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GATE 2026 Important Questions in Mechanical Engineering – ME Welcome to EII - Your Gateway to Success!
Gear up for GATE 2026 with confidence through a collection of carefully curated important questions in Mechanical Engineering (ME), designed by the esteemed faculty of Engineers Institute of India (EII). Renowned for its specialized and high-quality coaching, EII is dedicated to empowering Mechanical Engineering aspirants to achieve top results in the upcoming GATE examination.
Q.1 Which word completes the analogy "Fish is to Shoal as Lion is to _______"?
Answer: (A)
Explanation:
Analogies are based on relationships between pairs of words, so we need to determine the specific relationship and apply it consistently.
Step 1: Analyze the Relationship
Step 2: Apply the Relationship to Lion
Q.2 Which sentence is grammatically correct?
Answer: (A)
Explanation:
A - "It is I who am responsible" translates to "I am the one who am responsible," which is grammatically consistent:
Other options fail:
Q.3 Cars P and Q start from point X in Gurugram at 10 AM. Car P heads North at 25 km/h and travels continuously, while Car Q heads East at 30 km/h but stops after 1 hour. If both are equidistant from X at 11:30 AM, how many minutes did Car Q stop for?
Answer: (C)
Explanation:
Step 1: Distance by car P at 11:30 AM
Step 2: Distance by car Q
Step 3: Calculate Q’s travel time
Step 4: Find stoppage time
Q.4 Which statement is NOT true for all real 𝑥 regarding floor and ceiling functions?
Answer: (D)
Explanation:
The ceiling function ⌈x⌉ is the smallest integer ≥ x, and the floor function ⌊x⌋ is the largest integer ≤ x. We need to identify a statement that’s NOT true for all real x.
Common statement to test: ⌊x⌋ + 1 = ⌈x⌉
For x = 2.3:
For x = 2:
The statement ⌊x⌋ + 1 = ⌈x⌉ is NOT correct for all x.
Q.5 P and Q play chess. P wins 80%, draws 15%, and loses 5%. If they play 3 more matches, what is the probability that P wins exactly 2?
Answer: (A)
Explanation:
To find the probability that P wins exactly 2 of 3 chess matches against Q, given P's win rate is 80%, draw rate is 15%, and loss rate is 5%, we use the binomial probability formula. The outcomes are win, draw, or loss, but the question asks for the probability of exactly 2 wins, so we focus on wins versus non-wins.
Q.6 Select the most logical sentence sequence to form a paragraph.
P. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could.
Q. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts and inimical local lords – all of which would reduce their chances of getting gold to almost zero.
R. All of them thought that easily they could lay their hands on gold and become wealthy overnight.
S. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.
Answer: (D)
Explanation:
Step 1: Analyze Sentence Connections
Sequence and Flow
Q.7 If HIDE → 19-23-7-11 and CAGE → 5-2-17-11, what is the code for HIGH?
Answer: (D)
Explanation:
HIDE → 19-23-7-11
CAGE → 5-2-17-11
HIGH ⇒ 19-23-17-19
Q.8 A figure is reflected horizontally and then rotated 90° clockwise. Which is the resulting figure?
Answer: (Depends on actual figures shown)
Explanation:
Anti-clockwise figure
Reflection along horizontal line figure
Q.9 Arrange in increasing order of lines of symmetry: Isosceles triangle, Equilateral triangle, Square, Circle.
Answer: (B)
Explanation:
The Correct Sequence of Objects Based on Increasing Number of Mirror Lines (Lines of Symmetry)
Q.10 A student has 0.8 and 0.6 probability of job offers from Company S and T respectively. What is the probability of getting both?
Answer: (B)
Explanation: P (S) = 0.8 P (T) = 0.6 P (S∩T) = P (S) . P (T) = (0.8) . (0.6) = 0.48
Q.1 A free-body diagram of a block on a frictionless incline shows which forces acting on it?
Answer: A
Explanation: On a frictionless incline, only the weight (acting downward) and the normal force (perpendicular to the incline) act on the block. Friction is absent due to the frictionless surface.
Q.2 What condition must be satisfied for a body to be in static equilibrium?
Answer: C
Explanation: For static equilibrium, both the sum of all forces (ΣF = 0) and the sum of all moments (ΣM = 0) about any point must be zero.
Q.3 The coefficient of static friction between a block and a surface is 0.4. What is the maximum angle of incline before the block starts sliding?
Answer: A
Explanation: The maximum angle θ occurs when tan(θ) = μ_s = 0.4. Thus, θ = tan⁻¹(0.4) ≈ 21.8°.
Q.4 In a belt-pulley system, the tension in the tight side is 800 N, and in the slack side is 200 N. What is the torque transmitted if the pulley radius is 0.2 m?
Answer: A
Explanation: Torque = (T_tight - T_slack) × radius = (800 - 200) × 0.2 = 120 N·m.
Q.5 Which of the following is true for rolling friction?
Answer: C
Explanation: Rolling friction is generally much smaller than sliding friction due to minimal surface deformation compared to sliding.
Q.6 A screw jack has a pitch of 5 mm and a mean radius of 20 mm. What is the mechanical advantage if the coefficient of friction is negligible?
Answer: A
Explanation: Mechanical advantage = 2πr / p = 2π × 20 / 5 ≈ 25.13, assuming frictionless conditions.
Q.7 In a truss, which assumption is made about the joints?
Answer: A
Explanation: Truss joints are modeled as frictionless pins, allowing rotation but transmitting only forces, not moments.
Q.8 The virtual work principle is best applied to:
Answer: B
Explanation: The principle of virtual work is used for systems in static equilibrium, where the virtual work done by all forces is zero.
Q.9 A particle moves in a straight line with constant acceleration. Which quantity is conserved?
Answer: C
Explanation: With constant acceleration, external forces act, so neither linear momentum (ΣF ≠ 0) nor kinetic energy (work done changes KE) is conserved.
Q.10 The impulse-momentum theorem relates:
Answer: B
Explanation: The impulse-momentum theorem states that impulse (∫F dt) equals the change in momentum (mΔv).
Q.11 A rigid body rotates about a fixed axis. What is the relationship between angular and linear velocity?
Answer: B
Explanation: For a point on a rotating rigid body, linear velocity v = ω × r, where ω is angular velocity and r is the radius.
Q.12 In a clutch, the frictional torque depends on:
Answer: B
Explanation: Frictional torque in a clutch is T = μ × N × r, where μ is the coefficient of friction, N is the normal force, and r is the effective radius.
Q.13 Lagrange’s equation is derived from:
Answer: B
Explanation: Lagrange’s equation is derived using the principle of virtual work and D’Alembert’s principle for dynamic systems.
Q.14 A vehicle on a flat road experiences rolling friction. The rolling friction force is proportional to:
Answer: A
Explanation: Rolling friction force is proportional to the normal force and the coefficient of rolling friction, not velocity or wheel radius.
Q.15 A frame differs from a truss because:
Answer: B
Explanation: Frames may have rigid joints, unlike trusses, which assume pin joints, allowing frames to transmit moments.
Q.16 The work-energy principle states that the work done on a rigid body equals:
Answer: B
Explanation: The work-energy principle states that the net work done on a body equals the change in its kinetic energy.
Q.17 A wedge is used to lift a load. The mechanical advantage depends on:
Answer: A
Explanation: The mechanical advantage of a wedge depends on the wedge angle and the coefficient of friction between surfaces.
Q.18 In plane motion, the number of degrees of freedom for a rigid body is:
Answer: B
Explanation: A rigid body in plane motion has 3 degrees of freedom: two translational (x, y) and one rotational (about z-axis).
Q.19 The angular momentum of a rigid body is conserved if:
Answer: B
Explanation: Angular momentum is conserved when no external torques act (Στ = 0), per the angular impulse-momentum theorem.
Q.20 For a brake system, the braking torque is maximum when:
Answer: C
Explanation: Braking torque T = μ × N × r. Maximizing the coefficient of friction (μ) increases the torque for given N and r.
Q.21 Which of the following forces must be included in the free-body diagram of a block sliding down a rough incline?
Answer: A, B, C
Explanation: The free-body diagram includes weight (downward), normal force (perpendicular to incline), and frictional force (opposing motion). An external force is included only if applied.
Q.22 Which of the following are applications of friction in engineering mechanics?
Answer: A, B, C
Explanation: Belt-pulley systems, screw jacks, and vehicle rolling motion rely on friction for operation. Frictionless bearings are designed to minimize friction.
Q.23 Which quantities are conserved in a perfectly elastic collision between two rigid bodies in plane motion?
Answer: A, B, C
Explanation: In a perfectly elastic collision, linear momentum, angular momentum, and kinetic energy are conserved, assuming no external forces or torques. Potential energy is not relevant unless specified.
Q.24 Which of the following statements are true about Lagrange’s equation?
Answer: A, B, D
Explanation: Lagrange’s equation is used for dynamic systems, requires kinetic and potential energy, and can account for non-conservative forces via generalized forces. It is not limited to static systems.
Q.1 The ratio of lateral strain to axial strain in a material under uniaxial loading is known as:
Answer: B
Explanation: Poisson’s ratio is defined as the negative ratio of lateral strain to axial strain under uniaxial loading.
Q.2 Mohr’s circle is used to determine:
Answer: A
Explanation: Mohr’s circle is a graphical method to find principal stresses, maximum shear stress, and stresses on any plane for plane stress or strain conditions.
Q.3 A thin cylindrical pressure vessel with internal pressure p, diameter d, and thickness t has a hoop stress of:
Answer: C
Explanation: Hoop stress in a thin cylinder is given by σ_h = pd / (2t), but for the given options, the closest correct form is pd / t for longitudinal stress in some contexts. Assuming a typo, hoop stress is pd / (2t).
Q.4 The shear force diagram for a simply supported beam with a point load at the center is:
Answer: C
Explanation: For a point load at the center, the shear force diagram consists of two constant values (rectangles) with a step change at the load point.
Q.5 The maximum bending stress in a beam occurs at:
Answer: C
Explanation: Bending stress is maximum at the outermost fiber from the neutral axis, as per σ = My / I.
Q.6 The shear center of a cross-section is the point where:
Answer: B
Explanation: The shear center is the point where a shear force can be applied without causing torsion in the section.
Q.7 The deflection of a simply supported beam with a central point load is maximum at:
Answer: B
Explanation: For a simply supported beam with a central point load, maximum deflection occurs at the midpoint, as per beam deflection formulas.
Q.8 The torque transmitted by a circular shaft is related to the shear stress by:
Answer: A
Explanation: The torsion formula is T = τJ / r, where T is torque, τ is shear stress, J is the polar moment of inertia, and r is the radius.
Q.9 Euler’s critical load for a column with both ends pinned is:
Answer: A
Explanation: For a pinned-pinned column, Euler’s critical load is P_cr = π²EI / L², where E is Young’s modulus, I is the moment of inertia, and L is the length.
Q.10 The strain energy stored in a beam under bending is proportional to:
Answer: A
Explanation: Strain energy in bending is U = ∫ (M² / (2EI)) dx, so it is proportional to M² / EI.
Q.11 Thermal stress in a rod constrained at both ends due to a temperature rise ΔT is:
Answer: A
Explanation: Thermal stress in a fully constrained rod is σ = EαΔT, where E is Young’s modulus and α is the coefficient of thermal expansion.
Q.12 A strain gauge measures:
Answer: B
Explanation: A strain gauge measures strain in the direction of its alignment by detecting changes in electrical resistance.
Q.13 A universal testing machine is primarily used to test:
Answer: B
Explanation: A universal testing machine is used to perform tensile and compressive tests to determine material strength.
Q.14 The Brinell hardness test measures hardness by:
Answer: B
Explanation: The Brinell test uses a spherical indenter to create an indentation, and hardness is calculated based on the indentation size.
Q.15 The impact strength of a material is typically measured using:
Answer: A
Explanation: Charpy and Izod tests measure a material’s impact strength by determining the energy absorbed during fracture.
Q.16 The relationship between Young’s modulus (E), shear modulus (G), and Poisson’s ratio (ν) is:
Answer: A
Explanation: The relationship is E = 2G(1 + ν), derived from elastic constants.
Q.17 The bending moment diagram for a cantilever beam with a uniformly distributed load is:
Answer: B
Explanation: For a uniformly distributed load, the bending moment diagram is a parabola, as M(x) is a quadratic function.
Q.18 The maximum shear stress in a circular shaft under torsion occurs at:
Answer: C
Explanation: Shear stress due to torsion is maximum at the outermost surface, as τ = Tr / J.
Q.19 A strain rosette with three gauges at 0°, 45°, and 90° is used to determine:
Answer: A
Explanation: A strain rosette measures strains in multiple directions to calculate principal strains and their orientations.
Q.20 The deflection of a beam can be calculated using:
Answer: B
Explanation: The double integration method is used to find beam deflection by integrating the bending moment equation twice.
Q.21 Which of the following stresses are present in a thin cylindrical pressure vessel under internal pressure?
Answer: A, B, C
Explanation: A thin cylinder experiences hoop stress, longitudinal stress, and negligible radial stress (approximated as zero in thin-wall theory). Shear stress is absent unless torsion is applied.
Q.22 Which methods can be used to calculate the deflection of a beam?
Answer: A, B, C
Explanation: Beam deflection can be calculated using the double integration method, moment-area method, and energy methods (e.g., Castigliano’s theorem). Mohr’s circle is for stress/strain analysis, not deflection.
Q.23 Which of the following material properties can be determined using a universal testing machine?
Answer: A, B, D
Explanation: A universal testing machine measures tensile strength, compressive strength, and yield strength through stress-strain testing. Hardness is tested using other methods (e.g., Brinell, Rockwell).
Q.24 Which of the following factors influence thermal stresses in a constrained material?
Answer: A, B, C
Explanation: Thermal stress depends on temperature change (ΔT), Young’s modulus (E), and coefficient of thermal expansion (α), as per σ = EαΔT. Poisson’s ratio is not directly involved in thermal stress calculation.
Q.1 The instantaneous center of rotation in a plane mechanism is a point where:
Answer: B
Explanation: The instantaneous center of rotation is the point in a mechanism where the velocity of the body is zero, and all other points rotate about it.
Q.2 In a four-bar linkage, the Grashof condition determines:
Answer: A
Explanation: The Grashof condition determines whether a four-bar linkage can have a crank (shortest link rotates fully) based on the sum of the shortest and longest links compared to the other two.
Q.3 The velocity of a point in a mechanism can be found using:
Answer: B
Explanation: The instantaneous center method is used to find the velocity of points in a plane mechanism by considering rotation about the instantaneous center.
Q.4 A cam with a roller follower has a minimum radius of 20 mm. The follower radius is 5 mm. The minimum base circle radius is:
Answer: B
Explanation: The minimum base circle radius of the cam is the same as the minimum radius of the cam (20 mm), as the roller follower radius does not affect the base circle.
Q.5 In a spur gear, the pitch circle diameter is 100 mm. If the module is 5 mm, the number of teeth is:
Answer: B
Explanation: Number of teeth = Pitch circle diameter / Module = 100 / 5 = 20.
Q.6 The primary function of a flywheel is to:
Answer: B
Explanation: A flywheel stores kinetic energy to smooth out speed fluctuations in engines or machines with cyclic loads.
Q.7 A governor is used to:
Answer: A
Explanation: A governor regulates the speed of an engine by controlling fuel or power input based on load changes.
Q.8 Balancing of reciprocating masses in an engine is achieved by:
Answer: A
Explanation: Counterweights on the crankshaft are used to balance the inertia forces of reciprocating masses in an engine.
Q.9 The gyroscopic effect is significant in:
Answer: B
Explanation: The gyroscopic effect is prominent in rotating systems (e.g., ships, aircraft) where angular momentum causes stabilizing or destabilizing torques.
Q.10 In a single degree of freedom system, the natural frequency depends on:
Answer: A
Explanation: The natural frequency of an SDOF system is ω_n = √(k/m), where k is stiffness and m is mass.
Q.11 The effect of damping in a vibrating system is to:
Answer: B
Explanation: Damping dissipates energy, reducing the amplitude of vibration over time in a system.
Q.12 Vibration isolation is most effective when:
Answer: A
Explanation: Vibration isolation works best when the excitation frequency is much higher than the natural frequency (ω/ω_n > √2), minimizing transmitted vibrations.
Q.13 Resonance in a vibrating system occurs when:
Answer: B
Explanation: Resonance occurs when the excitation frequency matches the natural frequency, leading to large amplitudes.
Q.14 The critical speed of a rotating shaft is related to:
Answer: A
Explanation: The critical speed of a shaft is the rotational speed at which it matches the natural frequency of transverse vibration, causing resonance.
Q.15 In a gear train, the speed ratio is determined by:
Answer: A
Explanation: The speed ratio in a gear train is the ratio of the number of teeth on the driven gear to the driver gear.
Q.16 The acceleration analysis of a mechanism is used to find:
Answer: B
Explanation: Acceleration analysis determines the linear and angular accelerations of links in a mechanism, often using vector methods.
Q.17 A Scotch-Yoke mechanism converts:
Answer: A
Explanation: The Scotch-Yoke mechanism converts rotary motion (of a crank) into linear motion (of a slider).
Q.18 The logarithmic decrement is used to determine:
Answer: B
Explanation: Logarithmic decrement measures the rate of amplitude decay in free vibration, used to calculate the damping ratio.
Q.19 In a cam-follower system, the pressure angle is the angle between:
Answer: B
Explanation: The pressure angle is the angle between the direction of follower motion and the normal to the cam surface at the contact point.
Q.20 The dynamic analysis of a linkage involves:
Answer: B
Explanation: Dynamic analysis considers the forces, torques, and accelerations in a linkage under motion, using Newton’s laws or energy methods.
Q.21 Which of the following methods can be used for velocity analysis of a plane mechanism?
Answer: A, B, D
Explanation: Velocity analysis can be performed using the instantaneous center method, relative velocity method, and vector loop method. Mohr’s circle is used for stress analysis, not velocity.
Q.22 Which components in a machine are used to control or reduce vibrations?
Answer: B, C
Explanation: Vibration isolators and dampers are used to reduce or control vibrations. Flywheels reduce speed fluctuations, and governors control speed, not vibrations.
Q.23 Which of the following are affected by the balancing of rotating masses?
Answer: A, B
Explanation: Balancing rotating masses reduces bearing loads and vibration levels. Gear train efficiency and natural frequency are not directly affected by mass balancing.
Q.24 Which of the following are true for forced vibration in a single degree of freedom system?
Answer: A, B, D
Explanation: In forced vibration, amplitude depends on the frequency ratio (ω/ω_n), damping reduces amplitude at resonance, and an external force drives the system. Resonance occurs when ω = ω_n, not necessarily at critical speed.
Q.1 The factor of safety in machine design accounts for:
Answer: B
Explanation: The factor of safety is applied to account for uncertainties in loading, material properties, manufacturing tolerances, and other variables to ensure safe design.
Q.2 Which failure theory is most suitable for ductile materials under static loading?
Answer: A
Explanation: The maximum shear stress theory (Tresca) is commonly used for ductile materials under static loading, as it predicts yielding based on shear stress.
Q.3 The S-N diagram is used to represent:
Answer: B
Explanation: The S-N diagram (stress vs. number of cycles) shows the fatigue strength of a material as a function of the number of load cycles it can withstand.
Q.4 In a bolted joint, the primary load-carrying component under tensile loading is:
Answer: A
Explanation: The bolt shank carries the tensile load in a bolted joint, while the nut and washer distribute forces and prevent loosening.
Q.5 A riveted joint is preferred over a bolted joint for:
Answer: B
Explanation: Riveted joints are used for permanent connections in heavy structures (e.g., bridges, ships) due to their reliability and resistance to loosening.
Q.6 The design of a welded joint primarily depends on:
Answer: A
Explanation: The strength of a welded joint depends on the weld length and throat thickness, which determine the load-carrying capacity.
Q.7 The power transmitted by a shaft depends on:
Answer: A
Explanation: Power transmitted by a shaft is P = Tω, where torque T depends on the shaft diameter, and ω is the rotational speed.
Q.8 The module of a gear is defined as:
Answer: B
Explanation: Module (m) = Pitch circle diameter (D) / Number of teeth (N), a key parameter in gear design.
Q.9 Rolling contact bearings are preferred over sliding contact bearings for:
Answer: B
Explanation: Rolling contact bearings (e.g., ball or roller bearings) are used for high-speed and low-friction applications due to their reduced frictional losses.
Q.10 The primary function of a clutch is to:
Answer: A
Explanation: A clutch transmits power between two shafts, allowing engagement or disengagement of power transmission.
Q.11 The fatigue strength of a component can be improved by:
Answer: B
Explanation: Shot peening introduces compressive residual stresses on the surface, improving fatigue strength by reducing crack initiation.
Q.12 The design of a helical spring is primarily based on:
Answer: A
Explanation: Helical spring design considers shear stress (due to torsion) and deflection (based on spring stiffness) to ensure proper function.
Q.13 The endurance limit of a material is:
Answer: B
Explanation: The endurance limit is the stress level below which a material can withstand an infinite number of fatigue cycles without failure.
Q.14 A brake’s effectiveness depends on:
Answer: A
Explanation: Brake effectiveness is determined by the friction coefficient and the normal force, as per the frictional torque formula T = μFNr.
Q.15 The von Mises stress is used in:
Answer: B
Explanation: Von Mises stress is a criterion used to predict yielding in ductile materials under complex loading conditions.
Q.16 The dynamic load capacity of a bearing is:
Answer: B
Explanation: Dynamic load capacity is the load a bearing can sustain for a specified life (e.g., 1 million revolutions) at a given speed.
Q.17 The design of a shaft under combined loading considers:
Answer: B
Explanation: Shaft design accounts for combined bending and torsion, as these produce principal stresses that determine failure.
Q.18 The Lewis equation is used in the design of:
Answer: A
Explanation: The Lewis equation is used to calculate the bending stress in gear teeth, a critical factor in gear design.
Q.19 A keyway in a shaft reduces its strength due to:
Answer: A
Explanation: A keyway creates a stress concentration, reducing the shaft’s strength under cyclic loading.
Q.20 The primary purpose of a spring in a clutch is to:
Answer: B
Explanation: Springs in a clutch provide the necessary force to engage the friction surfaces, ensuring power transmission.
Q.21 Which of the following failure theories are commonly used for ductile materials?
Answer: A, C
Explanation: The maximum shear stress theory and von Mises yield criterion are widely used for ductile materials to predict yielding under complex loading.
Q.22 Which factors are considered in the design of a bolted joint?
Answer: A, B, D
Explanation: Bolt preload, thread friction, and joint stiffness are critical in bolted joint design to ensure proper clamping and prevent loosening. Material hardness is less directly relevant.
Q.23 Which of the following improve the fatigue life of a component?
Answer: A, B, C
Explanation: Shot peening, surface polishing, and case hardening improve fatigue life by reducing crack initiation and increasing surface strength. Increasing stress concentration worsens fatigue life.
Q.24 Which components are designed for dynamic loading in machine design?
Answer: A, B, C
Explanation: Shafts, gears, and springs are designed for dynamic loading due to cyclic stresses. Riveted joints are typically designed for static or quasi-static loads.
Q.1 Which of the following is the definition of fluid density?
Answer: A
Explanation: Density is defined as the mass per unit volume of a fluid, a fundamental property in fluid mechanics (Fluid Properties).
Q.2 The SI unit of dynamic viscosity is:
Answer: C
Explanation: Dynamic viscosity, which measures a fluid’s resistance to flow, is expressed in Pascal-seconds (Pa·s) in the SI system (Fluid Properties).
Q.3 Surface tension in fluids is caused by:
Answer: A
Explanation: Surface tension results from cohesive forces between fluid molecules, causing the surface to act like a stretched membrane (Fluid Properties).
Q.4 According to Pascal’s law, in a confined fluid, pressure applied to a fluid is:
Answer: A
Explanation: Pascal’s law states that pressure applied to a confined fluid is transmitted equally in all directions, a key principle in fluid statics (Fluid Statics).
Q.5 The buoyant force on a submerged object is equal to:
Answer: C
Explanation: Archimedes’ principle states that the buoyant force on a submerged object equals the weight of the fluid displaced, explaining why objects float or sink (Fluid Statics).
Q.6 For a floating body to be in stable equilibrium, the metacenter must be:
Answer: B
Explanation: A floating body is stable if the metacenter (M) is above the center of gravity (G), creating a restoring moment when tilted (Stability of Floating Bodies).
Q.7 The center of buoyancy of a floating body is:
Answer: D
Explanation: The center of buoyancy is the centroid of the displaced fluid volume, where the buoyant force acts (Stability of Floating Bodies).
Q.8 The continuity equation for a control volume states that:
Answer: A
Explanation: The continuity equation ensures mass conservation, stating that the mass flow rate entering a control volume equals the mass flow rate exiting (Control Volume Analysis).
Q.9 Bernoulli’s equation is derived from the conservation of:
Answer: C
Explanation: Bernoulli’s equation is a form of energy conservation for steady, incompressible, inviscid flow along a streamline (Control Volume Analysis).
Q.10 The continuity equation in differential form for an incompressible fluid is:
Answer: B
Explanation: For incompressible fluids, density is constant, simplifying the continuity equation to ∇·V = 0, indicating divergence-free flow (Navier-Stokes Equations).
Q.11 The Navier-Stokes equations describe the conservation of:
Answer: B
Explanation: The Navier-Stokes equations govern momentum conservation in fluid flow, accounting for viscous effects (Navier-Stokes Equations).
Q.12 The Reynolds number is the ratio of:
Answer: A
Explanation: Reynolds number (Re) = ρVD / μ compares inertial forces (ρVD²) to viscous forces (μVD/L), determining flow regime (Dimensional Analysis).
Q.13 In fluid mechanics, the Froude number is important for:
Answer: B
Explanation: Froude number (Fr) = V / √(gL) is significant in flows with free surfaces, like open channels or ship hydrodynamics, where gravity matters (Dimensional Analysis).
Q.14 The boundary layer thickness:
Answer: A
Explanation: The boundary layer grows thicker downstream due to cumulative viscous effects (Boundary Layer).
Q.15 Transition from laminar to turbulent flow in a boundary layer is influenced by:
Answer: C
Explanation: Transition to turbulence depends on Reynolds number and surface roughness, which can trigger instabilities (Boundary Layer).
Q.16 Flow is typically considered compressible when the Mach number is:
Answer: B
Explanation: Compressibility effects are significant when the Mach number exceeds 0.3, requiring compressible flow analysis (Compressible Flow).
Q.17 The Mach number is defined as:
Answer: B
Explanation: Mach number (Ma) = V / c, where V is the flow velocity and c is the speed of sound (Compressible Flow).
Q.18 The Darcy-Weisbach equation for head loss in pipe flow is:
Answer: A
Explanation: The Darcy-Weisbach equation, h_f = f (L/D) (V² / 2g), calculates frictional head loss in pipes (Pipe Flow).
Q.19 Minor losses in pipe flow are typically due to:
Answer: B
Explanation: Minor losses arise from flow disturbances caused by fittings, valves, and bends, expressed as K (V² / 2g) (Pipe Flow).
Q.20 In turbulent flow, the velocity profile in a pipe is:
Answer: C
Explanation: Turbulent flow in pipes has a logarithmic velocity profile near the wall, flatter in the center, unlike laminar flow’s parabolic profile (Pipe Flow).
Q.21 Which of the following are properties of fluids?
Answer: A, B, C
Explanation: Density, viscosity, and surface tension are key fluid properties, influencing flow behavior. Elasticity is primarily a solid property (Fluid Properties).
Q.22 In control volume analysis, which conservation laws are typically applied?
Answer: A, B, C
Explanation: Control volume analysis uses conservation of mass, momentum, and energy to analyze fluid systems. Charge conservation applies to electromagnetism (Control Volume Analysis).
Q.23 Which of the following are true for boundary layers?
Answer: A, B, C
Explanation: Boundary layers have zero velocity at the wall (no-slip condition), increase to free stream velocity, and grow thicker downstream. They can be laminar or turbulent (Boundary Layer).
Q.24 Compressibility effects become significant when:
Answer: A, B, D
Explanation: 
Q.1 How many distinct modes of heat transfer are generally recognized?
Answer: C
Explanation: The three modes of heat transfer are conduction (through solids), convection (via fluid motion), and radiation (via electromagnetic waves), as recognized in thermal engineering (Modes of Heat Transfer).
Q.2 What causes energy to flow from system A at temperature t to system B at temperature T (t > T) when they are in contact?
Answer: A
Explanation: Heat transfer occurs due to a temperature difference, driving energy from the hotter system A to the cooler system B (Modes of Heat Transfer).
Q.3 Which is an example of forced convection?
Answer: B
Explanation: Forced convection involves fluid motion driven by external means, such as pumps moving water through condenser tubes (Modes of Heat Transfer).
Q.4 In one-dimensional steady-state heat conduction through a plane wall, the temperature distribution is:
Answer: Yaml
Explanation: For steady-state conduction with constant thermal conductivity, the temperature varies linearly across the wall, per Fourier’s law (Conduction Basics).
Q.5 For two walls with thermal conductivity ratio 1/2, same thickness, area, and temperature difference, the heat flow ratio is:
Answer: B
Explanation: Heat flow Q = kA(ΔT)/L; with k1/k2 = 1/2, Q1/Q2 = k1/k2 = 1/2 (Conduction Basics).
Q.6 The thermal resistance of an oven wall (thickness 500 mm, k = 0.3 W/m·K) is:
Answer: B
Explanation: Thermal resistance R = L/(kA) = 0.5/(0.3·A) = 1.667/A K/W; assuming unit area, R = 1.667 K/W (Conduction Basics).
Q.7 The primary purpose of fins in heat transfer is to:
Answer: D
Explanation: Fins extend the surface area, enhancing convective heat transfer (Fins).
Q.8 For a steel fin (k = 30 W/m·K, diameter 1 cm, length 5 cm, wall at 10°C, air at 30°C, h = 50 W/m²·K, tip insulated), the fin efficiency is:
Answer: B
Explanation: Efficiency η = tanh(mL)/(mL), where m = √(hP/kA) ≈ 25.82 m⁻¹, mL ≈ 1.291, η ≈ 0.6657 or 66.57% (Fins).
Q.9 Heat flow in thin fins is primarily:
Answer: A
Explanation: Thin fins have negligible thickness, making heat flow one-dimensional along their length (Fins).
Q.10 The lumped capacitance method is valid when:
Answer: C
Explanation: Lumped capacitance assumes uniform temperature, valid when Bi = hL/k < 0.1 (Unsteady Conduction).
Q.11 The time constant of a thermocouple is the time to reach:
Answer: B
Explanation: Time constant τ = ρVc/hA is when the temperature difference reduces to 1/e ≈ 36.8% of initial, or reaches 63.2% (Unsteady Conduction).
Q.12 Heisler’s charts are used for:
Answer: B
Explanation: Heisler’s charts provide graphical solutions for transient temperature distributions in finite bodies (Unsteady Conduction).
Q.13 The thermal boundary layer represents the region where:
Answer: C
Explanation: Thermal boundary layer thickness is where the temperature difference ratio is 0.99 (Boundary Layer).
Q.14 The Prandtl number relates:
Answer: A
Explanation: Pr = ν/α compares momentum and thermal diffusivities, affecting boundary layer thickness (Boundary Layer).
Q.15 In laminar flow over a flat plate, the heat transfer coefficient varies with distance x as:
Answer: A
Explanation: For laminar flow, Nu ∝ Re^(1/2), so h = Nu·k/x ∝ x^(-1/2) (Convection Correlations).
Q.16 For turbulent flow in a pipe, the heat transfer coefficient is higher due to:
Answer: B
Explanation: Turbulence increases mixing, boosting the convective heat transfer coefficient (Convection Correlations).
Q.17 In a counter-flow heat exchanger with equal heat capacities and NTU = 0.5, the effectiveness is:
Answer: B
Explanation: For C_r = 1, ε = NTU/(1 + NTU) = 0.5/(1 + 0.5) ≈ 0.333 (Heat Exchangers).
Q.18 The Stefan-Boltzmann law states that a black body’s emissive power is proportional to:
Answer: D
Explanation: E = σT^4, where σ is the Stefan-Boltzmann constant (Radiation).
Q.19 Wien’s displacement law relates a black body’s temperature to:
Answer: B
Explanation: λ_max · T = constant, indicating the peak emission wavelength (Radiation).
Q.20 The view factor F_12 in radiative heat transfer is:
Answer: B
Explanation: F_12 is the fraction of radiation from surface 1 reaching surface 2, always ≤ 1 (Radiation).
Q.21 Which are dimensionless parameters in convective heat transfer?
Answer: A, B, C
Explanation: Re, Pr, and Nu are used in convection; Bi is for unsetady conduction (Convection).
Q.22 Which laws are relevant to radiative heat transfer?
Answer: A, B, D
Explanation: Stefan-Boltzmann, Wien’s, and Kirchhoff’s laws govern radiation; Fourier’s is for conduction (Radiation).
Q.23 Which factors affect fin efficiency?
Answer: A, B, C, D
Explanation: Efficiency depends on geometry, material, and convection conditions (Fins).
Q.24 Which statements are true for the lumped capacitance method?
Answer: A, B, C
Explanation: 
Q.1 A thermodynamic system is defined as:
Answer: A
Explanation: A thermodynamic system is the specific portion of matter or space selected for study, while everything outside is the surroundings (Thermodynamics Basics).
Q.2 Which of the following is an example of an open system?
Answer: B
Explanation: An open system allows mass and energy transfer. A pressure cooker with a safety valve permits steam escape, making it open (Thermodynamics Basics).
Q.3 The specific volume of a pure substance is:
Answer: A
Explanation: Specific volume is the volume per unit mass, typically in m³/kg, used in property tables (Gas Laws).
Q.4 For an ideal gas, the relationship between pressure, volume, and temperature is given by:
Answer: D
Explanation: The ideal gas law, PV = nRT, relates pressure, volume, temperature, and moles, encompassing other gas laws (Gas Laws).
Q.5 The zeroth law of thermodynamics states that:
Answer: C
Explanation: The zeroth law defines temperature through thermal equilibrium (Thermodynamics Laws).
Q.6 The first law of thermodynamics is a statement of:
Answer: B
Explanation: The first law states energy cannot be created or destroyed, only transferred (Thermodynamics Laws).
Q.7 In a constant volume process, the work done by the system is:
Answer: C
Explanation: Work is ∫PdV; with constant volume, dV = 0, so work is zero (Thermodynamics Laws).
Q.8 For an isentropic process, which is true?
Answer: B
Explanation: An isentropic process is adiabatic and reversible, with ΔS = 0 (Thermodynamics Laws).
Q.9 The second law of thermodynamics states that:
Answer: B
Explanation: The second law limits heat-to-work conversion due to entropy (Thermodynamics Laws).
Q.10 A heat engine operates between reservoirs at T_H and T_C. Maximum efficiency is:
Answer: A
Explanation: Carnot efficiency is η = (T_H - T_C)/T_H (Thermodynamics Laws).
Q.11 In a Mollier chart, coordinates typically used are:
Answer: C
Explanation: Mollier charts plot enthalpy vs. entropy for process analysis (Property Charts).
Q.12 The critical point on a phase diagram represents:
Answer: B
Explanation: At the critical point, liquid and vapor phases merge (Property Charts).
Q.13 Availability, or exergy, is defined as:
Answer: A
Explanation: Availability is the maximum work extractable as a system reaches equilibrium (Property Charts).
Q.14 Irreversibility in a process is due to:
Answer: C
Explanation: Irreversibility results from entropy generation, reducing available work (Property Charts).
Q.15 Maxwell relations are derived from:
Answer: B
Explanation: Maxwell relations come from thermodynamic potentials, linked to the second law (Thermodynamic Relations).
Q.16 The Clapeyron equation relates:
Answer: C
Explanation: Clapeyron equation describes phase boundary slopes (Thermodynamic Relations).
Q.17 Specific heat at constant volume (c_v) for an ideal gas is:
Answer: A
Explanation: c_v = (∂u/∂T)_v, where u is internal energy (Thermodynamic Relations).
Q.18 In a polytropic process, pV^n = constant. For isentropic, n is:
Answer: C
Explanation: Isentropic processes have n = γ = c_p/c_v (Thermodynamic Relations).
Q.19 The Joule-Thomson coefficient (μ) is defined as:
Answer: A
Explanation: μ measures temperature change with pressure at constant enthalpy (Thermodynamic Relations).
Q.20 The coefficient of performance (COP) of a Carnot refrigerator is:
Answer: B
Explanation: Carnot refrigerator COP = T_C / (T_H - T_C) (Thermodynamics Laws).
Q.21 Which are intensive properties?
Explanation: Intensive properties (pressure, temperature) are size-independent; volume and mass are extensive (Thermodynamics Basics).
Q.22 The first law of thermodynamics can be expressed as:
Answer: A, C, D
Explanation: The first law, ΔU = Q - W, can be rearranged as Q = ΔU + W or W = Q - ΔU (Thermodynamics Laws).
Q.23 Which processes are irreversible?
Answer: A, C, D
Explanation: Free expansion, adiabatic free expansion, and heat transfer with temperature differences generate entropy, making them irreversible (Property Charts).
Q.24 Thermodynamic equilibrium requires:
Answer: A, B, C, D
Explanation: Equilibrium involves mechanical, thermal, chemical, and phase balance (Thermodynamics Basics).
The questions comprehensively cover the thermodynamics syllabus, testing fundamental concepts and their applications in mechanical engineering. They are designed to be clear for students preparing for upcoming GATE, PSUs, State jobs or interviews, with explanations grounded in standard principles.
Q.1 What is the primary function of an air compressor?
Answer: B
Explanation: An air compressor increases air pressure by reducing its volume, essential for applications like pneumatic tools and refrigeration (Air Compressor).
Q.2 Which of the following is a positive displacement compressor?
Answer: C
Explanation: Reciprocating compressors use pistons to compress air, a hallmark of positive displacement compressors (Compressor).
Q.3 What is the purpose of intercooling in multi-stage compression?
Answer: B
Explanation: Intercooling cools air between compression stages, reducing the work required by lowering the temperature and volume (Air Compressor).
Q.4 In a vapour power cycle, regeneration aims to:
Answer: C
Explanation: Regeneration preheats the working fluid using turbine exhaust heat, improving efficiency (Vapour Power Cycles).
Q.5 Reheat in a Rankine cycle primarily:
Answer: A
Explanation: Reheat raises steam temperature after partial expansion, increasing turbine work and efficiency (Vapour Power Cycles).
Q.6 Which cycle is used in spark-ignition engines?
Answer: B
Explanation: The Otto cycle models spark-ignition engines, with constant-volume heat addition (Otto Cycle).
Q.7 In a Diesel cycle, heat addition occurs at:
Answer: B
Explanation: Fuel injection in a Diesel cycle causes heat addition at constant pressure (Diesel Cycle).
Q.8 The coefficient of performance (COP) of a refrigeration system is:
Answer: C
Explanation: COP measures efficiency as the ratio of heat absorbed from the cold space to work input (Refrigeration).
Q.9 On a psychrometric chart, dehumidification is shown as:
Answer: D
Explanation: Dehumidification reduces moisture content at constant dry bulb temperature, moving left on the chart (Refrigeration).
Q.10 The main difference between impulse and reaction turbines is:
Answer: B
Explanation: Impulse turbines (e.g., Pelton) use kinetic energy; reaction turbines (e.g., Francis) use both kinetic and pressure energy (Turbomachinery).
Q.11 Which turbine is best for high-head, low-flow applications?
Answer: C
Explanation: Pelton wheels are impulse turbines ideal for high-head, low-flow conditions (Turbomachinery).
Q.12 In a steam turbine, the governor’s role is to:
Answer: D
Explanation: The governor adjusts steam flow to control speed and prevent overload (Turbomachinery).
Q.13 The compression ratio in an Otto cycle is:
Answer: B
Explanation: Compression ratio is the ratio of initial to final volume (Otto Cycle).
Q.14 In a Brayton cycle, increasing the pressure ratio:
Answer: B
Explanation: Higher pressure ratios improve Brayton cycle efficiency (Gas Power Cycle).
Q.15 In a vapour compression refrigeration system, the expansion valve:
Answer: C
Explanation: The expansion valve regulates refrigerant flow and reduces pressure (Refrigeration).
Q.16 The dual cycle involves heat addition:
Answer: C
Explanation: The dual cycle combines Otto and Diesel cycles’ heat addition processes (Dual Cycle).
Q.17 A psychrometric chart is used to:
Answer: D
Explanation: The chart displays moist air properties and aids in system design and process analysis (Refrigeration).
Q.18 In a gas turbine, the compressor’s role is to:
Answer: B
Explanation: The compressor raises air pressure before combustion (Gas Turbine).
Q.19 Velocity diagrams in turbomachinery are used to:
Answer: D
Explanation: Velocity diagrams help analyze flow, calculate work, and assess efficiency (Turbomachinery).
Q.20 A heat pump’s primary function is to:
Answer: C
Explanation: Heat pumps transfer heat for both heating and cooling (Refrigeration).
Q.21 Which are types of air compressors?
Answer: A, B, C, D
Explanation: These are all compressor types, with reciprocating and screw being positive displacement, and centrifugal and axial being dynamic (Air Compressor).
Q.22 Which processes occur in a vapour compression refrigeration cycle?
Answer: A, C
Explanation: The cycle includes isentropic compression and isenthalpic expansion; heat transfer occurs in the condenser and evaporator (Refrigeration).
Q.23 Which properties are shown on a psychrometric chart?
Answer: A, B, C, D
Explanation: The chart displays these moist air properties for air-conditioning analysis (Refrigeration).
Q.24 Which are reaction turbines?
Answer: B, C
Explanation: Francis and Kaplan turbines are reaction turbines; Pelton and Turgo are impulse turbines (Turbomachinery).
Q.1 Which property measures a material's ability to resist deformation under load?
Answer: C
Explanation: Strength is the ability of a material to resist deformation under load without breaking, critical for structural applications.
Q.2 In a stress-strain diagram, what does the yield point indicate?
Answer: B
Explanation: The yield point marks the onset of plastic deformation, where the material no longer returns to its original shape.
Q.3 What does the area under the stress-strain curve represent?
Answer: B
Explanation: Toughness is the energy absorbed before fracture, represented by the area under the stress-strain curve.
Q.4 Which material type is known for high strength and ductility?
Answer: B
Explanation: Ductile materials, like many metals, can deform significantly before breaking, combining strength and ductility.
Q.5 In a phase diagram, what does the eutectic point represent?
Answer: B
Explanation: The eutectic point is where three phases (two solids and one liquid) are in equilibrium, as seen in alloy systems.
Q.6 What is the primary purpose of annealing in heat treatment?
Answer: C
Explanation: Annealing relieves internal stresses and enhances ductility by heating and slow cooling, improving workability.
Q.7 Which heat treatment process uses rapid cooling to increase hardness?
Answer: C
Explanation: Quenching rapidly cools the material, often in water or oil, to increase hardness by forming martensite.
Q.8 In the iron-carbon phase diagram, what is the carbon content at the eutectoid point?
Answer: A
Explanation: The eutectoid point occurs at 0.8% carbon, where austenite transforms into pearlite.
Q.9 Which is not a common crystal structure in metals?
Answer: D
Explanation: RCP is not a standard crystal structure; it describes amorphous solids, not crystalline metals.
Q.10 What is the process of adding elements to a metal to enhance its properties called?
Answer: A
Explanation: Alloying adds elements to improve properties like strength or corrosion resistance, as in stainless steel.
Q.11 Which property is measured by the Rockwell test?
Answer: B
Explanation: The Rockwell test measures hardness by indenting the material with a diamond or steel ball.
Q.12 What type of bonding is predominant in metals?
Answer: C
Explanation: Metallic bonding, with delocalized electrons, gives metals their conductivity and ductility.
Q.13 The ability to be drawn into wires is called:
Answer: B
Explanation: Ductility allows materials to be drawn into wires, while malleability allows shaping into sheets.
Q.14 Which material is classified as a ceramic?
Answer: C
Explanation: Glass is a ceramic, characterized by its inorganic, non-metallic composition and brittleness.
Q.15 Polymers are typically characterized by:
Answer: C
Explanation: Polymers have low density, making them lightweight compared to metals and ceramics.
Q.16 Hardening steel by heating and rapid cooling is called:
Answer: C
Explanation: Quenching rapidly cools steel to form a hard microstructure, often martensite.
Q.17 In a phase diagram, a single-phase region is:
Answer: B
Explanation: A single-phase region contains only one phase, such as a solid solution.
Q.18 The modulus of elasticity is also known as:
Answer: C
Explanation: Young's modulus measures stiffness, the ratio of stress to strain in the elastic region.
Q.19 Which heat treatment increases toughness after quenching?
Answer: B
Explanation: Tempering reduces brittleness and increases toughness in quenched steel.
Q.20 The ability to return to original shape after deformation is:
Answer: B
Explanation: Elasticity allows a material to recover its shape after elastic deformation.
Q.21 Which are typical properties of metals?
Answer: A, B, C
Explanation: Metals are conductive and ductile, allowing deformation without breaking. Brittleness is typical of ceramics.
Q.22 Which heat treatment processes involve heating and cooling?
Answer: A, B, C
Explanation: Annealing, quenching, and tempering involve heating and cooling to alter properties, unlike cold working.
Q.23 Which are types of phase diagrams?
Answer: A, B, C, D
Explanation: Phase diagrams include binary (two components), ternary (three), unary (one), and quaternary (four) types.
Q.24 Which materials are used for high-temperature applications?
Answer: A, C
Explanation: Ceramics and refractory metals withstand high temperatures due to high melting points, unlike most polymers.
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