GATE Mechanical Engineering

Consider a string P of length l that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Fig...

Domain A is bounded by curve x² = 4y, ordinate x = 2, and x axis. The value of ∫∫A y dxdy is

Let φ be a scalar function. Then, ∇φ is

The order and degree of the following differential equation are m and n, respectively. $\frac{\partial^3\varphi}{\partial x^3} + \frac{\partial^2\varphi}{\partial y^2}\frac{\partia...

Newton-Raphson method for solving algebraic equations is based on

The exact solution of $\int_0^4 \frac{dx}{1+x}$ is represented as n. If m represents numerically evaluated value of the above integral using Trapezoidal rule by considering four eq...

A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular velocity of 3 ra...

A gear train with five gears is shown in the figure below. The number of teeth on each gear is N1, N2, N3, N4, and N5. The idler gear in this gear train is

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is 350 N s/m and the damping coefficient is 35 N s/m. The logarithmic dec...

A closely coiled helical compression spring of mean coil diameter D and wire diameter d, is loaded by an axial force F. The maximum shear stress developed in the wire is

The rotor of an aeroplane engine has a mass moment of inertia 1.0 kg m². The engine rotates at a speed of 500 RPM in the clockwise direction if viewed from the front of the aeropla...

A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is l and the fillet weld leg size is...

Worm gearsets are used for transmitting rotary motion between

For an ideal gas, starting from state point 1, two different processes take place. The corresponding final states in these two processes are 2 and 3, lying on same isotherm. If P a...

A steady incompressible laminar flow passes through a 90° tube bend placed on a horizontal surface. In horizontal diametric plane, two pressure taps Pi and Po are provided across t...

An ideal gas passes isothermally through a long horizontal uniform cross-section pipe under steady flow. Consider that the pressure gradient in the pipe is sufficient for a finite...

Bernoulli's equation CANNOT be applied between

A quiescent fluid at temperature T3 is confined between two vertical parallel plates. While plate 1 is kept at temperature T1 and plate 2 is maintained at temperature T2, a velocit...

For the isothermal expansion of an ideal gas in a piston cylinder system, the net heat supplied during the process is equal to the net work. Which one of the following statements i...

A hydraulic crane supports a mass of 500 kg with its piston-cylinder actuator, inclined at 60° with horizontal, as shown in the figure below. The diameter of the piston is 30 cm an...

In relation to metal casting defects, match the following Defect P Dross Q Scab R Scar Description I Shallow blow found on a flat casting surface II Lighter impurities appearing on...

Which one of the following options is NOT an error associated with STereoLithography (STL) file in additive manufacturing?

A work piece is to be firmly held in a fixture. It is to be machined by using a plain slab milling cutter as shown in the figure below. Which one of the following options is the mo...

A two-dimensional surface profile is obtained over a sampling length by using a contact type stylus profilometer as shown in the figure below. A line AA parallel to the general lay...

A steel plate having yield strength of 550 MPa, is subjected to biaxial state of stress as σx = σ and σy = -2σ. Using distortion energy theory and considering the factor of safety...

A sphere of radius 5 mm is initially in equilibrium at 400 °C in a furnace. It is suddenly removed from the furnace and dipped in a well-stirred water bath at 20 °C, with a convect...

If $w = \log_e z = \log_e(x + iy)$, where $i = \sqrt{-1}$, then which one of the following statements is correct?

Consider the following differential equation $\frac{\partial y}{\partial x} = 3\frac{\partial y}{\partial t} + y$ If $y(x, 0) = 10e^{-2x}$, then the solution of the differential eq...

Let f(t) be a function of t defined for all positive values of t. The Laplace transform of f(t) denoted by L{f(t)} = ∫₀^∞ e^(-st)f(t)dt, provided that the integral exists where s i...

A student council of 10 members consists of two students from engineering school, three students from science school and five students from arts school. The university administrati...

A cantilever beam of length L is subjected to a concentrated load P and a moment M as shown in the figure below. Neglecting the mass of the beam, which one of the following options...

Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecting the mas...

A 5 kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young's modulus of the material o...

A very long fin of a uniform square cross-section is replaced by another very long fin of a uniform circular cross-section of the same material. Assume uniform and identical heat t...

For an ideal regenerative Rankine cycle, as shown in the figure below, which one of the following options is the correct representation of temperature-entropy (T-s) diagram?

Consider the Euler variables of polyhedral objects namely, P1, P2, P3, and P4 as given in the table below. Polyhedral objects (F) Faces (E) Edges (V) Vertices Faces' inner loops (L...

An objective function Z of primal variables (x₁ and x₂) is described below: Minimize Z = 0.07 x₁ + 0.05 x₂ subject to 0.1 x₁ ≥ 0.4 0.1 x₂ ≥ 0.6 0.1 x₁ + 0.2 x₂ ≥ 2.0 0.2 x₁ + 0.1 x...

Four jobs are on order in a factory. As on day 20 of the production calendar, the corresponding due date and work remaining to complete these jobs (in days) are given in the table...

A block of 50 kg mass is on an inclined plane. The block is connected to another hanging mass M by an inextensible massless string through two massless pulleys as shown in the figu...

A simply supported beam is subjected to an external point load P as shown in the figure below. The beam has a rectangular cross-section of 20 mm x 45 mm. A is a pin support and B i...

A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown in the figure below. The velocity of A in the downward direction at a given inst...

A cylindrical pressure vessel made of steel has diameter of 3 m and wall thickness of 15 mm. For steel, Young's modulus and Poisson's ratio are 210 GPa and 0.3, respectively. The c...

A welded square plate of 1 m × 1 m is subjected to biaxial stress of magnitude 6.5 MPa and 25 MPa, as shown in the figure below. The ratio of the normal stress acting in the perpen...

Water with a density of 1000 kg/m³ comes out of an industrial condenser through a horizontal pipe of 15 cm radius at the flow rate of 4.5 m³/min. The outlet of the pipe is connecte...

Two rectangular surfaces both having 1 m² area are placed perpendicular to each other with a common edge. One surface is hot, having a temperature of 1000 K and emissivity of 0.4,...

Convective heat transfer coefficients for Fluid 1 and Fluid 2 in a heat exchanger, as shown in the figure below, are 50 W/(m²K) and 80 W/(m²K), respectively. The inner tube is made...

A liquid comes out of the reactor of a chemical plant at 250 °C temperature with a flow rate of 100 LPM. The ambient temperature is 25 °C. Density and specific heat of the liquid r...

A rigid closed vertical cylindrical vessel of 15 cm diameter contains 5 kg water at 80 °C with 10% quality. The water is heated till its temperature reaches 130 °C. Considering onl...

An inward flow reaction turbine, having an outer diameter of 1 m, runs at 600 RPM. The normal component of absolute velocity at the inlet is 10 m/s. If the guide blade angle is 15°...

In a deep drawing operation of a rectangular sheet metal, 30% stretching in length results in 15% reduction in thickness. Assuming volume constancy, the normal anisotropy of the sh...

The actual demand for castings in a factory is 500 units and 635 units for the months of January 2026 and February 2026, respectively. The forecasted demand for January 2026 is 250...

The inventory holding cost of an item is ₹0.50 per unit per month and the ordering cost per order is ₹ 550. A stockist needs to supply 10000 units of the item per year to the custo...

A metal has FCC crystal structure with 2.71 g/cm³ of density and 26.98 g/mol of atomic weight. The Avogadro's number is 6.023 × 10^23. The atomic radius of the metal is ________ nm...

During orthogonal turning by using a single point cutting tool, feed rate is 0.24 mm/rev. The uncut chip thickness is 0.23 mm. The shear angle, tangential force component, and radi...

A drill bit during its lifetime can produce 150 through holes in a plate at a drill-speed of 200 RPM. If the drill-speed increases to 300 RPM, then it can produce 60 through holes...

The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic (t_o), most likely (t_m), and pessimistic (t_p) are given in the table...

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...

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

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...