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GATE Mechanical 2023 | Question: 1
A machine produces a defective component with a probability of $0.015$. The number of defective components in a packed box containing $200$ components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are $3$ ... $\sqrt{3}$, respectively $0.015$ and $0.015$, respectively $3$ and $9$, respectively

A machine produces a defective component with a probability of $0.015$. The number of defective components in a packed box containing $200$ components produced by the mac...

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GATE Mechanical 2023 | Question: 7
The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?

The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?

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GATE Mechanical 2023 | Question: 13
Two surfaces $\text{P}$ and $\text{Q}$ are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces $\text{P}$ and $\text{Q}$ for creating the joint? Arc welding Brazing Adhesive bonding Spot welding

Two surfaces $\text{P}$ and $\text{Q}$ are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces $\text{P}$ and $\tex...

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GATE Mechanical 2023 | Question: 9
Air (density $=1.2 \mathrm{~kg} / \mathrm{m}^3$, kinematic viscosity $=1.5 \times 10^{-5} \mathrm{~m}^2 / \mathrm{s}$ ) flows over a flat plate with a free-stream velocity of $2 \mathrm{~m} / \mathrm{s}$ ... at a location $30 \mathrm{~mm}$ from the leading edge? $\tau_w / 2$ $\sqrt{2} \tau_w$ $2 \tau_w$ $\tau_w / \sqrt{2}$

Air (density $=1.2 \mathrm{~kg} / \mathrm{m}^3$, kinematic viscosity $=1.5 \times 10^{-5} \mathrm{~m}^2 / \mathrm{s}$ ) flows over a flat plate with a free-stream velocit...

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GATE Mechanical 2023 | Question: 46
An optical flat is used to measure the height difference between a reference slip gauge $\text{A}$ and a slip gauge $\text{B}$. Upon viewing via the optical flat using a monochromatic light of wavelength $0.5 \mu \mathrm{m}, 12$ fringes were ... $45 \mathrm{~mm}$ apart, the height difference of the gauges is ____________ $\mu \mathrm{m}$. (Answer in integer)

An optical flat is used to measure the height difference between a reference slip gauge $\text{A}$ and a slip gauge $\text{B}$. Upon viewing via the optical flat using a ...

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GATE2020-ME-2: 12
The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications whose definitions are listed below. P: Maximum waviness Height (mm); Q: Maximum Roughness Height (mm); R: Minimum Roughness Height (mm) ... II-S, III-Q, IV-T, V-R, VI-P I-Q, II-U, III-R, IV-T, V-S, VI-P

The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various speci...

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GATE Mechanical 2023 | Question: 5
A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylinders with hemi-spherical tips are to be placed on the fixture for ... $\mathrm{P}1$ and $\mathrm{P}3$ are over-constrained and Configuration $\mathrm{P}2$ is under-constrained.

A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form...

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GATE Mechanical 2023 | Question: 17
Which of the plot(s) shown is/are valid Mohr's circle representations of a plane stress state in a material? (The center of each circle is indicated by $0$.) $\text{M1}$ $\text{M2}$ $\text{M3}$ $\text{M4}$

Which of the plot(s) shown is/are valid Mohr's circle representations of a plane stress state in a material? (The center of each circle is indicated by $0$.)$\text{M1}$$\...

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GATE Mechanical 2021 Set 2 | Question: 7
The machining process that involves ablation is Abrasive Jet Machining Chemical Machining Electrochemical Machining Laser Beam Machining

The machining process that involves ablation isAbrasive Jet MachiningChemical MachiningElectrochemical MachiningLaser Beam Machining

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GATE Mechanical 2023 | Question: 2
The figure shows the plot of a function over the interval $[-4,4]$. Which one of the options given $\text{CORRECTLY}$ identifies the function? $|2-x|$ $|2-| x||$ $|2+| x||$ $2-|x|$

The figure shows the plot of a function over the interval $[-4,4]$. Which one of the options given $\text{CORRECTLY}$$ identifies the function?$|2-x|$$|2-| x||$$|2+| x||$...

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GATE Mechanical 2023 | Question: 15
In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) given correctly describe(s) the mould and the pattern? Mould walls ... , while mould walls indicate boundaries of regions where mould material is not allowed. Patterns can be used to make moulds.

In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) gi...

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GATE Mechanical 2022 Set 2 | Question: 28
A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied ... $\sigma /2$ $\sigma \left ( 1-1/\sqrt{2} \right )$

A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresp...

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GATE Mechanical 2023 | Question: 11
Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profiles. The Nusselt number for this flow depends on neither the Reynolds ... and Prandtl numbers the Reynolds number but not the Prandtl number the Prandtl number but not the Reynolds number

Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and veloci...

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GATE Mechanical 2023 | Question: 28
The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity $\omega_1$. A rigid bar $\text{PQ}$ is pinned to the wheel at $\text{P}$ while the end $\text{Q}$ slides on the floor. What is the angular velocity $\omega_2$ ... bar $\text{PQ}$? $\omega_2=2 \omega_1$ $\omega_2=\omega_1$ $\omega_2=0.5 \omega_1$ $\omega_2=0.25 \omega_1$

The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity $\omega_1$. A rigid bar $\text{PQ}$ is pinned to the wheel at $\text{P}$ whi...

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GATE Mechanical 2023 | Question: 6
The effective stiffness of a cantilever beam of length $L$ and flexural rigidity $E I$ subjected to a transverse tip load $\mathrm{W}$ is $\frac{3 E I}{L^{3}}$ $\frac{2 E I}{L^{3}}$ $\frac{L^{3}}{2 E I}$ $\frac{L^{3}}{3 E I}$

The effective stiffness of a cantilever beam of length $L$ and flexural rigidity $E I$ subjected to a transverse tip load $\mathrm{W}$ is$\frac{3 E I}{L^{3}}$$\frac{2 E I...

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GATE Mechanical 2023 | Question: 4
Which one of the options given represents the feasible region of the linear programming model: $ \begin{gathered} \text { Maximize } 45 X_1+60 X_2 \\ X_1 \leq 45 \\ X_2 \leq 50 \\ 10 X_1+10 X_2 \geq 600 \\ 25 X_1+5 X_2 \leq 750 \end{gathered} $ Region $\mathrm{P}$ Region $\mathrm{Q}$ Region $\mathrm{R}$ Region $\mathrm{S}$

Which one of the options given represents the feasible region of the linear programming model:$$\begin{gathered}\text { Maximize } 45 X_1+60 X_2 \\X_1 \leq 45 \\X_2 \leq ...

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GATE Mechanical 2023 | Question: 16
The principal stresses at a point $\mathrm{P}$ in a solid are $70 ~ \mathrm{MPa},-70 ~ \mathrm{MPa}$ and $0$. The yield stress of the material is $100 ~ \mathrm{MPa}$. Which prediction(s) about material ... material fails Maximum normal stress theory predicts that the material does not fail Maximum shear stress theory predicts that the material does not fail

The principal stresses at a point $\mathrm{P}$ in a solid are $70 ~ \mathrm{MPa},-70 ~ \mathrm{MPa}$ and $0$. The yield stress of the material is $100 ~ \mathrm{MPa}$. Wh...

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GATE Mechanical 2023 | Question: 3
With reference to the Economic Order Quantity $\text{(EOQ)}$ model, which one of the options given is correct? $\text{Curve P1:}$ Total cost, $\text{Curve P2:}$ Holding cost, $\text{Curve P3:}$ Setup cost, and $\text{Curve P4:}$ Production cost. ... Total cost, $\text{Curve P2:}$ Production cost, $\text{Curve P3:}$ Holding cost, and $\text{Curve P4:}$ Setup cost.

With reference to the Economic Order Quantity $\text{(EOQ)}$ model, which one of the options given is correct?$\text{Curve P1:}$ Total cost, $\text{Curve P2:}$ Holding co...

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GATE Mechanical 2023 | Question: 27
A spherical ball weighing $2 \mathrm{~kg}$ is dropped from a height of $4.9 \mathrm{~m}$ onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in $\mathrm{kg} \; \mathrm{m} / \mathrm{s}$ ... $19.6 \hat{\jmath}$ $17.0 \hat{\imath}+9.8 \hat{\jmath}$ $9.8 \hat{\imath}+17.0 \hat{\jmath}$

A spherical ball weighing $2 \mathrm{~kg}$ is dropped from a height of $4.9 \mathrm{~m}$ onto an immovable rigid block as shown in the figure. If the collision is perfect...

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GATE Mechanical 2023 | Question: 21
A vector field $ \mathbf{B}(x, y, z)=x \; \hat{\imath}+y \; \hat{\jmath}-2 z \; \hat{\mathrm{k}} $ is defined over a conical region having height $h=2$, base radius $r=3$ and axis along $z$, as shown in the figure. The ... $S$ of the cone, the value of the integral $ \int_S \mathbf{B} \cdot \boldsymbol{n} \; \mathrm{dS} $ equals____________. (Answer in integer)

A vector field$$\mathbf{B}(x, y, z)=x \; \hat{\imath}+y \; \hat{\jmath}-2 z \; \hat{\mathrm{k}}$$is defined over a conical region having height $h=2$, base radius $r=3$ a...

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GATE Mechanical 2023 | Question: 24
The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force $\mathbf{P}$. The belt wraps around the pulley over an angle $\alpha=270$ degrees. The coefficient of friction ... $T_1$ to $T_2$ in the belt is equal to_____________. (Rounded off to two decimal places) Take $\pi=3.14$

The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force $\mathbf{P}$. The belt wraps ar...

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GATE Mechanical 2023 | Question: 18
Consider a laterally insulated rod of length $\mathrm{L}$ and constant thermal conductivity. Assuming one-dimensional heat conduction in the rod, which of the following steady-state temperature profile(s) can occur without internal heat generation?

Consider a laterally insulated rod of length $\mathrm{L}$ and constant thermal conductivity. Assuming one-dimensional heat conduction in the rod, which of the following s...

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GATE Mechanical 2022 Set 1 | Question: 20
The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the ... through the nozzle will increase. Mach number at the exit plane of the nozzle will become more than unity.

The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condi...

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GATE Mechanical 2023 | Question: 45
A solid part (see figure) of polymer material is to be fabricated by additive manufacturing $\text{(AM)}$ in square-shaped layers starting from the bottom of the part working upwards. The nozzle diameter of the $\text{(AM)}$ ... delays between layers or the serpentine scan lines. The time taken to fabricate this part is ____________ minutes. (Answer in integer)

A solid part (see figure) of polymer material is to be fabricated by additive manufacturing $\text{(AM)}$ in square-shaped layers starting from the bottom of the part wor...

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GATE Mechanical 2022 Set 2 | Question: 12
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine? Linear motor Ball screw Lead screw Chain and sprocket

Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine?Linear motorBall screwLead screwChain and sprocket

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GATE Mechanical 2022 Set 2 | Question: 16
A square plate is supported in four different ways (configurations $(P)$ to $(S)$ as shown in the figure). A couple moment $C$ is applied on the plate. Assume all the members to be rigid and mass-less, and all joints to ... one or more of the following support configurations? Configuration $(P)$ Configuration $(Q)$ Configuration $(R)$ Configuration $(S)$

A square plate is supported in four different ways (configurations $(P)$ to $(S)$ as shown in the figure). A couple moment $C$ is applied on the plate. Assume all the mem...

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GATE Mechanical 2023 | Question: 10
Consider an isentropic flow of air (ratio of specific heats $=1.4$ ) through a duct as shown in the figure. The variations in the flow across the cross-section are negligible. The flow conditions at Location $1$ ... $u_2<u_1, P_2<P_1$ $u_2<u_1, P_2>P_1$ $u_2>u_1, P_2<P_1$ $u_2>u_1, P_2>P_1$

Consider an isentropic flow of air (ratio of specific heats $=1.4$ ) through a duct as shown in the figure.The variations in the flow across the cross-section are negligi...

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GATE Mechanical 2023 | Question: 19
Two meshing spur gears $1$ and $2$ with diametral pitch of $8$ teeth per mm and an angular velocity ratio $\left|\omega_{2}\right| /\left|\omega_{1}\right|=1 / 4$, have their centers $30 \mathrm{~mm}$ apart. The number of teeth on the driver (gear $1$) is___________. (Answer in integer)

Two meshing spur gears $1$ and $2$ with diametral pitch of $8$ teeth per mm and an angular velocity ratio $\left|\omega_{2}\right| /\left|\omega_{1}\right|=1 / 4$, have t...

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GATE Mechanical 2022 Set 2 | Question: 37
The lengths of members $\text{BC}$ and $\text{CE}$ in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints is negligible. Two forces of magnitude $Q> 0$ are applied as shown, each at the ... the following members do not carry any load (force)? $\text{AB}$ $\text{CD}$ $\text{EF}$ $\text{GH}$

The lengths of members $\text{BC}$ and $\text{CE}$ in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints i...

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GATE Mechanical 2022 Set 1 | Question: 28
A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The $T$-shaped link $\text{CDEF}$ is constructed such that the ... $\text{AG and CDEF}$ on the border of Grashof and non-Grashof chains with uncertain configuration(s)

A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The ...

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GATE Mechanical 2023 | Question: 26
Which one of the options given is the inverse Laplace transform of $\frac{1}{s^3-S} ?$ $u(t)$ denotes the unit-step function. $\left(-1+\frac{1}{2} e^{-t}+\frac{1}{2} e^t\right) u(t)$ $\left(\frac{1}{3} e^{-t}-e^t\right) u(t)$ ... $\left(-1-\frac{1}{2} e^{-(t-1)}-\frac{1}{2} e^{(t-1)}\right) u(t-1)$

Which one of the options given is the inverse Laplace transform of $\frac{1}{s^3-S} ?$$u(t)$ denotes the unit-step function.$\left(-1+\frac{1}{2} e^{-t}+\frac{1}{2} e^t\r...

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GATE Mechanical 2022 Set 1 | Question: 14
A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\vec{V} = \left ( 2x\right ) \hat{i} + \left ( y + 3t \right )\hat{j}$, and the temperature field ... by the probe at $\left ( x = 1, y = 1, t = 1 \right )$ is _____________. $4$ $0$ $18$ $14$

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\ve...

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GATE Mechanical 2023 | Question: 14
A beam is undergoing pure bending as shown in the figure. The stress $(\sigma)$-strain $(\varepsilon)$ curve for the material is also given. The yield stress of the material is $\sigma_Y$. Which of the option(s) given represent(s) the bending stress distribution at crosssection $\text{AA}$ after plastic yielding?

A beam is undergoing pure bending as shown in the figure. The stress $(\sigma)$-strain $(\varepsilon)$ curve for the material is also given. The yield stress of the mater...

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GATE Mechanical 2023 | Question: 42
A steel sample with $1.5 \; \mathrm{wt}. \%$ carbon (no other alloying elements present) is slowly cooled from $1100^{\circ} \mathrm{C}$ ... the total cementite content in the microstructure that develops just below the eutectoid temperature is ___________. (Rounded off to two decimal places)

A steel sample with $1.5 \; \mathrm{wt}. \%$ carbon (no other alloying elements present) is slowly cooled from $1100^{\circ} \mathrm{C}$ to just below the eutectoid tempe...

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GATE Mechanical 2023 | Question: 12
A heat engine extracts heat $\left(Q_{\mathrm{H}}\right)$ from a thermal reservoir at a temperature of $1000 \mathrm{~K}$ and rejects heat $\left(Q_{\mathrm{L}}\right)$ to a thermal reservoir at a temperature of $100 \mathrm{~K}$, while producing work $(W)$. ... $Q_{\mathrm{H}}=6000 \mathrm{~J}, Q_{\mathrm{L}}=600 \mathrm{~J}, W=5500 \mathrm{~J}$

A heat engine extracts heat $\left(Q_{\mathrm{H}}\right)$ from a thermal reservoir at a temperature of $1000 \mathrm{~K}$ and rejects heat $\left(Q_{\mathrm{L}}\right)$ t...

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GATE Mechanical 2024 | GA Question: 1
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? reprove praise reprise grieve

If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [smile $\rightarrow$ giggle $\rightarrow$ laugh] is analogous to [disappro...

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GATE Mechanical 2023 | Question: 25
Consider a counter-flow heat exchanger with the inlet temperatures of two fluids $(1$ and $2)$ being $T_1$, in $=300 \mathrm{~K}$ and $T_2$, in $=350 \mathrm{~K}$ ... and the effectiveness of the heat exchanger is $0.5.$ The actual heat transfer rate is _________ $\mathrm{kW}$. (Answer in integer)

Consider a counter-flow heat exchanger with the inlet temperatures of two fluids $(1$ and $2)$ being $T_1$, in $=300 \mathrm{~K}$ and $T_2$, in $=350 \mathrm{~K}$. The he...

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GATE Mechanical 2022 Set 2 | Question: 20
A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each can be placed on the platforms. The number of discs placed ... $\text{(ii)}$ of the figure) required to prevent downward motion of the left side platform is _____________________(in integer).

A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each ca...

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GATE2019 ME-1: 4
The lengths of a large stock of titanium rods follow a normal distribution with a mean $(\mu)$ of $440$ mm and a standard deviation $(\sigma)$ of $1$ mm.What is the percentage of rods whose lengths lie between $438$ mm and $441$ mm? $81.85 \%$ $68.4 \%$ $99.75 \%$ $86.64 \%$

The lengths of a large stock of titanium rods follow a normal distribution with a mean $(\mu)$ of $440$ mm and a standard deviation $(\sigma)$ of $1$ mm.What is the perce...

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GATE Mechanical 2022 Set 2 | Question: 7
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings ... about the positive $y$-axis direction rotate slowly (compared to $\omega$) about the negative $y$-axis direction

A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in ...

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