GATE 2025 Mechanical Engineering
114 questions across 2 sessions
Gate Me 2025
Cylindrical workpieces of diameter 60 mm and length 400 mm are machined on a lathe at a cutting speed of $25 \mathrm{~m} \mathrm{~min}^{-1}$ and a feed of $0.2 \mathrm{~mm} \mathrm...
If HIDE and CAGE are coded as 19-23-7-11 and 5-2-17-11 respectively, then what is the code for HIGH ?
Let $A$ and $B$ be real symmetric matrices of same size. Which one of the following options is correct?
The endurance limit of a specific grade of steel is same as its yield strength. The ultimate strength of this grade of steel is twice of its yield strength. A component made of thi...
A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs Rs. 150 to place an order. Carrying costs are 40 percent of the purchase pr...
For the differential equation given below, which one of the following options is correct? $$ \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0,0 \leq x \leq 1,0...
Consider a Pelton wheel of 1 m diameter. The magnitude of relative velocity of water at the bucket inlet is same as the magnitude of relative velocity of water at the bucket exit....
Identify the grammatically correct sentence:
Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification tim...
Wire drawing operation is performed on a perfectly plastic metal without any strain hardening. Assuming no friction and no redundant work, the maximum possible percentage reduction...
If two unbiased coins are tossed, then what is the probability of having at least one head?
Among the following surface hardening processes, steel is heated to the lowest temperature in
A pair of spur gears is required to maintain a velocity ratio of $1: 2$. The module of the gears is 10 mm and the addendum is 10 mm . If the operating pressure angle is $15^{\circ}...
The ceiling function of a real number $x$, denoted by $\operatorname{ce}(x)$, is defined as the smallest integer that is greater than or equal to $x$. Similarly, the floor function...
In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100...
Ceramics and glass are machined by
The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j})$ is _______ (Rounded off to 1 decimal pla...
A shaft carries a helical spur gear. Which one of the following bearings can NOT be used to support it?
Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. At once, without thinking much, people rushed towards the city in hordes wit...
A plate of 30 mm thickness is fed through a rolling mill with two powered rolls. Each roll has a diameter of 500 mm . The plate thickness is to be reduced to 27 mm in a single pass...
For a fully-developed pipe flow, which of the following options is/are correct?
In computer aided design (CAD), solid models can be constructed using
The divergence of the curl of a vector field is
$$ \text { The values of a function } f \text { obtained for different values of } x \text { are shown in the table below. } $$ $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 0.25...
Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, are $$ \begin{array}{|...
$$ \text { In relation to additive manufacturing, match the following } $$ Process Layer creation technique Material P. Stereolithography 1. Injection of powder stream I. Paper Q....
P and Q play chess frequently against each other. Of these matches, P has won $80 \%$ of the matches, drawn $15 \%$ of the matches and lost $5 \%$ of the matches. If they play 3 mo...
The welding process commonly used for fabricating tailor-welded blanks of dissimilar thickness for automotive applications is
Consider a velocity field $\vec{V}=3 z \hat{i}+0 \hat{j}+C x \hat{k}$, where $C$ is a constant. if the flow is irrotational, the value of C is ________ (rounded off to 1 decimal pl...
$$ \text { Match the mold elements in the casting process with the most suitable function } $$ Column I Column II P. Blind riser I. Casting with internal cavity Q. Chill II. Molten...
Let $y$ be the solution of the differential equation with the initial conditions given below. If $y(x=2)=A \ln 2$, then the value of $A$ is _________ (rounded off to 2 decimal plac...
In the closed interval $[0,3]$, the minimum value of the function $f$ given below is $f(x)=2 x^3-9 x^2+12 x$
A final year student appears for placement interview in two companies, $S$ and $T$. Based on her interview performance, she estimates the probability of receiving job offers from c...
A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is __________hours (answer in integer)....
A liquid metal is poured in a mold cavity of size $200 \mathrm{~mm} \times 200 \mathrm{~mm} \times 200 \mathrm{~mm}$. The cooling is uniform in all directions with NO additional co...
A block of mass 1 kg connected to a spring of stiffness $10 \mathrm{~N} \mathrm{~m}^{-1}$ is operating in a viscous medium such that the damping ratio (or damping factor) is equal...
The yield stress of a metal in uniaxial tension is 200 MPa . According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to
In the context of balancing of rotating and reciprocating masses, which one of the following options is true?
A metallic square plate is subjected to a uniform hydrostatic pressure $(P)$. Choose the correct Mohr's circle representing the state of stress at any point in the plate from the o...
If $C$ is the unit circle in the complex plane with its center at the origin, then the value of $n$ in the equation given below is _______ (rounded off to 1 decimal place). $$ \oin...
Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?
Two cars, $P$ and $Q$, start from a point $X$ in India at 10 AM . Car $P$ travels North with a speed of $25 \mathrm{~km} / \mathrm{h}$ and car Q travels East with a speed of $30 \m...
Fish : Shoal :: Lion :_________ Select the correct option to complete the analogy.
When assembled, the hole $$ \begin{array}{r} +0.030 \\ 30+0.000 \end{array} $$. mm and shaft $$ \begin{array}{r} +0.020 \\ 30-0.020 \end{array} $$ mm will result in
The thermal efficiency of an ideal air-standard Otto cycle is 0.5 . The value of specific heat ratio of air is 1.4. The compression ratio of the cycle is _________ (rounded off to...
A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 4...
A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are $3344 \mathrm{~kJ} \mathrm{~kg}^{-1}$...
In a psychrometric chart, one axis represents dry-bulb temperature. The axis, that is perpendicular to the dry-bulb temperature axis, represents
A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air...
Set Master
Fish : Shoal :: Lion : ________ Select the correct option to complete the analogy.
Identify the grammatically correct sentence:
Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of 25 km/h and car Q travels East with a speed of 30 km/h. Car P travels continuously bu...
The ceiling function of a real number x, denoted by ce(x), is defined as the smallest integer that is greater than or equal to x. Similarly, the floor function, denoted by fl(x), i...
P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches and lost 5% of the matches. If they play 3 more matches,...
Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. At once, without thinking much, people rushed towards the city in hordes wit...
If HIDE and CAGE are coded as 19-23-7-11 and 5-2-17-11 respectively, then what is the code for HIGH?
The given figure is reflected about the horizontal dashed line and then rotated clockwise by 90° about an axis perpendicular to the plane of the figure. Which one of the following...
Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?
A final year student appears for placement interview in two companies, S and T. Based on her interview performance, she estimates the probability of receiving job offers from compa...
Let A and B be real symmetric matrices of same size. Which one of the following options is correct?
For the differential equation given below, which one of the following options is correct? ∂²u/∂x² + ∂²u/∂y² = 0 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
The divergence of the curl of a vector field is
If two unbiased coins are tossed, then what is the probability of having at least one head?
Let a spherical block of ice at -7 °C be exposed to atmospheric air at 30 °C with the gravitational direction as shown in the figure below. What will be the overall direction of ai...
Consider two identical tanks with a bottom hole of diameter d. One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column h is same...
In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100...
Air inside a rigid, thermally-insulated tank undergoes stirring as shown in the figure below. Which one of the following options is correct?
In a psychrometric chart, one axis represents dry-bulb temperature. The axis, that is perpendicular to the dry-bulb temperature axis, represents
Among the following surface hardening processes, steel is heated to the lowest temperature in
The welding process commonly used for fabricating tailor-welded blanks of dissimilar thickness for automotive applications is
The yield stress of a metal in uniaxial tension is 200 MPa. According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to
In computer aided design (CAD), solid models can be constructed using
Ceramics and glass are machined by
When assembled, the hole $30^{+0.030}_{+0.000}$ mm and shaft $30^{-0.020}$ mm will result in
A rigid circular disc of radius r (in m) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is ω (in rad s⁻¹). The velocit...
A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?
A metallic square plate is subjected to a uniform hydrostatic pressure (P). Choose the correct Mohr's circle representing the state of stress at any point in the plate from the opt...
In the context of balancing of rotating and reciprocating masses, which one of the following options is true?
A shaft carries a helical spur gear. Which one of the following bearings can NOT be used to support it?
The values of a function f obtained for different values of x are shown in the table below. Using Simpson's one-third rule, $\int_0^1 f(x) dx \approx$ ________ (rounded off to 2 de...
The thermal efficiency of an ideal air-standard Otto cycle is 0.5. The value of specific heat ratio of air is 1.4. The compression ratio of the cycle is ________ (rounded off to 1...
During a welding operation, thermal power of 2500 W is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular....
A liquid metal is poured in a mold cavity of size 200 mm × 200 mm × 200 mm. The cooling is uniform in all directions with NO additional compensation for shrinkage. Considering the...
A block of mass 1 kg connected to a spring of stiffness 10 N m⁻¹ is operating in a viscous medium such that the damping ratio (or damping factor) is equal to the ratio of the dampe...
In the closed interval [0,3], the minimum value of the function f given below is f(x) = 2x³ - 9x² + 12x
Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, are
Match the mold elements in the casting process with the most suitable function Mold element P Blind riser Q Chill R Skim bob S Core T Insulating sleeve U Inoculant Function I Casti...
Wire drawing operation is performed on a perfectly plastic metal without any strain hardening. Assuming no friction and no redundant work, the maximum possible percentage reduction...
In relation to additive manufacturing, match the following Process P Stereolithography Q Fused deposition modeling R Laminated object manufacturing S Laser-engineered net shaping L...
A plate of 30 mm thickness is fed through a rolling mill with two powered rolls. Each roll has a diameter of 500 mm. The plate thickness is to be reduced to 27 mm in a single pass....
The system shown in the figure below consists of a cantilever beam (with flexural rigidity $EI$ and negligible mass), a spring (with spring constant $K$ and negligible mass) and a...
The endurance limit of a specific grade of steel is same as its yield strength. The ultimate strength of this grade of steel is twice of its yield strength. A component made of thi...
For a fully-developed pipe flow, which of the following options is/are correct?
If C is the unit circle in the complex plane with its center at the origin, then the value of n in the equation given below is ________ (rounded off to 1 decimal place). $\oint_C \...
The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{i} + \sqrt{3} \hat{j})$ is ________ (rounded off to 1 decimal...
Let y be the solution of the differential equation with the initial conditions given below. If $y(x = 2) = A \ln 2$, then the value of A is ________ (rounded off to 2 decimal place...
Consider a cylindrical furnace of 5 m diameter and 5 m length with bottom, top and curved surfaces maintained at uniform temperatures of 800 K, 1500 K and 500 K, respectively. The...
A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in the wind tunnel as shown in the figure below. The density of air is 1.23 kg m⁻³ while the...
Consider a velocity field $\vec{V} = 3z\hat{i} + 0\hat{j} + Cx \hat{k}$, where C is a constant. If the flow is irrotational, the value of C is _________ (rounded off to 1 decimal p...
Water enters a tube of diameter, D = 60 mm with mass flow rate of 0.01 kg s⁻¹ as shown in the figure below. The inlet mean temperature is Tm,i = 293 K and the uniform heat flux at...
A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are 3344 kJ kg⁻¹ and 6.5 kJ kg⁻¹ K⁻¹, resp...
Consider a Pelton wheel of 1 m diameter. The magnitude of relative velocity of water at the bucket inlet is same as the magnitude of relative velocity of water at the bucket exit....
A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 4...
A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air...
The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction (εzz) is ________ (rounded off to...
A simply supported beam of length 1 m is subjected to a uniformly distributed bending moment of 1 N m per m throughout the length as shown in the figure given below. The bending mo...
An isotropic brittle material is tested in the universal testing machine. The stress-strain diagram for the material shows a bi-linear elastic behavior as shown in the figure given...
A pair of spur gears is required to maintain a velocity ratio of 1:2. The module of the gears is 10 mm and the addendum is 10 mm. If the operating pressure angle is 15°, the minimu...
An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is ________ mm (rounded off to nearest integer).
Two plates of thickness 10 mm each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below. If the ultimate tens...
Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification tim...
Cylindrical workpieces of diameter 60 mm and length 400 mm are machined on a lathe at a cutting speed of 25 m min⁻¹ and a feed of 0.2 mm rev⁻¹. The Taylor's tool life parameters C...
A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs ₹ 150 to place an order. Carrying costs are 40 percent of the purchase pric...
A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is ______ hours (answer in integer). Act...