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GATE ME 2014 Set 2

All 65 solved GATE ME 2014 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 29Medium 32Hard 4

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Choose the most appropriate word from the options given below to complete the following sentence.
    Communication and interpersonal skills are ________ important in their own ways.
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    Question

    Which of the options given below best completes the following sentence?
    She will feel much better if she ________________.
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    Question

    Choose the most appropriate pair of words from the options given below to complete the following sentence.
    She could not ___ the thought of _______ the election to her bitter rival.
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    Question

    A regular die has six sides with numbers 11 to 66 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1→0.1671 \rightarrow 0.167; 2→0.1672 \rightarrow 0.167; 3→0.1523 \rightarrow 0.152; 4→0.1664 \rightarrow 0.166; 5→0.1685 \rightarrow 0.168; 6→0.1806 \rightarrow 0.180. We call this die
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    Question

    Fill in the missing number in the series.
    2 \quad 3 \quad 6 \quad 15 \quad \text{___} \quad 157.5 \quad 630
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    Question

    Find the odd one in the following group
    Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X
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    Question

    Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct?
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    Question

    The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number?
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    Question

    The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg?
    Pie charts showing the percentage distribution of exports and revenues for six items
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    Question

    It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?
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MECHANICAL – ME

55
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    Question

    One of the eigenvectors of the matrix
    2x2 matrix
    is
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    Question

    lim⁡x→0(e2x−1sin⁡(4x))\lim_{x \to 0} \left( \frac{e^{2x} - 1}{\sin(4x)} \right) is equal to
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    Question

    Curl of vector F⃗=x2z2i^−2xy2zj^+2y2z3k^\vec{F} = x^2 z^2 \hat{i} - 2 x y^2 z \hat{j} + 2 y^2 z^3 \hat{k} is
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    Question

    A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is
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    Question

    The best approximation of the minimum value attained by e−xsin⁡(100x)e^{-x} \sin(100x) for x≥0x \geq 0 is _______
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    Question

    A steel cube, with all faces free to deform, has Young’s modulus, EE, Poisson’s ratio, ν\nu, and coefficient of thermal expansion, α\alpha. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, ΔT\Delta T, is given by
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    Question

    A two member truss ABCABC is shown in the figure. The force (in kN) transmitted in member ABAB is
    A two-member truss ABC with a 10 kN load at joint B
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    Question

    A 4-bar mechanism with all revolute pairs has link lengths lf=20 mml_f = 20 \text{ mm}, lin=40 mml_{in} = 40 \text{ mm}, lco=50 mml_{co} = 50 \text{ mm} and lout=60 mml_{out} = 60 \text{ mm}. The suffixes 'f', 'in', 'co' and 'out' denote the fixed link, the input link, the coupler and output link respectively. Which one of the following statements is true about the input and output links?
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    Question

    In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility (TT)?
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    Question

    In a structure subjected to fatigue loading, the minimum and maximum stresses developed in a cycle are 200 MPa and 400 MPa respectively. The value of stress amplitude (in MPa) is
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    Question

    A thin plate of uniform thickness is subject to pressure as shown in the figure below
    A thin plate in the xy-plane with pressure arrows acting on its edges and a coordinate system showing x, y, and z axes.
    Under the assumption of plane stress, which one of the following is correct?
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    Question

    For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of 22, the average heat transfer coefficient
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    Question

    The thermal efficiency of an air-standard Brayton cycle in terms of pressure ratio rpr_p and γ(=cp/cv)\gamma (= c_p/c_v) is given by
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    Question

    For an incompressible flow field, V⃗\vec{V}, which one of the following conditions must be satisfied?
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    Question

    A pure substance at 8 MPa8 \text{ MPa} and 400 °C400 \text{ °C} is having a specific internal energy of 2864 kJ/kg2864 \text{ kJ/kg} and a specific volume of 0.03432 m3/kg0.03432 \text{ m}^3\text{/kg}. Its specific enthalpy (in kJ/kg) is
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    Question

    In a heat exchanger, it is observed that ΔT1=ΔT2\Delta T_1 = \Delta T_2, where ΔT1\Delta T_1 is the temperature difference between the two single phase fluid streams at one end and ΔT2\Delta T_2 is the temperature difference at the other end. This heat exchanger is
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    Question

    The difference in pressure (in N/m2\text{N/m}^2) across an air bubble of diameter 0.001 m0.001\text{ m} immersed in water (surface tension =0.072 N/m= 0.072\text{ N/m}) is _______
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    Question

    If there are mm sources and nn destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is
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    Question

    A component can be produced by any of the four processes I, II, III and IV. The fixed cost and the variable cost for each of the processes are listed below. The most economical process for producing a batch of 100 pieces is
    ProcessFixed cost (in Rs.)Variable cost per piece (in Rs.)
    I203
    II501
    III402
    IV104
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    Question

    The flatness of a machine bed can be measured using
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    Question

    A robot arm PQPQ with end coordinates P(0,0)P(0,0) and Q(2,5)Q(2,5) rotates counter clockwise about PP in the XYXY plane by 90∘90^\circ. The new coordinate pair of the end point QQ is
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    Question

    Match the Machine Tools (Group A) with the probable Operations (Group B):
    Group AGroup B
    P: Centre Lathe1: Slotting
    Q: Milling2: Counter-boring
    R: Grinding3: Knurling
    S: Drilling4: Dressing
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    Question

    The following four unconventional machining processes are available in a shop floor. The most appropriate one to drill a hole of square cross section of 6 mm×6 mm6\text{ mm} \times 6\text{ mm} and 25 mm25\text{ mm} deep is
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    Question

    The relationship between true strain (ϵT\epsilon_T) and engineering strain (ϵE\epsilon_E) in a uniaxial tension test is given as
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    Question

    With respect to metal working, match Group A with Group B:
    Group AGroup B
    P: Defect in extrusionI: alligatoring
    Q: Defect in rollingII: scab
    R: Product of skew rollingIII: fish tail
    S: Product of rolling through cluster millIV: seamless tube
    V: thin sheet with tight tolerance
    VI: semi-finished balls of ball bearing
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    Question

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

    The general solution of the differential equation dydx=cos⁡(x+y)\frac{dy}{dx} = \cos(x + y), with cc as a constant, is
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    Question

    Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is _______
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    Question

    The value of ∫2.54ln⁡(x)dx\int_{2.5}^{4} \ln(x) dx calculated using the Trapezoidal rule with five subintervals is _______
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    Question

    The flexural rigidity (EIEI) of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load PP and bending moment PL/2PL/2 are applied at the free end of the beam then the value of the slope at the free end is
    Cantilever beam of length L with a point load P and a clockwise moment PL/2 at the free end
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    Question

    A cantilever beam of length, LL, with uniform cross-section and flexural rigidity, EIEI, is loaded uniformly by a vertical load, ww per unit length. The maximum vertical deflection of the beam is given by
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    Question

    For the three bolt system shown in the figure, the bolt material has shear yield strength of 200 MPa200\text{ MPa}. For a factor of safety of 2, the minimum metric specification required for the bolt is
    Diagram of a three-bolt lap joint system with a 19 kN load applied
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    Question

    Consider a flywheel whose mass MM is distributed almost equally between a heavy, ring-like rim of radius RR and a concentric disk-like feature of radius R/2R/2. Other parts of the flywheel, such as spokes, etc. have negligible mass. The best approximation for α\alpha, if the moment of inertia of the flywheel about its axis of rotation is expressed as αMR2\alpha MR^2, is _______
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    Question

    What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by mm and the spring constants are denoted by k1k_1 and k2k_2 as shown below.
    A spring-mass system on an inclined plane at an angle $\theta$. A block of mass $m$ is connected to two springs with constants $k_1$ and $k_2$. Spring $k_1$ is attached to the upper wall and the block, and spring $k_2$ is attached to the block and the lower wall.
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    Question

    A disc clutch with a single friction surface has coefficient of friction equal to 0.3. The maximum pressure which can be imposed on the friction material is 1.5 MPa. The outer diameter of the clutch plate is 200 mm and its internal diameter is 100 mm. Assuming uniform wear theory for the clutch plate, the maximum torque (in N⋅mN \cdot m) that can be transmitted is _______
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    Question

    A truck accelerates up a 10∘10^\circ incline with a crate of 100 kg. Value of static coefficient of friction between the crate and the truck surface is 0.3. The maximum value of acceleration (in m/s2m/s^2) of the truck such that the crate does not slide down is _______
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    Question

    Maximum fluctuation of kinetic energy in an engine has been calculated to be 26002600 J. Assuming that the engine runs at an average speed of 200200 rpm, the polar mass moment of inertia (in kg⋅m2kg \cdot m^2) of a flywheel to keep the speed fluctuation within ±0.5%\pm 0.5\% of the average speed is _______
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    Question

    Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true?
    Two states of stress: Configuration I shows a square element subjected to pure shear stress $\tau$. Configuration II shows a square element subjected to pure tensile stress $\sigma$.
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    Question

    A rigid link PQ of length 22 m rotates about the pinned end Q with a constant angular acceleration of 1212 rad/s2^2. When the angular velocity of the link is 44 rad/s, the magnitude of the resultant acceleration (in m/s2^2) of the end P is _______
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    Question

    A spur pinion of pitch diameter 5050 mm rotates at 200200 rad/s and transmits 33 kW power. The pressure angle of the tooth of the pinion is 20∘20^\circ. Assuming that only one pair of the teeth is in contact, the total force (in newton) exerted by a tooth of the pinion on the tooth on a mating gear is _______
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    Question

    A spherical balloon with a diameter of 10 m10 \text{ m}, shown in the figure below is used for advertisements. The balloon is filled with helium (RHe=2.08 kJ/kg.KR_{He} = 2.08 \text{ kJ/kg.K}) at ambient conditions of 15∘C15^\circ\text{C} and 100 kPa100 \text{ kPa}. Assuming no disturbances due to wind, the maximum allowable weight (in newton) of balloon material and rope required to avoid the fall of the balloon (Rair=0.289 kJ/kg.KR_{air} = 0.289 \text{ kJ/kg.K}) is _______
    spherical balloon diagram
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    Question

    A hemispherical furnace of 1 m1 \text{ m} radius has the inner surface (emissivity, ϵ=1\epsilon = 1) of its roof maintained at 800 K800 \text{ K}, while its floor (ϵ=0.5\epsilon = 0.5) is kept at 600 K600 \text{ K}. Stefan-Boltzmann constant is 5.668×10−8 W/m2.K45.668 \times 10^{-8} \text{ W/m}^2\text{.K}^4. The net radiative heat transfer (in kW) from the roof to the floor is _______
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    Question

    Water flows through a 10 mm10\text{ mm} diameter and 250 m250\text{ m} long smooth pipe at an average velocity of 0.1 m/s0.1\text{ m/s}. The density and the viscosity of water are 997 kg/m3997\text{ kg/m}^3 and 855×10−6 N.s/m2855 \times 10^{-6}\text{ N.s/m}^2, respectively. Assuming fully-developed flow, the pressure drop (in Pa) in the pipe is _______
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    Question

    A material P of thickness 1 mm1\text{ mm} is sandwiched between two steel slabs, as shown in the figure below. A heat flux 10 kW/m210\text{ kW/m}^2 is supplied to one of the steel slabs as shown. The boundary temperatures of the slabs are indicated in the figure. Assume thermal conductivity of this steel is 10 W/m.K10\text{ W/m.K}. Considering one-dimensional steady state heat conduction for the configuration, the thermal conductivity (kk, in W/m.K\text{W/m.K}) of material P is _______
    Diagram showing a material P of thickness 1 mm sandwiched between two steel slabs of 20 mm thickness each. Heat flux q'' = 10 kW/m^2 is applied to the left face. Boundary temperatures are T1 = 500 K and T2 = 360 K.
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    Question

    Consider laminar flow of water over a flat plate of length 1 m1\text{ m}. If the boundary layer thickness at a distance of 0.25 m0.25\text{ m} from the leading edge of the plate is 8 mm8\text{ mm}, the boundary layer thickness (in mm), at a distance of 0.75 m0.75\text{ m}, is _______
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    Question

    In an ideal Brayton cycle, atmospheric air (ratio of specific heats, cp/cv=1.4c_p/c_v = 1.4, specific heat at constant pressure = 1.005 kJ/kg.K1.005 \text{ kJ/kg.K}) at 1 bar1 \text{ bar} and 300 K300 \text{ K} is compressed to 8 bar8 \text{ bar}. The maximum temperature in the cycle is limited to 1280 K1280 \text{ K}. If the heat is supplied at the rate of 80 MW80 \text{ MW}, the mass flow rate (in kg/s) of air required in the cycle is _______
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    Question

    Steam at a velocity of 10 m/s10 \text{ m/s} enters the impulse turbine stage with symmetrical blading having blade angle 30∘30^\circ. The enthalpy drop in the stage is 100 kJ100 \text{ kJ}. The nozzle angle is 20∘20^\circ. The maximum blade efficiency (in percent) is _______
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    Question

    In a concentric counter flow heat exchanger, water flows through the inner tube at 25∘C25^\circ\text{C} and leaves at 42∘C42^\circ\text{C}. The engine oil enters at 100∘C100^\circ\text{C} and flows in the annular flow passage. The exit temperature of the engine oil is 50∘C50^\circ\text{C}. Mass flow rate of water and the engine oil are 1.5 kg/s1.5 \text{ kg/s} and 1 kg/s1 \text{ kg/s}, respectively. The specific heat of water and oil are 4178 J/kg.K4178 \text{ J/kg.K} and 2130 J/kg.K2130 \text{ J/kg.K}, respectively. The effectiveness of this heat exchanger is _______
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    Question

    A heat pump with refrigerant R22 is used for space heating between temperature limits of −20∘C-20^\circ\text{C} and 25∘C25^\circ\text{C}. The heat required is 200 MJ/h200\text{ MJ/h}. Assume specific heat of vapour at the time of discharge as 0.98 kJ/kg.K0.98\text{ kJ/kg.K}. Other relevant properties are given below. The enthalpy (in kJ/kg) of the refrigerant at isentropic compressor discharge is _______.
    Saturation temperature Tsat(∘C)T_{\text{sat}} (^\circ\text{C})Pressure P(MN/m2)P (\text{MN/m}^2)Specific enthalpy hf(kJ/kg)h_f (\text{kJ/kg})Specific enthalpy hg(kJ/kg)h_g (\text{kJ/kg})Specific entropy sf(kJ/kg.K)s_f (\text{kJ/kg.K})Specific entropy sg(kJ/kg.K)s_g (\text{kJ/kg.K})
    −20-200.24480.2448177.21177.21397.53397.530.91390.91391.78411.7841
    25251.0481.048230.07230.07413.02413.021.10471.10471.71831.7183
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    Question

    A project has four activities P, Q, R and S as shown below.
    ActivityNormal duration (days)PredecessorCost slope (Rs./day)
    P3-500
    Q7P100
    R4P400
    S5R200
    The normal cost of the project is Rs. 10,000/- and the overhead cost is Rs. 200/- per day. If the project duration has to be crashed down to 9 days, the total cost (in Rupees) of the project is _______.
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    Question

    Consider the following data with reference to elementary deterministic economic order quantity model
    Annual demand of an item100000
    Unit price of the item (in Rs.)10
    Inventory carrying cost per unit per year (in Rs.)1.5
    Unit order cost (in Rs.)30
    The total number of economic orders per year to meet the annual demand is _______.
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    Question

    For the CNC part programming, match Group A with Group B:
    Group AGroup B
    P: circular interpolation, counter clock wiseI: G02
    Q: dwellII: G03
    R: circular interpolation, clock wiseIII: G04
    S: point to point counteringIV: G00
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    Question

    A mild steel plate has to be rolled in one pass such that the final plate thickness is 2/3rd2/3^{rd} of the initial thickness, with the entrance speed of 10 m/min10\text{ m/min} and roll diameter of 500 mm500\text{ mm}. If the plate widens by 2%2\% during rolling, the exit velocity (in m/min) is _______
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    Question

    A hole of 20 mm20\text{ mm} diameter is to be drilled in a steel block of 40 mm40\text{ mm} thickness. The drilling is performed at rotational speed of 400 rpm400\text{ rpm} and feed rate of 0.1 mm/rev0.1\text{ mm/rev}. The required approach and over run of the drill together is equal to the radius of drill. The drilling time (in minute) is
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    Question

    A rectangular hole of size 100 mm×50 mm100\text{ mm} \times 50\text{ mm} is to be made on a 5 mm5\text{ mm} thick sheet of steel having ultimate tensile strength and shear strength of 500 MPa500\text{ MPa} and 300 MPa300\text{ MPa}, respectively. The hole is made by punching process. Neglecting the effect of clearance, the punching force (in kN) is
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