CSIT Entrance 2074

Mathematics

1. p/q ∈ R is defined if

2. [a,b] =

3. If f R⟶R defined by f(x) = $\sqrt{4-x^n}$ then f(-3) is

4. If |x| = 1 then x is

5. If log₂(x - 7) = 1 then x is

6. The value of sin(cos^-1 4/5) is

7. If tan²x = 3 then x is

8. If k + 2, 4k - 6, 3k - 2 and n are in AP then K is

9. Sum of infinity of 1 - 1/2 + 1/4 - 1/8 is

10. If A = $\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$ and B = ± $\left(\begin{array}{ccc}1& 2& 3\end{array}\right)$ then AB is

11. Value of $\left[\begin{array}{ccc}0& 2& 3\\ 1& 2& 3\\ 4& 8& 12\end{array}\right]$ is

12. Matrix $\left(\begin{array}{ccc}1& 2& 3\\ -1& 0& 4\\ -3& -4& 5\end{array}\right)$ is

13. [2(cos15 + isin15)]⁶ =

14. (1 + w + w²)³ + ( 1 + w - w²)³ =

15. Quadratic equation whose roots are -3 and n is

16. The line kx + 3y + 5 = 0 and 5x - 2y - 6 = 0 are perpendicular to each other for k =

17. The lines represented by 5x² + 3xy + ky² = 0 are perpendicular to each other for k =

18. The equation of tangent to circle x² + y ² = 9 at (1,1) is

19. ${\displaystyle \underset{x\to \infty }{lim}\frac{3x^2+2x-5}{6x^2+4x-7}=}$ =

20. ${\displaystyle \underset{x\to 0}{lim}\frac{1-coxax}{x^2}=}$

21. If x = t + sint, y = 1 - cost then $\frac{dy}{dx}$ is

22. Derivative of cosx w.r.t sinx is

23. The point of inflection of y = x³ - 12x² - 0 is

24. $\int \frac{dx}{si{n}^{2}x}=$

25. ${\int }_0^1\frac{dx}{1+x^2}=$

English

26. The word "commemorate" has the stress on __________ syllable

27. The word "go" has same vowel sound as the word _______

28. I hope that a school ______ for college children.

29 . One who is fond of fighting is _______

30. Select right synonym the word "analogus"

31. Give opposite meaning of "ominous"

32. He died ______ cancer but she died _____ the loss of blood.

33. Whom did you give it _______ ?

34. The dog sprang _______ a car

35. Insert missing vowel in these words: d_sease, d_ecease, suit_vs

36. Choose correct word from given option. Rice and curry _______ my favorite dish

37. There is a snag in it somewhere,

38. Custom of having many wives is called

39. Choose the right word: Monkeys _______

40. CHoose the right grammatical category of the underlined phrase.
Ram handed a book to his sister.

41. The car needs _____ hood repaired

42. These are two photographers are ______ same.

43. The girls is versatile, means

44. The word "aggresion" takes prefix

45. Fear of fire is called

46. Which of the following is noun?

47. We waited at the bus stop ______ the bus came.

48. One who travels from place to place

49. You're coming to the party ______ ?

50. Are you my friend or enemy? has a ______ tone

Physics

51. Order of magnitude of radius of an atom is

52. A projectile goes farthest away from Earth, when the angle of projection is

53. A simple pendulum where set into vibration comes to neat after sometimes because of

54. Powder cling to skin because of

55. Viscosity is inherent property of liquid and gases and is more closely related to

56. If a 200m bridge of steel has length from, temperature varies from 243K us 313K, The change of length of bridge for above seasonal variation in temperature (α_steel = 11 × 10^-6)

57. Internal Energy of perfect gas does not change during

58. Efficiency of steam engine is of order of

59. A gas maximum works when it expands

60. When two gases waves overlap the result is larger disturbance means

61. While standing still, an observer measures frequency of tuning fork to be 524 Hz. What frequency does he measure as he approaches the form at Sm/s ? (speed of sound in air = 340 m/s)

62. In longitudinal wave the displacement of the particles of medium is

63. The Illuminance at distance of 2 m from a 100 candle lamp is

64. When light beam is incident on a prism, it causes

65. If critical angle for a material placed in air is 30° the refractive index will be

66. A body has 1c of negative charge. How many excess electron it has as compared to its neutral state?

67. On heating a liquid, the refractive index generally

68. Torque on a electric dipole of moment vector (P) when paled in an electrical field vector (E) is proportional to

69. Wheat stone bridge is used to measure

70. Magnetism of a magnet

71. The self inductance of coil is MH. If a current of 2a is flown. What is the magnetic flux through coil?

72. Positive rays are

73. Wavelength of photon is 400Å. Its energy will be

74. According to Bohr's model of the H-atom, the radius of stationary orbit characterized by the principle of quantum number n is proportional to

75. In some substance, charges can flow at ordinary temperature but not at very low temperature. These are

Chemistry

76. Number of atoms of carbon present in 25 gm of Ca.CO₃ is

77. Electronic Configuration of chromium is

78. Structure of CO2 molecule is

79. Which element has highest electronic affinity?

80. Oxidation number Fe in compound Fe²O⁴

81. MgO is an example of

82. Down's process is used for the extraction of

83. IUPAC name of C-(CH₂)₄ is

84. Al₄C₃ reacts with water to give

85. Protein is polymer of

86. Which carbohydrates gives Tollen's Test?

87. DDT is an example of

88. Tranquilizers are substance used for treatment of

89. Each carbon atom in benzene is

90. 1°, 2° and 3° alcohols are distinguished by

91. Reduction of aldehyde by amalgamated zinc and conc. HCL to corresponding allcone is called as

92. Which is most basic?

93. Molecular formula of white vitrcol is

94. Cinnabar is an ore of

95. PH of 0.04M HNO₃

96. Unit of rte constant for first order reaction is

97. Which is an intensive property?

98. Unit of cell constant is

99. Unit of radioactivity is

100. Compound Na₂[Fe(CM)₅No] is known as