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ESE ECE Prelims practice questions

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Question 1General Studies and Engineering Aptitude (Paper I)

Under the Indian Constitution, which article guarantees the right to move the Supreme Court directly for enforcement of Fundamental Rights?

  1. Article 32 Correct answer.
  2. Article 143
  3. Article 226
  4. Article 136

Explanation

Article 32 confers the right to constitutional remedies, allowing a person to petition the Supreme Court directly when a Fundamental Right is violated. Dr. Ambedkar described it as the heart and soul of the Constitution because it makes the other rights enforceable.

Question 2General Studies and Engineering Aptitude (Paper I)

The Fundamental Duties of citizens were inserted into the Constitution of India by which amendment?

  1. 73rd Amendment, 1992
  2. 44th Amendment, 1978
  3. 52nd Amendment, 1985
  4. 42nd Amendment, 1976 Correct answer.

Explanation

The 42nd Amendment Act, 1976, added Part IVA (Article 51A) listing Fundamental Duties, following the recommendation of the Swaran Singh Committee. They are non-justiciable moral obligations that guide citizens' conduct.

Question 3General Studies and Engineering Aptitude (Paper I)

A body is thrown vertically upward with an initial speed of 20 m/s. Taking g = 10 m/s² and ignoring air resistance, the maximum height reached is:

  1. 20 m Correct answer.
  2. 40 m
  3. 5 m
  4. 10 m

Explanation

At maximum height the velocity becomes zero, so using v² = u² − 2gh gives 0 = 400 − 20h, hence h = 20 m. The result depends only on initial speed and g, not on the mass of the body.

Question 4General Studies and Engineering Aptitude (Paper I)

The SI unit of electrical conductance is the:

  1. farad
  2. siemens Correct answer.
  3. ohm
  4. henry

Explanation

Conductance is the reciprocal of resistance, so its SI unit is the reciprocal of the ohm, called the siemens. It measures how easily current flows through a component.

Question 5General Studies and Engineering Aptitude (Paper I)

Which of the following is a primary air pollutant rather than a secondary one?

  1. Sulphur dioxide Correct answer.
  2. Nitric acid vapour
  3. Peroxyacetyl nitrate
  4. Ozone at ground level

Explanation

Primary pollutants are emitted directly from a source, and sulphur dioxide from burning fossil fuels is a classic example. Secondary pollutants form in the atmosphere through chemical reactions among primary pollutants.

Question 6General Studies and Engineering Aptitude (Paper I)

The value of the expression 15% of 240 + 0.4 × 50 is:

  1. 36
  2. 66
  3. 46
  4. 56 Correct answer.

Explanation

Fifteen percent of 240 equals 36, and 0.4 × 50 equals 20. Adding the two parts gives 36 + 20 = 56, applying standard order of operations.

Question 7General Studies and Engineering Aptitude (Paper I)

Which gas is chiefly responsible for the greenhouse effect through its highest concentration-based contribution among the long-lived gases?

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

Explanation

Carbon dioxide is the principal long-lived greenhouse gas emitted by human activity and absorbs infrared radiation in key wavelength bands. Nitrogen and noble gases are essentially transparent to outgoing infrared radiation.

Question 8General Studies and Engineering Aptitude (Paper I)

In a standard IEEE 754 single-precision floating-point number, the number of bits allotted to the exponent is:

  1. 8 Correct answer.
  2. 32
  3. 23
  4. 11

Explanation

Single precision uses 1 sign bit, 8 exponent bits, and 23 fraction bits, totalling 32 bits. Double precision instead uses 11 exponent bits and 52 fraction bits.

Question 9General Studies and Engineering Aptitude (Paper I)

A sum of money doubles itself in 8 years under simple interest. In how many years will it become four times the original sum?

  1. 32 years
  2. 12 years
  3. 24 years Correct answer.
  4. 16 years

Explanation

Doubling under simple interest means the interest equals the principal in 8 years, giving a rate of 12.5% per annum. To become four times, the interest must equal three times the principal, requiring 3 × 8 = 24 years.

Question 10General Studies and Engineering Aptitude (Paper I)

A bag contains 5 red and 7 blue balls. Two balls are drawn at random without replacement. The probability that both are red is:

  1. 5/33 Correct answer.
  2. 5/12
  3. 10/144
  4. 25/144

Explanation

The probability of the first red ball is 5/12 and the second is 4/11, since one red ball is removed. Multiplying gives 20/132, which simplifies to 5/33.

Question 11General Studies and Engineering Aptitude (Paper I)

In an NPN bipolar junction transistor operating in the active region, the base-emitter junction and base-collector junction are respectively:

  1. Forward biased and reverse biased Correct answer.
  2. Both forward biased
  3. Reverse biased and forward biased
  4. Both reverse biased

Explanation

Active-region operation of an NPN transistor requires the base-emitter junction to be forward biased for carrier injection and the base-collector junction reverse biased to collect carriers. This configuration supports transistor action and current gain.

Question 12General Studies and Engineering Aptitude (Paper I)

The Nyquist sampling theorem states that a band-limited signal with maximum frequency fm must be sampled at a rate:

  1. At most fm
  2. At least fm/2
  3. Exactly fm
  4. At least 2fm Correct answer.

Explanation

To avoid aliasing, the sampling frequency must be at least twice the highest frequency present in the signal. Sampling below this rate causes spectral overlap and irreversible distortion.

Question 13General Studies and Engineering Aptitude (Paper I)

Which organisation publishes the Indian Standard codes for plain and reinforced concrete design, including IS 456?

  1. Indian Roads Congress
  2. National Building Construction Corporation
  3. Bureau of Indian Standards Correct answer.
  4. Central Public Works Department

Explanation

The Bureau of Indian Standards is the national standards body that formulates and issues IS codes such as IS 456 for concrete design. Other bodies issue their own specifications but do not publish the IS series.

Question 14General Studies and Engineering Aptitude (Paper I)

In a simply supported beam of span L carrying a central point load W, the maximum bending moment is:

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

Explanation

For a simply supported beam with a central point load, each reaction is W/2 and the maximum moment occurs at midspan. The value is (W/2)(L/2) = WL/4.

Question 15General Studies and Engineering Aptitude (Paper I)

The process of annealing in metallurgy is primarily carried out to:

  1. Improve electrical conductivity of the metal
  2. Relieve internal stresses and improve ductility Correct answer.
  3. Increase carbon content of the surface
  4. Increase hardness by rapid cooling

Explanation

Annealing involves controlled heating and slow cooling to soften the metal, relieve internal stresses, and improve machinability and ductility. Rapid cooling would instead produce hardening, as in quenching.

Question 16General Studies and Engineering Aptitude (Paper I)

Which of the following best describes a primary cell in the context of electrical sources?

  1. A cell that converts light directly to current
  2. A cell that can be recharged by reversing the current
  3. A cell that stores charge electrostatically
  4. A cell whose chemical reaction is irreversible and cannot be recharged Correct answer.

Explanation

In a primary cell the electrochemical reaction is not readily reversible, so the cell cannot be recharged and is discarded after use. Secondary cells, by contrast, can be recharged because their reactions are reversible.

Question 17General Studies and Engineering Aptitude (Paper I)

The time complexity of binary search on a sorted array of n elements is:

  1. O(log n) Correct answer.
  2. O(1)
  3. O(n log n)
  4. O(n)

Explanation

Binary search halves the search interval at each step, so the number of comparisons grows logarithmically with n. This logarithmic behaviour requires the array to be sorted beforehand.

Question 18General Studies and Engineering Aptitude (Paper I)

The Directive Principles of State Policy in the Indian Constitution are inspired chiefly by which model?

  1. The Irish Constitution Correct answer.
  2. The Australian Constitution
  3. The Canadian Constitution
  4. The Swiss Constitution

Explanation

The Directive Principles were borrowed largely from the Irish Constitution, which itself drew on the Spanish Constitution. They are non-justiciable guidelines aimed at social and economic democracy.

Question 19General Studies and Engineering Aptitude (Paper I)

A 3-phase, 400 V, 50 Hz induction motor has a synchronous speed of 1500 rpm and runs at 1440 rpm at full load. The percentage slip is:

  1. 10%
  2. 4% Correct answer.
  3. 6%
  4. 2.5%

Explanation

Slip is the difference between synchronous and actual speed divided by synchronous speed. Here (1500 − 1440)/1500 = 0.04, which is 4%.

Question 20General Studies and Engineering Aptitude (Paper I)

Which of the following is the correct order of increasing hardness on the Mohs scale?

  1. Gypsum, talc, quartz, calcite
  2. Calcite, quartz, talc, gypsum
  3. Talc, gypsum, calcite, quartz Correct answer.
  4. Quartz, calcite, gypsum, talc

Explanation

The Mohs scale ranks minerals from talc at hardness 1 through gypsum at 2, calcite at 3, and quartz at 7. The order talc, gypsum, calcite, quartz therefore reflects increasing hardness correctly.

Question 21General Studies and Engineering Aptitude (Paper I)

In a parallel RLC circuit at resonance, which statement about impedance is correct?

  1. Impedance is minimum and equals R
  2. Impedance is maximum and equals the dynamic resistance Correct answer.
  3. Impedance equals the reactance of the inductor
  4. Impedance is zero

Explanation

At resonance in a parallel RLC circuit, the inductive and capacitive susceptances cancel, leaving only the resistive path and giving maximum impedance. This behaviour contrasts with series resonance, where impedance is minimum.

Question 22General Studies and Engineering Aptitude (Paper I)

A signal x(t) has a Fourier transform X(f) that is zero for |f| > 5 kHz. If x(t) is sampled at 8 kHz, the resulting effect is:

  1. Aliasing because the sampling rate is below 10 kHz Correct answer.
  2. Perfect reconstruction with no error
  3. No effect because the signal is band-limited
  4. Only amplitude scaling of the spectrum

Explanation

The Nyquist rate for this signal is 2 × 5 kHz = 10 kHz, so sampling at 8 kHz falls below the required rate. Spectral replicas then overlap, causing aliasing that cannot be removed by ideal filtering.

Question 23General Studies and Engineering Aptitude (Paper I)

In reinforced concrete design, the term 'balanced section' refers to a section in which:

  1. Steel yields long before concrete crushes
  2. Concrete reaches its limiting strain simultaneously with steel reaching its yield strain Correct answer.
  3. Concrete crushes before steel yields
  4. Neither material reaches its limiting strain

Explanation

A balanced section is one where the tensile steel reaches its yield strain at the same load at which the extreme concrete fibre reaches its limiting compressive strain. This condition defines the limiting percentage of steel for a given grade combination.

Question 24General Studies and Engineering Aptitude (Paper I)

A Carnot engine operates between reservoirs at 600 K and 300 K. If it absorbs 1200 kJ from the hot reservoir, the work output is:

  1. 600 kJ Correct answer.
  2. 300 kJ
  3. 800 kJ
  4. 400 kJ

Explanation

Carnot efficiency is 1 − Tc/Th = 1 − 300/600 = 0.5. Multiplying by the heat absorbed, 0.5 × 1200 kJ gives 600 kJ of work.

Question 25General Studies and Engineering Aptitude (Paper I)

In a CMOS inverter, the principal reason for the brief flow of short-circuit current during switching is that:

  1. The threshold voltages of both transistors are zero
  2. The supply voltage exceeds the breakdown rating
  3. Both the NMOS and PMOS transistors conduct simultaneously during the input transition Correct answer.
  4. The output load capacitance discharges through the substrate

Explanation

During an input transition, there is an interval when the input voltage lies between the thresholds of the NMOS and PMOS devices, so both conduct. This creates a direct path from supply to ground, causing short-circuit power dissipation that grows with switching frequency.

Question 26General Studies and Engineering Aptitude (Paper I)

In the context of the Indian Constitution, the term 'basic structure doctrine' was articulated by the Supreme Court in which case?

  1. Golaknath v. State of Punjab
  2. Minerva Mills Ltd. v. Union of India
  3. Kesavananda Bharati v. State of Kerala Correct answer.
  4. Indira Nehru Gandhi v. Raj Narain

Explanation

The basic structure doctrine was laid down in Kesavananda Bharati (1973), where a thirteen-judge bench held that Parliament's amending power under Article 368 cannot destroy the Constitution's essential features. This established a judicially enforceable limit on constitutional amendments.

Question 27General Studies and Engineering Aptitude (Paper I)

A body starts from rest and moves with uniform acceleration. The ratio of the distance covered in the first 2 seconds to that covered in the first 4 seconds is:

  1. 1:2
  2. 1:16
  3. 1:4 Correct answer.
  4. 1:8

Explanation

For motion from rest under uniform acceleration, distance is proportional to the square of elapsed time since s = ½at². Hence the ratio is (2²):(4²) = 4:16 = 1:4.

Question 28General Studies and Engineering Aptitude (Paper I)

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

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

Explanation

Conductance is the reciprocal of resistance, and its SI unit is the siemens (symbol S), formerly called the mho. One siemens equals one ampere per volt.

Question 29General Studies and Engineering Aptitude (Paper I)

The value of log₁₀ 1000 + log₂ 32 is:

  1. 7
  2. 8 Correct answer.
  3. 9
  4. 6

Explanation

log₁₀ 1000 = 3 because 10³ = 1000, and log₂ 32 = 5 because 2⁵ = 32. Their sum is 8.

Question 30General Studies and Engineering Aptitude (Paper I)

Which data structure is most appropriate for implementing the undo feature of a text editor?

  1. Hash table
  2. Queue
  3. Stack Correct answer.
  4. Binary search tree

Explanation

Undo operations require the most recent action to be reversed first, which is last-in-first-out behaviour. A stack supports LIFO access in constant time, making it ideal for this purpose.

Question 31General Studies and Engineering Aptitude (Paper I)

In a transformer, the core is laminated primarily to reduce which loss?

  1. Hysteresis loss
  2. Stray load loss
  3. Eddy current loss Correct answer.
  4. Copper loss

Explanation

Laminating the core increases the resistance of the eddy current paths, reducing the magnitude of circulating currents and hence the eddy current loss. Hysteresis loss depends on the core material's magnetic properties, not on lamination.

Question 32General Studies and Engineering Aptitude (Paper I)

The chemical formula of ordinary Portland cement's most abundant hydraulic compound, tricalcium silicate, is:

  1. 3CaO·Al₂O₃
  2. 3CaO·SiO₂ Correct answer.
  3. 2CaO·SiO₂
  4. 4CaO·Al₂O₃·Fe₂O₃

Explanation

Tricalcium silicate is written as 3CaO·SiO₂, abbreviated C₃S, and it is the major compound responsible for early strength development in cement. It typically constitutes roughly half of the clinker by mass.

Question 33General Studies and Engineering Aptitude (Paper I)

In a first-order system with time constant τ, the steady-state error to a unit step input under unity negative feedback is:

  1. Infinite
  2. 1
  3. 0.5
  4. Zero Correct answer.

Explanation

A first-order system of the form K/(τs+1) is a type-0 system with finite non-zero gain, so it tracks a step input with zero steady-state error. The final value theorem confirms that the error tends to 1/(1+K) only if the loop gain is finite; with the standard unity-gain closed-loop form the error is zero.

Question 34General Studies and Engineering Aptitude (Paper I)

Which of the following is the primary greenhouse gas emitted during the anaerobic decomposition of organic matter in landfills?

  1. Nitrous oxide
  2. Methane Correct answer.
  3. Sulphur hexafluoride
  4. Carbon dioxide

Explanation

Anaerobic decomposition of biodegradable waste in landfills produces methane (CH₄) as the principal product, along with carbon dioxide. Methane has a much higher global warming potential than carbon dioxide over a twenty-year horizon.

Question 35General Studies and Engineering Aptitude (Paper I)

A simply supported rectangular beam of width 230 mm and effective depth 450 mm carries a factored shear force of 100 kN. The nominal shear stress is approximately:

  1. 0.97 N/mm² Correct answer.
  2. 1.45 N/mm²
  3. 0.48 N/mm²
  4. 1.93 N/mm²

Explanation

Nominal shear stress τv equals Vu divided by b·d, so 100000/(230×450) equals about 0.966 N/mm². This is the value compared with τc to decide whether shear reinforcement is required.

Question 36General Studies and Engineering Aptitude (Paper I)

In a JK flip-flop, when both J and K inputs are held HIGH and the clock is applied, the output:

  1. Resets to 0
  2. Sets to 1
  3. Toggles on each clock edge Correct answer.
  4. Remains unchanged

Explanation

With J = K = 1, the JK flip-flop operates in toggle mode, so the output complements itself at every active clock edge. This behaviour is used to build ripple and synchronous counters.

Question 37General Studies and Engineering Aptitude (Paper I)

The Laplace transform of the unit impulse function δ(t) is:

  1. 1 Correct answer.
  2. 1/s²
  3. s
  4. 1/s

Explanation

The unit impulse has unit area concentrated at t = 0, so its Laplace transform evaluates to 1 for all s. This makes the impulse response the inverse transform of the system transfer function.

Question 38General Studies and Engineering Aptitude (Paper I)

Which of the following best describes the role of a commutator in a DC machine?

  1. It converts alternating armature current into direct current in the external circuit Correct answer.
  2. It regulates the field current automatically
  3. It reduces the eddy current loss in the field poles
  4. It provides mechanical support to the armature winding

Explanation

The commutator, together with the brushes, acts as a mechanical rectifier in a generator and as an inverter in a motor, reversing the connections so that the external circuit sees direct current. This is essential for unidirectional torque production.

Question 39General Studies and Engineering Aptitude (Paper I)

The oxidation state of chromium in potassium dichromate, K₂Cr₂O₇, is:

  1. +2
  2. +7
  3. +3
  4. +6 Correct answer.

Explanation

Let the oxidation state of chromium be x. With two potassium ions at +1 each and seven oxygen atoms at −2 each, the equation 2(+1) + 2x + 7(−2) = 0 gives 2x = 12, so x = +6.

Question 40General Studies and Engineering Aptitude (Paper I)

In a class B push-pull amplifier, the maximum theoretical collector efficiency is:

  1. 25%
  2. 78.5% Correct answer.
  3. 100%
  4. 50%

Explanation

Class B operation conducts for half of each cycle, and the maximum theoretical efficiency is π/4, approximately 78.5%. This is higher than the 50% limit of a class A amplifier.

Question 41General Studies and Engineering Aptitude (Paper I)

The minimum number of NAND gates required to implement a two-input XOR function is:

  1. 6
  2. 4 Correct answer.
  3. 5
  4. 3

Explanation

A two-input XOR can be built from four NAND gates: two to generate the complemented products and two to combine them. This is the standard minimal NAND-only realisation.

Question 42General Studies and Engineering Aptitude (Paper I)

The 'Preamble' of the Indian Constitution declares India to be a:

  1. Sovereign, democratic, federal, secular monarchy
  2. Sovereign, socialist, theocratic, democratic republic
  3. Sovereign, socialist, secular, democratic republic Correct answer.
  4. Sovereign, capitalist, secular, democratic republic

Explanation

The Preamble, as amended by the 42nd Amendment, describes India as a sovereign, socialist, secular, democratic republic. It also commits to justice, liberty, equality and fraternity.

Question 43General Studies and Engineering Aptitude (Paper I)

A 3-phase, 50 Hz, 4-pole induction motor has a full-load slip of 4%. The rotor speed is:

  1. 1200 rpm
  2. 1440 rpm Correct answer.
  3. 1380 rpm
  4. 1500 rpm

Explanation

Synchronous speed is 120f/P = 120×50/4 = 1500 rpm. Rotor speed equals Ns(1 − s) = 1500 × 0.96 = 1440 rpm.

Question 44General Studies and Engineering Aptitude (Paper I)

The process of galvanising steel involves coating it with:

  1. Chromium
  2. Tin
  3. Zinc Correct answer.
  4. Nickel

Explanation

Galvanising deposits a zinc coating on steel, which protects it both as a barrier and by sacrificial cathodic protection because zinc is more anodic than iron.

Question 45General Studies and Engineering Aptitude (Paper I)

In a series RLC circuit, the circuit behaves as purely resistive at resonance because:

  1. Inductance becomes zero
  2. Capacitance becomes infinite
  3. Resistance becomes zero
  4. Inductive and capacitive reactances cancel each other Correct answer.

Explanation

At resonance the inductive reactance jωL and capacitive reactance 1/(jωC) are equal in magnitude and opposite in phase, so they cancel and the impedance reduces to R. The current is then in phase with the supply voltage.

Question 46General Studies and Engineering Aptitude (Paper I)

A 2-bit comparator compares two 2-bit numbers A and B. Which Boolean expression represents the condition A > B when A = A₁A₀ and B = B₁B₀?

  1. A₁'B₁ + (A₁ ⊕ B₁)'A₀'B₀
  2. A₁B₁' + (A₁ ⊕ B₁)'A₀B₀' Correct answer.
  3. A₁B₁' + (A₁ ⊕ B₁)A₀B₀'
  4. A₁B₁ + (A₁ ⊕ B₁)'A₀B₀

Explanation

A is greater than B if the most significant bit of A is 1 while that of B is 0, or if the MSBs are equal and A₀ exceeds B₀. The expression A₁B₁' + (A₁ ⊕ B₁)'A₀B₀' captures exactly these two cases.

Question 47General Studies and Engineering Aptitude (Paper I)

A discrete memoryless source emits four symbols with probabilities 1/2, 1/4, 1/8 and 1/8. The entropy of the source in bits per symbol is:

  1. 1.75 Correct answer.
  2. 1.50
  3. 2.25
  4. 2.00

Explanation

Entropy equals −Σp log₂p, so (1/2)(1) + (1/4)(2) + (1/8)(3) + (1/8)(3) = 0.5 + 0.5 + 0.375 + 0.375 = 1.75 bits per symbol. This is below the maximum of 2 bits for four equiprobable symbols.

Question 48General Studies and Engineering Aptitude (Paper I)

In a common-emitter amplifier, the Miller effect causes the effective input capacitance to increase because:

  1. The emitter bypass capacitor is reflected to the input
  2. The load resistance is reflected to the input
  3. The base-collector capacitance is multiplied by the voltage gain Correct answer.
  4. The base-emitter capacitance is multiplied by the current gain

Explanation

The collector voltage is an inverted, amplified version of the base voltage, so the voltage across the base-collector capacitance is (1 + |Av|) times the input voltage. This makes the effective input capacitance Cbc(1 + |Av|), which is the Miller effect.

Question 49General Studies and Engineering Aptitude (Paper I)

A control system has the open-loop transfer function G(s)H(s) = K/[s(s+2)(s+4)]. Using the Routh-Hurwitz criterion, the range of K for closed-loop stability is:

  1. K > 48
  2. 0 < K < 24
  3. 0 < K < 12
  4. 0 < K < 48 Correct answer.

Explanation

The characteristic equation is s³ + 6s² + 8s + K = 0. The Routh array requires all first-column terms positive, giving K > 0 and K < 48 from the row (48 − K)/6, so the stable range is 0 < K < 48.

Question 50General Studies and Engineering Aptitude (Paper I)

A simply supported beam of rectangular cross-section is subjected to pure bending. If the depth is doubled while the width and bending moment are kept constant, the maximum bending stress becomes:

  1. Twice the original
  2. One-fourth of the original Correct answer.
  3. Four times the original
  4. One-half of the original

Explanation

Bending stress equals My/I, and for a rectangle I = bd³/12, so stress is proportional to 1/d² for constant moment and width. Doubling the depth reduces the maximum stress to one-quarter.