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GATE ME 2019 Set 2

All 65 solved GATE ME 2019 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 24Medium 36Hard 5

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Once the team of analysts identify the problem, we __________ in a better position to comment on the issue.
    Which one of the following choices CANNOT fill the given blank?
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    Question

    A final examination is the __________ of a series of evaluations that a student has to go through.
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    Question

    If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
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    Question

    The product of three integers XX, YY and ZZ is 192. ZZ is equal to 4 and PP is equal to the average of XX and YY. What is the minimum possible value of PP?
    1. A.
      6
    2. B.
      7
    3. C.
      8
    4. D.
      9.5

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    Question

    Are there enough seats here? There are ______ people here than I expected.
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    Question

    Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ______.
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    Question

    Two pipes PP and QQ can fill a tank in 6 hours and 9 hours respectively, while a third pipe RR can empty the tank in 12 hours. Initially, PP and RR are open for 4 hours. Then PP is closed and QQ is opened. After 6 more hours RR is closed. The total time taken to fill the tank (in hours) is ______.
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    Question

    While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and in Manhattan penthouses with clinking ice cubes. This was, till an eminent Caribbean writer gave the writers in the once-colonised countries the confidence to see the shabby lives around them as worthy of being "told".
    The writer of this passage is surprised by the creative writing assignments of his students, because ______.
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    Question

    Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?
    TypeJanuaryFebruaryMarchApril
    Pool170320215190
    Mini11022018070
    Prime7518012090
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    Question

    XX is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, XX is almost forcing its customers towards its loyalty membership. If its loyalty membership continues to grow at its current rate, within the next eight years more households will be watching XX than cable television.
    Which one of the following statements can be inferred from the above paragraph?
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Mechanical Engineering (Set 3)

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    Question

    In matrix equation [A]{X}={R}[A]\{X\}=\{R\},[A]=[484816−44−415],{X}=[214] and {R}=[321664].[A]=\begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix}, \{X\}=\begin{bmatrix} 2 \\ 1 \\ 4 \end{bmatrix} \text{ and } \{R\} = \begin{bmatrix} 32 \\ 16 \\ 64 \end{bmatrix}.One of the eigenvalues of matrix [A][A] is
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    Question

    The directional derivative of the function f(x,y)=x2+y2f(x, y) = x^2 + y^2 along a line directed from (0,0)(0, 0) to (1,1)(1, 1), evaluated at the point x=1,y=1x = 1, y = 1 is
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    Question

    The differential equation dydx+4y=5\frac{dy}{dx} + 4y = 5 is valid in the domain 0≤x≤10 \leq x \leq 1 with y(0)=2.25y(0) = 2.25. The solution of the differential equation is
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    Question

    An analytic function f(z)f(z) of complex variable z=x+iyz=x+iy may be written as f(z)=u(x,y)+iv(x,y)f(z)=u(x,y)+iv(x,y). Then, u(x,y)u(x,y) and v(x,y)v(x,y) must satisfy
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    Question

    A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the xx-axis, and the body moves such that velocities of points P and R are VPV_P and VRV_R, in the xx and yy directions, respectively. The magnitude of the angular velocity of the body is
    A rigid triangular body PQR with velocity vectors $V_P$ and $V_R$
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    Question

    Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young's modulus E=200E = 200 GPa and Poisson's ratio ν=0.3\nu = 0.3 are given. The principal strains in the plane of the sheet are
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    Question

    A spur gear has pitch circle diameter DD and number of teeth TT. The circular pitch of the gear is
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    Question

    Endurance limit of a beam subjected to pure bending decreases with
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    Question

    A two-dimensional incompressible frictionless flow field is given by u⃗=xi^−yj^\vec{u} = x\hat{i} - y\hat{j}. If ρ\rho is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
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    Question

    Sphere 1 with a diameter of 0.1 m0.1\text{ m} is completely enclosed by another sphere 2 of diameter 0.4 m0.4\text{ m}. The view factor F12F_{12} is
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    Question

    One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is
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    Question

    For a simple compressible system, vv, ss, pp and TT are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell's relations, (∂v∂s)p\left( \frac{\partial v}{\partial s} \right)_p is equal to
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    Question

    Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet?
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    Question

    Hardenability of steel is a measure of
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    Question

    The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in
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    Question

    The cold forming process in which a hardened tool is pressed against a workpiece (when there is relative motion between the tool and the workpiece) to produce a roughened surface with a regular pattern is
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    Question

    The most common limit gage used for inspecting the hole diameter is
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    Question

    The transformation matrix for mirroring a point in x−yx - y plane about the line y=xy = x is given by
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    Question

    If xx is the mean of data 3, xx, 2 and 4, then the mode is ______
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    Question

    The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A, then the magnitude of the force produced in member CD is ______ N.
    Idealized plane truss with a horizontal force at the apex
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    Question

    The state of stress at a point in a component is represented by a Mohr's circle of radius 100100 MPa centered at 200200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260260 MPa. The magnitude of the shear stress on the same plane at the same point is ________ MPa.
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    Question

    A wire of circular cross-section of diameter 1.0 mm1.0\text{ mm} is bent into a circular arc of radius 1.0 m1.0\text{ m} by application of pure bending moments at its ends. The Young's modulus of the material of the wire is 100 GPa100\text{ GPa}. The maximum tensile stress developed in the wire is ______ MPa.
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    Question

    Water enters a circular pipe of length L=5.0L = 5.0 m and diameter D=0.20D = 0.20 m with Reynolds number ReD=500Re_D = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is ______.
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    Question

    A thin vertical flat plate of height LL, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings, and the properties of the surrounding fluid, are constant. The relationship between the average Nusselt and Rayleigh numbers is given as Nu=KRa1/4Nu = K Ra^{1/4}, where KK is a constant. The length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the plate is increased to 16L16L keeping all other factors constant.
    A diagram showing a vertical plate of height L and gravity vector g=9.8 m/s^2
    If the average heat transfer coefficient for the first plate is h1h_1 and that for the second plate is h2h_2, the value of the ratio h1/h2h_1/h_2 is ______.
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    Question

    In an electrical discharge machining process, the breakdown voltage across inter electrode gap (IEG) is 200 V200\text{ V} and the capacitance of the RC circuit is 50 μF50\text{ }\mu\text{F}. The energy (in J) released per spark across the IEG is ______
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    Question

    Given a vector u⃗=13(−y3i^+x3j^+z3k^)\vec{u} = \frac{1}{3}(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k}) and n^\hat{n} as the unit normal vector to the surface of the hemisphere (x2+y2+z2=1;z≥0)(x^2 + y^2 + z^2 = 1; z \geq 0), the value of integral ∫(∇×u⃗)⋅n^ dS\int (\nabla \times \vec{u}) \cdot \hat{n} \, dS evaluated on the curved surface of the hemisphere SS is
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    Question

    A differential equation is given asx2d2ydx2−2xdydx+2y=4x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 4The solution of the differential equation in terms of arbitrary constants C1C_1 and C2C_2 is
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    Question

    The derivative of f(x)=cos⁡(x)f(x) = \cos(x) can be estimated using the approximationf′(x)=f(x+h)−f(x−h)2hf'(x) = \frac{f(x+h)-f(x-h)}{2h}The percentage error is calculated as(Exact value−Approximate valueExact value)×100\left( \frac{\text{Exact value} - \text{Approximate value}}{\text{Exact value}} \right) \times 100The percentage error in the derivative of f(x)f(x) at x=π/6x = \pi/6 radian, choosing h=0.1h = 0.1 radian, is
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    Question

    A ball of mass 3 kg3\text{ kg} moving with a velocity of 4 m/s4\text{ m/s} undergoes a perfectly-elastic direct-central impact with a stationary ball of mass mm. After the impact is over, the kinetic energy of the 3 kg3\text{ kg} ball is 6 J6\text{ J}. The possible value(s) of mm is/are
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    Question

    Consider two concentric circular cylinders of different materials MM and NN in contact with each other at r=br = b, as shown below. The interface at r=br = b is frictionless. The composite cylinder system is subjected to internal pressure PP. Let (urM,uθM)(u_r^M, u_\theta^M) and (σrrM,σθθM)(\sigma_{rr}^M, \sigma_{\theta\theta}^M) denote the radial and tangential displacement and stress components, respectively, in material MM. Similarly, (urN,uθN)(u_r^N, u_\theta^N) and (σrrN,σθθN)(\sigma_{rr}^N, \sigma_{\theta\theta}^N) denote the radial and tangential displacement and stress components, respectively, in material NN. The boundary conditions that need to be satisfied at the frictionless interface between the two cylinders are:
    Two concentric circular cylinders M and N with interface at radius b
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    Question

    A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is LL, Young's modulus EE, and area moment of inertia II, the magnitude of the maximum deflection is
    A cantilever beam of length L, fixed at the left end and free at the right end. A triangularly distributed load is applied, with its maximum value q at the fixed end and decreasing linearly to zero at the free end. A coordinate system (x, y) is shown at the free end.
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    Question

    A slender uniform rigid bar of mass mm is hinged at O and supported by two springs, with stiffnesses 3k3k and kk, and a damper with damping coefficient cc, as shown in the figure. For the system to be critically damped, the ratio c/kmc/\sqrt{km} should be
    A slender rigid bar of length L is hinged at point O, which is at a distance L/4 from the left end. A spring of stiffness 3k is attached to the left end. A damper with coefficient c is attached at the midpoint of the bar (L/2 from the left end). A spring of stiffness k is attached to the right end.
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    Question

    The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (Q2Q_2) rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output (WW) of the heat engine. If temperatures, T1>T3>T2T_1 > T_3 > T_2, then the relation between the efficiency (η\eta) of the heat engine and the coefficient of performance (COP) of the heat pump is
    A schematic diagram showing a heat engine (HE) and a heat pump (HP). HE takes heat Q1 from reservoir T1, produces work W, and rejects heat Q2 to reservoir T2. HP takes heat Q2 from reservoir T2, receives work W from HE, and rejects heat Q3 to reservoir T3.
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    Question

    The binary phase diagram of metals PP and QQ is shown in the figure. An alloy XX containing 60%60\% PP and 40%40\% QQ (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in weight percent) at 12501250 ∘C^\circ\text{C}, respectively, will be
    Binary phase diagram of metals P and Q showing liquidus and solidus lines with temperature on y-axis and concentration of Q on x-axis
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    Question

    The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship "X<Y,ZX < Y, Z" means that XX is predecessor of activities YY and ZZ. The time to complete the activities along the critical path is ______ weeks.
    ActivityDuration (Weeks)Precedence Relationship
    A5A < B, C, D
    B7B < E, F, G
    C10C < I
    D6D < G
    E3E < H
    F9F < I
    G7G < I
    H4H < I
    I2----
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    Question

    The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity ω\omega, as shown. Assume the length of the crank to be rr.
    Diagram of an offset slider-crank mechanism with crank length r and connecting rod length √2r. The slider moves vertically.
    Using exact analysis, the acceleration of the slider in the yy-direction, at the instant shown, where the crank is parallel to xx-axis, is given by
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    Question

    A horizontal cantilever beam of circular cross-section, length 1.0 m1.0\text{ m} and flexural rigidity EI=200 N⋅m2EI = 200\text{ N}\cdot\text{m}^2 is subjected to an applied moment MA=1.0 N⋅mM_A = 1.0\text{ N}\cdot\text{m} at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is ______ mm (round off to one decimal place).
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    Two masses AA and BB having mass mam_a and mbm_b, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through OO perpendicular to the plane of the figure. The radii of rotation of the masses mam_a and mbm_b are rar_a and rbr_b, respectively. The angle between lines OAOA and OBOB is 90∘90^\circ. If ma=10 kgm_a = 10\text{ kg}, mb=20 kgm_b = 20\text{ kg}, ra=200 mmr_a = 200\text{ mm} and rb=400 mmr_b = 400\text{ mm}, then the balance mass to be placed at a radius of 200 mm200\text{ mm} is ______ kg (round off to two decimal places).
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    Question

    A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed ω2\omega_2. Length of different links are:
    O2O4=O2A=LO_2O_4 = O_2A = L,
    AB=O4B=2LAB = O_4B = \sqrt{2}L.
    The magnitude of the angular speed of the output link 4 is ω4\omega_4 at the instant when link 2 makes an angle of 90∘90^\circ with O2O4O_2O_4 as shown. The ratio ω4ω2\frac{\omega_4}{\omega_2} is ______ (round off to two decimal places).
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    The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts will be defective is ______ (round off to two decimal places).
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    Question

    A uniform disc with radius rr and a mass of mm kg is mounted centrally on a horizontal axle of negligible mass and length of 1.5r1.5r. The disc spins counter-clockwise about the axle with angular speed ω\omega, when viewed from the right-hand side bearing, QQ. The axle precesses about a vertical axis at ωp=ω/10\omega_p = \omega / 10 in the clockwise direction when viewed from above. Let RPR_P and RQR_Q (positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings PP and QQ, respectively. Assuming ω2r=300 m/s2\omega^2 r = 300 \text{ m/s}^2 and g=10 m/s2g = 10 \text{ m/s}^2, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is ______.
    Diagram showing a uniform disc of radius r on an axle of length 1.5r between bearings P and Q. Spin direction ω and precession direction ωp are indicated.
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    Question

    A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500 mm. The dimensions a=1000a = 1000 mm, b=500b = 500 mm and c=200c = 200 mm. The coefficient of friction between the drum and the shoe is 0.35. The force applied on the lever F=100F = 100 N as shown in the figure. The drum is rotating anti-clockwise. The braking torque on the drum is ______ N·m (round off to two decimal places).
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    Question

    Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QAQ_B/Q_A is ______ (round off to two decimal places).
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    The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1 with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same amount of power needed to overcome the aerodynamic drag, the speed of the car with the windows and roof open (round off to two decimal places), is ______ km/h (The density of air and the frontal area may be assumed to be constant).
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    Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor FIJF_{IJ} is defined as the fraction of radiation leaving plate II that is intercepted by plate JJ. Assume that the values of FLMF_{LM} and FNRF_{NR} are 0.80.8 and 0.40.4, respectively. The value of FPQF_{PQ} (round off to one decimal place) is ______.
    Three sets of parallel plates LM, NR and PQ in Figures 1, 2 and 3 showing dimensions and relative positions
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    Hot and cold fluids enter a parallel flow double tube heat exchanger at 100 ∘C100\text{ }^\circ\text{C} and 15 ∘C15\text{ }^\circ\text{C}, respectively. The heat capacity rates of hot and cold fluids are Ch=2000 W/KC_h = 2000\text{ W/K} and Cc=1200 W/KC_c = 1200\text{ W/K}, respectively. If the outlet temperature of the cold fluid is 45 ∘C45\text{ }^\circ\text{C}, the log mean temperature difference (LMTD) of the heat exchanger is ______ K (round off to two decimal places).
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    Water flowing at the rate of 1 kg/s1\text{ kg/s} through a system is heated using an electric heater such that the specific enthalpy of the water increases by 2.50 kJ/kg2.50\text{ kJ/kg} and the specific entropy increases by 0.007 kJ/kg⋅K0.007\text{ kJ/kg}\cdot\text{K}. The power input to the electric heater is 2.50 kW2.50\text{ kW}. There is no other work or heat interaction between the system and the surroundings. Assuming an ambient temperature of 300 K300\text{ K}, the irreversibility rate of the system is ______ kW (round off to two decimal places).
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    An idealized centrifugal pump (blade outer radius of 50 mm50\text{ mm}) consumes 2 kW2\text{ kW} power while running at 3000 rpm3000\text{ rpm}. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is _______ kg/s (round off to two decimal places).
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    An air standard Otto cycle has thermal efficiency of 0.50.5 and the mean effective pressure of the cycle is 1000 kPa1000 \text{ kPa}. For air, assume specific heat ratio γ=1.4\gamma = 1.4 and specific gas constant R=0.287 kJ/kg⋅KR = 0.287 \text{ kJ/kg}\cdot\text{K}. If the pressure and temperature at the beginning of the compression stroke are 100 kPa100 \text{ kPa} and 300 K300 \text{ K}, respectively, the specific net work output of the cycle is ______ kJ/kg\text{kJ/kg} (round off to two decimal places).
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    The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is 9.81 m/s29.81 \text{ m/s}^2. The time (in s, round off to two decimal places) to fill up the mold cavity (of size 40 cm×30 cm×15 cm40 \text{ cm} \times 30 \text{ cm} \times 15 \text{ cm}) is ______
    Pouring arrangement for casting showing a basin, sprue, and mold cavity with dimensions
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    A gas tungsten arc welding operation is performed using a current of 250 A250\text{ A} and an arc voltage of 20 V20\text{ V} at a welding speed of 5 mm/s5\text{ mm/s}. Assuming that the arc efficiency is 70%70\%, the net heat input per unit length of the weld will be _______ kJ/mm (round off to one decimal place).
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    The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ______ mm (round off to two decimal places).
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    A through hole is drilled in an aluminum alloy plate of 15 mm thickness with a drill bit of diameter 10 mm, at a feed of 0.25 mm/rev and a spindle speed of 1200 rpm. If the specific energy required for cutting this material is 0.7 N⋅m/mm30.7 \text{ N}\cdot\text{m/mm}^3, the power required for drilling is ______ W (round off to two decimal places).
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    In an orthogonal machining with a single point cutting tool of rake angle 10∘10^\circ, the uncut chip thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchant's first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool interface is ______ (round off to two decimal places).
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    The annual demand of valves per year in a company is 10,000 units. The current order quantity is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs. 400 per order. If the current order quantity is changed to Economic Order Quantity, then the saving in the total cost of inventory per year will be Rs. ______ (round off to two decimal places).
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