NFAT B. Tech. - M.Tech. Computer Science and Engineering (Cyber Security) Mock Test 2025

NFAT BTech Computer Science Entrance Exam Mock Test 2025

Physics (27 Questions)

1. A particle moves in a circular path of radius \( R = 2 \, \text{m} \) with angular velocity \( \omega(t) = 3t^2 + 2t \). What is the magnitude of its centripetal acceleration at \( t = 2 \, \text{s} \)?

A) \( 64 \, \text{m/s}^2 \)

B) \( 128 \, \text{m/s}^2 \)

C) \( 256 \, \text{m/s}^2 \)

D) \( 32 \, \text{m/s}^2 \)

2. In a Young's double-slit experiment, slits are 0.2 mm apart, the screen is 1.5 m away, and the wavelength is 600 nm. A glass plate (\( \mu = 1.5 \), thickness 0.1 mm) is placed in front of one slit. What is the fringe shift?

A) 0.75 mm

B) 1.5 mm

C) 2.25 mm

D) 3 mm

3. A charged particle (\( q = 2 \, \mu \text{C} \), \( m = 1 \, \text{mg} \)) moves with velocity \( \vec{v} = 5 \hat{i} \, \text{m/s} \) in a magnetic field \( \vec{B} = 0.2 \hat{k} \, \text{T} \) and electric field \( \vec{E} = 1000 \hat{j} \, \text{V/m} \). What is the force on the particle?

A) \( (2 \hat{j} + 0.002 \hat{j}) \, \text{N} \)

B) \( 2 \hat{j} \, \text{N} \)

C) \( 0.002 \hat{j} \, \text{N} \)

D) Zero

4. A Carnot engine operates between 800 K and 400 K, absorbing 200 J of heat per cycle. What is the work done per cycle?

A) 100 J

B) 50 J

C) 150 J

D) 75 J

5. A satellite orbits a planet at radius \( R \). If its orbital period is \( T \), what is the period of another satellite at radius \( 2R \)?

A) \( 2\sqrt{2} T \)

B) \( 2T \)

C) \( \sqrt{2} T \)

D) \( 4T \)

6. A convex lens (focal length 20 cm) and a concave mirror (focal length 15 cm) are 10 cm apart. An object is placed 30 cm from the lens. Where is the final image?

A) 60 cm from the mirror

B) 30 cm from the lens

C) 45 cm from the mirror

D) 20 cm from the lens

7. A solenoid (2000 turns, 1 m length) carries 3 A. What is the magnetic field at its center?

A) \( 7.54 \times 10^{-3} \, \text{T} \)

B) \( 7.54 \times 10^{-3} \, \text{T} \)

C) \( 3.77 \times 10^{-3} \, \text{T} \)

D) \( 1.26 \times 10^{-3} \, \text{T} \)

8. The de Broglie wavelength of an electron accelerated through 200 V is:

A) 0.086 nm

B) 0.086 nm

C) 8.6 nm

D) 0.86 nm

9. A disc (radius 1 m) rotates with angular acceleration \( 4 \, \text{rad/s}^2 \). Starting from rest, what is the tangential acceleration at the edge after 2 s?

A) 4 m/s\(^2\)

B) 8 m/s\(^2\)

C) 2 m/s\(^2\)

D) 16 m/s\(^2\)

10. A sound wave (frequency 1000 Hz, speed 340 m/s) travels in a medium. What is the phase difference between two points 0.34 m apart?

A) \( \pi/2 \)

B) \( 2\pi \)

C) \( \pi \)

D) \( \pi/4 \)

11. A capacitor (20 µF) is charged to 200 V and connected to an inductor (0.2 H). What is the frequency of oscillation in the LC circuit?

A) 112.5 Hz

B) 225 Hz

C) 56.25 Hz

D) 450 Hz

12. A projectile is launched at 45° with 30 m/s. What is its range on a horizontal plane (\( g = 10 \, \text{m/s}^2 \))?

A) 90 m

B) 45 m

C) 60 m

D) 120 m

13. A photon has energy 2.48 eV. What is its wavelength?

A) 500 nm

B) 250 nm

C) 750 nm

D) 1000 nm

14. In an adiabatic process (\( \gamma = 1.4 \)), if volume decreases to \( \frac{1}{4} \) of initial volume, what is the final pressure ratio to initial?

A) 4

B) 16

C) 8

D) 2

15. A particle (\( q = 3 \, \mu \text{C} \)) moves with velocity \( \vec{v} = (4 \hat{i} + 2 \hat{j}) \, \text{m/s} \) in a magnetic field \( \vec{B} = 0.5 \hat{k} \, \text{T} \). What is the force?

A) \( (3 \hat{i} - 6 \hat{j}) \times 10^{-6} \, \text{N} \)

B) \( (6 \hat{i} - 3 \hat{j}) \times 10^{-6} \, \text{N} \)

C) \( (-6 \hat{i} + 3 \hat{j}) \times 10^{-6} \, \text{N} \)

D) Zero

16. A thin lens has power +4 D. What is its focal length?

A) 25 cm

B) 20 cm

C) 50 cm

D) 10 cm

17. A simple pendulum (length 2 m) oscillates on a planet with \( g = 5 \, \text{m/s}^2 \). What is its time period?

A) 2 s

B) 4 s

C) 1 s

D) 8 s

18. A transformer has 300 primary and 1200 secondary turns. If input voltage is 220 V, what is the output voltage?

A) 880 V

B) 55 V

C) 440 V

D) 1760 V

19. In Young’s experiment, if wavelength doubles, the fringe width:

A) Halves

B) Doubles

C) Remains same

D) Quadruples

20. A body (mass 10 kg) falls from 15 m. What is its kinetic energy just before hitting the ground (\( g = 10 \, \text{m/s}^2 \))?

A) 1500 J

B) 750 J

C) 3000 J

D) 375 J

21. A radioactive isotope has a half-life of 3 hours. What fraction remains after 12 hours?

A) 1/16

B) 1/8

C) 1/4

D) 1/2

22. A wire (resistance 20 Ω) is stretched to triple its length. What is the new resistance?

A) 180 Ω

B) 60 Ω

C) 90 Ω

D) 30 Ω

23. A particle in SHM has amplitude 10 cm and frequency 5 Hz. What is its maximum acceleration?

A) 10 m/s\(^2\)

B) 100 m/s\(^2\)

C) 50 m/s\(^2\)

D) 25 m/s\(^2\)

24. A concave mirror has a focal length of 25 cm. An object is placed 15 cm from the mirror. Where is the image?

A) 37.5 cm behind the mirror

B) 37.5 cm in front of the mirror

C) 15 cm behind the mirror

D) 15 cm in front of the mirror

25. A rocket ejects gas at 1000 m/s relative to itself with a mass ejection rate of 5 kg/s. What is the thrust?

A) 5000 N

B) 2500 N

C) 10000 N

D) 1250 N

26. A block (mass 2 kg) slides down a frictionless incline at 30° with a constant acceleration. What is its acceleration?

A) 9.8 m/s\(^2\)

B) 4.9 m/s\(^2\)

C) 2.45 m/s\(^2\)

D) 19.6 m/s\(^2\)

27. A parallel plate capacitor has plates of area 0.01 m\(^2\) separated by 0.1 mm with a dielectric (\( \kappa = 2 \)). What is its capacitance?

A) 1.77 nF

B) 0.885 nF

C) 1.77 nF

D) 3.54 nF

Chemistry (26 Questions)

28. A cell with \( \text{Zn}|\text{Zn}^{2+} (0.2 \, \text{M}) || \text{Cu}^{2+} (0.02 \, \text{M})|\text{Cu} \), \( E^\circ_{\text{cell}} = 1.10 \, \text{V} \). What is the cell potential at 298 K?

A) 1.07 V

B) 1.13 V

C) 1.04 V

D) 1.16 V

29. A reaction \( \text{A} + \text{B} \to \text{C} \) has rate law \( \text{Rate} = k[\text{A}]^2[\text{B}] \). If [A] and [B] are tripled, by what factor does the rate increase?

A) 27

B) 9

C) 81

D) 3

30. Which compound has the highest dipole moment?

A) \( \text{CCl}_4 \)

B) \( \text{CHCl}_3 \)

C) \( \text{CH}_4 \)

D) \( \text{CO}_2 \)

31. The major product of 1-butene with HBr in the presence of peroxides is:

A) 1-Bromobutane

B) 2-Bromobutane

C) 1,2-Dibromobutane

D) 2,2-Dibromobutane

32. For a reaction, \( \Delta H = -50 \, \text{kJ/mol} \), \( \Delta S = -150 \, \text{J/mol} \cdot \text{K} \). At what temperature is it spontaneous?

A) Below 333 K

B) Above 333 K

C) Below 500 K

D) Above 500 K

33. A cubic crystal has a lattice parameter of 5 Å. What is the distance between (111) planes?

A) 2.89 Å

B) 5 Å

C) 1.44 Å

D) 3.54 Å

34. The magnetic moment of \( [\text{Ni}(\text{CN})_4]^{2-} \) is:

A) 0 BM

B) 2.83 BM

C) 1.73 BM

D) 3.87 BM

35. Toluene with \( \text{Cl}_2 \) in the presence of \( \text{FeCl}_3 \) yields:

A) Chlorotoluene

B) Benzyl chloride

C) 1,2-Dichlorotoluene

D) Hexachlorotoluene

36. If a galvanic cell’s salt bridge is removed, what happens?

A) Cell potential increases

B) Cell stops functioning

C) Current increases

D) Electrodes dissolve

37. The pH of a 0.01 M solution of a weak base (pKb = 5) is:

A) 9

B) 10

C) 8

D) 11

38. The hybridization of carbon in ethene is:

A) sp\(^2\)

B) sp

C) sp\(^3\)

D) dsp\(^2\)

39. For \( \text{N}_2 + \text{O}_2 \to 2\text{NO} \), if \( \Delta H = 180 \, \text{kJ/mol} \), what is \( \Delta H_f \) of \( \text{NO} \)?

A) 90 kJ/mol

B) 180 kJ/mol

C) 45 kJ/mol

D) 360 kJ/mol

40. Which gas deviates most from ideal behavior at low temperature?

A) He

B) N\( _2 \)

C) NH\( _3 \)

D) H\( _2 \)

41. The oxidation state of Mn in \( \text{KMnO}_4 \) is:

A) +5

B) +7

C) +6

D) +4

42. The rate constant of a first-order reaction is 0.0346 min\(^{-1}\). What is its half-life?

A) 20 min

B) 10 min

C) 30 min

D) 40 min

43. The IUPAC name of \( \text{CH}_3\text{COCH}_2\text{CH}_2\text{OH} \) is:

A) 4-Hydroxybutan-2-one

B) 3-Hydroxybutan-2-one

C) 4-Hydroxybutanal

D) 2-Hydroxybutan-4-one

44. In a titration of HCl with NaOH, the indicator methyl orange changes color at pH:

A) 7

B) 4

C) 9

D) 2

45. The bond order of N\( _2^+ \) is:

A) 2.5

B) 3

C) 2

D) 1.5

46. The solubility product of \( \text{BaSO}_4 \) is \( 1.1 \times 10^{-10} \). What is its solubility in 0.01 M \( \text{Na}_2\text{SO}_4 \)?

A) \( 1.1 \times 10^{-8} \, \text{M} \)

B) \( 1.1 \times 10^{-10} \, \text{M} \)

C) \( 1.1 \times 10^{-12} \, \text{M} \)

D) \( 1.1 \times 10^{-6} \, \text{M} \)

47. The primary standard used in acid-base titration is:

A) HCl

B) Na\( _2 \)CO\( _3 \)

C) NaOH

D) H\( _2 \)SO\( _4 \)

48. The structure of \( \text{XeF}_2 \) is:

A) Linear

B) Trigonal bipyramidal

C) T-shaped

D) Square planar

49. The enthalpy of neutralization of a weak acid and strong base is:

A) Less than -57.3 kJ/mol

B) -57.3 kJ/mol

C) More than -57.3 kJ/mol

D) Zero

50. The catalyst used in the contact process is:

A) V\( _2 \)O\( _5 \)

B) Fe

C) Ni

D) Pt

51. The number of stereoisomers of 2,3-butanediol is:

A) 2

B) 3

C) 4

D) 6

52. The boiling point of ethanol is higher than diethyl ether due to:

A) Hydrogen bonding

B) Dipole-dipole interactions

C) London forces

D) Covalent bonding

53. The coordination number of \( \text{Fe} \) in \( [\text{Fe}(\text{EDTA})]^{2-} \) is:

A) 4

B) 6

C) 8

D) 5

Mathematics (27 Questions)

54. If \( z = x + iy \) satisfies \( |z - 4i| = 3 \), what is the maximum value of \( |z| \)?

A) 4

B) 7

C) 5

D) 3

55. The number of ways to distribute 8 identical balls into 3 distinct boxes with at least one ball per box is:

A) \( \binom{7}{2} \)

B) \( \binom{8}{2} \)

C) \( \binom{7}{3} \)

D) \( \binom{8}{3} \)

56. If \( \int_{0}^{1} \frac{\ln(1 + x)}{x^2 + 1} \, dx = k\pi \), what is \( k \)?

A) \( \frac{1}{8} \)

B) \( \frac{1}{4} \)

C) \( \frac{1}{2} \)

D) 1

57. The sum of the series \( 1 + \frac{2}{3} + \frac{4}{9} + \frac{8}{27} + \dots \) to infinity is:

A) 2

B) 3

C) 1.5

D) 4

58. The eccentricity of the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \) is:

A) \( \frac{5}{4} \)

B) \( \frac{4}{3} \)

C) \( \frac{5}{3} \)

D) \( \frac{3}{2} \)

59. If \( \tan^{-1}x + \tan^{-1}y = \frac{\pi}{4} \), what is the value of \( x + y + xy \)?

A) 0

B) 1

C) -1

D) 2

60. The number of solutions to \( \sin x + \cos x = 1 \) in \( [0, 2\pi] \) is:

A) 2

B) 1

C) 3

D) 4

61. If \( A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \), what is the determinant of \( A^2 \)?

A) 25

B) 49

C) 36

D) 16

62. The probability that a leap year has 53 Sundays is:

A) \( \frac{2}{7} \)

B) \( \frac{1}{7} \)

C) \( \frac{3}{7} \)

D) \( \frac{4}{7} \)

63. The area enclosed by \( |x| + |y| = 4 \) is:

A) 8

B) 16

C) 32

D) 4

64. If \( f(x) = x^3 - 3x + 1 \), how many real roots does it have?

A) 3

B) 1

C) 2

D) 0

65. The value of \( \lim_{x \to 0} \frac{\sin x - x}{x^3} \) is:

A) \( \frac{1}{6} \)

B) \( -\frac{1}{6} \)

C) 0

D) \( \frac{1}{3} \)

66. The number of ways to arrange 5 distinct books on a shelf is:

A) 120

B) 60

C) 24

D) 720

67. If \( \vec{a} = \hat{i} + 2\hat{j} \) and \( \vec{b} = 2\hat{i} - \hat{j} \), what is the angle between them?

A) 0°

B) 90°

C) 45°

D) 180°

68. The value of \( \int_{0}^{\pi/2} \sin^3 x \, dx \) is:

A) \( \frac{2}{3} \)

B) \( \frac{4}{3} \)

C) \( \frac{1}{3} \)

D) 1

69. The radius of the circle \( x^2 + y^2 - 4x + 6y - 12 = 0 \) is:

A) 2

B) 5

C) 3

D) 4

70. If \( f(x) = x^2 + 2x + 1 \), what is the inverse function?

A) \( f^{-1}(x) = \sqrt{x} - 1 \)

B) \( f^{-1}(x) = x - 1 \)

C) \( f^{-1}(x) = \sqrt{x} + 1 \)

D) \( f^{-1}(x) = x + 1 \)

71. The sum of the roots of \( x^2 - 5x + k = 0 \) is 5. If one root is 2, what is \( k \)?

A) 6

B) 6

C) 8

D) 4

72. The value of \( \cos^{-1}(\cos 5\pi/3) \) is:

A) \( \pi/3 \)

B) \( 5\pi/3 \)

C) \( 2\pi/3 \)

D) \( 4\pi/3 \)

73. The number of solutions to \( |x - 1| + |x - 2| = 1 \) is:

A) 0

B) 1

C) 2

D) Infinite

74. The differential equation \( \frac{dy}{dx} = y \) has the solution:

A) \( y = Ce^x \)

B) \( y = Ce^{-x} \)

C) \( y = Cx \)

D) \( y = C/x \)

75. If \( P(A) = 0.4 \), \( P(B) = 0.5 \), and \( P(A \cap B) = 0.2 \), what is \( P(A \cup B) \)?

A) 0.6

B) 0.7

C) 0.8

D) 0.9

76. The slope of the tangent to \( y = x^3 - 2x \) at \( x = 1 \) is:

A) 1

B) 2

C) 3

D) 0

77. The value of \( \sum_{n=1}^{\infty} \frac{1}{n^2} \) is:

A) \( \pi^2/12 \)

B) \( \pi^2/6 \)

C) \( \pi^2/8 \)

D) \( \pi^2/4 \)

78. The number of ways to choose 3 items from 5 is:

A) 10

B) 15

C) 20

D) 5

79. The equation of the plane through (1, 2, 3) and perpendicular to \( \vec{n} = \hat{i} + \hat{j} + \hat{k} \) is:

A) \( x + y + z = 5 \)

B) \( x + y + z = 6 \)

C) \( x + y + z = 7 \)

D) \( x + y + z = 8 \)

80. The value of \( \lim_{x \to \infty} \left(1 + \frac{2}{x}\right)^x \) is:

A) \( e^2 \)

B) \( e \)

C) \( e^4 \)

D) 1

Reasoning, English Grammar, General Knowledge & Awareness (20 Questions)

81. If APPLE is coded as BQQMF, how is ORANGE coded?

A) PSBOHF

B) PQBOHF

C) PSBOIF

D) PQAOIF

82. Choose the correct sentence:

A) Either the teacher or the students was present.

B) Either the teacher or the students were present.

C) Either the teacher or the students is present.

D) Either the teacher nor the students were present.

83. Who won the Nobel Prize in Chemistry for the discovery of the structure of DNA?

A) Linus Pauling

B) Watson and Crick

C) Marie Curie

D) Rosalind Franklin

84. As of May 2025, which country is the current chair of the G20?

A) Brazil

B) India

C) South Africa

D) Germany

85. If the day after tomorrow is Wednesday, what day is it today?

A) Monday

B) Monday

C) Tuesday

D) Sunday

86. Choose the word that best completes the analogy: Big : Small :: Fast : ?

A) Slow

B) Quick

C) Rapid

D) Large

87. The synonym of "ephemeral" is:

A) Permanent

B) Transient

C) Eternal

D) Constant

88. Which Indian state has the highest literacy rate as of 2025?

A) Kerala

B) Tamil Nadu

C) Maharashtra

D) Karnataka

89. In a group of 5 people, A speaks to B, B speaks to C, C speaks to D, and D speaks to E. If A wants to send a message to E, how many intermediaries are needed?

A) 1

B) 2

C) 3

D) 4

90. The antonym of "ameliorate" is:

A) Improve

B) Worsen

C) Maintain

D) Enhance

91. The headquarters of the United Nations is located in:

A) New York

B) Geneva

C) Paris

D) Vienna

92. If 3 cats catch 3 mice in 3 minutes, how many minutes will 6 cats take to catch 6 mice?

A) 6

B) 3

C) 1.5

D) 12

93. Choose the correctly spelled word:

A) Accommodate

B) Acommodate

C) Accomodate

D) Acomodate

94. The first Indian woman to win an Olympic medal is:

A) P.T. Usha

B) Karnam Malleswari

C) Saina Nehwal

D) Mary Kom

95. If the sequence is 1, 4, 10, 19, 31, …, what is the next term?

A) 46

B) 48

C) 50

D) 52

96. The meaning of the idiom "to beat around the bush" is:

A) To be aggressive

B) To avoid the main topic

C) To be confused

D) To be decisive

97. The currency of Japan is:

A) Yen

B) Won

C) Yuan

D) Ringgit

98. A clock shows 3:00. After 2 hours and 15 minutes, what is the angle between the hour and minute hands?

A) 30°

B) 22.5°

C) 45°

D) 60°

99. The author of "India Wins Freedom" is:

A) Maulana Abul Kalam Azad

B) Jawaharlal Nehru

C) Sardar Patel

D) Subhas Chandra Bose

100. If all roses are flowers and some flowers are red, which statement is true?

A) All roses are red

B) Some roses may be red

C) No roses are red

D) All flowers are roses

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