LPUNEST 2027 Sample Paper B.Tech

ADMISSION
LPUNEST B.Tech Sample Paper 2027
LPUNEST 2027 · B.Tech · Physics, Chemistry, Mathematics, English · Practice Paper

Questions Marks Time Negative marking
100 (25 per subject) 400 (4 each) 150 minutes None

Part Section Questions Q. No.
Part I: Physics Physics – MCQ (one correct option) 16 1 to 16
Part I: Physics Physics – MSQ (one or more correct options) 4 17 to 20
Part I: Physics Physics – Fill in the blanks (numerical answer) 5 21 to 25
Part II: Chemistry Chemistry – MCQ (one correct option) 16 26 to 41

Part II: Chemistry Chemistry – MSQ (one or more correct options) 4 42 to 45
Part II: Chemistry Chemistry – Fill in the blanks (numerical answer) 5 46 to 50
Part III: Mathematics Mathematics – MCQ (one correct option) 16 51 to 66
Part III: Mathematics Mathematics – MSQ (one or more correct options) 4 67 to 70
Part III: Mathematics Mathematics – Fill in the blanks (numerical answer) 5 71 to 75
Part IV: English English – MCQ (one correct option) 20 76 to 95

Part IV: English English – MSQ (one or more correct options) 5 96 to 100

Instructions
1. This paper has 100 questions in four subjects: Physics (Q1–25), Chemistry (Q26–50), Mathematics (Q51–75) and
English (Q76–100).
2. Each question carries 4 marks. There is no negative marking for wrong or unanswered questions, so attempt every
question.
3. MCQ (multiple choice): four options, only ONE is correct.
4. MSQ (multiple select): ONE OR MORE of the options (A)–(D) may be correct. Marks are given only if you select all
the correct options and no wrong option; there are no partial marks.
5. FIB (fill in the blank): type (here, write) the numerical answer in the box. Marks are given for the correct value.
6. Time: 150 minutes for the whole paper. Calculators are not allowed.
7. The answer key and short solutions are at the end. For MSQ and FIB questions the key shows the correct options
or value.

This is an AglaSem practice paper written on the official LPUNEST 2027 B.Tech pattern (100 questions, 400 marks, 150
minutes, no negative marking) and the LPUNEST B.Tech syllabus. It is not an official Lovely Professional University paper, and
its questions are original. This is the Mathematics version; candidates for programmes that need Biology take a Biology section
(25 MCQs/MSQs) in place of Mathematics.

Part I: Physics

Physics – MCQ (one correct option)
1. The dimensional formula of Planck's constant is:
(A) [MLT⁻¹] (B) [ML²T⁻³]
(C) [ML²T⁻¹] (D) [ML²T⁻²]

2. A projectile is fired with a speed of 30 m/s at 30° above the horizontal. Taking g = 10 m/s², its horizontal
range is:
(A) 45 m (B) 90√3 m
(C) 45√3 m (D) 90 m

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3. A 5 kg block on a rough horizontal floor (coefficient of kinetic friction 0.2) is pulled by a horizontal force
of 20 N. Taking g = 10 m/s², its acceleration is:
(A) 3 m/s² (B) 1 m/s²
(C) 4 m/s² (D) 2 m/s²

4. The moment of inertia of a uniform solid sphere of mass M and radius R about a tangent to its surface
is:
(A) (3/5)MR² (B) (7/2)MR²
(C) (2/5)MR² (D) (7/5)MR²

5. The escape velocity from the Earth is 11.2 km/s. For a planet with the same mean density as the Earth
but twice its radius, the escape velocity is:
(A) 11.2 km/s (B) 15.8 km/s
(C) 22.4 km/s (D) 44.8 km/s

6. A mass m on a spring of force constant k oscillates with period T. If the same mass hangs from two
such springs joined in series, the new period is:
(A) √2 T (B) 2T
(C) T/√2 (D) T

7. A Carnot engine works between a source at 527 °C and a sink at 127 °C. Its efficiency is:
(A) 24% (B) 50%
(C) 76% (D) 25%

8. Two point charges separated by a distance r repel each other with a force F. If each charge is doubled
and the distance is halved, the force becomes:
(A) 16F (B) F/4
(C) 8F (D) 4F

9. A wire of resistance R is stretched uniformly until its length doubles. Its new resistance is:
(A) 2R (B) 8R
(C) 4R (D) R/2

10. The magnetic field at the centre of a circular loop of radius r carrying a current I is:
(A) μ₀I/(4r) (B) μ₀I/(2πr)
(C) μ₀I/(2r) (D) μ₀I/r

11. In a series LCR circuit at resonance, the phase difference between the current and the applied voltage
is:
(A) π/2 (B) π
(C) 0 (D) π/4

12. A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 40 cm. The
power of the combination is:
(A) −2.5 D (B) +2.5 D
(C) +5 D (D) +7.5 D

13. A Young's double-slit apparatus is completely immersed in water (refractive index 4/3). The fringe width
becomes:
(A) 3/4 of its value in air (B) 4/3 of its value in air
(C) 9/16 of its value in air (D) unchanged

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14. Photons of energy 5 eV fall on a metal surface of work function 3 eV. The stopping potential for the
emitted photoelectrons is:
(A) 2 V (B) 3 V
(C) 5 V (D) 8 V

15. A radioactive substance has a half-life of 10 days. The fraction of the original sample left undecayed
after 30 days is:
(A) 1/6 (B) 1/4
(C) 1/8 (D) 1/3

16. A p-type semiconductor is obtained when pure silicon is doped with:
(A) aluminium (B) phosphorus
(C) antimony (D) arsenic

Physics – MSQ (one or more correct options)

17. Which of the following physical quantities is/are vectors? (One or more options may be correct.)
(A) Displacement
(B) Work
(C) Torque
(D) Electric current

18. An ideal gas undergoes an isothermal process. Which of the following statements is/are correct? (One
or more options may be correct.)
(A) The change in internal energy of the gas is zero.
(B) The heat absorbed by the gas equals the work done by it.
(C) PV remains constant.
(D) The temperature of the gas rises when it is compressed.

19. Which of the following electromagnetic waves has/have a wavelength shorter than that of visible light?
(One or more options may be correct.)
(A) Microwaves
(B) X-rays
(C) Infrared rays
(D) Gamma rays

20. A charged particle enters a uniform magnetic field with its velocity perpendicular to the field. Which of
the following statements is/are correct? (One or more options may be correct.)
(A) Its speed remains constant.
(B) Its kinetic energy increases.
(C) It moves in a circular path.
(D) Its time period of revolution does not depend on its speed.

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Physics – Fill in the blanks (numerical answer)

21. A car starts from rest and accelerates uniformly to 20 m/s in 5 s. The distance (in m) covered in this time
is _____.

22. A 2 kg body moving at 3 m/s collides with a 1 kg body at rest and the two stick together. Their common
velocity (in m/s) just after the collision is _____.

23. Resistors of 6 Ω and 3 Ω are connected in parallel, and this combination is connected in series with a 4
Ω resistor. The equivalent resistance (in Ω) is _____.

24. The radius of the first Bohr orbit of hydrogen is 0.53 Å. The radius (in Å) of its third orbit (n = 3) is _____.

25. An ideal transformer has 100 turns in its primary coil and 500 turns in its secondary coil. If the primary is
connected to 220 V AC, the secondary voltage (in V) is _____.

Part II: Chemistry

Chemistry – MCQ (one correct option)

26. The number of moles in 4.4 g of carbon dioxide is:
(A) 1.0 (B) 0.2
(C) 0.4 (D) 0.1

27. The maximum number of electrons that can be present in the shell with principal quantum number n = 3
is:
(A) 9 (B) 8
(C) 18 (D) 32

28. Which of the following molecules is linear?
(A) SO₂ (B) NO₂
(C) H₂O (D) CO₂

29. The enthalpies of combustion of C(graphite), H₂(g) and CH₄(g) are −394, −286 and −890 kJ mol⁻¹. The
enthalpy of formation of CH₄(g) is:
(A) −210 kJ mol⁻¹ (B) −76 kJ mol⁻¹
(C) +76 kJ mol⁻¹ (D) −1856 kJ mol⁻¹

30. Which of the following 0.1 M aqueous solutions has the highest boiling point?
(A) 0.1 M AlCl₃ (B) 0.1 M glucose
(C) 0.1 M NaCl (D) 0.1 M MgSO₄

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31. The pH of a 0.001 M aqueous solution of HCl at 25 °C is:
(A) 3 (B) 0.001
(C) 1 (D) 11

32. For the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g), ΔH < 0, the yield of ammonia at equilibrium is increased by:
(A) adding a catalyst (B) removing some N₂
(C) increasing the temperature (D) increasing the pressure

33. The quantity of electricity needed to deposit 1 mol of aluminium from Al³⁺ ions is:
(A) 2 F (B) 1 F
(C) 3 F (D) 6 F

34. A first-order reaction has a half-life of 69.3 s. Its rate constant is:
(A) 0.1 s⁻¹ (B) 1.0 s⁻¹
(C) 0.01 s⁻¹ (D) 0.001 s⁻¹

35. Among B, C, N and O, the element with the highest first ionisation enthalpy is:
(A) O (B) C
(C) B (D) N

36. Which of the following oxoacids of phosphorus is monobasic?
(A) H₄P₂O₇ (B) H₃PO₃
(C) H₃PO₄ (D) H₃PO₂

37. Which of the following ions is colourless in aqueous solution?
(A) Fe³⁺ (B) Cu²⁺
(C) Zn²⁺ (D) Ti³⁺

38. The oxidation state of iron in K₄[Fe(CN)₆] is:
(A) +2 (B) +3
(C) +4 (D) +6

39. The IUPAC name of CH₃–CH(CH₃)–CH₂–OH is:
(A) 1,1-dimethylethanol (B) butan-1-ol
(C) 2-methylpropan-2-ol (D) 2-methylpropan-1-ol

40. Propene reacts with HBr in the presence of an organic peroxide to give mainly:
(A) propane (B) 1-bromopropane
(C) 2-bromopropane (D) 1,2-dibromopropane

41. The Lucas test (conc. HCl + anhydrous ZnCl₂) is used to distinguish between:
(A) 1°, 2° and 3° amines (B) 1°, 2° and 3° alcohols
(C) phenol and benzoic acid (D) aldehydes and ketones

Chemistry – MSQ (one or more correct options)
42. Which of the following is/are reducing sugars? (One or more options may be correct.)
(A) Glucose
(B) Sucrose
(C) Fructose
(D) Maltose

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43. Which of the following compounds give(s) a positive carbylamine (isocyanide) test? (One or more
options may be correct.)
(A) Aniline
(B) N-Methylaniline
(C) Ethylamine
(D) Triethylamine

44. Which of the following is/are redox reactions? (One or more options may be correct.)
(A) NaOH + HCl → NaCl + H₂O
(B) Zn + CuSO₄ → ZnSO₄ + Cu
(C) AgNO₃ + NaCl → AgCl + NaNO₃
(D) 2H₂ + O₂ → 2H₂O

45. Which of the following diatomic molecules is/are paramagnetic? (One or more options may be correct.)
(A) O₂
(B) N₂
(C) F₂
(D) H₂

Chemistry – Fill in the blanks (numerical answer)

46. 4 g of NaOH (molar mass 40 g/mol) is dissolved in water to make 250 mL of solution. The molarity (in
mol/L) of the solution is _____.

47. The number of unpaired electrons in the Fe³⁺ ion (atomic number of Fe = 26) is _____.

48. The hydroxide ion concentration of an aqueous solution at 25 °C is 1 × 10⁻⁴ M. The pH of the solution is
_____.

49. A first-order reaction is 75% complete in 60 minutes. Its half-life (in minutes) is _____.

50. When excess AgNO₃ solution is added to a solution containing 1 mol of [Co(NH₃)₅Cl]Cl₂, the number of
moles of AgCl precipitated is _____.

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Part III: Mathematics

Mathematics – MCQ (one correct option)

51. If a set A has 3 elements, the number of elements in the power set of A × A is:
(A) 64 (B) 512
(C) 81 (D) 256

52. The domain of the real function f(x) = √(4 − x²) is:
(A) (−∞, −2] ∪ [2, ∞) (B) [−2, 2]
(C) (−2, 2) (D) [0, 2]

53. The value of lim (x → 0) (sin 3x)/x is:
(A) 1/3 (B) 3
(C) 1 (D) 0

54. If z = (1 + i)/(1 − i), then z⁴ equals:
(A) −i (B) 1
(C) i (D) −1

55. If the roots of x² − kx + 9 = 0 are real and equal, then k equals:
(A) ±6 (B) ±9
(C) 6 only (D) ±3

56. The sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + … is:
(A) 3 (B) 2/3
(C) 3/2 (D) 4/3

57. If A is a square matrix of order 3 with |A| = 4, then |adj A| equals:
(A) 16 (B) 8
(C) 64 (D) 4

58. The general solution of tan x = √3 is:
(A) x = nπ + π/3, n ∈ Z (B) x = nπ + π/6, n ∈ Z
(C) x = 2nπ + π/3, n ∈ Z (D) x = nπ − π/3, n ∈ Z

59. The angle between the vectors a = î + ĵ and b = ĵ + k̂ is:
(A) 30° (B) 60°
(C) 90° (D) 45°

60. The number of diagonals of a regular decagon (10 sides) is:
(A) 45 (B) 70
(C) 40 (D) 35

61. The middle term in the expansion of (x + 1/x)¹⁰ is:
(A) 462 (B) 210
(C) 126 (D) 252

62. If y = xˣ (x > 0), then dy/dx at x = 1 is:
(A) e (B) 0
(C) 2 (D) 1

63. The maximum value of f(x) = x(12 − x) for real x is:
(A) 24 (B) 36
(C) 72 (D) 144

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64. The value of ∫₀^(π/2) sin²x dx is:
(A) π (B) π/2
(C) 1/2 (D) π/4

65. The order and degree of the differential equation (d²y/dx²)³ + (dy/dx)² + y = 0 are:
(A) order 2, degree 3 (B) order 3, degree 2
(C) order 3, degree 3 (D) order 2, degree 2

66. The distance between the parallel lines 3x + 4y = 5 and 3x + 4y = 15 is:
(A) 2 (B) 1
(C) 5 (D) 10

Mathematics – MSQ (one or more correct options)
67. For the parabola y² = 8x, which of the following statements is/are correct? (One or more options may be
correct.)
(A) Its focus is (2, 0).
(B) Its directrix is x = 2.
(C) The length of its latus rectum is 8.
(D) The point (2, 4) lies on it.

68. Which of the following statements is/are correct (principal values)? (One or more options may be
correct.)
(A) sin⁻¹x + cos⁻¹x = π/2 for every x in [−1, 1]
(B) tan⁻¹(1) = π/2
(C) cos⁻¹(−1) = π
(D) sin⁻¹(1/2) = π/3

69. A and B are independent events with P(A) = 0.5 and P(B) = 0.4. Which of the following is/are correct?
(One or more options may be correct.)
(A) P(A ∪ B) = 0.9
(B) P(A ∩ B) = 0.2
(C) A and B are mutually exclusive.
(D) P(A | B) = 0.5

70. For the line (x − 1)/2 = (y + 1)/3 = (z − 2)/6, which of the following is/are correct? (One or more options
may be correct.)
(A) Its direction cosines are 2/7, 3/7, 6/7.
(B) It passes through the point (1, −1, 2).
(C) It passes through the point (3, 2, 8).
(D) It is parallel to the plane 2x + 3y + 6z = 0.

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Mathematics – Fill in the blanks (numerical answer)

71. The sum of the first 15 terms of the arithmetic progression 2, 5, 8, 11, … is _____.

72. The value of the determinant with rows (1, 2, 3), (0, 4, 5) and (0, 0, 6) is _____.

73. The variance of the observations 2, 4, 6, 8, 10 is _____.

74. The radius of the circle x² + y² − 4x + 6y − 12 = 0 is _____.

75. The value of sin²30° + cos²60° + tan²45° is _____.

Part IV: English

English – MCQ (one correct option)
76. Choose the word closest in meaning to BENEVOLENT.
(A) hostile (B) fearful
(C) greedy (D) kindly

77. Choose the word opposite in meaning to SCARCE.
(A) plentiful (B) rare
(C) insufficient (D) meagre

78. Choose the correctly spelt word.
(A) Ocurrence (B) Occurrence
(C) Occurrance (D) Occurence

79. Choose the one word for: a person who can speak two languages.
(A) bilingual (B) monolingual
(C) linguist (D) polyglot

80. Choose the correct meaning of the idiom: to beat around the bush.
(A) to avoid coming to the main point
(B) to search for something carefully
(C) to waste money on useless things
(D) to work very hard

81. Fill in the blank: By the time we reached the station, the train ______.
(A) has left (B) had left
(C) left (D) was leaving

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82. Choose the correct passive form of: They are building a new bridge.
(A) A new bridge has been built by them.
(B) A new bridge is built by them.
(C) A new bridge is being built by them.
(D) A new bridge was being built by them.

83. Fill in the blank: You ______ wear a helmet while riding a motorcycle; it is the law.
(A) might (B) must
(C) would (D) can

84. Fill in the blank: There is ______ milk left in the jug, so we need to buy some.
(A) a little (B) few
(C) little (D) many

85. Fill in the blank: She has been working in this company ______ 2019.
(A) from (B) until
(C) for (D) since

86. Fill in the blank with the correct article: He is ______ honest man.
(A) no article (B) the
(C) an (D) a

87. Find the part of the sentence that has an error:
(P) Neither of the two boys / (Q) have finished / (R) the assigned work.
(A) Part (R) (B) Part (P)
(C) Part (Q) (D) No error

88. Find the part of the sentence that has an error:
(P) The news are / (Q) very encouraging / (R) for all of us.
(A) Part (P) (B) Part (Q)
(C) Part (R) (D) No error

89. Fill in the blank: Each of the players ______ given a medal after the match.
(A) are (B) have been
(C) was (D) were

90. Complete the analogy: AUTHOR : BOOK :: COMPOSER : ______
(A) piano (B) symphony
(C) concert (D) orchestra

91. Fill in the blank: The ______ of the story is that honesty is always rewarded.
(A) mortal (B) moral
(C) mural (D) morale

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Read the passage and answer the questions that follow.
Bamboo has long been called the poor man's timber, but engineers are now taking a fresh look at it. A
clump of bamboo can be harvested every three to five years, whereas a hardwood tree may need several
decades to mature. Its hollow, jointed stem is light, yet some species are remarkably strong in tension for
their weight. These qualities make bamboo attractive for scaffolding, low-cost housing and even bridges.
The material does have weaknesses. Untreated bamboo is attacked by insects and fungi, and it absorbs
moisture, which makes it swell and crack. Because each stem differs in thickness and strength, it is also
hard to write the precise design rules that builders rely on for steel or concrete. Researchers are therefore
working on simple chemical treatments and on laminated bamboo boards of uniform quality. If these
efforts succeed, a plant that grows in thousands of villages could become a mainstream building material.

92. The main idea of the passage is that bamboo:
(A) is too weak and irregular to be used for any kind of construction
(B) grows much faster than hardwood and so should replace all timber
(C) is already replacing steel and concrete in most new buildings
(D) has real strengths as a building material, but its weaknesses must be overcome first

93. According to the passage, why is it hard to write precise design rules for bamboo?
(A) Each stem differs in thickness and strength.
(B) Bamboo is heavier than steel.
(C) Builders do not trust laminated boards.
(D) Bamboo grows only in a few villages.

94. The word 'mainstream' in the last line of the passage most nearly means:
(A) costly and rare (B) found near rivers
(C) used only in villages (D) widely accepted and used

95. Which of the following uses of bamboo is NOT mentioned in the passage?
(A) low-cost housing (B) scaffolding
(C) furniture (D) bridges

English – MSQ (one or more correct options)

96. Which of the following words is/are similar in meaning to OBSTINATE? (One or more options may be
correct.)
(A) stubborn
(B) flexible
(C) headstrong
(D) docile

97. Which of the following sentences is/are grammatically correct? (One or more options may be correct.)
(A) She doesn't like coffee.
(B) He don't know the answer.
(C) Each of the girls have a book.
(D) The children are playing outside.

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98. Which of the following words is/are correctly spelt? (One or more options may be correct.)
(A) Necessary
(B) Seperate
(C) Embarrass
(D) Definately

99. Which of the following words is/are opposite in meaning to EXPAND? (One or more options may be
correct.)
(A) enlarge
(B) contract
(C) extend
(D) shrink

100. In which of the following sentences is the word 'bear' used as a verb? (One or more options may be
correct.)
(A) I cannot bear this noise any longer.
(B) A brown bear lives in that cave.
(C) These mango trees bear fruit in summer.
(D) The company will bear the cost of the repairs.

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Answer Key

1 C 2 C 3 D 4 D 5 C 6 A 7 B 8 A 9 C 10 C
11 C 12 B 13 A 14 A 15 C 16 A 17 A,C 18 A,B,C 19 B,D 20 A,C,D
21 50 22 2 23 6 24 4.77 25 1100 26 D 27 C 28 D 29 B 30 A
31 A 32 D 33 C 34 C 35 D 36 D 37 C 38 A 39 D 40 B
41 B 42 A,C,D 43 A,C 44 B,D 45 A 46 0.4 47 5 48 10 49 30 50 2
51 B 52 B 53 B 54 B 55 A 56 C 57 A 58 A 59 B 60 D
61 D 62 D 63 B 64 D 65 A 66 A 67 A,C,D 68 A,C 69 B,D 70 A,B,C
71 345 72 24 73 8 74 5 75 1.5 76 D 77 A 78 B 79 A 80 A
81 B 82 C 83 B 84 C 85 D 86 C 87 C 88 A 89 C 90 B
91 B 92 D 93 A 94 D 95 C 96 A,C 97 A,D 98 A,C 99 B,D 100 A,C,D

Solutions

Physics – MCQ (one correct option)
1. (C) From E = hν, h = E/ν, so its unit is J s = kg m² s⁻¹, i.e. [ML²T⁻¹].
2. (C) R = u² sin 2θ / g = (900 × sin 60°)/10 = 90 × (√3/2) = 45√3 m (about 78 m).
3. (D) Friction = μmg = 0.2 × 5 × 10 = 10 N. Net force = 20 − 10 = 10 N, so a = 10/5 = 2 m/s².
4. (D) About a diameter I = (2/5)MR². By the parallel axis theorem, about a tangent I = (2/5)MR² + MR² = (7/5)MR².
5. (C) vₑ = √(2GM/R) and M = (4/3)πR³ρ, so vₑ = R√(8πGρ/3) ∝ R for the same density. Doubling R doubles vₑ to 22.4
km/s.
6. (A) Two springs of constant k in series give k/2. T = 2π√(m/k) becomes 2π√(2m/k) = √2 T.
7. (B) Use kelvin: T₁ = 800 K, T₂ = 400 K. η = 1 − T₂/T₁ = 1 − 400/800 = 0.5 = 50%.
8. (A) F ∝ q₁q₂/r². The product of charges becomes 4 times and 1/r² becomes 4 times, so the force becomes 16F.
9. (C) The volume stays the same, so doubling the length halves the area. R = ρl/A becomes ρ(2l)/(A/2) = 4R.
10. (C) From the Biot–Savart law, B at the centre of a circular loop = μ₀I/(2r). (μ₀I/(2πr) is the field near a long straight
wire.)
11. (C) At resonance X_L = X_C, so the impedance is purely resistive (Z = R) and the current is in phase with the
voltage.
12. (B) P = 1/f₁ + 1/f₂ (in metres) = 1/0.20 − 1/0.40 = 5 − 2.5 = +2.5 D.
13. (A) β = λD/d. In water the wavelength becomes λ/μ = 3λ/4, so the fringe width becomes 3/4 of its value in air.
14. (A) K_max = hν − φ = 5 − 3 = 2 eV, so the stopping potential is 2 V.
15. (C) 30 days = 3 half-lives, so the fraction left is (1/2)³ = 1/8.
16. (A) p-type needs a trivalent (Group 13) impurity, which creates holes. Aluminium is trivalent; phosphorus, arsenic
and antimony are pentavalent and give n-type.

Physics – MSQ (one or more correct options)
17. (A,C) Correct options: (A), (C). Displacement and torque have direction and add by the vector law. Work is a scalar
(dot product), and electric current, though it has a sense of flow, does not add by the vector law, so it is a scalar.
18. (A,B,C) Correct options: (A), (B), (C). Internal energy of an ideal gas depends only on T, so ΔU = 0; then the first law
gives Q = W. Boyle's law (PV = constant) holds at constant T. By definition T does not change, so (D) is wrong.
19. (B,D) Correct options: (B), (D). In order of decreasing wavelength: radio, microwaves, infrared, visible, ultraviolet, X-
rays, gamma rays. X-rays and gamma rays are shorter than visible light; microwaves and infrared are longer.

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20. (A,C,D) Correct options: (A), (C), (D). The magnetic force qv × B is always perpendicular to the velocity, so it does
no work: speed and kinetic energy stay constant and the path is a circle. T = 2πm/(qB), which does not depend on the
speed.

Physics – Fill in the blanks (numerical answer)
21. (50) Answer: 50. Distance = average velocity × time = ((0 + 20)/2) × 5 = 50 m.
22. (2) Answer: 2. Momentum is conserved: 2 × 3 = (2 + 1)v, so v = 2 m/s.
23. (6) Answer: 6. 6 Ω ∥ 3 Ω = (6 × 3)/(6 + 3) = 2 Ω; 2 + 4 = 6 Ω.
ₙ
24. (4.77) Answer: 4.77. In the Bohr model r = n²r₁, so r₃ = 9 × 0.53 = 4.77 Å.
25. (1100) Answer: 1100. Vs/Vp = Ns/Np = 500/100 = 5, so Vs = 5 × 220 = 1100 V.

Chemistry – MCQ (one correct option)
26. (D) Molar mass of CO₂ = 12 + 2 × 16 = 44 g/mol. Moles = 4.4/44 = 0.1.
27. (C) The maximum number of electrons in a shell is 2n² = 2 × 9 = 18 (3s², 3p⁶, 3d¹⁰).
28. (D) In CO₂ the carbon has two bonding domains and no lone pair (sp), so O=C=O is linear (180°). H₂O, SO₂ and
NO₂ are bent because of lone pairs or an odd electron on the central atom.
29. (B) By Hess's law, ΔHf(CH₄) = ΔHc(C) + 2ΔHc(H₂) − ΔHc(CH₄) = −394 + 2(−286) − (−890) = −394 − 572 + 890 = −76
kJ mol⁻¹.
30. (A) Elevation of boiling point ∝ i × concentration. AlCl₃ gives 4 ions (i = 4); NaCl and MgSO₄ give 2; glucose does
not dissociate (i = 1).
31. (A) HCl is a strong acid, so [H⁺] = 10⁻³ M and pH = −log(10⁻³) = 3.
32. (D) The forward reaction reduces the number of gas moles (4 → 2), so higher pressure shifts it forward (Le
Chatelier). Being exothermic, it is favoured by lower temperature. A catalyst does not change the equilibrium yield, and
removing N₂ shifts it backward.
33. (C) Al³⁺ + 3e⁻ → Al. One mole of Al needs 3 mol of electrons, i.e. 3 faradays.
34. (C) For a first-order reaction k = 0.693/t½ = 0.693/69.3 = 0.01 s⁻¹.
35. (D) Ionisation enthalpy generally rises across the period, but N (2p³, half-filled) has a higher value than O (2p⁴),
since removing one paired 2p electron from O is easier.
36. (D) Basicity equals the number of P–OH groups. H₃PO₂ (hypophosphorous acid) has one P–OH and two P–H
bonds, so it is monobasic. H₃PO₃ is dibasic, H₃PO₄ tribasic and H₄P₂O₇ tetrabasic.
37. (C) Colour comes from d–d transitions, which need a partly filled d subshell. Zn²⁺ is 3d¹⁰ (full), so it is colourless.
Cu²⁺ (3d⁹), Fe³⁺ (3d⁵) and Ti³⁺ (3d¹) are coloured.
38. (A) 4(+1) + x + 6(−1) = 0 gives x = +2.
39. (D) The longest chain containing the C–OH carbon has 3 carbons (propanol), with OH on C-1 and a methyl group
on C-2: 2-methylpropan-1-ol.
40. (B) In the presence of peroxide, HBr adds by a free-radical mechanism (peroxide or Kharasch effect), giving the
anti-Markovnikov product CH₃CH₂CH₂Br, 1-bromopropane.
41. (B) With Lucas reagent, 3° alcohols turn turbid at once, 2° alcohols in about five minutes, and 1° alcohols do not
react at room temperature. So it distinguishes 1°, 2° and 3° alcohols.

Chemistry – MSQ (one or more correct options)
42. (A,C,D) Correct options: (A), (C), (D). Glucose, fructose and maltose have a free (potential) aldehyde or ketone
group and reduce Tollens' and Fehling's reagents. In sucrose both anomeric carbons are joined in the glycosidic bond,
so it is non-reducing.
43. (A,C) Correct options: (A), (C). The carbylamine test (CHCl₃ + alcoholic KOH, foul smell of isocyanide) is given only
by primary amines, aliphatic or aromatic. Aniline and ethylamine are primary; N-methylaniline is secondary and
triethylamine is tertiary.
44. (B,D) Correct options: (B), (D). In (B) Zn goes from 0 to +2 and Cu from +2 to 0; in (D) H goes from 0 to +1 and O
from 0 to −2. (A) is neutralisation and (C) is precipitation: no oxidation number changes.

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45. (A) Correct option: (A). By molecular orbital theory O₂ has two unpaired electrons in the π*2p orbitals, so it is
paramagnetic. N₂, F₂ and H₂ have all electrons paired and are diamagnetic.

Chemistry – Fill in the blanks (numerical answer)
46. (0.4) Answer: 0.4. Moles = 4/40 = 0.1 mol; volume = 0.25 L; molarity = 0.1/0.25 = 0.4 M.
47. (5) Answer: 5. Fe is [Ar]3d⁶4s²; Fe³⁺ is [Ar]3d⁵, with five singly occupied d orbitals (Hund's rule).
48. (10) Answer: 10. pOH = 4, so pH = 14 − 4 = 10.
49. (30) Answer: 30. 75% completion leaves 1/4 = (1/2)², i.e. two half-lives in 60 minutes, so t½ = 30 minutes.
50. (2) Answer: 2. The complex ionises as [Co(NH₃)₅Cl]²⁺ + 2Cl⁻. Only the two ionisable chloride ions (outside the
coordination sphere) are precipitated as AgCl.

Mathematics – MCQ (one correct option)
51. (B) A × A has 3 × 3 = 9 elements, so its power set has 2⁹ = 512 elements.
52. (B) We need 4 − x² ≥ 0, i.e. x² ≤ 4, so −2 ≤ x ≤ 2.
53. (B) (sin 3x)/x = 3 × (sin 3x)/(3x) → 3 × 1 = 3.
54. (B) z = (1 + i)²/((1 − i)(1 + i)) = 2i/2 = i, so z⁴ = i⁴ = 1.
55. (A) Equal roots need discriminant = 0: k² − 36 = 0, so k = ±6.
56. (C) S∞ = a/(1 − r) = 1/(1 − 1/3) = 3/2.
57. (A) |adj A| = |A|ⁿ⁻¹ for a matrix of order n. Here 4² = 16.
58. (A) tan x = tan(π/3), and tan has period π, so x = nπ + π/3 for any integer n. (2nπ + π/3 misses the solutions 4π/3,
10π/3, ….)
59. (B) cos θ = (a·b)/(|a||b|) = 1/(√2 × √2) = 1/2, so θ = 60°.
60. (D) Number of diagonals = ¹⁰C₂ − 10 = 45 − 10 = 35 (or n(n − 3)/2 = 10 × 7/2 = 35).
61. (D) There are 11 terms, so the middle term is T₆ = ¹⁰C₅ x⁵(1/x)⁵ = ¹⁰C₅ = 252.
62. (D) ln y = x ln x, so y′/y = ln x + 1 and y′ = xˣ(1 + ln x). At x = 1: 1 × (1 + 0) = 1.
63. (B) f′(x) = 12 − 2x = 0 at x = 6, and f″(x) = −2 < 0, so the maximum is f(6) = 6 × 6 = 36.
64. (D) sin²x = (1 − cos 2x)/2. ∫₀^(π/2) (1 − cos 2x)/2 dx = (1/2)[x − (sin 2x)/2] from 0 to π/2 = π/4.
65. (A) The highest derivative is d²y/dx² (order 2), and its power is 3 (degree 3), since the equation is a polynomial in the
derivatives.
66. (A) Distance = |c₁ − c₂|/√(a² + b²) = |15 − 5|/√(9 + 16) = 10/5 = 2.

Mathematics – MSQ (one or more correct options)
67. (A,C,D) Correct options: (A), (C), (D). y² = 4ax with 4a = 8 gives a = 2: focus (2, 0), directrix x = −2 (not x = 2), latus
rectum 4a = 8. For (2, 4): 4² = 16 = 8 × 2, so it lies on the parabola.
68. (A,C) Correct options: (A), (C). (A) is a standard identity. tan⁻¹(1) = π/4, not π/2. cos π = −1 and π lies in [0, π], so
cos⁻¹(−1) = π. sin⁻¹(1/2) = π/6, not π/3.
69. (B,D) Correct options: (B), (D). P(A ∩ B) = 0.5 × 0.4 = 0.2, so P(A ∪ B) = 0.5 + 0.4 − 0.2 = 0.7 (not 0.9). Since P(A ∩
B) ≠ 0 they are not mutually exclusive. P(A | B) = 0.2/0.4 = 0.5 = P(A).
70. (A,B,C) Correct options: (A), (B), (C). Direction ratios 2, 3, 6 have magnitude √(4 + 9 + 36) = 7, giving direction
cosines 2/7, 3/7, 6/7. Putting each ratio = 0 gives (1, −1, 2); each = 1 gives (3, 2, 8). The plane's normal (2, 3, 6) is along
the line, so the line is perpendicular to the plane, not parallel.

Mathematics – Fill in the blanks (numerical answer)
71. (345) Answer: 345. a = 2, d = 3: S₁₅ = (15/2)[2 × 2 + 14 × 3] = (15/2) × 46 = 345.
72. (24) Answer: 24. The matrix is upper triangular, so the determinant is the product of the diagonal entries: 1 × 4 × 6
= 24.
73. (8) Answer: 8. Mean = 30/5 = 6. Squared deviations: 16, 4, 0, 4, 16, total 40. Variance = 40/5 = 8.
74. (5) Answer: 5. (x − 2)² + (y + 3)² = 12 + 4 + 9 = 25, so the centre is (2, −3) and the radius is 5.

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75. (1.5) Answer: 1.5. sin²30° = 1/4, cos²60° = 1/4, tan²45° = 1. Sum = 1/4 + 1/4 + 1 = 1.5.

English – MCQ (one correct option)
76. (D) Benevolent means well-meaning and kind, so 'kindly' is the synonym. Hostile is its opposite.
77. (A) Scarce means in short supply. Its opposite is plentiful. Rare, meagre and insufficient are close in meaning to
scarce.
78. (B) The correct spelling has double c, double r and ends in -ence: occurrence.
79. (A) Bilingual means able to speak two languages. A polyglot knows many languages, a linguist studies languages,
and monolingual means speaking only one.
80. (A) To beat around the bush is to talk about other things and avoid the main point.
81. (B) Of two past actions, the earlier one (the train leaving) takes the past perfect: 'had left'.
82. (C) Present continuous active (are building) becomes present continuous passive: is/are + being + past participle,
so 'is being built'.
83. (B) A legal obligation is expressed by 'must'. 'Might' shows possibility, 'can' ability or permission, and 'would' a
condition or habit.
84. (C) Milk is uncountable, so few and many are wrong. 'Little' means hardly any, which fits 'we need to buy some'; 'a
little' would mean there is still some.
85. (D) With the present perfect continuous, a point of time (2019) takes 'since'; 'for' is used with a period, such as 'for
six years'.
86. (C) 'Honest' begins with a vowel sound (the h is silent), so the indefinite article is 'an'.
87. (C) 'Neither' is singular and takes a singular verb: 'Neither of the two boys has finished the assigned work.'
88. (A) 'News' is an uncountable noun and takes a singular verb: 'The news is very encouraging for all of us.'
89. (C) 'Each' is singular and takes a singular verb; the past context needs 'was'.
90. (B) An author creates a book; a composer creates a symphony. An orchestra performs it, a piano is an instrument
and a concert is an event.
91. (B) The 'moral' of a story is the lesson it teaches. Morale is spirit or confidence, mortal means subject to death, and
a mural is a wall painting.
92. (D) The passage describes bamboo's advantages, then its weaknesses, then the research to overcome them,
ending with 'if these efforts succeed'. The other options are either too negative or claim more than the passage says.
93. (A) The passage says: 'Because each stem differs in thickness and strength, it is also hard to write the precise
design rules.'
94. (D) A mainstream building material is one that is normally and widely used, as steel and concrete are now.
95. (C) The passage mentions scaffolding, low-cost housing and even bridges. Furniture is not mentioned.

English – MSQ (one or more correct options)
96. (A,C) Correct options: (A), (C). Obstinate means refusing to change one's mind. Stubborn and headstrong mean
the same; flexible and docile are opposites.
97. (A,D) Correct options: (A), (D). (B) should be 'He doesn't know', since a third person singular subject takes 'does'.
(C) should be 'Each of the girls has a book', since 'each' is singular.
98. (A,C) Correct options: (A), (C). The correct spellings of the other two are 'separate' and 'definitely'.
99. (B,D) Correct options: (B), (D). To expand is to become larger. Contract and shrink mean to become smaller;
enlarge and extend are synonyms of expand.
100. (A,C,D) Correct options: (A), (C), (D). In (A) bear means tolerate, in (C) produce, and in (D) pay for: all are verbs. In
(B) 'bear' is a noun, the animal.

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