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GATE ME 2014 Set 1

All 65 solved GATE ME 2014 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 28Medium 34Hard 3

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Choose the most appropriate phrase from the options given below to complete the following sentence.
    The aircraft __________ take off as soon as its flight plan was filed.
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    Question

    Read the statements:
    All women are entrepreneurs.
    Some women are doctors.
    Which of the following conclusions can be logically inferred from the above statements?
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    Question

    Choose the most appropriate word from the options given below to complete the following sentence.
    Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped _________ such notions.
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    Question

    The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?
    BatsmanAverageStandard deviation
    K31.25.21
    L46.06.35
    M54.46.22
    N17.95.90
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    Question

    What is the next number in the series?
    12 35 81 173 357 ____
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    Question

    Find the odd one from the following group:
    W,E,K,O I,Q,W,A F,N,T,X N,V,B,D
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    Question

    For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs 15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who should fill Form T is
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    Question

    A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?
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    Question

    The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5th1/5^{th} of the exports?
    Bar chart showing Exports and Imports in crores of Rs. from 2000 to 2007
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    Question

    You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is
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MECHANICAL – ME

55
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    Question

    Given that the determinant of the matrix [130264−102]\begin{bmatrix} 1 & 3 & 0 \\ 2 & 6 & 4 \\ -1 & 0 & 2 \end{bmatrix} is −12-12, the determinant of the matrix [2604128−204]\begin{bmatrix} 2 & 6 & 0 \\ 4 & 12 & 8 \\ -2 & 0 & 4 \end{bmatrix} is
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    Question

    lim⁡x→0x−sin⁡x1−cos⁡x\lim_{x \to 0} \frac{x - \sin x}{1 - \cos x} is
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    Question

    The argument of the complex number 1+i1−i\frac{1+i}{1-i}, where i=−1i = \sqrt{-1}, is
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    Question

    The matrix form of the linear system dxdt=3x−5y\frac{dx}{dt} = 3x - 5y and dydt=4x+8y\frac{dy}{dt} = 4x + 8y is
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    Question

    Which one of the following describes the relationship among the three vectors, i^+j^+k^\hat{i} + \hat{j} + \hat{k}, 2i^+3j^+k^2\hat{i} + 3\hat{j} + \hat{k} and 5i^+6j^+4k^5\hat{i} + 6\hat{j} + 4\hat{k}?
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    Question

    A circular rod of length ‘LL’ and area of cross-section ‘AA’ has a modulus of elasticity ‘EE’ and coefficient of thermal expansion ‘α\alpha’. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by ΔT\Delta T, then
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    Question

    A metallic rod of 500 mm500\text{ mm} length and 50 mm50\text{ mm} diameter, when subjected to a tensile force of 100 kN100\text{ kN} at the ends, experiences an increase in its length by 0.5 mm0.5\text{ mm} and a reduction in its diameter by 0.015 mm0.015\text{ mm}. The Poisson’s ratio of the rod material is _______
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    Question

    Critical damping is the
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    Question

    A circular object of radius rr rolls without slipping on a horizontal level floor with the center having velocity VV. The velocity at the point of contact between the object and the floor is
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    Question

    For the given statements:
    I. Mating spur gear teeth is an example of higher pair
    II. A revolute joint is an example of lower pair
    Indicate the correct answer.
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    Question

    A rigid link PQ is 2 m long and oriented at 20∘20^\circ to the horizontal as shown in the figure. The magnitude and direction of velocity VQV_Q, and the direction of velocity VPV_P are given. The magnitude of VPV_P (in m/s) at this instant is
    Rigid link PQ with velocity vectors $V_Q$ and $V_P$ and orientation angles
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    Question

    Biot number signifies the ratio of
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    Question

    The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called
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    Question

    Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below. The free stream velocity is U∞U_\infty and the free stream temperature T∞T_\infty is lower than the cylinder surface temperature TsT_s. The local heat transfer coefficient is minimum at point
    A cylinder in cross-flow with points 1, 2, 3, and 4 marked on its surface.
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    Question

    For a completely submerged body with centre of gravity ‘G’ and centre of buoyancy ‘B’, the condition of stability will be
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    Question

    In a power plant, water (density = 1000 kg/m31000\text{ kg/m}^3) is pumped from 80 kPa80\text{ kPa} to 3 MPa3\text{ MPa}. The pump has an isentropic efficiency of 0.850.85. Assuming that the temperature of the water remains the same, the specific work (in kJ/kg) supplied to the pump is
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    Question

    Which one of the following is a CFC refrigerant?
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    Question

    The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is
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    Question

    In exponential smoothening method, which one of the following is true?
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    Question

    For machining a rectangular island represented by coordinates P(0,0), Q(100,0), R(100,50) and S(0,50) on a casting using CNC milling machine, an end mill with a diameter of 16 mm is used. The trajectory of the cutter centre to machine the island PQRS is
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    Question

    Which one of the following instruments is widely used to check and calibrate geometric features of machine tools during their assembly?
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    Question

    The major difficulty during welding of aluminium is due to its
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    Question

    The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is 400400 N. The turning was performed using 22 mm depth of cut and 0.10.1 mm/rev feed rate. The specific cutting pressure (in N/mm2N/mm^2) is
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    Question

    The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness is
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    Question

    In solid-state welding, the contamination layers between the surfaces to be welded are removed by
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    Question

    The integral ∮C(ydx−xdy)\oint_C (y dx - x dy) is evaluated along the circle x2+y2=14x^2 + y^2 = \frac{1}{4} traversed in counter clockwise direction. The integral is equal to
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    Question

    If y=f(x)y = f(x) is the solution of d2ydx2=0\frac{d^2y}{dx^2} = 0 with the boundary conditions y=5y = 5 at x=0x = 0, and dydx=2\frac{dy}{dx} = 2 at x=10,f(15)=_______x = 10, f(15) = \_\_\_\_\_\_\_
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    Question

    In the following table, xx is a discrete random variable and p(x)p(x) is the probability density. The standard deviation of xx is
    xx123
    p(x)p(x)0.30.60.1
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    Question

    Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral ∫−1+1∣x∣dx\int_{-1}^{+1} |x| dx is _______
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    Question

    The state of stress at a point is given by σx=−6\sigma_x = -6 MPa, σy=4\sigma_y = 4 MPa, and τxy=−8\tau_{xy} = -8 MPa. The maximum tensile stress (in MPa) at the point is _______
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    Question

    A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a massless and inextensible string PQ. If the coefficient of static friction for all surfaces is 0.4, the minimum force F (in kN) needed to move the block S is
    A diagram showing block R on top of block S. Block R is connected to a wall by a string PQ. A horizontal force F is applied to block S. Both blocks are on a horizontal surface.
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    Question

    A pair of spur gears with module 55 mm and a center distance of 450450 mm is used for a speed reduction of 5:15:1. The number of teeth on pinion is _______
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    Question

    Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length 0.01 m. The frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip, is 100 Hz. The flexural rigidity (in N.m2^2) of the beam is _______
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    Question

    An ideal water jet with volume flow rate of 0.05 m3/s0.05\text{ m}^3/\text{s} strikes a flat plate placed normal to its path and exerts a force of 1000 N1000\text{ N}. Considering the density of water as 1000 kg/m31000\text{ kg/m}^3, the diameter (in mm) of the water jet is _______
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    Question

    A block weighing 200 N200\text{ N} is in contact with a level plane whose coefficients of static and kinetic friction are 0.40.4 and 0.20.2, respectively. The block is acted upon by a horizontal force (in newton) P=10tP=10t, where tt denotes the time in seconds. The velocity (in m/s) of the block attained after 10 seconds is _______
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    Question

    A slider crank mechanism has slider mass of 10 kg10\text{ kg}, stroke of 0.2 m0.2\text{ m} and rotates with a uniform angular velocity of 10 rad/s10\text{ rad/s}. The primary inertia forces of the slider are partially balanced by a revolving mass of 6 kg6\text{ kg} at the crank, placed at a distance equal to crank radius. Neglect the mass of connecting rod and crank. When the crank angle (with respect to slider axis) is 30∘30^\circ, the unbalanced force (in newton) normal to the slider axis is _______
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    Question

    An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is _______
    Offset slider-crank mechanism with dimensions 20 mm crank, 40 mm connecting rod, and 10 mm offset
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    Question

    A rigid uniform rod ABAB of length LL and mass mm is hinged at CC such that AC=L/3AC = L/3, CB=2L/3CB = 2L/3. Ends AA and BB are supported by springs of spring constant kk. The natural frequency of the system is given by
    Rigid uniform rod AB hinged at C with springs at ends A and B
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    Question

    A hydrodynamic journal bearing is subject to 2000 N load at a rotational speed of 2000 rpm. Both bearing bore diameter and length are 40 mm. If radial clearance is 20 μm20\ \mu\text{m} and bearing is lubricated with an oil having viscosity 0.03 Pa.s, the Sommerfeld number of the bearing is _______
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    Question

    A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by 250°C. If the Young’s modulus and coefficient of thermal expansion are 200 GPa and 1×10−5/∘C1 \times 10^{-5}/^\circ\text{C}, respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is _______
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    Question

    1.5 kg of water is in saturated liquid state at 2 bar (vf=0.001061 m3/kgv_f = 0.001061 \text{ m}^3/\text{kg}, uf=504.0 kJ/kgu_f = 504.0 \text{ kJ/kg}, hf=505 kJ/kgh_f = 505 \text{ kJ/kg}). Heat is added in a constant pressure process till the temperature of water reaches 400°C (v=1.5493 m3/kgv = 1.5493 \text{ m}^3/\text{kg}, u=2967.0 kJ/kgu = 2967.0 \text{ kJ/kg}, h=3277.0 kJ/kgh = 3277.0 \text{ kJ/kg}). The heat added (in kJ) in the process is _______
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    Question

    Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness 30 mm and thermal conductivity 15 W/m.K. At x=0x = 0, a constant heat flux, q′′=1×105 W/m2q'' = 1 \times 10^5 \text{ W/m}^2 is applied. On the other side of the wall, heat is removed from the wall by convection with a fluid at 25°C and heat transfer coefficient of 250 W/m2^2.K. The temperature (in °C), at x=0x = 0 is _______
    Diagram showing a wall of thickness $L$ with constant heat flux $q''$ applied at $x=0$ (temperature $T_1$) and convection to a fluid at $T_\infty$ from the surface at $x=L$ (temperature $T_2$)
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    Question

    Water flows through a pipe having an inner radius of 10 mm10\text{ mm} at the rate of 36 kg/hr36\text{ kg/hr} at 25∘C25^\circ\text{C}. The viscosity of water at 25∘C25^\circ\text{C} is 0.001 kg/m.s0.001\text{ kg/m.s}. The Reynolds number of the flow is _______
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    Question

    For a fully developed flow of water in a pipe having diameter 10 cm10\text{ cm}, velocity 0.1 m/s0.1\text{ m/s} and kinematic viscosity 10−5 m2/s10^{-5}\text{ m}^2\text{/s}, the value of Darcy friction factor is _______
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    Question

    In a simple concentric shaft-bearing arrangement, the lubricant flows in the 2 mm2\text{ mm} gap between the shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure gradient. The diameter of the shaft is 100 mm100\text{ mm} and its tangential speed is 10 m/s10\text{ m/s}. The dynamic viscosity of the lubricant is 0.1 kg/m.s0.1\text{ kg/m.s}. The frictional resisting force (in newton) per 100 mm100\text{ mm} length of the bearing is _______
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    Question

    The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by TW−TTW−T∞=a+byL+c(yL)2\frac{T_W - T}{T_W - T_\infty} = a + b \frac{y}{L} + c \left( \frac{y}{L} \right)^2, where yy is measured perpendicular to the plate, LL is the plate length, and aa, bb and cc are arbitrary constants. TWT_W and T∞T_\infty are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is kk and the wall heat flux is q′′q'', the Nusselt number Nu=q′′TW−T∞LkNu = \frac{q''}{T_W - T_\infty} \frac{L}{k} is equal to
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    Question

    In an air-standard Otto cycle, air is supplied at 0.10.1 MPa and 308308 K. The ratio of the specific heats (γ\gamma) and the specific gas constant (RR) of air are 1.41.4 and 288.8288.8 J/kg.K, respectively. If the compression ratio is 88 and the maximum temperature in the cycle is 26602660 K, the heat (in kJ/kg) supplied to the engine is _______
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    Question

    A reversible heat engine receives 2 kJ2\text{ kJ} of heat from a reservoir at 1000 K1000\text{ K} and a certain amount of heat from a reservoir at 800 K800\text{ K}. It rejects 1 kJ1\text{ kJ} of heat to a reservoir at 400 K400\text{ K}. The net work output (in kJ) of the cycle is
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    Question

    An ideal reheat Rankine cycle operates between the pressure limits of 10 kPa and 8 MPa, with reheat being done at 4 MPa. The temperature of steam at the inlets of both turbines is 500°C and the enthalpy of steam is 3185 kJ/kg at the exit of the high pressure turbine and 2247 kJ/kg at the exit of low pressure turbine. The enthalpy of water at the exit from the pump is 191 kJ/kg. Use the following table for relevant data.
    Superheated steam temperature (∘^\circ C)Pressure (MPa)ν\nu (m3/kgm^3/kg)hh (kJ/kg)ss (kJ/kg.K)
    50040.0864434467.0922
    50080.0417733996.7266
    Disregarding the pump work, the cycle efficiency (in percentage) is _______
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    Question

    Jobs arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is 40 minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be
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  51. Think it through. Then check your answer.

    Question

    A metal rod of initial length L0L_0 is subjected to a drawing process. The length of the rod at any instant is given by the expression, L(t)=L0(1+t2)L(t) = L_0(1 + t^2), where tt is the time in minutes. The true strain rate (in min−1min^{-1}) at the end of one minute is _______
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    Question

    During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness of the chip produced is 0.50.5 mm. The feed given to the zero degree rake angle tool is 0.20.2 mm/rev. The shear strain produced during the operation is _______
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    Question

    For the given assembly: 25 H7/g825\text{ H7/g8}, match Group A with Group B
    Group AGroup B
    P. HI. Shaft Type
    Q. IT8II. Hole Type
    R. IT7III. Hole Tolerance Grade
    S. gIV. Shaft Tolerance Grade
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  54. Think it through. Then check your answer.

    Question

    If the Taylor’s tool life exponent nn is 0.20.2, and the tool changing time is 1.51.5 min, then the tool life (in min) for maximum production rate is _______
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    Question

    An aluminium alloy (density 2600 kg/m32600\text{ kg/m}^3) casting is to be produced. A cylindrical hole of 100 mm100\text{ mm} diameter and 100 mm100\text{ mm} length is made in the casting using sand core (density 1600 kg/m31600\text{ kg/m}^3). The net buoyancy force (in newton) acting on the core is _______
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