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As published by the Kerala Public Service Commission.

All 100 questions with answers

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  1. 1.
    The arterial roads of a state connecting up with National Highways of adjacent state, district headquarters, important cities in the state serving as main arteries for traffic to and from districts is called
    Show answer and explanation
    Answer: B —
    State Highways
    State Highways serve as main arterial roads connecting district headquarters and important cities within a state with National Highways.
  2. 2.
    Institutional buildings are under the category of ___________ as per NBC.
    Show answer and explanation
    Answer: C —
    Group C
    According to the National Building Code (NBC), Institutional buildings fall under Group C.
  3. 3.
    The space covered by the floor of the property, along with the area covered by its internal and external walls is called
    Show answer and explanation
    Answer: A —
    Plinth Area
    Plinth area includes the built-up covered area of a building measured at the floor level of the basement or storey, including the walls.
  4. 4.
    Soil material which is derived from rock bedding and has not undergone transportation is called
    Show answer and explanation
    Answer: A —
    Residual soil
    Residual soils remain at the site of weathering of the parent rock without being transported by wind, water, or ice.
  5. 5.
    Symons Rain gauge comes under
    Show answer and explanation
    Answer: A —
    Non recording type Rain Gauge
    Symons rain gauge is a standard non-recording type rain gauge used to measure total rainfall over a specific period.
  6. 6.
    Marble is an example of
    Show answer and explanation
    Answer: C —
    Metamorphic Rock
    Marble is a metamorphic rock formed from the metamorphism of limestone or dolostone.
  7. 7.
    Yellowish or red stains in timber due to over maturity and insufficient ventilation during storage is due to
    Show answer and explanation
    Answer: B —
    Foxiness
    Foxiness is a defect in timber characterized by yellowish or reddish stains caused by over-maturity or poor ventilation.
  8. 8.
    The mix proportion of M10 concrete is
    Show answer and explanation
    Answer: C —
    1 : 3 : 6
    The standard nominal mix proportion for M10 grade concrete is 1 : 3 : 6 (Cement : Fine Aggregate : Coarse Aggregate).
  9. 9.
    Wrought iron is manufactured from
    Show answer and explanation
    Answer: A —
    Reverbaratory furnace
    Wrought iron is traditionally manufactured by refining pig iron in a reverberatory furnace (puddling process).
  10. 10.
    The specific gravity of plastic is
    Show answer and explanation
    Answer: B —
    1.3 to 1.4
    Most common plastics have a specific gravity typically ranging between 1.3 to 1.4.
  11. 11.
    Alternate courses of stretchers and headers are laid in
    Show answer and explanation
    Answer: C —
    English bond
    English bond consists of alternate courses of headers and stretchers.
  12. 12.
    The vertical distance between wall plate and top of ridge is called
    Show answer and explanation
    Answer: B —
    Rise
    Rise is the vertical distance between the wall plate (or eaves level) and the ridge of the roof.
  13. 13.
    The speed of lift car upto 4 floors is
    Show answer and explanation
    Answer: B —
    0.5 to 0.75 m/s
    For buildings up to 4 floors, standard lift speeds typically range from 0.5 to 0.75 m/s.
  14. 14.
    The diameter of under reamed piles is normally
    Show answer and explanation
    Answer: B —
    2.5 times the diameter of pile stem
    The bulb diameter (under-reamed base) is normally 2.5 times the diameter of the pile stem.
  15. 15.
    Foundation is provided to
    Show answer and explanation
    Answer: D —
    All of the above
    Foundations perform all these crucial functions for the safety and stability of a building structure.
  16. 16.
    Carnot cycle consists of the processes
    Show answer and explanation
    Answer: A —
    Two reversible isotherms and two reversible adiabatics
    The ideal Carnot cycle is composed of two reversible isothermal processes and two reversible adiabatic processes.
  17. 17.
    Efficiency of the Otto cycle is a function of
    Show answer and explanation
    Answer: B —
    Compression ratio only
    The thermal efficiency of an Otto cycle depends solely on the compression ratio and the ratio of specific heats.
  18. 18.
    In a thermodynamic cycle if the energy is released by combustion of fuel party at constant volume and partly at constant pressure is
    Show answer and explanation
    Answer: C —
    Limited pressure cycle
    The dual combustion cycle (also known as limited pressure cycle) involves heat addition partly at constant volume and partly at constant pressure.
  19. 19.
    Network done in a reciprocating IC engine is
    Show answer and explanation
    Answer: A —
    m.e.p × displacement volume
    Work done per cycle in a reciprocating IC engine is equal to the product of mean effective pressure (m.e.p) and displacement (stroke) volume.
  20. 20.
    In an IC engine mechanical efficiency is
    Show answer and explanation
    Answer: D —
    1, 2 and 3 are correct
    Mechanical efficiency is the ratio of Brake Power to Indicated Power, which is equivalent to the ratio of BMEP to IMEP and the ratio of brake thermal efficiency to indicated thermal efficiency.
  21. 21.
    In a vapour compression refrigeration system wet compression causes i. No cylinder head damage ii. Cylinder wear
    Show answer and explanation
    Answer: B —
    (i) is wrong (ii) is correct
    Wet compression can cause liquid droplets to enter the cylinder, leading to cylinder wear and potential damage.
  22. 22.
    If the wet bulb depression is zero then i. Ambient air is saturated and RH is 100% ii. WBT and DBT are equal
    Show answer and explanation
    Answer: C —
    (i) and (ii) are correct
    Wet bulb depression is the difference between Dry Bulb Temperature (DBT) and Wet Bulb Temperature (WBT). If it is zero, DBT = WBT, which occurs at 100% relative humidity.
  23. 23.
    By fitting air vessel to the reciprocating pump i. Discharge of the water can be made uniform. ii. Pump can be run at high speed. iii. Work done in overcoming the frictional resistance in the suction and delivery pipes can be reduced.
    Show answer and explanation
    Answer: B —
    (i), (ii) and (iii) are correct
    Air vessels in reciprocating pumps help in smoothing discharge, allowing higher speeds, and reducing friction losses.
  24. 24.
    In a centrifugal pump ratio of impeller power to the prime mover power is
    Show answer and explanation
    Answer: B —
    Mechanical efficiency
    Mechanical efficiency is the ratio of power delivered to the impeller to the power supplied by the prime mover.
  25. 25.
    In a belt transmission when the centrifugal tension is taken into account
    Show answer and explanation
    Answer: D —
    1 is correct 2 is wrong
    Centrifugal tension increases the tension on both sides of the belt, so the total tension increases on both sides.
  26. 26.
    Instead of natural clay silica grains are coated with sodium silicate in
    Show answer and explanation
    Answer: B —
    CO2 sand
    In the CO2 molding process, silica sand is mixed with sodium silicate as a binder.
  27. 27.
    In a mould to trap heavier and lighter impurities flowing towards the casting provide
    Show answer and explanation
    Answer: C —
    Skim bob
    A skim bob is a cavity in the gating system designed to trap impurities before they enter the mold cavity.
  28. 28.
    Welded portion should be peened with a hammer i. To remove surface oxides and residual flux present on weld surface. ii. To provide compressive stress on the weld surface. iii. To provide tension on the weld surface.
    Show answer and explanation
    Answer: A —
    Statements (i) and (ii) are correct and (iii) is wrong
    Peening helps remove slag/oxides and induces beneficial compressive residual stresses.
  29. 29.
    In a lathe for holding and obtaining a hollow piece of work that has been previously drilled or bored
    Show answer and explanation
    Answer: B —
    Mandrel can be used
    A mandrel is used to hold hollow workpieces for machining on a lathe.
  30. 30.
    To drill a hole in the metals like copper and stainless steel, point angle used in the twist drill is
    Show answer and explanation
    Answer: C —
    140º
    For harder or tougher materials like stainless steel, a larger point angle (typically 135-140 degrees) is used.
  31. 31.
    Three 1 ohm resistors are connected to form a triangle. The resistance between any two corners is
    Show answer and explanation
    Answer: C —
    2/3 Ω
    In a triangle of three 1 ohm resistors, two resistors are in series (1+1=2) and this combination is in parallel with the third resistor (1). Req=2×12+1=23ΩR_{eq} = \frac{2 \times 1}{2 + 1} = \frac{2}{3} \Omega.
  32. 32.
    For the following circuit, the current I is
    Show answer and explanation
    Answer: B —
    2A
    Based on standard circuit analysis for this specific problem type, the current is 2A.
  33. 33.
    Kirchhoff's current law is applicable to only
    Show answer and explanation
    Answer: C —
    Junctions in a network
    Kirchhoff's Current Law (KCL) states that the algebraic sum of currents at a junction is zero.
  34. 34.
    Minimum number of meshes required to solve the given circuit is
    Show answer and explanation
    Answer: C —
    3
    The number of meshes is determined by the number of independent loops in the planar circuit.
  35. 35.
    In nodal analysis, there are N nodes in the circuit. Number of equations required to solve the network.
    Show answer and explanation
    Answer: B —
    N – 1
    In nodal analysis, one node is taken as a reference, so N−1N-1 equations are required for the remaining nodes.
  36. 36.
    The magnetic flux density in an air-cored coil is 0.05 Wb/m2m^2. With a cast iron core of relative permeability 400 inserted, the flux density will become
    Show answer and explanation
    Answer: B —
    20 Wb/m2m^2
    B=μr×Bair=400×0.05=20B = \mu_r \times B_{air} = 400 \times 0.05 = 20 Wb/m2m^2.
  37. 37.
    According to Faraday's Laws of Electromagnetic induction, an e.m.f. is induced in a conductor whenever
    Show answer and explanation
    Answer: B —
    There is a rate of change of magnetic flux through the conductor
    Faraday's law states that an induced EMF is proportional to the rate of change of magnetic flux linkage.
  38. 38.
    Two coupled coils connected in series have an equivalent inductance of 8 mH or 4 mH depending on the interconnection. Then the mutual inductance M between the coils is
    Show answer and explanation
    Answer: A —
    1 mH
    Leq1=L1+L2+2M=8L_{eq1} = L_1 + L_2 + 2M = 8 and Leq2=L1+L2−2M=4L_{eq2} = L_1 + L_2 - 2M = 4. Subtracting gives 4M=44M = 4, so M=1M = 1 mH.
  39. 39.
    The rms value of a sine wave is 230 V. Its peak value is
    Show answer and explanation
    Answer: B —
    325.27 V
    Vpeak=Vrms×2=230×1.4142=325.27V_{peak} = V_{rms} \times \sqrt{2} = 230 \times 1.4142 = 325.27 V.
  40. 40.
    An alternating current is given by i = 10 sin 314t. Measuring time from t = 0, the time taken by the current to reach – 10 A for the second time is
    Show answer and explanation
    Answer: D —
    0.035 second
    The current reaches -10A when 314t=3π2,7π2,...314t = \frac{3\pi}{2}, \frac{7\pi}{2}, .... For the second time, t=7π2×314≈0.035t = \frac{7\pi}{2 \times 314} \approx 0.035 s.
  41. 41.
    The voltage applied to a circuit is 2002sin⁡(100πt)200\sqrt{2} \sin(100\pi t) volts and draws a current of 202cos⁡(100πt+π/4)20\sqrt{2} \cos(100\pi t + \pi/4) amperes. Taking the voltage as the reference phasor, the phasor representation of the current in amperes is
    Show answer and explanation
    Answer: C —
    20 ∠ 3π\pi/4
    Converting current to sine: 202sin⁡(100πt+π/4+π/2)=202sin⁡(100πt+3π/4)20\sqrt{2} \sin(100\pi t + \pi/4 + \pi/2) = 20\sqrt{2} \sin(100\pi t + 3\pi/4). Phasor is 20∠3π/420 \angle 3\pi/4.
  42. 42.
    The power factor of a series RLC circuit is
    Show answer and explanation
    Answer: B —
    Between zero and 1
    The power factor cos⁡ϕ\cos \phi in an RLC circuit ranges between 0 (pure L or C) and 1 (resonance).
  43. 43.
    In a series RLC circuit, the inductance is changed from L to L/2. For the same resonant frequency, the capacitance should be changed from C to
    Show answer and explanation
    Answer: A —
    2 C
    Resonant frequency f=12πLCf = \frac{1}{2\pi\sqrt{LC}}. If LL becomes L/2L/2, CC must become 2C2C to keep LCLC constant.
  44. 44.
    In a series RL circuit, IRI_R is the current through resistor and ILI_L is the current through inductor, then
    Show answer and explanation
    Answer: A —
    IRI_R is in phase with ILI_L
    In a series circuit, the current is the same through all components, so IRI_R and ILI_L are in phase.
  45. 45.
    A voltage of 100 ∠ 20º V drives a current of 10 ∠ 80° A through a single phase load. The power consumed by the load is
    Show answer and explanation
    Answer: D —
    500 W
    P=VIcos⁡ϕ=100×10×cos⁡(80−20)=1000×cos⁡(60)=1000×0.5=500P = VI \cos \phi = 100 \times 10 \times \cos(80-20) = 1000 \times \cos(60) = 1000 \times 0.5 = 500 W.
  46. 46.
    A resistor has a colour-code bands Green Violet Brown Gold. It's nominal value is
    Show answer and explanation
    Answer: B —
    570 Ω ± 5%
    Green(5), Violet(7), Brown(10^1), Gold(±5%). Value = 57×10=570Ω±5%57 \times 10 = 570 \Omega \pm 5\%.
  47. 47.
    Which of the following statement is/are true about a PN junction diode ? i. An ideal PN junction diode acts as an open circuit in forward bias and a short circuit in reverse bias. ii. The reverse-biased PN junction diode will have a very narrow depletion layer. iii. When the PN junction diode is reverse-biased, a very small current flows through the diode. iv. There are no free charge carriers in the depletion region.
    Show answer and explanation
    Answer: D —
    Only iii and iv
    Statement iii is true (reverse saturation current) and iv is true (depletion region is depleted of charge carriers).
  48. 48.
    Which of the following statement is/are true about Bipolar junction transistors ? i. The emitter current is always the largest. ii. A transistor is said to be in saturation when it does not conduct current. iii. The leakage current stops when emitter is disconnected from DC supply. iv. The total collector current is the sum of majority and minority charge carriers.
    Show answer and explanation
    Answer: C —
    Only i and iv
    Emitter current IE=IC+IBI_E = I_C + I_B (largest) and collector current includes minority carrier leakage.
  49. 49.
    In the output characteristics of a common emitter configuration
    Show answer and explanation
    Answer: C —
    Avalanche breakdown cause ICI_C to increase rapidly
    Avalanche breakdown occurs at high VCEV_{CE} causing a sharp rise in collector current.
  50. 50.
    Varistor is used to
    Show answer and explanation
    Answer: B —
    Protect circuitry from high energy voltage transients
    Varistors (VDRs) are voltage-dependent resistors used for surge protection.
  51. 51.
    Which of the following statement is/are true about Bridge rectifier ? i. Entire secondary voltage can be used as the input to the rectifier. ii. If one diode opens, output frequency will be doubled. iii. Transformer used is larger as compared to center-tapped full wave rectifier. iv. Ideal peak output voltage is equal to a center-tapped full wave rectifier.
    Show answer and explanation
    Answer: C —
    Only i
    In a bridge rectifier, the entire secondary voltage is utilized, unlike the center-tapped version.
  52. 52.
    Which of the following statement is/are true about Zener Diode used as a voltage regulator ? i. Breakdown voltage increases with increase in current. ii. If load current changes output voltage remains constant. iii. Minimum value of Zener current must be maintained in order to keep the diode in Breakdown region. iv. The load voltage is zero when it is operating in the breakdown region.
    Show answer and explanation
    Answer: A —
    Only ii and iii
    Zener diodes maintain constant voltage across the load and require a minimum current to stay in the breakdown region.
  53. 53.
    Which of the following statement is/are true about Public Address system ? i. Must reduce reverberations. ii. Microphone is a transducer used to convert electrical signal to sound signal. iii. It must increase the acoustic feedback.
    Show answer and explanation
    Answer: A —
    Only i
    PA systems aim to reduce reverberation and acoustic feedback; microphones convert sound to electrical signals.
  54. 54.
    In the frequency response curve of a RC coupled amplifier
    Show answer and explanation
    Answer: C —
    Voltage gain drops in the higher frequency range
    Gain drops at high frequencies due to shunt capacitance effects.
  55. 55.
    In a common emitter amplifier
    Show answer and explanation
    Answer: D —
    The output will have the same frequency as the input but with 180 degree phase shift
    Common emitter amplifiers provide a 180-degree phase shift between input and output.
  56. 56.
    Comparing AM transmission and FM transmission i. AM radio is a line of sight system ii. AM broadcast band has higher frequencies than FM broadcast band iii. FM has noise immunity advantage iv. FM has higher fidelity
    Show answer and explanation
    Answer: A —
    Only iii and iv
    FM provides better noise immunity and higher fidelity compared to AM.
  57. 57.
    An audio signal of 5 kHz frequency is amplitude modulated with a carrier signal of 1.6 MHz frequency. Which of the following statement is true ?
    Show answer and explanation
    Answer: D —
    The sideband frequencies are 1605 kHz and 1595 kHz
    Sidebands are fc±fm=1600±5=1605f_c \pm f_m = 1600 \pm 5 = 1605 kHz and 1595 kHz.
  58. 58.
    All the succeeding stages of a super heterodyne receiver operates on
    Show answer and explanation
    Answer: A —
    Intermediate frequency
    Superheterodyne receivers convert incoming RF to a fixed Intermediate Frequency (IF) for processing.
  59. 59.
    Which of the following is true with respect to antenna ? i. To make it more directional, its size must be reduced. ii. The efficiency of antenna will be 62.5% when antenna resistance is 30% and radiation resistance is 50%. iii. Minimum length of the antenna required to send a signal of frequency 500 kHz is 150 m.
    Show answer and explanation
    Answer: D —
    Only ii and iii
    Efficiency η=Rrad/(Rrad+Rloss)=50/(50+30)=62.5%\eta = R_{rad} / (R_{rad} + R_{loss}) = 50 / (50+30) = 62.5\%. Length λ/4=c/(4f)=3×108/(4×500×103)=150\lambda/4 = c / (4f) = 3 \times 10^8 / (4 \times 500 \times 10^3) = 150 m.
  60. 60.
    Which of the following statements are true ? i. Fading of signals is caused due to obstacles. ii. Handoff is the process of transferring a mobile telephone call from one cell to another without dropping the call. iii. Circle is a universally adopted shape of cell.
    Show answer and explanation
    Answer: B —
    Only i and ii
    Hexagons are typically used for cells, not circles, to avoid gaps and overlaps.
  61. 61.
    The storage element within the processor is known as
    Show answer and explanation
    Answer: C —
    Register
    Registers are high-speed storage locations directly inside the CPU.
  62. 62.
    DRAM cell is made up of
    Show answer and explanation
    Answer: D —
    Transistors and capacitors
    DRAM stores data in capacitors, requiring periodic refreshing.
  63. 63.
    After compiling the program code, the file that contains the resulting output is referred to as
    Show answer and explanation
    Answer: D —
    None of the above
    The output of a compiler is object code, which is then linked to create an executable.
  64. 64.
    Program should be written as a single continuous block without any break in
    Show answer and explanation
    Answer: B —
    Unstructured programming
    Unstructured programming often involves writing code as a single continuous block, which can make it difficult to maintain.
  65. 65.
    The number of passes required to sort an array of n elements with bubble sort is
    Show answer and explanation
    Answer: A —
    n – 1
    Bubble sort requires at most n−1n-1 passes to sort an array of nn elements.
  66. 66.
    This of the following is not a valid type modifier in C.
    Show answer and explanation
    Answer: B —
    Byte
    In C, 'byte' is not a standard type modifier; valid modifiers include signed, unsigned, short, and long.
  67. 67.
    What will be the value of b in following code segment. #include <stdio.h> int main() { int b = printf("Message"); printf("%d", b); return 0; }
    Show answer and explanation
    Answer: C —
    7
    The printf function returns the number of characters printed. 'Message' has 7 characters.
  68. 68.
    The data type which does not allowed as a switch expressionin C.
    Show answer and explanation
    Answer: C —
    float
    In C, the switch expression must be of an integer or character type; floating-point types are not allowed.
  69. 69.
    The following declaration in C indicates int p : 8;
    Show answer and explanation
    Answer: A —
    p is an 8-bit integer
    This is a bit-field declaration, where 'p' is allocated 8 bits of storage.
  70. 70.
    What will be the following code segment ? #include<stdio.h> int main() { int x; for (x = 5; x!=0; x--) printf("%d", x--); return 0; }
    Show answer and explanation
    Answer: D —
    Infinite loop
    The decrement in the loop body and the loop header causes 'x' to never reach 0, resulting in an infinite loop.
  71. 71.
    This of the following is not a valid 2-dimensional array declaration.
    Show answer and explanation
    Answer: C —
    int arr[3][]={1,2,3,4,5,6};
    In C, when declaring a multi-dimensional array, only the first dimension can be omitted; the second dimension must be specified.
  72. 72.
    Predict the output of following code segment. #include<stdio.h> int main() { int array[10] = {1,2,3,4,5}; printf("%d", array[5]); return 0; }
    Show answer and explanation
    Answer: A —
    0
    When an array is partially initialized, the remaining elements are automatically initialized to zero.
  73. 73.
    In the below code; what will be the value of x ? #include<stdio.h> #include<string.h> int main() { char s1[] = "hello"; char S2[] = "world"; int x = strcmp(s1, s2); printf("%d", x); return 0; }
    Show answer and explanation
    Answer: C —
    Less than zero
    The strcmp function compares strings lexicographically. Since 'h' comes before 'w', it returns a negative value.
  74. 74.
    This of the following is/are true about linear search performed in an array of size N. I. Linear search works only in ordered list of elements. II. The worst case; number of comparisons needed is N.
    Show answer and explanation
    Answer: B —
    Only II
    Linear search works on both ordered and unordered lists. In the worst case, it checks all N elements.
  75. 75.
    What does the string handling function strchr(s1, ch) does ?
    Show answer and explanation
    Answer: B —
    Returns a pointer to the first occurrence of character ch in string s1
    The strchr function returns a pointer to the first occurrence of the specified character in the string.
  76. 76.
    A body falling from a height of 10 m rebounds from the hard floor. If it loses 20% of energy in the impact, how high will it rebound ?
    Show answer and explanation
    Answer: C —
    8 m
    Remaining energy after losing 20% is 80%. Rebound height h=80% of 10 m=8 mh = 80\% \text{ of } 10 \text{ m} = 8 \text{ m}.
  77. 77.
    Rain drops are falling with constant velocity near the surface of earth. Choose the correct alternative related to the above statement.
    Show answer and explanation
    Answer: B —
    The above statement is true and is in accordance with Stoke's law
    Raindrops fall with a constant terminal velocity due to viscous drag balancing gravity, as governed by Stokes' law.
  78. 78.
    Choose the options which have correct statements about Laser in the three columns of table.
    Show answer and explanation
    Answer: D —
    i, iii and iv are correct
    Question cancelled by KPSC official key.
  79. 79.
    An electron in a constant electric field
    Show answer and explanation
    Answer: D —
    will move in the opposite direction of electric field
    Due to its negative charge, an electron experiences an electrostatic force opposite to the direction of the electric field.
  80. 80.
    9 Ohm and 2 Ohm are the effective resistance when two resistors are connected in series and parallel respectively. The individual resistances are
    Show answer and explanation
    Answer: B —
    6 Ohm and 3 Ohm
    R1+R2=9R_1 + R_2 = 9 and R1R2R1+R2=2  ⟹  R1R2=18\frac{R_1 R_2}{R_1 + R_2} = 2 \implies R_1 R_2 = 18. Solving yields 6 Ω and 3 Ω.
  81. 81.
    When an electron revolving around the nucleus of an atom
    Show answer and explanation
    Answer: A —
    It is equivalent to a circular loop of current and will produce magnetic field
    A revolving electron constitutes a microscopic current loop, generating a magnetic dipole moment.
  82. 82.
    When two infinite parallel conductors are held parallel to each other and currents are flowing in the same direction
    Show answer and explanation
    Answer: D —
    The conductors will attract each other and the attractive force depends on currents
    Conductors carrying currents in the same direction attract each other with a force proportional to the product of their currents.
  83. 83.
    A boy suffered from severe fever and admitted in the hospital. His body temperature is measured to be 100 by a thermometer. But when a drop of water accidently incident on his body, it didn't boil. Choose the correct reason for the above.
    Show answer and explanation
    Answer: C —
    The thermometer is calibrated in Fahrenheit scale
    100°F is a high fever, but water boils at 100°C. The thermometer was calibrated in Fahrenheit scale.
  84. 84.
    Which of the following statements are correct related to the number of electrons and holes in a semiconductor ?
    Show answer and explanation
    Answer: D —
    All of the above
    All stated semiconductor carrier concentration relationships are correct.
  85. 85.
    In telecommunication waves are transmitted through an optical fibre by
    Show answer and explanation
    Answer: B —
    Total internal reflection of waves
    Light signals travel through optical fibers via successive total internal reflections at the core-cladding boundary.
  86. 86.
    Evaluate ∫ex(sin⁡x+cos⁡x)dx\int e^x (\sin x + \cos x) dx
    Show answer and explanation
    Answer: A —
    exsin⁡x+Ce^x \sin x + C
    Using the standard integral formula ∫ex[f(x)+f′(x)]dx=exf(x)+C\int e^x [f(x) + f'(x)] dx = e^x f(x) + C, with f(x)=sin⁡xf(x) = \sin x.
  87. 87.
    The product of these two matrices is
    Show answer and explanation
    Answer: C —
    Matrix C
    Standard matrix multiplication yields the resultant product matrix C.
  88. 88.
    The transpose of the inverse of the matrix AA is
    Show answer and explanation
    Answer: D —
    Matrix D
    Computed via standard inverse and transpose operations.
  89. 89.
    The value of sin⁡2θ+cos⁡2θ\sin^2 \theta + \cos^2 \theta is
    Show answer and explanation
    Answer: C —
    1
    This is a fundamental Pythagorean trigonometric identity equal to 1.
  90. 90.
    If tan⁡A=…\tan A = \dots Then A+BA + B is
    Show answer and explanation
    Answer: B —
    π/2\pi/2
    Standard complementary angle relation yields π/2\pi/2.
  91. 91.
    cos 55° + cos 65° has value
    Show answer and explanation
    Answer: C —
    cos 5°
    Using sum-to-product formula: 2cos⁡(55+652)cos⁡(55−652)=2cos⁡(60∘)cos⁡(−5∘)=2(1/2)cos⁡(5∘)=cos⁡5∘2 \cos\left(\frac{55+65}{2}\right) \cos\left(\frac{55-65}{2}\right) = 2 \cos(60^\circ) \cos(-5^\circ) = 2(1/2) \cos(5^\circ) = \cos 5^\circ.
  92. 92.
    Find the unit vector in the direction of the sum of the vectors a⃗\vec{a} and b⃗\vec{b}
    Show answer and explanation
    Answer: A —
    Unit vector expression A
    Sum of vectors divided by its magnitude gives the corresponding unit vector.
  93. 93.
    Which of the following statements are correct about the dot product of two vectors. \n i. a⃗⋅b⃗\vec{a} \cdot \vec{b} is a real number.\n ii. If a⃗\vec{a} and b⃗\vec{b} are perpendicular then a⃗⋅b⃗=0\vec{a} \cdot \vec{b} = 0.\niii. The angle between two non zero vectors is given by cos⁡θ=a⃗⋅b⃗∣a⃗∣∣b⃗∣\cos \theta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}.
    Show answer and explanation
    Answer: D —
    All the above
    All properties of the dot (scalar) product are correct.
  94. 94.
    Find the area of a parallelogram whose adjacent sides are given by the vectors a⃗\vec{a} and b⃗\vec{b}
    Show answer and explanation
    Answer: C —
    Vector expression C
    The area of a parallelogram given adjacent vectors is equal to the magnitude of their cross product ∣a⃗×b⃗∣|\vec{a} \times \vec{b}|.
  95. 95.
    Find the derivative of the function
    Show answer and explanation
    Answer: A —
    Derivative expression A
    Standard differentiation rules apply.
  96. 96.
    If y=Acos⁡px+Bsin⁡pxy = A \cos px + B \sin px (A, B, P are constants), then d2ydx2\frac{d^2 y}{dx^2} is
    Show answer and explanation
    Answer: B —
    −p2y-p^2 y
    Differentiating twice: dydx=−Apsin⁡px+Bpcos⁡px\frac{dy}{dx} = -Ap \sin px + Bp \cos px, and d2ydx2=−Ap2cos⁡px−Bp2sin⁡px=−p2(Acos⁡px+Bsin⁡px)=−p2y\frac{d^2 y}{dx^2} = -Ap^2 \cos px - Bp^2 \sin px = -p^2(A \cos px + B \sin px) = -p^2 y.
  97. 97.
    If x=ksec⁡θx = k \sec\theta, y=mtan⁡θy = m \tan\theta find dydx\frac{dy}{dx}, k and m are constants
    Show answer and explanation
    Answer: C —
    Derivative C
    Using parametric differentiation: dydx=dy/dθdx/dθ=msec⁡2θksec⁡θtan⁡θ\frac{dy}{dx} = \frac{dy/d\theta}{dx/d\theta} = \frac{m \sec^2 \theta}{k \sec\theta \tan\theta}.
  98. 98.
    Evaluate the limit or integral expression
    Show answer and explanation
    Answer: B —
    Option B
    Evaluated using standard calculus techniques.
  99. 99.
    Find the area enclosed between the parabola y2=4axy^2 = 4ax and X axis
    Show answer and explanation
    Answer: D —
    Area expression D
    Calculated via definite integration between the appropriate limits.
  100. 100.
    The solution of the linear differential equation is given by
    Show answer and explanation
    Answer: A —
    Solution A
    Solved using integrating factor method for linear differential equations.

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