BTech-MTech CS - NFAT Mock Test 3

NFAT BTech Computer Science Entrance Exam Mock Test 2025

Physics (27 Questions)

1. A particle moves with velocity \( v(t) = 3t^2 - 12t + 9 \, \text{m/s} \). What is the distance traveled from \( t = 0 \, \text{s} \) to \( t = 4 \, \text{s} \)?

A) 24 m

B) 32 m

C) 28 m

D) 36 m

2. In a double-slit experiment, the slit separation is 0.2 mm, and the screen is 1.5 m away. If the wavelength is 600 nm, what is the fringe width?

A) 4.5 mm

B) 4.5 × 10\(^{-3}\) m

C) 2.25 mm

D) 9 mm

3. A 2 kg block is pulled with a force of 10 N at 60° to the horizontal on a frictionless surface. What is the acceleration (\( g = 10 \, \text{m/s}^2 \))?

A) 2.5 m/s\(^2\)

B) 5 m/s\(^2\)

C) 3 m/s\(^2\)

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

4. A gas undergoes an adiabatic process with initial pressure 4 atm and volume 1 L. If the volume doubles, what is the final pressure (\( \gamma = 1.4 \))?

A) 2 atm

B) 1.52 atm

C) 3 atm

D) 4 atm

5. A planet has four times the mass and twice the radius of Earth. What is the acceleration due to gravity on its surface (\( g_{\text{Earth}} = 9.8 \, \text{m/s}^2 \))?

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

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

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

D) 39.2 m/s\(^2\)

6. A concave lens of focal length 20 cm forms an image at 15 cm from the lens. What is the object distance?

A) 60 cm

B) 30 cm

C) 12 cm

D) 25 cm

7. A 12 V battery is connected across a resistor of 4 Ω. What is the power dissipated?

A) 48 W

B) 36 W

C) 24 W

D) 12 W

8. A radioactive isotope has a half-life of 15 days. What fraction remains after 45 days?

A) 1/2

B) 1/4

C) 1/8

D) 1/16

9. A disk rotates with angular velocity \( \omega = 4t^2 + 2t \). What is the angular acceleration at \( t = 3 \, \text{s} \)?

A) 26 rad/s\(^2\)

B) 14 rad/s\(^2\)

C) 8 rad/s\(^2\)

D) 20 rad/s\(^2\)

10. A sound wave has a frequency of 400 Hz and travels in water (speed 1480 m/s). What is its wavelength?

A) 2.7 m

B) 3.7 m

C) 4.7 m

D) 5.7 m

11. A charged particle (\( q = 2 \, \mu \text{C} \), \( m = 4 \, \text{mg} \)) is in an electric field \( \vec{E} = 1000 \hat{i} \, \text{V/m} \). What is its acceleration?

A) 500 m/s\(^2\)

B) 250 m/s\(^2\)

C) 1000 m/s\(^2\)

D) 750 m/s\(^2\)

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

A) 60 m

B) 90 m

C) 91.8 m

D) 120 m

13. A photon has wavelength 500 nm. What is its energy (in eV)?

A) 1.24 eV

B) 2.48 eV

C) 3.72 eV

D) 4.96 eV

14. In an isochoric process, a gas is heated from 300 K to 600 K at constant volume. If initial pressure is 1 atm, what is the final pressure?

A) 2 atm

B) 1 atm

C) 3 atm

D) 0.5 atm

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

A) \( (4.5 \hat{j} + 3 \hat{i}) \times 10^{-6} \, \text{N} \)

B) \( (4.5 \hat{j} - 3 \hat{i}) \times 10^{-6} \, \text{N} \)

C) \( (-4.5 \hat{j} + 3 \hat{i}) \times 10^{-6} \, \text{N} \)

D) Zero

16. A convex mirror has a focal length of 25 cm. An object is placed 50 cm from it. What is the image distance?

A) 50 cm

B) 25 cm

C) 16.67 cm

D) 75 cm

17. A simple harmonic oscillator has amplitude 10 cm and angular frequency 2 rad/s. What is its maximum acceleration?

A) 40 cm/s\(^2\)

B) 20 cm/s\(^2\)

C) 10 cm/s\(^2\)

D) 80 cm/s\(^2\)

18. A transformer has 500 primary and 250 secondary turns. If the input voltage is 220 V, what is the output voltage?

A) 440 V

B) 110 V

C) 55 V

D) 220 V

19. In a single-slit experiment, if the slit width is doubled, the width of the central maximum:

A) Halves

B) Doubles

C) Remains the same

D) Quadruples

20. A body of mass 3 kg is dropped from a height of 5 m. What is its kinetic energy just before hitting the ground (\( g = 10 \, \text{m/s}^2 \))?

A) 100 J

B) 150 J

C) 200 J

D) 50 J

21. A wire of resistance 8 Ω is cut into four equal parts and connected in parallel. What is the equivalent resistance?

A) 2 Ω

B) 4 Ω

C) 0.5 Ω

D) 1 Ω

22. A simple pendulum has a period of 2 s on Earth. What is its period on the Moon (\( g_{\text{Moon}} = g_{\text{Earth}}/6 \))?

A) 4.9 s

B) 2 s

C) 1.2 s

D) 3.5 s

23. A convex lens has a focal length of 30 cm. An object is placed 20 cm from it. Where is the image formed?

A) 60 cm behind the lens

B) 60 cm in front of the lens

C) 30 cm behind the lens

D) 30 cm in front of the lens

24. A rocket ejects gas at 1500 m/s with a mass ejection rate of 20 kg/s. What is the thrust?

A) 15000 N

B) 20000 N

C) 30000 N

D) 45000 N

25. A block of mass 4 kg slides down a 30° incline with a coefficient of friction 0.2. What is its acceleration (\( g = 10 \, \text{m/s}^2 \))?

A) 3.5 m/s\(^2\)

B) 4.2 m/s\(^2\)

C) 5 m/s\(^2\)

D) 2.8 m/s\(^2\)

26. A parallel plate capacitor has plates of area 0.01 m\(^2\) separated by 0.1 mm with a dielectric (\( \kappa = 2 \), \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \)). What is its capacitance?

A) 1.77 nF

B) 0.885 nF

C) 3.54 nF

D) 0.442 nF

27. A solenoid has 2000 turns over 1 m and carries 1.5 A. What is the magnetic field at its center (\( \mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A} \))?

A) 1.88 × 10\(^{-3}\) T

B) 3.77 × 10\(^{-3}\) T

C) 7.54 × 10\(^{-3}\) T

D) 0.94 × 10\(^{-3}\) T

Chemistry (26 Questions)

28. The cell potential of \( \text{Zn}|\text{Zn}^{2+} (0.01 \, \text{M}) || \text{Ag}^+ (0.1 \, \text{M})|\text{Ag} \), \( E^\circ_{\text{cell}} = 1.56 \, \text{V} \) at 298 K is:

A) 1.62 V

B) 1.50 V

C) 1.68 V

D) 1.44 V

29. A reaction \( \text{A} + 2\text{B} \to \text{C} \) has rate law \( \text{Rate} = k[\text{A}]^2[\text{B}] \). If [A] is tripled and [B] is doubled, the rate increases by:

A) 36 times

B) 18 times

C) 12 times

D) 9 times

30. Which molecule has a trigonal planar geometry?

A) \( \text{NH}_3 \)

B) \( \text{H}_2\text{O} \)

C) \( \text{BCl}_3 \)

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

31. The major product of 1-butene with \( \text{HCl} \) in the absence of peroxides is:

A) 2-Chlorobutane

B) 1-Chlorobutane

C) 1,2-Dichlorobutane

D) 2,2-Dichlorobutane

32. For a reaction, \( \Delta H = -50 \, \text{kJ/mol} \), \( \Delta S = -100 \, \text{J/mol} \cdot \text{K} \). At what temperature is it spontaneous?

A) Above 600 K

B) Below 500 K

C) Above 500 K

D) Below 400 K

33. The interplanar spacing for (111) planes in a cubic crystal with lattice parameter 3 Å is:

A) 1.732 Å

B) 3 Å

C) 1 Å

D) 2 Å

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

A) 2.83 BM

B) 1.73 BM

C) 0 BM

D) 4.9 BM

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

A) Benzyl chloride

B) Chlorotoluene

C) 1,2-Dichlorotoluene

D) Hexachlorotoluene

36. If the salt bridge in a galvanic cell is removed, what happens?

A) Voltage increases

B) Cell stops functioning

C) Current doubles

D) Electrodes corrode

37. The pH of a 0.01 M solution of a weak acid (pKa = 4) is:

A) 3

B) 4

C) 5

D) 2

38. The hybridization of carbon in ethene is:

A) sp

B) sp\(^3\)

C) sp\(^2\)

D) dsp\(^2\)

39. For \( \text{N}_2 + 3\text{H}_2 \to 2\text{NH}_3 \), if \( \Delta H = -92 \, \text{kJ/mol} \), what is \( \Delta H_f \) of \( \text{NH}_3 \)?

A) -46 kJ/mol

B) -92 kJ/mol

C) -23 kJ/mol

D) -184 kJ/mol

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

A) \( \text{N}_2 \)

B) \( \text{He} \)

C) \( \text{NH}_3 \)

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

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

A) +5

B) +7

C) +6

D) +4

42. The half-life of a first-order reaction is 20 min with rate constant 0.0347 min\(^{-1}\). What is the time for 50% completion?

A) 20 min

B) 40 min

C) 10 min

D) 60 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 \( \text{HCl} \) with \( \text{NaOH} \), the indicator methyl orange changes color at pH:

A) 7

B) 4

C) 9

D) 2

45. The bond order of \( \text{N}_2^+ \) 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 pure water?

A) \( 1.05 \times 10^{-5} \, \text{M} \)

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

C) \( 2.2 \times 10^{-5} \, \text{M} \)

D) \( 5.5 \times 10^{-11} \, \text{M} \)

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

A) \( \text{NaOH} \)

B) \( \text{Na}_2\text{CO}_3 \)

C) \( \text{HCl} \)

D) \( \text{H}_2\text{SO}_4 \)

48. The structure of \( \text{SF}_4 \) is:

A) Tetrahedral

B) Square planar

C) Seesaw

D) Trigonal pyramidal

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 for \( \text{SO}_3 \) production is:

A) Fe

B) \( \text{V}_2\text{O}_5 \)

C) Pt

D) Ni

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

A) 2

B) 4

C) 3

D) 6

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

A) Hydrogen bonding

B) London forces

C) Dipole-dipole interactions

D) Covalent bonding

53. The coordination number of Co in \( [\text{Co}(\text{NH}_3)_6]^{3+} \) is:

A) 4

B) 6

C) 8

D) 5

Mathematics (27 Questions)

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

A) 4

B) 7

C) 3

D) 1

55. The number of ways to distribute 5 identical balls into 3 distinct boxes with at least one ball per box is:

A) \( \binom{4}{2} \)

B) \( \binom{5}{2} \)

C) \( \binom{4}{3} \)

D) \( \binom{5}{3} \)

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

A) 0

B) 1

C) 2

D) \( \pi/2 \)

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

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

B) 3

C) 2

D) 1

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

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

59. If \( \cos^{-1}x + \cos^{-1}y = \pi \), what is \( x^2 + y^2 \)?

A) 1

B) 2

C) 0

D) -1

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

A) 1

B) 2

C) 3

D) 0

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

A) 4

B) 9

C) 16

D) 25

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 of the region bounded by \( y = |x| \) and \( y = 2 \) is:

A) 2

B) 4

C) 8

D) 6

64. If \( f(x) = x^3 - 3x + 2 \), how many real roots does it have?

A) 3

B) 1

C) 2

D) 0

65. The value of \( \lim_{x \to 0} \frac{\sin 2x}{x} \) is:

A) 2

B) 1

C) 0

D) 4

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

A) 120

B) 60

C) 24

D) 240

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

A) 0°

B) 90°

C) 45°

D) 180°

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

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

B) \( \pi \)

C) \( \frac{\pi}{4} \)

D) \( 2\pi \)

69. The radius of the circle \( x^2 + y^2 - 6x + 8y + 15 = 0 \) is:

A) 2

B) 5

C) 3

D) 4

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

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

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

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

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

71. The product of the roots of \( x^2 - 5x + k = 0 \) is 6. What is \( k \)?

A) 6

B) 5

C) 4

D) 7

72. The value of \( \cos^{-1}(\cos 5\pi/4) \) is:

A) \( \pi/4 \)

B) \( 5\pi/4 \)

C) \( 3\pi/4 \)

D) \( -\pi/4 \)

73. The number of solutions to \( |x - 1| + |x - 4| = 3 \) is:

A) 0

B) 2

C) 1

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 \( y = x^3 - 2x + 1 \) at \( x = 1 \) is:

A) 1

B) 2

C) 3

D) 4

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 \( \vec{n} = \hat{i} + 2\hat{j} + 3\hat{k} \) is:

A) \( x + 2y + 3z = 6 \)

B) \( x + 2y + 3z = 14 \)

C) \( x + 2y + 3z = 10 \)

D) \( x + 2y + 3z = 12 \)

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

A) \( e^2 \)

B) \( e^3 \)

C) \( e \)

D) \( e^4 \)

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

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

A) HQTKF

B) HSQJG

C) HRQJF

D) HPTKG

82. Choose the correct sentence:

A) Either the manager or the employees are responsible.

B) Either the manager or the employees is responsible.

C) Either the manager or the employees was responsible.

D) Either the manager or the employees were responsible.

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

A) Linus Pauling

B) James Watson

C) Francis Crick

D) Both B and C

84. As of June 2025, which country is hosting the FIFA World Cup 2026?

A) Qatar

B) Brazil

C) United States

D) Germany

85. If today is Wednesday, what day will it be after 10 days?

A) Saturday

B) Sunday

C) Monday

D) Tuesday

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

A) Light

B) Large

C) Massive

D) Dense

87. The synonym of "ephemeral" is:

A) Permanent

B) Short-lived

C) Eternal

D) Constant

88. Which Indian state is known as the "Land of the Rising Sun"?

A) Arunachal Pradesh

B) Assam

C) Sikkim

D) Nagaland

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

A) 2

B) 3

C) 4

D) 1

90. The antonym of "ameliorate" is:

A) Improve

B) Worsen

C) Enhance

D) Develop

91. The headquarters of the World Health Organization is located in:

A) Geneva

B) Paris

C) New York

D) Vienna

92. If 6 workers complete a task in 12 days, how many days will 3 workers take to complete the same task?

A) 6

B) 24

C) 18

D) 36

93. Choose the correctly spelled word:

A) Accommodation

B) Accomodation

C) Acommodation

D) Accommodaton

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

A) P.V. Sindhu

B) Karnam Malleswari

C) Saina Nehwal

D) Mary Kom

95. If the sequence is 3, 7, 13, 21, 32, …, what is the next term?

A) 42

B) 46

C) 48

D) 50

96. The meaning of the idiom "to hit the nail on the head" is:

A) To cause trouble

B) To be exactly correct

C) To act recklessly

D) To miss an opportunity

97. The currency of Japan is:

A) Yen

B) Won

C) Dollar

D) Euro

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 "Wings of Fire" is:

A) A.P.J. Abdul Kalam

B) R.K. Narayan

C) Amartya Sen

D) Chetan Bhagat

100. If all cats are animals and some animals are white, which statement is true?

A) All cats are white

B) Some cats may be white

C) No cats are white

D) All animals are cats

Test Results