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Question 1General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The Bihar Public Service Commission derives its constitutional authority from which Article of the Indian Constitution?

  1. Article 324
  2. Article 312
  3. Article 320
  4. Article 315 Correct answer.

Explanation

Article 315 provides for the establishment of Public Service Commissions for the Union and for each State, and it is the provision under which the BPSC was constituted. The Commission's functions are further detailed in Articles 320 and 321.

Question 2General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which river, rising near Fatuha in Bihar, joins the Ganga near Hajipur and is sometimes called the 'Sorrow of Bihar'?

  1. Kosi
  2. Son Correct answer.
  3. Gandak
  4. Punpun

Explanation

The Son, though usually associated with its course through Jharkhand and Uttar Pradesh, is often confused with flood-prone rivers; the true 'Sorrow of Bihar' is the Kosi, which shifts course and floods north Bihar. The stem's description of a river near Fatuha fits the Punpun, a small tributary of the Ganga.

Question 3General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which session of the Indian National Congress, held in 1927, passed a resolution calling for complete independence for the first time as its goal?

  1. Calcutta session
  2. Lahore session
  3. Madras session Correct answer.
  4. Karachi session

Explanation

At the Madras session of 1927, under the presidency of M. A. Ansari, the Congress for the first time adopted complete independence as its goal, though the formal Purna Swaraj declaration came at Lahore in 1929. This distinction between the 1927 resolution and the 1929 declaration is frequently tested.

Question 4General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

In the context of the Indian economy, 'fiscal deficit' is best defined as which of the following?

  1. Total revenue receipts minus total revenue expenditure
  2. The gap between exports and imports of goods and services
  3. The excess of capital expenditure over capital receipts
  4. Total expenditure minus total receipts excluding borrowings Correct answer.

Explanation

Fiscal deficit measures the government's total borrowing requirement, computed as total expenditure minus total receipts other than borrowings. It indicates how much the government must borrow to meet its expenditure.

Question 5General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following is the SI unit of electric conductance?

  1. Ohm
  2. Farad
  3. Siemens Correct answer.
  4. Henry

Explanation

Conductance is the reciprocal of resistance, and its SI unit is the siemens, formerly called the mho. It measures how easily a conductor allows current to flow.

Question 6General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The Tropic of Cancer passes through which of the following districts of Bihar?

  1. Bhagalpur
  2. Gaya Correct answer.
  3. Patna
  4. Darbhanga

Explanation

The Tropic of Cancer, at roughly 23.5 degrees north latitude, passes through the southern districts of Bihar, with Gaya lying close to that latitude. This makes Gaya the district among the options that the line crosses.

Question 7General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following is a Directive Principle of State Policy that was added by the 42nd Constitutional Amendment Act of 1976?

  1. Uniform civil code throughout the territory of India
  2. Protection and improvement of environment and safeguarding of forests and wildlife Correct answer.
  3. Organisation of village panchayats
  4. Promotion of international peace and security

Explanation

The 42nd Amendment of 1976 inserted Article 48A, directing the State to protect and improve the environment and to safeguard forests and wildlife. It also added Article 39A on free legal aid and moved education to the Concurrent List.

Question 8General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The Quit India Movement was launched by the Indian National Congress in August 1942 following the failure of which mission?

  1. Cripps Mission Correct answer.
  2. Cabinet Mission
  3. Wavell Plan
  4. Simon Commission

Explanation

The Cripps Mission of 1942 failed to secure Indian cooperation for the war effort, prompting the Congress to launch the Quit India Movement in August 1942. The Cabinet Mission came in 1946, after the war.

Question 9General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following is the correct sequence of states in descending order of literacy rate as per the 2011 Census among the options given?

  1. Mizoram, Kerala, Bihar, Rajasthan
  2. Kerala, Rajasthan, Mizoram, Bihar
  3. Kerala, Bihar, Mizoram, Rajasthan
  4. Kerala, Mizoram, Rajasthan, Bihar Correct answer.

Explanation

As per the 2011 Census, Kerala had the highest literacy rate at about 94 percent, followed by Mizoram at about 91 percent, then Rajasthan at about 66 percent, with Bihar lowest at about 62 percent. This ordering reflects the widely reported comparative figures.

Question 10General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The 'Repo Rate' in Indian monetary policy refers to which of the following?

  1. The interest paid by the government on its treasury bills
  2. The rate at which commercial banks lend to their most creditworthy customers
  3. The rate at which the RBI lends short-term funds to commercial banks against government securities Correct answer.
  4. The rate at which the RBI absorbs liquidity from commercial banks

Explanation

Repo rate is the policy rate at which the Reserve Bank of India lends short-term funds to banks against eligible collateral, chiefly government securities. It is the principal tool through which the Monetary Policy Committee signals its stance.

Question 11General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following statements about the Fundamental Duties in the Indian Constitution is accurate?

  1. They were part of the original Constitution of 1950
  2. They are enforceable directly by writs under Article 32
  3. They apply only to citizens holding public office
  4. They were included by the 42nd Amendment on the recommendation of the Swaran Singh Committee Correct answer.

Explanation

Fundamental Duties were added by the 42nd Amendment Act of 1976 on the recommendation of the Swaran Singh Committee, which drew on the earlier idea of duties. Article 51A lists these duties for citizens.

Question 12General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following pairs of biosphere reserves and their states is correctly matched?

  1. Sundarbans - Odisha
  2. Nilgiri - Kerala only
  3. Simlipal - West Bengal
  4. Nokrek - Meghalaya Correct answer.

Explanation

Nokrek Biosphere Reserve is located in the Garo Hills of Meghalaya and is part of India's UNESCO-recognised biosphere reserves. Matching reserves to their correct states is a common general studies question.

Question 13General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The Battle of Buxar, fought in 1764, was significant because it led to which outcome?

  1. Transfer of the capital of British India from Calcutta to Delhi
  2. Grant of Diwani rights over Bengal, Bihar and Orissa to the East India Company Correct answer.
  3. Establishment of the dual government in Bengal by Warren Hastings
  4. Abolition of the East India Company's trading monopoly

Explanation

Following the victory at Buxar, the Treaty of Allahabad in 1765 granted the East India Company the Diwani, or revenue rights, over Bengal, Bihar and Orissa. This transformed the Company from a trading body into a territorial power.

Question 14General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following is the most abundant gas in the Earth's atmosphere by volume?

  1. Nitrogen Correct answer.
  2. Argon
  3. Oxygen
  4. Carbon dioxide

Explanation

Nitrogen constitutes about 78 percent of the atmosphere by volume, making it the most abundant gas. Oxygen follows at about 21 percent, with argon and carbon dioxide present in much smaller amounts.

Question 15General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The 'Green Revolution' in India during the late 1960s was most closely associated with which crop?

  1. Rice
  2. Sugarcane
  3. Wheat Correct answer.
  4. Cotton

Explanation

The Green Revolution in India centred on high-yielding varieties of wheat, introduced with the help of Norman Borlaug's research and promoted by C. Subramaniam. It dramatically raised wheat output in Punjab, Haryana and western Uttar Pradesh.

Question 16General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which Article of the Constitution provides for the appointment of a Governor for each state?

  1. Article 155
  2. Article 153 Correct answer.
  3. Article 161
  4. Article 163

Explanation

Article 153 provides that there shall be a Governor for each state, and the same person may be appointed Governor for two or more states. Articles 155 and 156 deal with appointment and tenure respectively.

Question 17General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following is a Kharif crop in Bihar's agricultural calendar?

  1. Barley
  2. Mustard
  3. Wheat
  4. Maize Correct answer.

Explanation

Kharif crops are sown with the onset of the monsoon and harvested in autumn, and maize is a typical Kharif crop in Bihar. Wheat, mustard and barley are Rabi crops grown in the winter season.

Question 18General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The 'Doctrine of Lapse' used by Lord Dalhousie to annex Indian states was based on which principle?

  1. Revenue collection would be transferred to the British after every decade
  2. Treaties with Indian states would be renewed every twenty years
  3. Indian rulers must maintain a standing army for the British
  4. A state without a natural heir would lapse to the British Correct answer.

Explanation

The Doctrine of Lapse held that any princely state whose ruler died without a natural heir would be annexed by the British, with adopted sons denied recognition. Dalhousie applied it to states such as Satara, Jhansi and Nagpur.

Question 19General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following phenomena explains why the sky appears blue during the day?

  1. Rayleigh scattering of shorter wavelengths by air molecules Correct answer.
  2. Absorption of blue light by the ozone layer
  3. Refraction of white light through water vapour
  4. Total internal reflection within the atmosphere

Explanation

Rayleigh scattering causes shorter wavelengths, such as blue, to scatter far more strongly than longer wavelengths when sunlight interacts with air molecules. The scattered blue light reaches the observer from all directions, giving the sky its colour.

Question 20General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following is the correct chronological order of the following events in Indian history, from earliest to latest?

  1. Partition of Bengal, Revolt of 1857, Quit India Movement, Jallianwala Bagh massacre
  2. Revolt of 1857, Partition of Bengal, Jallianwala Bagh massacre, Quit India Movement Correct answer.
  3. Jallianwala Bagh massacre, Revolt of 1857, Partition of Bengal, Quit India Movement
  4. Revolt of 1857, Jallianwala Bagh massacre, Partition of Bengal, Quit India Movement

Explanation

The Revolt of 1857 came first, followed by the Partition of Bengal in 1905, the Jallianwala Bagh massacre in 1919, and the Quit India Movement in 1942. This sequence reflects the standard chronology of modern Indian history.

Question 21General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

In the Indian Constitution, the concept of 'basic structure' was propounded in which case?

  1. Kesavananda Bharati v. State of Kerala Correct answer.
  2. Golaknath v. State of Punjab
  3. Minerva Mills v. Union of India
  4. Maneka Gandhi v. Union of India

Explanation

The doctrine of basic structure was laid down in Kesavananda Bharati v. State of Kerala (1973), where the Supreme Court held that Parliament cannot amend the Constitution in a way that destroys its essential features. It was a response to the earlier Golaknath ruling and later reaffirmed in Minerva Mills.

Question 22General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The 'Kisan Credit Card' scheme, launched in 1998, was primarily designed to provide which of the following to farmers?

  1. Timely and adequate credit for agricultural needs Correct answer.
  2. Subsidised electricity for irrigation pumps
  3. Crop insurance against natural calamities
  4. Guaranteed minimum support prices for produce

Explanation

The Kisan Credit Card scheme, introduced in 1998 on the recommendation of the R. V. Gupta Committee, provides farmers with timely and adequate short-term credit for cultivation and related needs. It is a credit-delivery mechanism rather than an insurance or price-support scheme.

Question 23General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following mountain passes connects the Lahaul valley with the Spiti valley in Himachal Pradesh?

  1. Rohtang Pass
  2. Kunzum Pass Correct answer.
  3. Nathu La
  4. Zoji La

Explanation

Kunzum Pass, at over 4,500 metres, links the Lahaul valley with the Spiti valley in Himachal Pradesh. Rohtang connects Kullu with Lahaul, while Nathu La and Zoji La lie in Sikkim and Ladakh respectively.

Question 24General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following statements about the Fundamental Right to Constitutional Remedies under Article 32 is correct?

  1. It is available only against the Union government and not against states
  2. It is available only to citizens and not to foreigners
  3. It can be enforced only through the High Courts and not the Supreme Court
  4. It can be suspended during a national emergency by the President under Article 359 Correct answer.

Explanation

Article 359 empowers the President, during a national emergency, to suspend the right to move any court for enforcement of specified Fundamental Rights, including those under Article 32. This was invoked during the Emergency of 1975-77.

Question 25General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following is the correct order of the layers of the atmosphere from the Earth's surface upward?

  1. Stratosphere, Troposphere, Mesosphere, Thermosphere, Exosphere
  2. Troposphere, Stratosphere, Mesosphere, Thermosphere, Exosphere Correct answer.
  3. Troposphere, Stratosphere, Thermosphere, Mesosphere, Exosphere
  4. Troposphere, Mesosphere, Stratosphere, Exosphere, Thermosphere

Explanation

The atmosphere is layered, from the surface upward, as troposphere, stratosphere, mesosphere, thermosphere and exosphere. Weather phenomena occur mainly in the troposphere, while the ozone layer lies in the stratosphere.

Question 26General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which body is constitutionally empowered to recommend the imposition of President's Rule in a state under Article 356?

  1. The Governor of the state Correct answer.
  2. The Supreme Court
  3. The Election Commission of India
  4. The Union Cabinet

Explanation

Under Article 356, the President acts on a report from the Governor of the state, who certifies that governance cannot be carried on in accordance with the Constitution. The Governor's report is the constitutional trigger, though the Union Council of Ministers advises the President formally. Judicial review of such proclamation was upheld in S.R. Bommai v. Union of India (1994).

Question 27General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The Chhota Nagpur Plateau, which extends into parts of Bihar, is composed chiefly of which type of rock formation?

  1. Cretaceous limestone
  2. Archaean granite and gneiss Correct answer.
  3. Deccan trap basalt
  4. Tertiary sedimentary sandstone

Explanation

The Chhota Nagpur Plateau is part of the ancient peninsular shield and is dominated by Archaean granites, gneisses and schists, along with Gondwana coal-bearing sediments in its basins. These crystalline rocks are among the oldest in India. The Deccan traps lie far to the west in Maharashtra, not in this plateau.

Question 28General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following best explains why a lunar eclipse can occur only on a full moon night?

  1. The Earth lies between the Sun and the Moon, so the Moon can enter the Earth's shadow. Correct answer.
  2. The Moon is closest to Earth on a full moon night.
  3. The Moon's orbital plane is inclined at 5 degrees to the ecliptic.
  4. The Moon reflects maximum sunlight on a full moon night.

Explanation

A lunar eclipse requires the Earth to come between the Sun and the Moon so that the Moon passes through the Earth's umbra. That alignment is geometrically possible only when the Moon is opposite the Sun, that is, at full moon. Because the Moon's orbit is tilted about 5 degrees to the ecliptic, eclipses do not occur every full moon.

Question 29General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

The 'Hindu rate of growth', a phrase used to describe India's sluggish GDP growth in the first four decades after independence, was coined by which economist?

  1. Amartya Sen
  2. V.K.R.V. Rao
  3. Raj Krishna Correct answer.
  4. Jagdish Bhagwati

Explanation

The term 'Hindu rate of growth' was coined by economist Raj Krishna to describe the low trend growth of around 3.5 per cent per annum in the Indian economy between the 1950s and the 1980s. It was a descriptive label for the pre-liberalisation growth pattern, not a formal policy concept. The phrase is often cited in discussions of the 1991 reforms.

Question 30General Studies (general awareness, current affairs, Indian polity, geography, history, economy, science)

Which of the following is the primary function of the Reserve Bank of India's Monetary Policy Committee?

  1. To set the policy repo rate to achieve the inflation target Correct answer.
  2. To fix the exchange rate of the rupee against the dollar
  3. To regulate the capital market and stock exchanges
  4. To approve the Union Budget before presentation

Explanation

The Monetary Policy Committee, constituted under the RBI Act as amended in 2016, is mandated to determine the policy repo rate to keep consumer price inflation within the target set with the Government. The committee has six members and meets at least four times a year. Its framework is inflation targeting, with a flexible tolerance band.

Question 31General Engineering Science (common engineering fundamentals across disciplines)

A simply supported beam of span L carries a central point load W. What is the maximum bending moment?

  1. WL/4 Correct answer.
  2. WL/2
  3. WL²/8
  4. WL/8

Explanation

For a simply supported beam with a central point load, the reactions are W/2 each and the maximum moment occurs at midspan, equal to (W/2)(L/2) = WL/4. The parabolic value WL²/8 applies only to a uniformly distributed load, not a point load.

Question 32General Engineering Science (common engineering fundamentals across disciplines)

In a rectangular beam of width b and depth d, the section modulus about the centroidal axis parallel to the width is:

  1. bd²/6 Correct answer.
  2. bd/6
  3. bd³/12
  4. bd²/3

Explanation

The second moment of area is bd³/12 and the extreme fibre distance is d/2, so section modulus Z = I/y = (bd³/12)/(d/2) = bd²/6. This value is used to convert bending moment into extreme fibre stress via σ = M/Z.

Question 33General Engineering Science (common engineering fundamentals across disciplines)

A steel bar of length 2 m and cross-sectional area 500 mm² carries an axial tensile load of 50 kN. Taking E = 200 GPa, the elongation is:

  1. 1.0 mm Correct answer.
  2. 0.5 mm
  3. 2.0 mm
  4. 0.25 mm

Explanation

Axial elongation is δ = PL/(AE). Substituting P = 50,000 N, L = 2000 mm, A = 500 mm² and E = 200,000 N/mm² gives δ = (50,000 × 2000)/(500 × 200,000) = 1.0 mm.

Question 34General Engineering Science (common engineering fundamentals across disciplines)

For a circular shaft of diameter d transmitting torque T, the maximum shear stress is:

  1. 32T/(πd³)
  2. 8T/(πd³)
  3. T/(πd³)
  4. 16T/(πd³) Correct answer.

Explanation

Torsion theory gives τ = T·r/J with polar moment J = πd⁴/32 and radius r = d/2, so τ = 16T/(πd³). The factor 32 appears in the polar moment itself, not in the stress expression.

Question 35General Engineering Science (common engineering fundamentals across disciplines)

A closed cylindrical thin-walled pressure vessel has internal diameter 1 m and wall thickness 10 mm, with internal pressure 2 MPa. The hoop stress is approximately:

  1. 200 MPa
  2. 50 MPa
  3. 100 MPa Correct answer.
  4. 25 MPa

Explanation

Thin-cylinder hoop stress is σ = pd/(2t). With p = 2 MPa, d = 1000 mm and t = 10 mm, σ = (2 × 1000)/(2 × 10) = 100 MPa. The longitudinal stress would be half of this value.

Question 36General Engineering Science (common engineering fundamentals across disciplines)

In a first law analysis of a closed system undergoing a process with no change in kinetic or potential energy, which relation holds?

  1. Q = W at constant volume
  2. Q + W = ΔU
  3. Q − W = ΔU Correct answer.
  4. Q − W = ΔH

Explanation

For a closed system, the first law states that net heat added minus net work done by the system equals the change in internal energy, Q − W = ΔU. Enthalpy appears in open-system (flow) energy balances, not in the closed-system form.

Question 37General Engineering Science (common engineering fundamentals across disciplines)

An ideal Carnot engine operates between 600 K and 300 K. Its thermal efficiency is:

  1. 50% Correct answer.
  2. 75%
  3. 100%
  4. 25%

Explanation

Carnot efficiency is η = 1 − T_C/T_H, using absolute temperatures. Here η = 1 − 300/600 = 0.5, that is 50 percent, which is the maximum possible efficiency for these reservoirs.

Question 38General Engineering Science (common engineering fundamentals across disciplines)

For an ideal gas undergoing an isothermal process, which quantity remains constant?

  1. Volume
  2. Internal energy Correct answer.
  3. Entropy
  4. Pressure

Explanation

For an ideal gas, internal energy depends only on temperature, so it stays constant when temperature is held constant. Pressure and volume vary inversely along the isotherm, and entropy increases as the gas expands.

Question 39General Engineering Science (common engineering fundamentals across disciplines)

In a Rankine cycle, the purpose of the condenser is to:

  1. Raise the pressure of the working fluid
  2. Add heat to the boiler feedwater
  3. Superheat the steam before expansion
  4. Reject heat and condense the exhaust steam to liquid Correct answer.

Explanation

The condenser is the low-pressure heat rejection component where turbine exhaust steam gives up latent heat to cooling water and becomes saturated liquid. Lowering condenser pressure also lowers the turbine exit enthalpy and improves cycle efficiency.

Question 40General Engineering Science (common engineering fundamentals across disciplines)

Heat transfer through a plane wall of thickness L and thermal conductivity k has a thermal resistance per unit area equal to:

  1. k/L
  2. 1/(kL)
  3. L/k Correct answer.
  4. kL

Explanation

For one-dimensional conduction, the heat flux is q'' = ΔT/(L/k), so the thermal resistance per unit area is L/k. Resistance rises with thickness and falls with conductivity, which matches physical intuition.

Question 41General Engineering Science (common engineering fundamentals across disciplines)

In forced convection over a flat plate, the local Nusselt number is correlated with the local Reynolds and Prandtl numbers. Which dimensionless group represents the ratio of momentum diffusivity to thermal diffusivity?

  1. Reynolds number
  2. Nusselt number
  3. Prandtl number Correct answer.
  4. Grashof number

Explanation

The Prandtl number Pr = μc_p/k compares momentum diffusivity to thermal diffusivity and depends only on the fluid. The Reynolds number compares inertia to viscous forces, while the Nusselt number expresses convective to conductive heat transfer.

Question 42General Engineering Science (common engineering fundamentals across disciplines)

The equivalent resistance of two resistors of 6 Ω and 3 Ω connected in parallel is:

  1. 2 Ω Correct answer.
  2. 1.5 Ω
  3. 4.5 Ω
  4. 9 Ω

Explanation

For a parallel combination, 1/R = 1/6 + 1/3 = 1/2, so the equivalent resistance is 2 Ω. The result is always smaller than the smallest branch resistance, which confirms the answer.

Question 43General Engineering Science (common engineering fundamentals across disciplines)

In a balanced three-phase star-connected load supplied from a 400 V line voltage, the phase voltage is approximately:

  1. 400 V
  2. 200 V
  3. 231 V Correct answer.
  4. 693 V

Explanation

In a star connection the phase voltage is the line voltage divided by √3, so 400/1.732 ≈ 231 V. The line current equals the phase current in star, unlike the delta connection.

Question 44General Engineering Science (common engineering fundamentals across disciplines)

The unit of magnetic flux density in SI is:

  1. Weber
  2. Tesla Correct answer.
  3. Ampere-turn per metre
  4. Henry

Explanation

Magnetic flux density B is measured in tesla, equal to one weber per square metre. Flux itself is in webers, inductance in henries, and magnetic field strength in amperes per metre.

Question 45General Engineering Science (common engineering fundamentals across disciplines)

A single-phase transformer has 500 primary turns and 100 secondary turns. If the primary is connected to 230 V, the secondary no-load voltage is approximately:

  1. 23 V
  2. 46 V Correct answer.
  3. 1150 V
  4. 230 V

Explanation

The voltage ratio equals the turns ratio, so V₂ = V₁·N₂/N₁ = 230 × 100/500 = 46 V. This is a step-down transformer because the secondary turns are fewer than the primary turns.

Question 46General Engineering Science (common engineering fundamentals across disciplines)

A DC shunt motor draws armature current I_a with back emf E_b and armature resistance R_a. The torque developed is proportional to:

  1. I_a²R_a
  2. E_b/R_a
  3. Φ·I_a Correct answer.
  4. E_b·I_a/R_a

Explanation

Developed torque is proportional to the product of air-gap flux per pole and armature current, T ∝ ΦI_a. For a shunt motor the flux is nearly constant, so torque is approximately proportional to armature current alone.

Question 47General Engineering Science (common engineering fundamentals across disciplines)

In a series RLC circuit at resonance, which statement is true?

  1. Impedance is maximum and purely capacitive
  2. The power factor is zero
  3. Impedance is minimum and purely resistive Correct answer.
  4. Current is minimum

Explanation

At resonance the inductive and capacitive reactances cancel, leaving only resistance, so impedance is minimum and purely resistive. Consequently current is maximum and the power factor is unity.

Question 48General Engineering Science (common engineering fundamentals across disciplines)

The relationship between Young's modulus E, shear modulus G and Poisson's ratio ν for an isotropic material is:

  1. E = 2G(1 + ν) Correct answer.
  2. E = G/(2(1 + ν))
  3. E = G(1 + ν)
  4. E = 3G(1 − 2ν)

Explanation

For an isotropic elastic material the moduli are linked by E = 2G(1 + ν). A typical metal with ν ≈ 0.3 gives G ≈ 0.4E, consistent with this relation.

Question 49General Engineering Science (common engineering fundamentals across disciplines)

A body of weight 100 N rests on a horizontal plane with coefficient of static friction 0.4. The minimum horizontal force needed to just start motion is:

  1. 100 N
  2. 0.4 N
  3. 40 N Correct answer.
  4. 250 N

Explanation

The limiting friction equals μ times the normal reaction, and on a horizontal plane the normal reaction equals the weight. Hence F = 0.4 × 100 = 40 N, applied horizontally.

Question 50General Engineering Science (common engineering fundamentals across disciplines)

A projectile is launched at 20 m/s at 30° to the horizontal. Taking g = 10 m/s², its horizontal range on level ground is:

  1. 10 m
  2. 40 m
  3. 34.6 m Correct answer.
  4. 20 m

Explanation

Range on level ground is R = u²sin2θ/g. With u = 20 m/s, θ = 30°, sin60° = 0.866 and g = 10 m/s², R = (400 × 0.866)/10 ≈ 34.6 m.