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GATE ME 2024 Set 1

All 65 solved GATE ME 2024 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

3

MCQ · NAT · MSQ

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 16Medium 41Hard 8

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    If ‘→\rightarrow’ denotes increasing order of intensity, then the meaning of the words
    [smile →\rightarrow giggle →\rightarrow laugh] is analogous to [disapprove →\rightarrow ________ →\rightarrow chide].
    Which one of the given options is appropriate to fill the blank?
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    Question

    Find the odd one out in the set: {19,37,21,17,23,29,31,11}\{19, 37, 21, 17, 23, 29, 31, 11\}
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    Question

    In the following series, identify the number that needs to be changed to form the Fibonacci series.
    1,1,2,3,6,8,13,21,…1, 1, 2, 3, 6, 8, 13, 21, \dots
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    Question

    The real variables x,y,zx, y, z, and the real constants p,q,rp, q, r satisfyxpq−r2=yqr−p2=zrp−q2\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}Given that the denominators are non-zero, the value of px+qy+rzpx + qy + rz is
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    Question

    Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4 probability of landing on any of the four rectangular faces. The label on the top face of the dice is the score of the throw.
    If thrown together, what is the probability of getting the sum of the two long dice scores greater than 11?
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    Question

    In the given text, the blanks are numbered (i)−(iv). Select the best match for all the blanks.
    Prof. P (i) merely a man who narrated funny stories. (ii) in his blackest moments he was capable of self-deprecating humor.
    Prof. Q (iii) a man who hardly narrated funny stories. (iv) in his blackest moments was he able to find humor.
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    Question

    How many combinations of non-null sets A,B,CA, B, C are possible from the subsets of {2,3,5}\{2, 3, 5\} satisfying the conditions: (i) AA is a subset of BB, and (ii) BB is a subset of CC?
    1. A.
      28
    2. B.
      27
    3. C.
      18
    4. D.
      19

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    Question

    The bar chart gives the batting averages of VK and RS for 11 calendar years from 2012 to 2022. Considering that 2015 and 2019 are world cup years, which one of the following options is true?
    Bar chart showing batting averages of VK and RS from 2012 to 2022
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    Question

    A planar rectangular paper has two V-shaped pieces attached as shown below.
    Net of a V-shaped object
    This piece of paper is folded to make the following closed three-dimensional object.
    3D V-shaped object
    The number of folds required to form the above object is
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    Question

    Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is
    1. A.
      30∘30^\circ
    2. B.
      60∘60^\circ
    3. C.
      45∘45^\circ
    4. D.
      90∘90^\circ

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Mechanical Engineering (ME)

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    Question

    In order to numerically solve the ordinary differential equation dydt=−y\frac{dy}{dt} = -y for t>0t > 0, with an initial condition y(0)=1y(0) = 1, the following scheme is employedyn+1−ynΔt=−12(yn+1+yn).\frac{y_{n+1} - y_n}{\Delta t} = -\frac{1}{2}(y_{n+1} + y_n).Here, Δt\Delta t is the time step and yn=y(nΔt)y_n = y(n\Delta t) for n=0,1,2,…n = 0, 1, 2, \dots. This numerical scheme will yield a solution with non-physical oscillations for Δt>h\Delta t > h. The value of hh is
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    Question

    The value of the surface integral∯Szdxdy\oiint_S z dx dywhere SS is the external surface of the sphere x2+y2+z2=R2x^2 + y^2 + z^2 = R^2 is
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    Question

    Let f(z)f(z) be an analytic function, where z=x+iyz = x + iy. If the real part of f(z)f(z) is cosh⁡xcos⁡y\cosh x \cos y, and the imaginary part of f(z)f(z) is zero for y=0y = 0, then f(z)f(z) is
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    Question

    Consider the system of linear equations x+2y+z=5x + 2y + z = 52x+ay+4z=122x + ay + 4z = 122x+4y+6z=b2x + 4y + 6z = bThe values of aa and bb such that there exists a non-trivial null space and the system admits infinite solutions are
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    Question

    Let f(.)f(.) be a twice differentiable function from R2→R\mathbb{R}^2 \to \mathbb{R}. If p,x0∈R2\mathbf{p}, \mathbf{x_0} \in \mathbb{R}^2 where ∥p∥\|\mathbf{p}\| is sufficiently small (here ∥.∥\|. \| is the Euclidean norm or distance function), then f(x0+p)=f(x0)+∇f(x0)Tp+12pT∇2f(ψ)pf(\mathbf{x_0} + \mathbf{p}) = f(\mathbf{x_0}) + \nabla f(\mathbf{x_0})^T \mathbf{p} + \frac{1}{2} \mathbf{p}^T \nabla^2 f(\boldsymbol{\psi}) \mathbf{p}where oldsymbol{\psi} \in \mathbb{R}^2 is a point on the line segment joining x0\mathbf{x_0} and x0+p\mathbf{x_0} + \mathbf{p}. If x0\mathbf{x_0} is a strict local minimum of f(x)f(\mathbf{x}), then which one of the following statements is TRUE?
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    Question

    The velocity field of a two-dimensional, incompressible flow is given byV⃗=2sinh⁡xi^+v(x,y)j^\vec{V} = 2 \sinh x \hat{i} + v(x, y) \hat{j}where i^\hat{i} and j^\hat{j} denote the unit vectors in xx and yy directions, respectively. If v(x,0)=cosh⁡xv(x, 0) = \cosh x, then v(0,−1)v(0, -1) is
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    Question

    A plane, solid slab of thickness LL, shown in the figure, has thermal conductivity kk that varies with the spatial coordinate xx as k=A+Bxk = A + Bx, where AA and BB are positive constants (A>0,B>0A > 0, B > 0). The slab walls are maintained at fixed temperatures of T(x=0)=0T(x = 0) = 0 and T(x=L)=T0>0T(x = L) = T_0 > 0. The slab has no internal heat sources. Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?
    A diagram showing a rectangular slab of thickness L. The x-axis starts at x=0 (left wall) where T=0 and ends at x=L (right wall) where T=T0. The thermal conductivity k varies as A+Bx.
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    Question

    Consider incompressible laminar flow over a flat plate with freestream velocity of u∞u_\infty. The Nusselt number corresponding to this flow velocity is Nu1Nu_1. If the freestream velocity is doubled, the Nusselt number changes to Nu2Nu_2. Choose the correct option for Nu2/Nu1Nu_2/Nu_1.
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    Question

    Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., zz direction). In the following statements, TT is the temperature of the fluid, TwT_w is the wall temperature and TmT_m is the bulk mean temperature of the fluid. Which one of the following statements is TRUE?
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    Question

    A furnace can supply heat steadily at 1200 K1200\text{ K} at a rate of 24000 kJ/min24000\text{ kJ/min}. The maximum amount of power (in kW\text{kW}) that can be produced by using the heat supplied by this furnace in an environment at 300 K300\text{ K} is
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    Question

    Which one of the following statements regarding a Rankine cycle is FALSE?
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    Question

    For a ball bearing, the fatigue life in millions of revolutions is given by L=(CP)nL = \left( \frac{C}{P} \right)^n, where PP is the constant applied load and CC is the basic dynamic load rating. Which one of the following statements is TRUE?
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    Question

    The change in kinetic energy ΔE\Delta E of an engine is 300 J300\text{ J}, and minimum and maximum shaft speeds are ωmin=220 rad/s\omega_{min} = 220\text{ rad/s} and ωmax=280 rad/s\omega_{max} = 280\text{ rad/s}, respectively. Assume that the torque-time function is purely harmonic. To achieve a coefficient of fluctuation of 0.050.05, the moment of inertia (in kg⋅m2\text{kg}\cdot\text{m}^2) of the flywheel to be mounted on the engine shaft is
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    Question

    A ram in the form of a rectangular body of size l=9 ml = 9\text{ m} and b=2 mb = 2\text{ m} is suspended by two parallel ropes of lengths 7 m7\text{ m}. Assume the center-of-mass of the body is at its geometric center and g=9.81 m/s2g = 9.81\text{ m/s}^2. For striking the object P with a horizontal velocity of 5 m/s5\text{ m/s}, what is the angle θ\theta with the vertical from which the ram should be released from rest?
    A diagram showing a rectangular ram suspended by two parallel ropes of length 7m at an angle theta to the vertical, positioned to strike an object P.
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    Question

    A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitudes of two successive cycles measured are 7.75 mm and 7.20 mm, the coefficient of viscous damping (in N.s/m) is
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    Question

    Which one of the following failure theories is the most conservative design approach against fatigue failure?
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    Question

    A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at A along xx-axis and another at point B along yy-axis. For the body to be in equilibrium, the third point load acting at point O must be
    A rigid massless tetrahedron with vertex O at the origin and vertices A, B, C on the x, y, z axes respectively. Forces are applied at A and B.
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    Question

    The phases present in pearlite are
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    Question

    The “Earing” phenomenon in metal forming is associated with
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    Question

    The grinding wheel used to provide the best surface finish is
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    Question

    The allowance provided to a pattern for easy withdrawal from a sand mold is
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    The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding (GMAW) process is
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    The preparatory functions in Computer Numerical Controlled (CNC) machine programing are denoted by the alphabet
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    Question

    A set of jobs U,V,W,X,Y,ZU, V, W, X, Y, Z arrive at time t=0t = 0 to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.
    JobUVWXYZ
    Workstation 1573468
    Workstation 2466857
    The sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is
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    Question

    A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a mean of 5 jobs/hour. The service time of the server is exponentially distributed with a mean of 6 minutes. In steady state operation of the queueing system, the probability that the server is not busy at any point in time is
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    Question

    The matrix [1a83]\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix} (where a>0a > 0) has a negative eigenvalue if aa is greater than
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    Question

    In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points WW, NN, and SS with point JJ have an equal length LL. The pipe connecting points JJ and EE has a length 10L10L. The pressures at the ends NN, EE, and SS are equal. The flow rate in the pipe connecting WW and JJ is QQ. Assume that the fluid flow is steady, incompressible, and the pressure losses at the pipe entrance and junction are negligible. Consider the following statements:
    I : The flow rate in pipe connecting JJ and EE is Q/21Q/21.
    II: The pressure difference between JJ and NN is equal to the pressure difference between JJ and EE.
    Which one of the following options is CORRECT?
    Pipe network diagram showing points W, N, S, J, E and lengths L, 10L
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    Question

    A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per order is 300 rupees, and the holding cost is 12 rupees per month per gear. The company uses an order size that is 25% more than the optimal order quantity determined by the EOQ model. The percentage change in the total cost of ordering and holding inventory from that associated with the optimal order quantity is
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    Question

    At the current basic feasible solution (bfs) v0\mathbf{v}_0 (v0∈R5\mathbf{v}_0 \in \mathbb{R}^5), the simplex method yields the following form of a linear programming problem in standard form.minimize z=−x1−2x2\text{minimize } z = -x_1 - 2x_2s. t. x3=2+2x1−x2\text{s. t. } x_3 = 2 + 2x_1 - x_2x4=7+x1−2x2x_4 = 7 + x_1 - 2x_2x5=3−x1x_5 = 3 - x_1x1,x2,x3,x4,x5≥0x_1, x_2, x_3, x_4, x_5 \geq 0Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs v1\mathbf{v}_1 (v1∈R5\mathbf{v}_1 \in \mathbb{R}^5) that best improves the objective function, which of the following represents the objective function at v1\mathbf{v}_1, assuming that the objective function is written in the same manner as above?
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    Question

    Steady, compressible flow of air takes place through an adiabatic converging-diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If EE and FF denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?
    Converging-diverging nozzle with a normal shock wave at the diverging section, with points E and F marked upstream and downstream of the shock respectively.
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    Which of the following beam(s) is/are statically indeterminate?
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    If the value of the double integral∫x=34∫y=12dydx(x+y)2\int_{x=3}^{4} \int_{y=1}^{2} \frac{dydx}{(x + y)^2}is log⁡e(a/24)\log_e(a/24), then aa is ___________ (answer in integer).
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    If x(t)x(t) satisfies the differential equationtdxdt+(t−x)=0t \frac{dx}{dt} + (t - x) = 0subject to the condition x(1)=0x(1) = 0, then the value of x(2)x(2) is ________ (rounded off to 2 decimal places).
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    Let XX be a continuous random variable defined on [0,1][0,1] such that its probability density function f(x)=1f(x) = 1 for 0≤x≤10 \leq x \leq 1 and 00 otherwise. Let Y=log⁡e(X+1)Y = \log_e(X + 1). Then the expected value of YY is_____. (rounded off to 2 decimal places)
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    Consider an air-standard Brayton cycle with adiabatic compressor and turbine, and a regenerator, as shown in the figure. Air enters the compressor at 100 kPa and 300 K and exits the compressor at 600 kPa and 550 K. The air exits the combustion chamber at 1250 K and exits the adiabatic turbine at 100 kPa and 800 K. The exhaust air from the turbine is used to preheat the air in the regenerator. The exhaust air exits the regenerator (state 6) at 600 K. There is no pressure drop across the regenerator and the combustion chamber. Also, there is no heat loss from the regenerator to the surroundings. The ratio of specific heats at constant pressure and volume is cp/cv=1.4c_p/c_v = 1.4. The thermal efficiency of the cycle is _________ % (answer in integer).
    Schematic diagram of a Brayton cycle with a regenerator showing compressor, regenerator, combustion chamber, and turbine with state points 1 to 6.
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    A piston-cylinder arrangement shown in the figure has a stop located 2 m2 \text{ m} above the base. The cylinder initially contains air at 140 kPa140 \text{ kPa} and 350∘C350 ^\circ\text{C} and the piston is resting in equilibrium at a position which is 1 m1 \text{ m} above the stops. The system is now cooled to the ambient temperature of 25∘C25 ^\circ\text{C}. Consider air to be an ideal gas with a value of gas constant R=0.287 kJ/(kg.K)R = 0.287 \text{ kJ/(kg.K)}.
    The absolute value of specific work done during the process is________kJ/kg\text{kJ/kg} (rounded off to 11 decimal place)
    Piston-cylinder arrangement with stops
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    A heat pump (H.P.) is driven by the work output of a heat engine (H.E.) as shown in the figure. The heat engine extracts 150 kJ150\text{ kJ} of heat from the source at 1000 K1000\text{ K}. The heat pump absorbs heat from the ambient at 280 K280\text{ K} and delivers heat to the room which is maintained at 300 K300\text{ K}. Considering the combined system to be ideal, the total amount of heat delivered to the room together by the heat engine and heat pump is _______kJ\text{kJ} (answer in integer).
    Schematic diagram showing a Heat Engine (H.E.) operating between 1000 K and 300 K, driving a Heat Pump (H.P.) operating between 280 K and 300 K.
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    Question

    Consider a slab of 20 mm20\text{ mm} thickness. There is a uniform heat generation of q˙=100 MW/m3\dot{q} = 100\text{ MW/m}^3 inside the slab. The left and right faces of the slab are maintained at 150 ∘C150\text{ }^\circ\text{C} and 110 ∘C110\text{ }^\circ\text{C}, respectively. The plate has a constant thermal conductivity of 200 W/(m.K)200\text{ W/(m.K)}. Considering a 1-D steady state heat conduction, the location of the maximum temperature from the left face will be at _____mm\text{mm} (answer in integer).
    A slab of thickness 20 mm with heat generation q_dot, left face at 150 °C and right face at 110 °C.
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    Question

    A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of 1 shell and 20,000 tubes. Water flows through each of the tubes at a rate of 1 kg/s with an inlet temperature of 30 °C. The steam in the condenser shell condenses at the rate of 430 kg/s at a temperature of 50 °C. If the heat of vaporization is 2.326 MJ/kg and specific heat of water is 4 kJ/(kg.K), the effectiveness of the heat exchanger is ________ (rounded off to 3 decimal places).
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    Consider a hemispherical furnace of diameter D=6D = 6 m with a flat base. The dome of the furnace has an emissivity of 0.7 and the flat base is a blackbody. The base and the dome are maintained at uniform temperature of 300 K and 1200 K, respectively. Under steady state conditions, the rate of radiation heat transfer from the dome to the base is ________kW (rounded off to the nearest integer).
    Use Stefan-Boltzmann constant = 5.67×10−85.67 \times 10^{-8} W/(m2^2 K4^4)
    Hemispherical furnace with dome and base
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    A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance LL travelled by the liquid meniscus inside the capillary in time tt is given byL=kγaRbμct,L = k \gamma^a R^b \mu^c \sqrt{t},where γ\gamma is the surface tension, RR is the inner radius of the capillary, and μ\mu is the dynamic viscosity of the liquid. If kk is a dimensionless constant, then the exponent aa is __________ (rounded off to 1 decimal place).
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    The Levai type-A train illustrated in the figure has gears with module m=8m = 8 mm/tooth. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates at 20 rev/min counter-clockwise. The magnitude of angular velocity of the arm is__________ rev/min. (rounded off to 2 decimal places)
    Diagram of a Levai type-A epicyclic gear train showing arm 1, fixed sun gear 2, planet gear 3, and internal ring gear 4.
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    A horizontal beam of length 1200 mm is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distributed load is applied on the beam. The magnitude of maximum bending moment acting on the beam is _______ N.m. (round off to 1 decimal place)
    Simply supported beam of length 1200 mm with a triangularly distributed load increasing from 0 at the left support to 100 N/m at the right support.
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    At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate ω=7\omega = 7 rad/s. Pin P on link OD slides in the slot BC of link ABC which is hinged at A, and causes a clockwise rotation of the link ABC. The magnitude of angular velocity of link ABC for this instant is _________________ rad/s (rounded off to 2 decimal places).
    Mechanism diagram showing link OD rotating about O, with pin P sliding in a slot BC of triangular link ABC hinged at A. Dimensions: OP = 150 mm, AP = 150 mm, slot angle = 60 degrees.
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    A vibratory system consists of mass mm, a vertical spring of stiffness 2k2k and a horizontal spring of stiffness kk. The end A of the horizontal spring is given a horizontal motion xA=asin⁡ωtx_A = a \sin \omega t. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown. Assume m=10m = 10 kg, k=1.5k = 1.5 kN/m, and neglect friction. The magnitude of critical driving frequency for which the oscillations of mass mm tend to become excessively large is _________ rad/s (answer in integer).
    Diagram of a vibratory system with mass m, springs, and pulleys
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    A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force P=100P = 100 kN and a torque T=600T = 600 N. m at the other end as shown. Assume that the axis of the cylinder is normal to the support. Considering distortion energy theory with allowable yield stress as 300 MPa, the factor of safety in the design is _____ (rounded off to 1 decimal place).
    A cantilevered cylinder subjected to axial force P and torque T
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    The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle α=60∘\alpha = 60^\circ with the horizontal. The closed vessel has a wall thickness of 10 mm and diameter of 2 m. When subjected to an internal pressure of 200 kPa, the magnitude of the normal stress acting on the weld is _________ MPa (rounded off to 1 decimal place).
    Thin cylindrical pressure vessel with a weld line at angle alpha
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    A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of P=100 kNP = 100\text{ kN} and Q=50 kNQ = 50\text{ kN}. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is ______ kN (rounded off to 1 decimal place).
    A semi-circular three-hinged arch ABC with vertical loads P and Q applied at 3 m from the center on either side.
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    A band brake shown in the figure has a coefficient of friction of 0.3. The band can take a maximum force of 1.5 kN. The maximum braking force (F) that can be safely applied is _______ N (rounded off to the nearest integer).
    A band brake system with a lever of length 1000 mm and a drum rotating counter-clockwise.
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    A cutting tool provides a tool life of 60 minutes while machining with the cutting speed of 60 m/min. When the same tool is used for machining the same material, it provides a tool life of 10 minutes for a cutting speed of 100 m/min. If the cutting speed is changed to 80 m/min for the same tool and work material combination, the tool life computed using Taylor’s tool life model is____________ minutes (rounded off to 2 decimal places).
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    Aluminium is casted in a cube-shaped mold having dimensions as 20 mm×20 mm×20 mm20\text{ mm} \times 20\text{ mm} \times 20\text{ mm}. Another mold of the same mold material is used to cast a sphere of aluminium having a diameter of 20 mm20\text{ mm}. The pouring temperature for both cases is the same. The ratio of the solidification times of the cube-shaped mold to the spherical mold is ________ (answer in integer).
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    A blanking operation is performed on C20 steel sheet to obtain a circular disc having a diameter of 2020 mm and a thickness of 22 mm. An allowance of 0.040.04 is provided. The punch size used for the operation is ___________ mm (rounded off to 22 decimal places).
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    In an arc welding process, the voltage and current are 3030 V and 200200 A, respectively. The cross-sectional area of the joint is 2020 mm2^2 and the welding speed is 55 mm/s. The heat required to melt the material is 2020 J/mm3^3. The percentage of heat lost to the surrounding during the welding process is _________ (rounded off to 22 decimal places).
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    A flat surface of a C60 steel having dimensions of 100 mm100\text{ mm} (length) ×200 mm\times 200\text{ mm} (width) is produced by a HSS slab mill cutter. The 8-toothed cutter has 100 mm100\text{ mm} diameter and 200 mm200\text{ mm} width. The feed per tooth is 0.1 mm0.1\text{ mm}, cutting velocity is 20 m/min20\text{ m/min} and depth of cut is 2 mm2\text{ mm}. The machining time required to remove the entire stock is _____________ minutes (rounded off to 2 decimal places).
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    In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer are tabulated below. The supply chain manager wishes to minimize the total cost of transportation across the supply chain.
    Retailer IRetailer IIRetailer IIIRetailer IVCapacity
    Supplier A11161913300
    Supplier B51078300
    Supplier C12141711300
    Supplier D815119300
    Demand300300300300
    The optimal cost of satisfying the total demand from all retailers is _____ rupees (answer in integer).
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