GATE 2024 Mechanical Engineering
109 questions across 2 sessions
Gate Me 2024
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
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, …
Let $X$ be a continuous random variable defined on $[0, 1]$ such that its probability density function $f(x) = 1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y = \log_e (X + 1)$....
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...
If ‘→’ denotes increasing order of intensity, then the meaning of the words [smile → giggle → laugh] is analogous to [disapprove → _______ → ch...
Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}
The real variables $x, y, z$, and the real constants $p, q, r$ satisfy $\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}$ Given that the denominators are non-zero, the...
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...
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 mom...
How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?
In order to numerically solve the ordinary differential equation dy/dt = -y for t > 0 , with an initial condition y(0) = 1 , the following scheme is employed: $\frac{y_{n+1} - y_{n...
Let f(z) be an analytic function, where z = x + iy . If the real part of f(z) is cosh x cos y , and the imaginary part of f(z) is zero for y = 0 , then f(z) is
Consider the system of linear equations x + 2y + z = 5 2x + ay + 4z = 12 2x + 4y + 6z = b The values of a and b such that there exists a non-trivial null space and the system admit...
Let $f(.)$ be a twice differentiable function from $ \mathbb{R}^{2} \rightarrow \mathbb{R}$. If $P, \mathbf{x}_{0} \in \mathbb{R}^{2}$ where $\vert \vert P\vert \vert$ is sufficien...
The velocity field of a two-dimensional, incompressible flow is given by $\overrightarrow{V} = \ 2sin{h}\,x\,\hat{i} + v(x,y)\hat{j}$ where $ \hat{i}$ and $\underset{\dot{}}{j}$ de...
Consider incompressible laminar flow over a flat plate with freestream velocity of $u_{\infty}$. The Nusselt number corresponding to this flow velocity is $Nu_1$. If the freestream...
Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., z direction). In the following statements, $T$ is the temperatu...
For a ball bearing, the fatigue life in millions of revolutions is given by $L = \left(\frac{C}{P}\right)^n$, where $P$ is the constant applied load and $C$ is the basic dynamic lo...
Which one of the following failure theories is the most conservative design approach against fatigue failure?
The "Earing" phenomenon in metal forming is associated with
The grinding wheel used to provide the best surface finish is
The allowance provided to a pattern for easy withdrawal from a sand mold is
The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding (GMAW) process is
The preparatory functions in Computer Numerical Controlled (CNC) machine programming are denoted by the alphabet
If $x(t)$ satisfies the differential equation $t \frac{dx}{dt} + (t - x) = 0$ subject to the condition $x(1) = 0$, then the value of $x(2)$ is __________ (rounded off to 2 decimal...
A set of jobs $U, V, W, X, Y, Z$ arrive at time $t = 0$ to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (...
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...
The matrix $\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix}$ (where $a > 0$) has a negative eigenvalue if $a$ is greater than
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 or...
At the current basic feasible solution (bfs) $v_0 (v_0 \in \mathbb{R}^5)$, the simplex method yields the following form of a linear programming problem in standard form: minimize $...
If the value of the double integral $\int_{x=3}^{4} \int_{y=1}^{2} \frac{dydx}{(x + y)^2}$ is $\log_e(\frac{a}{24})$, then $a$ is __________ (answer in integer).
A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance $L$ travelled by the liquid meniscus inside the...
A flat surface of a C60 steel having dimensions of 100 mm (length) × 200 mm (width) is produced by a HSS slab mill cutter. The 8-toothed cutter has 100 mm diameter and 200 mm width...
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...
Aluminium is casted in a cube-shaped mold having dimensions as 20 mm × 20 mm × 20 mm. Another mold of the same mold material is used to cast a sphere of aluminium having a diameter...
A blanking operation is performed on C20 steel sheet to obtain a circular disc having a diameter of 20 mm and a thickness of 2 mm. An allowance of 0.04 is provided. The punch size...
In an arc welding process, the voltage and current are 30 V and 200 A, respectively. The cross-sectional area of the joint is 20 mm 2 and the welding speed is 5 mm/s. The heat requ...
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...
A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an en...
Which one of the following statements regarding a Rankine cycle is FALSE?
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 measur...
The change in kinetic energy $\Delta E$ of an engine is $300$ J, and minimum and maximum shaft speeds are $\omega_{min} = 220$ rad/s and $\omega_{max} = 280$ rad/s, respectively. A...
The phases present in pearlite are
Which of the following beam(s) is/are statically indeterminate?
Set Master
If '→' denotes increasing order of intensity, then the meaning of the words [smile → giggle → laugh] is analogous to [disapprove → _______ → chide]. Which one of the given options...
Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}
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,...
The real variables x, y, z, and the real constants p, q, r satisfy $\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}$ Given that the denominators are non-zero, the valu...
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...
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...
How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?
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 option...
A planar rectangular paper has two V-shaped pieces attached as shown below. This piece of paper is folded to make the following closed three-dimensional object. The number of folds...
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
In order to numerically solve the ordinary differential equation dy/dt = -y for t > 0, with an initial condition y(0) = 1, the following scheme is employed (y_{n+1} - y_n) / Δt = -...
The value of the surface integral ∬_S z dx dy where S is the external surface of the sphere x² + y² + z² = R² is
Let f(z) be an analytic function, where z = x + iy. If the real part of f(z) is cosh x cos y, and the imaginary part of f(z) is zero for y = 0, then f(z) is
Consider the system of linear equations x + 2y + z = 5 2x + ay + 4z = 12 2x + 4y + 6z = b The values of a and b such that there exists a non-trivial null space and the system admit...
Let f(.) be a twice differentiable function from R² → R. If p, x₀ ∈ R² where ||p|| is sufficiently small (here ||. || is the Euclidean norm or distance function), then f(x₀ + p) =...
The velocity field of a two-dimensional, incompressible flow is given by V⃗ = 2 sinh x î + v(x, y) ĵ where î and ĵ denote the unit vectors in x and y directions, respectively. If v...
A plane, solid slab of thickness L, shown in the figure, has thermal conductivity k that varies with the spatial coordinate x as k = A + Bx, where A and B are positive constants (A...
Consider incompressible laminar flow over a flat plate with freestream velocity of u∞. The Nusselt number corresponding to this flow velocity is Nu₁. If the freestream velocity is...
Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., z direction). In the following statements, T is the temperature...
A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an en...
Which one of the following statements regarding a Rankine cycle is FALSE?
For a ball bearing, the fatigue life in millions of revolutions is given by L = (C/P)^n, where P is the constant applied load and C is the basic dynamic load rating. Which one of t...
The change in kinetic energy ΔE of an engine is 300 J, and minimum and maximum shaft speeds are ω_min = 220 rad/s and ω_max = 280 rad/s, respectively. Assume that the torque-time f...
A ram in the form of a rectangular body of size l = 9 m and b = 2 m is suspended by two parallel ropes of lengths 7 m. Assume the center-of-mass of the body is at its geometric cen...
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 measur...
Which one of the following failure theories is the most conservative design approach against fatigue failure?
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 a...
The phases present in pearlite are
The "Earing" phenomenon in metal forming is associated with
The grinding wheel used to provide the best surface finish is
The allowance provided to a pattern for easy withdrawal from a sand mold is
The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding (GMAW) process is
The preparatory functions in Computer Numerical Controlled (CNC) machine programing are denoted by the alphabet
A set of jobs U, V, W, X, Y, Z arrive at time t = 0 to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e....
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...
The matrix $\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix}$ (where $a > 0$) has a negative eigenvalue if $a$ is greater than
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 W, N, and S with poi...
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 or...
At the current basic feasible solution (bfs) $\boldsymbol{v_0}$ ($\boldsymbol{v_0} \in \mathbb{R}^5$), the simplex method yields the following form of a linear programming problem...
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 nozz...
Which of the following beam(s) is/are statically indeterminate?
If the value of the double integral $\int_{x=3}^{4}\int_{y=1}^{2}\frac{dydx}{(x+y)^2}$ is $\log_e (a/24)$, then $a$ is ________ (answer in integer).
If $x(t)$ satisfies the differential equation $t\frac{dx}{dt} + (t - x) = 0$ subject to the condition $x(1) = 0$, then the value of $x(2)$ is ________ (rounded off to 2 decimal pla...
Let X be a continuous random variable defined on [0,1] such that its probability density function f(x) = 1 for 0 ≤ x ≤ 1 and 0 otherwise. Let Y = loge(X + 1). Then the expected val...
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 th...
A piston-cylinder arrangement shown in the figure has a stop located 2 m above the base. The cylinder initially contains air at 140 kPa and 350 °C and the piston is resting in equi...
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 kJ of heat from the source at 1000 K. The heat pump abs...
Consider a slab of 20 mm thickness. There is a uniform heat generation of $\dot{q}$ = 100 MW/m$^3$ inside the slab. The left and right faces of the slab are maintained at 150 °C an...
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...
Consider a hemispherical furnace of diameter D = 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...
A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance L travelled by the liquid meniscus inside the c...
The Levai type-A train illustrated in the figure has gears with module m = 8 mm/tooth. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates...
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...
At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate $\omega$ = 7 rad/s. Pin P on link OD slides in the slot BC of...
A vibratory system consists of mass m, a vertical spring of stiffness 2k and a horizontal spring of stiffness k. The end A of the horizontal spring is given a horizontal motion x_A...
A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force P = 100 kN and a torque T = 600 N. m at the other end as sh...
The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha = 60^{\circ}$ with the horizontal. The closed ve...
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 kN and Q = 50 kN. Neglect friction at...
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 ____...
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...
Aluminium is casted in a cube-shaped mold having dimensions as 20 mm × 20 mm × 20 mm. Another mold of the same mold material is used to cast a sphere of aluminium having a diameter...
A blanking operation is performed on C20 steel sheet to obtain a circular disc having a diameter of 20 mm and a thickness of 2 mm. An allowance of 0.04 is provided. The punch size...
In an arc welding process, the voltage and current are 30 V and 200 A, respectively. The cross-sectional area of the joint is 20 mm² and the welding speed is 5 mm/s. The heat requi...
A flat surface of a C60 steel having dimensions of 100 mm (length) x 200 mm (width) is produced by a HSS slab mill cutter. The 8-toothed cutter has 100 mm diameter and 200 mm width...
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...