ECAT — Engineering College Admission Test (UET)
Take the ECAT Full-Length Mock Test 3 (100 MCQs): 100 multiple-choice questions (110 minutes) with instant scoring and a full answer review. Covers 30…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. The general solution of sin x = −1 is (n ∈ ℤ):
Answer: B. x = 2nπ − π/2
Explanation: sin x = −1 only at x = 3π/2 (equivalently −π/2) in each period of 2π, so x = 2nπ − π/2.
Q2. A bag contains 4 white and 6 black balls. Two balls are drawn at random together. The probability that both are black is:
Answer: A. 1/3
Explanation: P = ⁶C₂/¹⁰C₂ = 15/45 = 1/3.
Q3. One radian is approximately equal to:
Answer: C. 57.3°
Explanation: 1 rad = 180°/π ≈ 57.3°.
Q4. If ω is a complex cube root of unity, then ω¹⁰ + ω²⁰ equals:
Answer: A. −1
Explanation: ω³ = 1 gives ω¹⁰ = ω and ω²⁰ = ω², and ω + ω² = −1.
Q5. The correct form of the partial fractions of 1/(x²(x + 1)) is:
Answer: C. A/x + B/x² + C/(x + 1)
Explanation: The repeated factor x² needs one term for each power, A/x + B/x², plus C/(x + 1) for the linear factor.
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Q6. If the roots of x² + kx + 8 = 0 are in the ratio 1 : 2, then k equals:
Q7. The 10th term of the A.P. whose first term is −3 and common difference is 4 is:
Q8. The expression (1 − tan²θ)/(1 + tan²θ) is equal to:
Q9. A card is drawn from a well-shuffled pack of 52. The probability that it is either a red card or a face card (J, Q, K) is:
Q10. If z = 1 + i, then z²/z̄ equals:
Q11. The value of cos 20° cos 40° cos 80° is:
Q12. If tan θ = 5/12 and θ lies in the third quadrant, then sin θ equals:
Q13. If ⁿC₃ = 20, then n equals:
Q14. If A = [2 0; 0 −1], then A³ is:
Q15. The determinant of every skew-symmetric matrix of odd order is:
Q16. The line through (2, −1) and (−2, 3) is:
Q17. The perpendicular distance of the point (1, 2) from the line 4x − 3y + 12 = 0 is:
Q18. The midpoint of the segment joining (−3, 4) and (5, −2) is:
Q19. Maximise z = 4x + y subject to x + y ≤ 5, x ≤ 3, x ≥ 0, y ≥ 0. The maximum value of z is:
Q20. The angle of inclination of the line x − √3y + 1 = 0 is:
Q21. The radius of the circle x² + y² − 10x = 0 is:
Q22. The focus of the parabola x² = −4y is:
Q23. The eccentricity of the ellipse x²/169 + y²/144 = 1 is:
Q24. The asymptotes of the hyperbola x²/16 − y²/25 = 1 are:
Q25. The centre of the ellipse (x − 1)²/4 + (y + 2)²/9 = 1 is:
Q26. The circle with centre (3, −4) passing through the origin is:
Q27. The angle between a = i + j − k and b = 2i − j + k is:
Q28. If a = 2i − j and b = i + 3j, then |a + b| equals:
Q29. The volume of the rectangular box with edges 2i, 3j and 4k (the scalar triple product [2i 3j 4k]) is:
Q30. The area of the parallelogram with adjacent sides a = 2i + j and b = i + 3j is:
Q31. A proton and an α-particle enter the same uniform magnetic field at right angles with the same speed. What is the ratio of the radii of their paths (proton : α)?
Q32. A proton moves in a circle at right angles to a uniform 1 T magnetic field. How many revolutions does it make per second? (q = 1.6 × 10⁻¹⁹ C, mₚ = 1.67 × 10⁻²⁷ kg)
Q33. A galvanometer of resistance 20 Ω gives full-scale deflection at 5 mA. What resistance must be connected in series with it to make a voltmeter of range 0–10 V?
Q34. In a cathode-ray oscilloscope, the time-base voltage applied to the X-plates has the waveform of a:
Q35. A 2 m long conductor moves at 10 m/s at right angles to a uniform magnetic field of 0.05 T. What emf is induced across its ends?
Q36. The henry, the SI unit of inductance, is equivalent to:
Q37. The primary of an ideal transformer has 2200 turns and is connected to 220 V AC. How many secondary turns are needed for a 12 V output?
Q38. The peak emf of an AC generator is 100 V. What is the instantaneous emf when the plane of the rotating coil makes an angle of 30° with the magnetic field?
Q39. Which device makes use of eddy currents?
Q40. What is the reactance of an ideal inductor in a steady DC circuit?
Q41. A series circuit has a resistance of 8 Ω and an inductive reactance of 6 Ω. What is its power factor?
Q42. What is the resonant frequency of a series circuit with L = 0.4 H and C = 0.1 μF?
Q43. A capacitor of capacitance (100/π) μF is connected to a 220 V (r.m.s.), 50 Hz supply. What r.m.s. current flows?
Q44. A wire 2 m long with cross-sectional area 1 mm² stretches by 1 mm under a load of 100 N. What is its Young's modulus?
Q45. A wire stretches by 1 mm when a load gradually increased to 100 N is applied (within the elastic limit). How much strain energy is stored in it?
Q46. Below its critical temperature, a superconductor has:
Q47. The area enclosed by the hysteresis loop of a ferromagnetic material represents:
Q48. A brittle material such as glass, when stressed beyond its elastic limit:
Q49. When a ferromagnetic material such as iron is heated above its Curie temperature, it:
Q50. The potential barrier of a silicon p–n junction at room temperature is about:
Q51. When a transistor used as a switch is driven into saturation, it behaves like:
Q52. What is the energy of a photon of violet light of wavelength 400 nm? (hc = 1240 eV nm)
Q53. An electron and a proton are accelerated from rest through the same potential difference. What is the ratio of their de Broglie wavelengths (electron : proton)? (mₚ/mₑ ≈ 1836)
Q54. What is the shortest wavelength in the Balmer series of hydrogen (the series limit)? (E₁ = −13.6 eV, hc = 1240 eV nm)
Q55. According to Bohr's postulate, what is the angular momentum of the electron in the second orbit of hydrogen?
Q56. What fraction of a radioactive sample has decayed after three half-lives?
Q57. What is the function of the moderator (e.g. graphite or heavy water) in a nuclear reactor?
Q58. Energy is released when two light nuclei such as deuterium fuse because:
Q59. β⁻ particles emitted by radioactive nuclei are:
Q60. Which kind of radiation is most dangerous when its source is taken inside the body (e.g. inhaled or swallowed)?
Q61. In the complex [Fe(C₂O₄)₃]³⁻, oxalate is a bidentate ligand. The coordination number of iron is:
Q62. The correct order of carbon content in the forms of iron is:
Q63. The IUPAC name of CH₃COOCH₃ is:
Q64. Successive members of a homologous series differ by:
Q65. How many primary carbon atoms are present in 2,2-dimethylbutane?
Q66. Which species can act as a nucleophile?
Q67. Which compound contains a chiral (asymmetric) carbon atom?
Q68. Complete combustion of 0.1 mol of a hydrocarbon gives 8.8 g of CO₂ and 3.6 g of H₂O. The hydrocarbon is:
Q69. How many moles of H₂ are needed to convert 1 mol of benzene completely into cyclohexane (Ni catalyst, high temperature and pressure)?
Q70. Ethyne reacts with excess bromine to give:
Q71. A colourless gas decolourizes bromine water without the evolution of HBr. This indicates that the gas:
Q72. Bromoethane reacts with alcoholic KCN to give:
Q73. CH₃MgI reacts with water to give:
Q74. Bromoethane heated with excess alcoholic ammonia in a sealed tube gives mainly:
Q75. Ethanol (b.p. 78°C) boils much higher than its isomer dimethyl ether (b.p. −24°C) because:
Q76. Phenol reacts with dilute HNO₃ at room temperature to give a mixture of:
Q77. Formalin, used to preserve biological specimens, is:
Q78. Ethanal reacts with HCN to give a cyanohydrin, which on acid hydrolysis forms:
Q79. Propanal is oxidized by acidified K₂Cr₂O₇ to:
Q80. Which of these carboxylic acids has the lowest pKa (is the strongest acid)?
Q81. Ethanoic acid is heated with ethanol and a few drops of concentrated H₂SO₄. The sweet-smelling product is:
Q82. Ethanoic acid is converted into ethanoyl chloride by treatment with:
Q83. Which naturally occurring amino acid is optically inactive?
Q84. Reduction of a carboxylic acid with LiAlH₄ gives:
Q85. Nylon-6,6 is made by condensation polymerization of hexamethylenediamine with:
Q86. The monomer of PVC is:
Q87. Sucrose does not reduce Fehling's or Tollens' reagent because:
Q88. Biochemical oxygen demand (BOD) of a water sample is a measure of:
Q89. CO₂ and CH₄ contribute to the greenhouse effect because they:
Q90. Calcium ammonium nitrate (CAN) is preferred over pure ammonium nitrate as a fertilizer because:
Q91. Choose the word most nearly opposite in meaning to VAGUE.
Q92. Choose the word most nearly opposite in meaning to SCARCITY.
Q93. Choose the word that best completes the sentence: The doctor said the wound was only ___ and would heal within a week.
Q94. Choose the word that best completes the sentence: The new metro service has made commuting far more ___; journeys that took an hour now take twenty minutes.
Q95. In the sentence below, what does the word in capitals mean? 'The boxer was INVINCIBLE that season; no one could defeat him.'
Q96. Choose the correct passive form: The cook is preparing the dinner.
Q97. Choose the correct passive form: They will have finished the work by noon.
Q98. Choose the correct indirect (reported) speech: She said to him, "Do you like mangoes?"
Q99. Choose the correct indirect (reported) speech: He said to me, "Don't touch the wire."
Q100. Which sentence about attendance at the meeting is grammatically correct?