the accused be _____________ without trial.
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    Question

    Choose the statement(s) where the underlined word is used correctly:
    (i) A prone is a dried plum.
    (ii) He was lying prone on the floor.
    (iii) People who eat a lot of fat are prone to heart disease.
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    Question

    Fact: If it rains, then the field is wet.
    Read the following statements:
    (i) It rains
    (ii) The field is not wet
    (iii) The field is wet
    (iv) It did not rain
    Which one of the options given below is NOT logically possible, based on the given fact?
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    Question

    A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in m2m^2 is __________.
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    Question

    Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE?
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    Question

    A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the city, something which critics argue, will lead to a surveillance state.
    Which of the following can be logically inferred from the above paragraph?
    (i) All smart cities encourage the formation of surveillance states.
    (ii) Surveillance is an integral part of a smart city.
    (iii) Sustainability and surveillance go hand in hand in a smart city.
    (iv) There is a perception that smart cities promote surveillance.
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    Question

    Find the missing sequence in the letter series.
    B, FH, LNP, .
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    Question

    The binary operation □\square is defined as a□b=ab+(a+b)a \square b = ab+(a+b), where aa and bb are any two real numbers. The value of the identity element of this operation, defined as the number xx such that a□x=aa \square x = a, for any aa, is ________.
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    Question

    Which of the following curves represents the function y=ln⁡(∣e∣sin⁡(∣x∣)∣∣)y = \ln(|e^{|\sin(|x|)|}|) for ∣x∣<2π|x| < 2\pi?
    Here, xx represents the abscissa and yy represents the ordinate.
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Mechanical Engineering (ME)

55
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    Question

    The condition for which the eigenvalues of the matrix A=[211k]A = \begin{bmatrix} 2 & 1 \\ 1 & k \end{bmatrix}are positive, is
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    Question

    The values of xx for which the function f(x)=x2−3x−4x2+3x−4f(x) = \frac{x^2 - 3x - 4}{x^2 + 3x - 4}is NOT continuous are
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    Question

    Laplace transform of cos⁡(ωt)\cos(\omega t) is
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    Question

    A function ff of the complex variable z=x+iyz = x + i y, is given as f(x,y)=u(x,y)+iv(x,y)f(x, y) = u(x, y) + i v(x, y), where u(x,y)=2kxyu(x, y) = 2kxy and v(x,y)=x2−y2v(x, y) = x^2 - y^2. The value of kk, for which the function is analytic, is _____
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    Question

    Numerical integration using trapezoidal rule gives the best result for a single variable function, which is
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    Question

    A point mass having mass MM is moving with a velocity VV at an angle θ\theta to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is
    A point mass moving towards a horizontal wall at an angle theta
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    Question

    A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is
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    Question

    A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is
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    Question

    The forces F1F_1 and F2F_2 in a brake band and the direction of rotation of the drum are as shown in the figure. The coefficient of friction is 0.25. The angle of wrap is 3π/23\pi /2 radians. It is given that R=1R = 1 m and F2=1F_2 = 1 N. The torque (in N-m) exerted on the drum is _________
    Band brake diagram showing forces F1, F2 and clockwise drum rotation
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    Question

    A single degree of freedom mass-spring-viscous damper system with mass mm, spring constant kk and viscous damping coefficient qq is critically damped. The correct relation among mm, kk, and qq is
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    Question

    A machine element XY, fixed at end X, is subjected to an axial load PP, transverse load FF, and a twisting moment TT at its free end Y. The most critical point from the strength point of view is
    Machine element XY fixed at X with loads P, F, and T at Y
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    Question

    For the brake shown in the figure, which one of the following is TRUE?
    A brake shoe and drum assembly with a lever pivoted at one end and a force applied at the other.
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    Question

    The volumetric flow rate (per unit depth) between two streamlines having stream functions ψ1\psi_1 and ψ2\psi_2 is
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    Question

    Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is
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    Question

    A hollow cylinder has length LL, inner radius r1r_1, outer radius r2r_2, and thermal conductivity kk. The thermal resistance of the cylinder for radial conduction is
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    Question

    Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is RoR_o and that of the inner cylinder is RiR_i. The radiation view factor of the outer cylinder onto itself is
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    Question

    The internal energy of an ideal gas is a function of
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    Question

    The heat removal rate from a refrigerated space and the power input to the compressor are 7.2 kW and 1.8 kW, respectively. The coefficient of performance (COP) of the refrigerator is ______
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    Question

    The error in numerically computing the integral ∫0π(sin⁡x+cos⁡x)dx\int_{0}^{\pi} (\sin x + \cos x) dx using the trapezoidal rule with three intervals of equal length between 00 and π\pi is ________.
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    Question

    A mass of 20002000 kg is currently being lowered at a velocity of 22 m/s from the drum as shown in the figure. The mass moment of inertia of the drum is 150150 kg-m2^2. On applying the brake, the mass is brought to rest in a distance of 0.50.5 m. The energy absorbed by the brake (in kJ) is ________.
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    Question

    A system of particles in motion has mass center GG as shown in the figure. The particle ii has mass mim_i and its position with respect to a fixed point OO is given by the position vector r⃗i\vec{r}_i. The position of the particle ii with respect to GG is given by the vector ρ⃗i\vec{\rho}_i. The time rate of change of the angular momentum of the system of particles about GG is
    (The quantity ρ¨i\ddot{\rho}_i indicates second derivative of ρi\rho_i with respect to time and likewise for r¨i\ddot{r}_i).
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    Question

    The welding process which uses a blanket of fusible granular flux is
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    Question

    The value of true strain produced in compressing a cylinder to half its original length is
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    Question

    The following data is applicable for a turning operation. The length of job is 900 mm900 \text{ mm}, diameter of job is 200 mm200 \text{ mm}, feed rate is 0.25 mm/rev0.25 \text{ mm/rev} and optimum cutting speed is 300 m/min300 \text{ m/min}. The machining time (in min) is __________
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    Question

    In an ultrasonic machining (USM) process, the material removal rate (MRR) is plotted as a function of the feed force of the USM tool. With increasing feed force, the MRR exhibits the following behavior:
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    Question

    A scalar potential ϕ\phi has the following gradient: ∇ϕ=yzi^+xzj^+xyk^\nabla\phi = yz\hat{i} + xz\hat{j} + xy\hat{k}. Consider the integral ∫C∇ϕ⋅dr\int_C \nabla\phi \cdot d\mathbf{r} on the curve r=xi^+yj^+zk^\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}.
    The curve CC is parameterized as follows: {x=ty=t2z=3t2\begin{cases} x = t \\ y = t^2 \\ z = 3t^2 \end{cases} and 1≤t≤31 \leq t \leq 3.
    The value of the integral is ________
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    The value of ∮Γ3z−5(z−1)(z−2)dz\oint_\Gamma \frac{3z-5}{(z-1)(z-2)} dz along a closed path Γ\Gamma is equal to 4πi4\pi i, where z=x+iyz = x + iy and i=−1i = \sqrt{-1}. The correct path Γ\Gamma is
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    Question

    The probability that a screw manufactured by a company is defective is 0.1. The company sells screws in packets containing 5 screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________
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    Question

    The error in numerically computing the integral ∫0π(sin⁡x+cos⁡x)dx\int_0^\pi (\sin x + \cos x) dx using the trapezoidal rule with three intervals of equal length between 0 and π\pi is ___________
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    Question

    A mass of 2000 kg is currently being lowered at a velocity of 2 m/s from the drum as shown in the figure. The mass moment of inertia of the drum is 150 kg-m2^2. On applying the brake, the mass is brought to rest in a distance of 0.5 m. The energy absorbed by the brake (in kJ) is __________
    A schematic showing a drum of diameter 2 m with a mass of 2000 kg being lowered at 2 m/s. A brake is applied to the drum.
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    Question

    A system of particles in motion has mass center GG as shown in the figure. The particle ii has mass mim_i and its position with respect to a fixed point OO is given by the position vector rir_i. The position of the particle with respect to GG is given by the vector ρi\rho_i. The time rate of change of the angular momentum of the system of particles about GG is
    (The quantity ρ¨i\ddot{\rho}_i indicates second derivative of ρi\rho_i with respect to time and likewise for rir_i).
    A system of particles with mass center G, fixed point O, and vectors r_i and rho_i
    1. A.
      ∑iri×miρ¨i\sum_i r_i \times m_i \ddot{\rho}_i
    2. B.
      ∑iρi×mir¨i\sum_i \rho_i \times m_i \ddot{r}_i
    3. C.
      ∑iri×mir¨i\sum_i r_i \times m_i \ddot{r}_i
    4. D.
      ∑iρi×miρ¨i\sum_i \rho_i \times m_i \ddot{\rho}_i

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    Question

    A rigid horizontal rod of length 2L2L is fixed to a circular cylinder of radius RR as shown in the figure. Vertical forces of magnitude PP are applied at the two ends as shown in the figure. The shear modulus for the cylinder is GG and the Young’s modulus is EE.
    A rigid horizontal rod of length 2L fixed to a circular cylinder of radius R with vertical forces P at ends
    The vertical deflection at point A is
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    Question

    A simply supported beam of length 2L2L is subjected to a moment MM at the mid-point x=0x = 0 as shown in the figure. The deflection in the domain 0≤x≤L0 \leq x \leq L is given byw=−Mx12EIL(L−x)(x+c),w = \frac{-Mx}{12 EIL} (L - x)(x + c),where EE is the Young’s modulus, II is the area moment of inertia and cc is a constant (to be determined).
    Simply supported beam with moment M at center
    The slope at the center x=0x = 0 is
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    Question

    In the figure, the load P=1 NP = 1\text{ N}, length L=1 mL = 1\text{ m}, Young’s modulus E=70 GPaE = 70\text{ GPa}, and the cross-section of the links is a square with dimension 10 mm×10 mm10\text{ mm} \times 10\text{ mm}. All joints are pin joints.
    The stress (in Pa) in the link AB is ___________
    (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)
    Truss diagram with links AB and BC, and a load P applied at joint B
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    Question

    A circular metallic rod of length 250 mm250\text{ mm} is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of 0.2 mm0.2\text{ mm} between the rod and the wall on the right side. If the temperature of the rod is increased by 200∘C200^\circ\text{C}, the axial stress developed in the rod is __________ MPa.
    Young’s modulus of the material of the rod is 200 GPa200\text{ GPa} and the coefficient of thermal expansion is 10−510^{-5} per ∘C^\circ\text{C}.
    Diagram of a rod of length 250 mm between two walls with a 0.2 mm gap on the right side
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    Question

    The rod AB, of length 1 m1\text{ m}, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along QP and QR. If the velocity VAV_A of the slider at A is 2 m/s2\text{ m/s}, the velocity of the midpoint of the rod at this instant is ___________ m/s.
    Kinematic diagram showing rod AB with sliders at A and B moving along paths QP and QR, both at 60 degrees to the horizontal
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    Question

    The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing over pulley B of radius rr and mass 20 kg. The spring constant kk is 1500 N/m. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ rad/s.
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    Question

    In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are 50 MPa and 150 MPa, respectively. The endurance, yield, and the ultimate strengths of the material are 200 MPa, 300 MPa and 400 MPa, respectively. The factor of safety using modified Goodman criterion is
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    Question

    The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that 45 percent of its volume is in oil while the rest is in water. The density of the body is _________ kg/m3^3.
    The specific gravity of oil is 0.7 and density of water is 1000 kg/m3^3.
    Acceleration due to gravity g=10g = 10 m/s2^2.
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    Question

    Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being 50 mm). The top plate is sliding parallel to the stationary bottom plate at a speed of 3 m/s. The flow between the plates is solely due to the motion of the top plate. The force per unit area (magnitude) required to maintain the bottom plate stationary is _________ N/m2^2.
    Viscosity of the fluid μ=0.44\mu = 0.44 kg/m-s and density ρ=888\rho = 888 kg/m3^3.
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    Question

    Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions 2R×L2R \times L at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius RR. The tank is filled with a liquid of density ρ\rho up to the tip of the plug. The gravitational acceleration is gg. Neglect the effect of the atmospheric pressure.
    Sectional view A-A of a tank with a semi-cylindrical plug blocking a hole
    The force FF required to hold the plug in its position is
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    Question

    Consider a parallel-flow heat exchanger with area ApA_p and a counter-flow heat exchanger with area AcA_c. In both the heat exchangers, the hot stream flowing at 1 kg/s cools from 80 ∘^\circ C to 50 ∘^\circ C. For the cold stream in both the heat exchangers, the flow rate and the inlet temperature are 2 kg/s and 10 ∘^\circ C, respectively. The hot and cold streams in both the heat exchangers are of the same fluid. Also, both the heat exchangers have the same overall heat transfer coefficient. The ratio Ac/ApA_c/A_p is _________
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    Question

    Two cylindrical shafts A and B at the same initial temperature are simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperature at all times after they are introduced into the furnace. The temperature variation in the axial direction of the shafts can be assumed to be negligible. The data related to shafts A and B is given in the following Table.
    QuantityShaft AShaft B
    Diameter (m)0.40.1
    Thermal conductivity (W/m-K)4020
    Volumetric heat capacity (J/m3^3-K)2×1062 \times 10^62×1072 \times 10^7
    The temperature at the centerline of the shaft A reaches 400 ∘^\circ C after two hours. The time required (in hours) for the centerline of the shaft B to attain the temperature of 400 ∘^\circ C is _______
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    Question

    A piston-cylinder device initially contains 0.4 m3^3 of air (to be treated as an ideal gas) at 100 kPa and 80 ∘^\circ C. The air is now isothermally compressed to 0.1 m3^3. The work done during this process is ________ kJ.
    (Take the sign convention such that work done on the system is negative)
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    Question

    A reversible cycle receives 40 kJ of heat from one heat source at a temperature of 127 ∘^\circ C and 37 kJ from another heat source at 97 ∘^\circ C. The heat rejected (in kJ) to the heat sink at 47 ∘^\circ C is __________
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    A refrigerator uses R-134a as its refrigerant and operates on an ideal vapour-compression refrigeration cycle between 0.140.14 MPa and 0.80.8 MPa. If the mass flow rate of the refrigerant is 0.050.05 kg/s, the rate of heat rejection to the environment is _________ kW.
    Given data:
    At P=0.14P = 0.14 MPa, h=236.04h = 236.04 kJ/kg, s=0.9322s = 0.9322 kJ/kg-K
    At P=0.8P = 0.8 MPa, h=272.05h = 272.05 kJ/kg (superheated vapour)
    At P=0.8P = 0.8 MPa, h=93.42h = 93.42 kJ/kg (saturated liquid)
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    The partial pressure of water vapour in a moist air sample of relative humidity 70%70\% is 1.61.6 kPa, the total pressure being 101.325101.325 kPa. Moist air may be treated as an ideal gas mixture of water vapour and dry air. The relation between saturation temperature (TsT_s in K) and saturation pressure (psp_s in kPa) for water is given by ln⁡(ps/po)=14.317−5304/Ts\ln(p_s / p_o) = 14.317 - 5304/T_s, where po=101.325p_o = 101.325 kPa. The dry bulb temperature of the moist air sample (in ∘^\circ C) is __________
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    In a binary system of A and B, a liquid of 20% A (80% B) is coexisting with a solid of 70% A (30% B). For an overall composition having 40% A, the fraction of solid is
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    Gray cast iron blocks of size 100 mm×50 mm×10 mm100\text{ mm} \times 50\text{ mm} \times 10\text{ mm} with a central spherical cavity of diameter 4 mm4\text{ mm} are sand cast. The shrinkage allowance for the pattern is 3%3\%. The ratio of the volume of the pattern to volume of the casting is _________
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    The voltage-length characteristic of a direct current arc in an arc welding process is V=100+40lV = 100 + 40l, where ll is the length of the arc in mm and VV is arc voltage in volts. During a welding operation, the arc length varies between 11 and 2 mm2\text{ mm} and the welding current is in the range 200-250 A200\text{-}250\text{ A}. Assuming a linear power source, the short circuit current is_________ A.
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    For a certain job, the cost of metal cutting is Rs. 18C/V18C/V and the cost of tooling is Rs. 270C/(TV)270C/(TV), where CC is a constant, VV is the cutting speed in m/min and TT is the tool life in minutes. The Taylor's tool life equation is VT0.25=150VT^{0.25} = 150. The cutting speed (in m/min) for the minimum total cost is _______
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    The surface irregularities of electrodes used in an electrochemical machining (ECM) process are 3 μm3\ \mu\text{m} and 6 μm6\ \mu\text{m} as shown in the figure. If the work-piece is of pure iron and 12V DC12\text{V DC} is applied between the electrodes, the largest feed rate is ___________ mm/min\text{mm/min}.
    Conductivity of the electrolyte0.02 ohm−1mm−10.02\ \text{ohm}^{-1}\text{mm}^{-1}
    Over-potential voltage1.5 V1.5\ \text{V}
    Density of iron7860 kg/m37860\ \text{kg/m}^3
    Atomic weight of iron55.85 gm55.85\ \text{gm}
    Assume the iron to be dissolved as Fe+2\text{Fe}^{+2} and the Faraday constant to be 96500 Coulomb96500\ \text{Coulomb}.
    Diagram showing tool and work-piece with surface irregularities and nominal gap
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    For the situation shown in the figure below the expression for HH in terms of rr, RR and DD is
    Two circles of radii $r$ and $R$ inside a rectangle of width $D$ and height $H$. The larger circle is tangent to the bottom and left sides, and the smaller circle is tangent to the top and right sides. The circles are tangent to each other.
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    A food processing company uses 25,000 kg25,000\ \text{kg} of corn flour every year. The quantity-discount price of corn flour is provided in the table below:
    Quantity (kg)Unit price (Rs/kg)
    1-74970
    750-149965
    1500 and above60
    The order processing charges are Rs. 500/order\text{Rs. } 500/\text{order}. The handling plus carry-over charge on an annual basis is 20%20\% of the purchase price of the corn flour per kg. The optimal order quantity (in kg) is _____________
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    A project consists of 14 activities, A to N. The duration of these activities (in days) are shown in brackets on the network diagram. The latest finish time (in days) for node 10 is __________
    Network diagram showing activities A to N with durations between nodes 1 to 12
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