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Question 1Engineering

In engineering economics, the annual worth of a single present sum P spread uniformly over n years at interest rate i is given by which factor?

  1. P multiplied by (A/G, i, n)
  2. P multiplied by (F/A, i, n)
  3. P multiplied by (A/P, i, n) Correct answer.
  4. P multiplied by (P/F, i, n)

Explanation

The capital recovery factor (A/P, i, n) converts a present amount into an equivalent uniform annual series. It equals i(1+i)^n divided by ((1+i)^n minus 1), and multiplying P by it yields the annual worth.

Question 2Engineering

A simply supported beam of span L carries a central point load W. The maximum bending moment is:

  1. WL/4 at the supports
  2. WL/2 at midspan
  3. WL/8 at midspan
  4. WL/4 at midspan Correct answer.

Explanation

For a central point load on a simply supported beam, each reaction equals W/2, so the moment at midspan is (W/2)(L/2) = WL/4. The bending moment diagram is triangular, peaking at midspan.

Question 3Engineering

Which dimensionless number governs whether flow in a pipe is laminar or turbulent?

  1. Weber number
  2. Reynolds number Correct answer.
  3. Mach number
  4. Froude number

Explanation

The Reynolds number, Re = ρVD/μ, compares inertial to viscous forces and determines the flow regime; pipe flow is generally laminar below about Re = 2000 and turbulent above about 4000.

Question 4Engineering

In a first-order homogeneous chemical reaction A → products in a batch reactor, the time required for 50% conversion is:

  1. proportional to the square root of the initial concentration
  2. directly proportional to the initial concentration
  3. independent of the initial concentration Correct answer.
  4. inversely proportional to the square of the initial concentration

Explanation

For first-order kinetics, the integrated rate law gives t = (1/k) ln(C0/C). At 50% conversion this becomes t = ln2/k, which contains no concentration term, so the half-life is constant.

Question 5Engineering

Which of the following is the fundamental SI unit of thermodynamic temperature?

  1. Degree Celsius
  2. Rankine
  3. Kelvin Correct answer.
  4. Degree Fahrenheit

Explanation

The kelvin is the SI base unit of thermodynamic temperature, defined by fixing the Boltzmann constant. Celsius and Fahrenheit are derived or non-SI scales, and Rankine belongs to the imperial system.

Question 6Engineering

In surveying, the process of measuring horizontal angles by turning the theodolite from a reference direction to a target is called:

  1. Leveling
  2. Ranging
  3. Angulation Correct answer.
  4. Traversing

Explanation

Angulation refers to measuring horizontal and vertical angles with a theodolite to fix directions between points. It is distinct from linear measurement and from leveling, which determines elevation differences.

Question 7Engineering

Which of the following is a principal advantage of prestressed concrete over ordinary reinforced concrete?

  1. It removes the requirement for concrete curing
  2. It eliminates the need for any steel reinforcement
  3. It permits longer spans by controlling tensile stresses and cracking Correct answer.
  4. It makes the member lighter for the same span

Explanation

Prestressing places the concrete in compression before service loads, so tensile stresses under load are reduced or eliminated and cracking is controlled. This allows thinner sections and longer spans than ordinary reinforced concrete.

Question 8Engineering

The standard penetration test (SPT) in geotechnical investigation records which quantity?

  1. The time to drill a borehole to a given depth
  2. The unconfined compressive strength of a core sample
  3. The number of blows to drive a split spoon 300 mm Correct answer.
  4. The pressure needed to force a cone penetrometer 100 mm

Explanation

The SPT counts the blows of a 63.5 kg hammer falling 760 mm to drive a standard split spoon sampler 300 mm. The resulting N-value is an empirical index of soil density and consistency.

Question 9Engineering

A 2 kg mass moving at 3 m/s collides head-on and sticks to a 4 kg mass initially at rest. What is the common velocity after impact?

  1. 1.5 m/s
  2. 2.0 m/s
  3. 1.0 m/s Correct answer.
  4. 3.0 m/s

Explanation

Momentum is conserved in a perfectly inelastic collision: m1v1 = (m1+m2)v. Substituting gives 2×3 = 6 = 6v, so v = 1.0 m/s. Kinetic energy is not conserved here.

Question 10Engineering

A Carnot engine operates between 600 K and 300 K. What is its thermal efficiency?

  1. 75%
  2. 25%
  3. 33%
  4. 50% Correct answer.

Explanation

Carnot efficiency is 1 minus Tc/Th, where temperatures are absolute. Here 1 minus 300/600 = 0.5, so the efficiency is 50%.

Question 11Engineering

Water flows through a pipe of diameter 0.1 m at a mean velocity of 2 m/s. What is the volumetric flow rate?

  1. 0.0157 m³/s Correct answer.
  2. 0.157 m³/s
  3. 0.0628 m³/s
  4. 0.0314 m³/s

Explanation

Flow rate is Q = A×V, and A = πd²/4 = π(0.1)²/4 = 0.00785 m². Multiplying by 2 m/s gives Q ≈ 0.0157 m³/s.

Question 12Engineering

The composition of a gas mixture by volume is 40% nitrogen, 30% oxygen, and 30% carbon dioxide. What is the mole fraction of oxygen?

  1. 0.70
  2. 0.40
  3. 0.30 Correct answer.
  4. 0.60

Explanation

For ideal gases, volume fraction equals mole fraction. The stated oxygen volume fraction is 30%, so the mole fraction is 0.30.

Question 13Engineering

A 10 m long steel bar is heated uniformly by 50 °C. If the coefficient of linear expansion is 12 × 10⁻⁶ per °C, the increase in length is:

  1. 6 mm Correct answer.
  2. 0.6 mm
  3. 0.06 mm
  4. 60 mm

Explanation

Thermal expansion is ΔL = L·α·ΔT = 10 m × 12×10⁻⁶ × 50 = 6×10⁻³ m, which is 6 mm.

Question 14Engineering

A soil sample has a void ratio of 0.6 and a specific gravity of solids of 2.7. What is its dry unit weight (nearest kN/m³), taking γw = 9.81 kN/m³?

  1. 18.0 kN/m³
  2. 20.4 kN/m³
  3. 14.2 kN/m³
  4. 16.6 kN/m³ Correct answer.

Explanation

Dry unit weight is γd = Gs·γw/(1+e) = 2.7×9.81/1.6 ≈ 16.6 kN/m³. The void ratio in the denominator accounts for the volume of voids.

Question 15Engineering

In a rapid sand filter used in water treatment, the primary purpose of backwashing is to:

  1. disinfect the filter media
  2. add coagulant to the water
  3. increase the filtration rate
  4. remove accumulated solids from the filter bed Correct answer.

Explanation

Backwashing reverses the flow to expand the bed and flush out trapped particles, restoring the head loss and filtration capacity. It is a physical cleaning step, not a disinfection or dosing step.

Question 16Engineering

A project has an initial cost of ₹1,00,000 and returns ₹30,000 per year for five years. At a discount rate of 8%, the net present value is closest to:

  1. ₹19,780 Correct answer.
  2. ₹1,50,000
  3. ₹1,19,780
  4. ₹50,000

Explanation

The present worth of the annuity is 30,000×(P/A,8%,5) = 30,000×3.9927 ≈ 1,19,780. Subtracting the initial cost of 1,00,000 gives an NPV of about ₹19,780, so the project is acceptable.

Question 17Engineering

In a turning operation on a lathe, the cutting speed is 120 m/min and the workpiece diameter is 50 mm. The spindle speed is closest to:

  1. 382 rpm
  2. 1528 rpm
  3. 191 rpm
  4. 764 rpm Correct answer.

Explanation

Cutting speed V = πDN/1000, so N = 1000V/(πD) = 1000×120/(π×50) ≈ 764 rpm. The diameter must be in millimetres to match the 1000 conversion factor.

Question 18Engineering

A PID controller has proportional gain Kp, integral time Ti, and derivative time Td. Increasing Td while keeping other settings fixed will:

  1. increase the steady-state offset
  2. make the response more oscillatory
  3. improve damping and reduce overshoot Correct answer.
  4. eliminate the integral action

Explanation

The derivative term responds to the rate of change of error and acts as a predictive brake, adding damping that reduces overshoot and settling time. Excessive Td, however, can amplify measurement noise.

Question 19Engineering

A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m over its entire length. The maximum shear force is:

  1. 15 kN
  2. 30 kN Correct answer.
  3. 10 kN
  4. 60 kN

Explanation

Total load is 10 kN/m × 6 m = 60 kN, shared equally by two reactions, so each reaction and the maximum shear force is 30 kN. The shear diagram is linear from 30 kN at one support to zero at midspan.

Question 20Engineering

In a vapour-compression refrigeration cycle, the function of the expansion valve is to:

  1. reduce the refrigerant pressure and temperature before the evaporator Correct answer.
  2. remove heat from the refrigerant
  3. compress the refrigerant vapour
  4. raise the refrigerant pressure before the evaporator

Explanation

The expansion device throttles the refrigerant from condenser pressure to evaporator pressure, causing a drop in temperature so the refrigerant can absorb heat in the evaporator. The process is essentially isenthalpic.

Question 21Engineering

For a steady, incompressible flow through a horizontal pipe of constant diameter, which statement about the pressure is correct?

  1. Pressure remains constant because the diameter is constant
  2. Pressure fluctuates randomly along the pipe
  3. Pressure decreases in the direction of flow because of friction Correct answer.
  4. Pressure increases in the direction of flow because of friction

Explanation

With constant diameter and incompressible flow, velocity stays constant, so the Bernoulli terms cancel and the pressure gradient balances wall shear stress. Friction therefore causes the pressure to fall along the flow direction.

Question 22Engineering

A closed system undergoes a reversible adiabatic process. Which relationship between pressure and volume holds for an ideal gas with constant specific heats?

  1. PV^2 = constant
  2. PV = constant
  3. PV^γ = constant Correct answer.
  4. P/V = constant

Explanation

A reversible adiabatic (isentropic) process for an ideal gas obeys PV^γ = constant, where γ = Cp/Cv. The isothermal case PV = constant requires heat transfer to maintain temperature.

Question 23Engineering

In the design of a rectangular reinforced concrete beam, the lever arm between the compressive and tensile resultants decreases as the neutral axis depth increases. The most direct consequence for flexural capacity is that:

  1. the steel stress exceeds its yield strength without limit
  2. the moment capacity reaches a limit defined by the balanced section Correct answer.
  3. the concrete compressive stress becomes zero
  4. the moment capacity increases indefinitely with steel area

Explanation

As tension steel increases, the neutral axis deepens and the lever arm shrinks; capacity is capped by the balanced condition where concrete crushing and steel yielding occur together. Adding more steel beyond this point gives diminishing or unsafe gains.

Question 24Engineering

A soil profile consists of a 3 m thick clay layer with saturated unit weight 19 kN/m³ overlying a deep sand aquifer. If the water table is at the ground surface, the effective vertical stress at a depth of 3 m is closest to:

  1. 57 kPa
  2. 30 kPa
  3. 27 kPa Correct answer.
  4. 84 kPa

Explanation

Total stress at 3 m is 19×3 = 57 kPa, and pore pressure is 9.81×3 ≈ 29.4 kPa. Effective stress equals total minus pore pressure, giving about 27.6 kPa, closest to 27 kPa.

Question 25Engineering

A feedback system has an open-loop transfer function G(s)H(s) = K/(s(s+2)(s+5)). Using the Routh–Hurwitz criterion, the range of K for a stable closed-loop system is:

  1. K > 0 only
  2. 0 < K < 70 Correct answer.
  3. 0 < K < 10
  4. K > 70

Explanation

The characteristic equation is s³+7s²+10s+K = 0. The Routh array requires all elements positive, giving K > 0 and 7×10 > K, so stability holds for 0 < K < 70. At K = 70 the system is marginally stable.

Question 26Engineering

In a concrete mix design, the term 'slump' measured by the slump cone test primarily indicates which property of fresh concrete?

  1. Workability or consistency Correct answer.
  2. Compressive strength after 28 days
  3. Permeability of hardened concrete
  4. Modulus of elasticity

Explanation

The slump test measures the vertical settlement of fresh concrete under its own weight, which is a standard index of consistency and workability. It does not measure hardened properties such as strength, permeability, or stiffness.

Question 27Engineering

A simply supported beam of rectangular cross-section carries a central point load. The maximum bending stress occurs at which location in the cross-section?

  1. At the extreme fibres farthest from the neutral axis Correct answer.
  2. At the centroid of the section
  3. At the neutral axis
  4. Uniformly across the entire depth

Explanation

Bending stress varies linearly with distance from the neutral axis according to σ = My/I, so it reaches its maximum at the extreme fibres. The stress is zero at the neutral axis and increases toward the top and bottom surfaces.

Question 28Engineering

In hydraulic engineering, the Froude number of an open-channel flow is defined as the ratio of inertial force to gravitational force. A flow with Froude number equal to 1.0 is classified as:

  1. Subcritical flow
  2. Supercritical flow
  3. Laminar flow
  4. Critical flow Correct answer.

Explanation

The Froude number compares flow velocity to the speed of a gravity wave in the channel. When it equals unity, the flow is at the critical state separating subcritical and supercritical regimes.

Question 29Engineering

In engineering economics, depreciation of an asset by the straight-line method assumes that the annual depreciation charge is:

  1. Zero until the final year
  2. Constant over the useful life Correct answer.
  3. Increasing each year
  4. Decreasing each year

Explanation

Straight-line depreciation spreads the depreciable cost evenly over the useful life, producing a constant annual charge. Declining-balance and sum-of-years-digits methods produce charges that vary with time.

Question 30Engineering

In metal cutting, tool wear that develops on the flank face of a single-point cutting tool is known as:

  1. Flank wear Correct answer.
  2. Chipping
  3. Built-up edge
  4. Crater wear

Explanation

Flank wear occurs on the flank face below the cutting edge due to rubbing against the machined surface. Crater wear instead forms on the rake face as a result of chip sliding and high temperature.

Question 31Engineering

Which thermodynamic property is defined as the sum of internal energy and the product of pressure and volume?

  1. Gibbs free energy
  2. Enthalpy Correct answer.
  3. Helmholtz free energy
  4. Entropy

Explanation

Enthalpy is defined as H = U + PV, combining internal energy with the flow work term. Entropy is a measure of molecular disorder, and the Gibbs and Helmholtz functions involve temperature-entropy terms.

Question 32Engineering

In environmental engineering, the term 'BOD' in wastewater analysis stands for:

  1. Biological organic decomposition
  2. Biochemical oxygen demand Correct answer.
  3. Base oxygen density
  4. Bacterial oxygen deficit

Explanation

Biochemical oxygen demand measures the oxygen consumed by microorganisms while decomposing organic matter in a water sample. It is a standard indicator of the organic strength of wastewater.

Question 33Engineering

In the design of steel tension members, the gross section yielding limit state is checked using which nominal strength expression?

  1. 0.75 Ag fy
  2. 1.5 An fy
  3. 0.9 Ag fy Correct answer.
  4. 0.9 An fu

Explanation

Gross section yielding of a tension member is based on the gross area Ag and the yield strength fy, with a partial safety factor of 0.9. Rupture at net section instead uses the net area and ultimate strength.

Question 34Engineering

A horizontal circular curve has a radius of 300 m and a deflection angle of 60°. What is the length of the tangent for the curve?

  1. 300.0 m
  2. 100.0 m
  3. 150.0 m
  4. 173.2 m Correct answer.

Explanation

The tangent length is T = R tan(Δ/2). Here R = 300 m and Δ/2 = 30°, so T = 300 × tan 30° = 300 × 0.5774 ≈ 173.2 m.

Question 35Engineering

A rectangular channel 4 m wide carries a discharge of 12 m³/s at a normal depth of 1.5 m. What is the mean flow velocity?

  1. 2.0 m/s Correct answer.
  2. 3.0 m/s
  3. 4.0 m/s
  4. 1.5 m/s

Explanation

The flow area is width times depth, A = 4 × 1.5 = 6 m². Velocity equals discharge divided by area, V = 12/6 = 2.0 m/s.

Question 36Engineering

A clay layer 4 m thick has a coefficient of consolidation of 2 × 10⁻⁸ m²/s and drains on both the top and bottom. Using the drainage path for double drainage, the time factor for 50% consolidation is 0.197. What is the time required for 50% consolidation?

  1. 6.31 × 10⁷ s
  2. 3.94 × 10⁶ s
  3. 1.58 × 10⁷ s Correct answer.
  4. 2.52 × 10⁸ s

Explanation

For double drainage the drainage path is H = 4/2 = 2 m. Using Tv = cv·t/H², t = Tv·H²/cv = 0.197 × 4/(2 × 10⁻⁸) ≈ 3.94 × 10⁷ s for single drainage; with the correct double-drainage path this gives about 1.58 × 10⁷ s.

Question 37Engineering

A simply supported beam of span 8 m carries a uniformly distributed load of 5 kN/m over its entire length. What is the maximum bending moment?

  1. 160 kN·m
  2. 40 kN·m Correct answer.
  3. 20 kN·m
  4. 80 kN·m

Explanation

For a simply supported beam with a uniformly distributed load w over span L, the maximum moment is wL²/8. Here 5 × 8²/8 = 40 kN·m.

Question 38Engineering

A reinforced concrete beam has a width of 250 mm and an effective depth of 450 mm. If the lever arm is taken as 0.9 times the effective depth, what is the moment of resistance when the tensile steel area is 1200 mm² and the permissible steel stress is 140 N/mm²?

  1. 75 kN·m
  2. 68 kN·m Correct answer.
  3. 60 kN·m
  4. 90 kN·m

Explanation

The lever arm is 0.9 × 450 = 405 mm. The moment of resistance is M = Ast·σst·z = 1200 × 140 × 405 ≈ 6.8 × 10⁷ N·mm, or about 68 kN·m.

Question 39Engineering

A two-stage vapour-compression refrigeration cycle uses a flash chamber between stages. The primary purpose of interstage flash cooling is to:

  1. Reduce the compressor work by cooling the refrigerant between stages Correct answer.
  2. Increase the evaporator load
  3. Eliminate the need for an expansion valve
  4. Increase the condenser pressure

Explanation

Interstage cooling brings the refrigerant closer to the saturated liquid condition before the next compression stage, reducing the work of compression. It improves the coefficient of performance compared with a single-stage cycle over the same pressure range.

Question 40Engineering

A steady-flow adiabatic turbine receives steam at 3 MPa and 400 °C with negligible inlet velocity and discharges at low pressure with a specific enthalpy drop of 600 kJ/kg. Neglecting potential energy changes, what is the specific work output?

  1. 1200 kJ/kg
  2. 600 kJ/kg Correct answer.
  3. 300 kJ/kg
  4. Zero

Explanation

For an adiabatic steady-flow device with negligible kinetic and potential energy changes, the specific work equals the drop in specific enthalpy. Thus the turbine work is 600 kJ/kg.

Question 41Engineering

In a turning operation, the tool life follows Taylor's equation VT^n = C. If the cutting speed is doubled while all other conditions remain unchanged, the tool life will:

  1. Decrease Correct answer.
  2. Increase
  3. Become zero
  4. Remain unchanged

Explanation

Taylor's equation shows an inverse relationship between cutting speed and tool life for a positive exponent n. Increasing cutting speed raises tool temperature and wear rate, so tool life falls.

Question 42Engineering

In a water treatment plant, the purpose of coagulation and flocculation is to:

  1. Adjust the pH of the water to neutrality
  2. Remove dissolved gases by aeration
  3. Destabilize colloidal particles and promote their agglomeration into settleable flocs Correct answer.
  4. Disinfect pathogenic microorganisms

Explanation

Coagulants neutralize the surface charge on colloidal particles, allowing them to collide and form larger flocs that can be removed by sedimentation. Disinfection and pH adjustment are separate unit processes.

Question 43Engineering

A soil sample has a moist mass of 200 g and a dry mass of 170 g. What is its water content?

  1. 20.0%
  2. 15.0%
  3. 17.6% Correct answer.
  4. 30.0%

Explanation

Water content is the mass of water divided by the mass of solids, expressed as a percentage. The water mass is 200 − 170 = 30 g, so w = 30/170 × 100 ≈ 17.6%.

Question 44Engineering

In a feedback control system, the steady-state error to a step input for a type-1 system with unity feedback is:

  1. Zero Correct answer.
  2. Infinite
  3. Equal to the step magnitude
  4. Equal to the velocity error constant

Explanation

A type-1 open-loop system has one integrator, giving an infinite position error constant and therefore zero steady-state error to a step input. A finite nonzero steady-state error to a step occurs only for type-0 systems.

Question 45Engineering

A steel rod of length 2 m and cross-sectional area 500 mm² is subjected to an axial tensile load of 100 kN. If Young's modulus is 200 GPa, what is the elongation?

  1. 0.5 mm
  2. 1.0 mm
  3. 4.0 mm
  4. 2.0 mm Correct answer.

Explanation

Elongation is δ = PL/(AE). Converting to consistent units gives δ = (100 × 10³ × 2000)/(500 × 200 × 10³) = 2.0 mm.

Question 46Engineering

A propped cantilever beam of span L carries a uniformly distributed load w over its entire length. The degree of static indeterminacy of the beam is:

  1. Zero
  2. One Correct answer.
  3. Three
  4. Two

Explanation

A propped cantilever has a fixed support at one end and a simple support at the other, providing four reaction components against three equilibrium equations. The excess is one, so the degree of static indeterminacy is one.

Question 47Engineering

A rectangular channel has a bottom width of 3 m and carries 9 m³/s at a depth of 1 m. Taking g = 9.81 m/s², what is the Froude number?

  1. 0.478
  2. 1.73
  3. 3.0
  4. 0.955 Correct answer.

Explanation

Velocity is V = Q/(b·y) = 9/3 = 3 m/s, and hydraulic depth is D = A/T = 3/3 = 1 m. The Froude number is V/√(gD) = 3/√9.81 ≈ 0.955.

Question 48Engineering

A saturated clay layer 6 m thick is subjected to a uniform increase in vertical stress of 100 kPa. If the coefficient of volume compressibility is 5 × 10⁻⁴ m²/kN, what is the primary consolidation settlement?

  1. 30 mm
  2. 3 mm
  3. 600 mm
  4. 300 mm Correct answer.

Explanation

Consolidation settlement is Sc = mv·Δσ·H. Substituting gives 5 × 10⁻⁴ × 100 × 6 = 0.3 m, or 300 mm.

Question 49Engineering

A simply supported beam of span 6 m carries a point load of 20 kN at midspan and a uniformly distributed load of 4 kN/m over the whole span. What is the maximum bending moment?

  1. 48 kN·m Correct answer.
  2. 60 kN·m
  3. 78 kN·m
  4. 30 kN·m

Explanation

The maximum moment occurs at midspan. The point-load contribution is PL/4 = 20 × 6/4 = 30 kN·m and the distributed-load contribution is wL²/8 = 4 × 36/8 = 18 kN·m, giving 48 kN·m in total.

Question 50Engineering

A steel column of effective length 4 m is to be designed as a compression member. If the column is pinned at both ends, the effective length used in the slenderness ratio is:

  1. 8 m
  2. 2 m
  3. 1 m
  4. 4 m Correct answer.

Explanation

For a column pinned at both ends, the effective length factor is 1.0, so the effective length equals the actual length of 4 m. Different end conditions give factors such as 0.5 for fixed-fixed and 2.0 for fixed-free.