CSIT Entrance 2071

Mathematics

1. If (x-3) = 4 then x is

7 and -1

7 and 1

2. If {x-x² = 9 and 2x = 6}, then

Null Set

{3}

{3,-3}

{4,3}

3. If R⟶R defined by f(x)=x² + 3 then f^-1(4) is

Null

{-1,1}

{1,0}

{4,3}

4. The value of log2 is

3/2

-3/2

π/6

5. If cos2θ = 1/2, then θ is

nπ ± π/4

nπ + π/4

nπ ± π/3

2nπ

6. cos(sin-13/5) =

3/5

4/5

9/25

4/25

7. If a², b², c² are in H.P. then

2a²x² = b²(a² + c²)

a²c² = b²(a² + c²)

2b²c² = a²(b² + c²)

c²a² = 2b²(a² + c²)

8. If $A = [\begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}]$ , then A² - nA - I = 0, then the value of n is

-4

9. If $A = [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \end{matrix}]$ , then A is

Symmetric

Skew-Symmetric

Singular

Non Singular

10. The system of equation 2x + y = 5; 4x + 2 = 8 is

Consistent and dependent

Inconsistent and Independent

Inconsistent and dependent

Consistent and independent

11. The value of i⁷ + 1/i⁴ is

-1

-i

-i+1

12. The value of x - wy - x2zy + wz + w2x, where w is the cube root of unity is

x + y + z

w²

13. If the roots of x² + 4x + k = 0, are equal then k is

-4

14. The two line a1x + b1y +c1 = 0 and a2x + b2y + c2 = 0 are identical if

$\frac{a 1}{a 2} = \frac{b 1}{b 2} = \frac{c 1}{c 2}$

$\frac{a 1}{a 2} = 0$

$\frac{b 1}{b 2} = 0$

$\frac{c 1}{c 2} = 0$

15. The two line 2x² - 2xy + ky² = 0 are perpendicular to each other if k is

-2

16. The equation of the circle touching the positive x-axis and y-axis with radius 2 units is

x² + y² - 4x - 4y + 4 = 0

x² + y² + 4x + 4y - 4 = 0

x² + y² - 4x + 4y + 4 = 0

x² + y² - 4x + 4x - 4 = 0

17. If the line 4x + 3y = k is tangent to the circle x² + y² = 2S at (2,1) then k is

-25

± 25

± 11

18. The value of $lim_{x \to 2} \frac{x^{5} - 2^{5}}{x - 2} =$ is

19. The value of $lim_{x \to 0} \frac{3 x + 4 t a n 2 x}{x}$ is

20. The derivative of y = b^x is

xb^x-1

x^bln|b|

b^xln|b|

21. The derivative of $y = c o s (c o s \sqrt{x})$ is

$\frac{s i n (c o s \sqrt{x}) . s i n (\sqrt{x})}{2 \sqrt{x}}$

$s i n (c o s \sqrt{x})$

$s i n (s i n \sqrt{x})$

$\frac{s i n (c o s \sqrt{x})}{2 \sqrt{x}}$

22. The value of x for which the derivative of x²+2x+2 is zero is

23. The point of inflection of the curve x²+3x²-9x+2 is

-1

24. $\int \frac{d x}{1 - c o s x}$ =

tan x/2

-cot x/2

cos x/2

-tan x/2

25. $\int_{0}^{\frac{1}{2}} \frac{c o s x}{1 + s i n x} d x$

∞

ln|2|

English

26. The word "education" has the stress on the ...... syllable

first

second

third

fourth

27. Select the right synonym to the word "ardous"

Simple

Diffcult

easy

strange

28. Give the opposite meaning of "obscure"

Pedantic

implicit

explicit

obnoxious

29. The initial consonant sound of "chef" is the same as that of ....

Chute

chess

child

cheap

30. Which of the following pair has the same vowel sound?

Hut/hot

sit/seat

salt/mark

pair/tear

31. I completely differ ..... you ...... this point.

From: at

from: in

from: on

to: at

32. We feel sympathy ........ the poor

With

about

for

33. He insisted ....... leaving immediately.

over

34. Tick the correct word to the underlined expression.
No one knows his hole and corner method of dealing with people.

strict

secret

servile

suspicious

35. Food that agree to one's taste is ......

Pungent

Edible

Servile

suspicious

36. The word "pleased" takes the prefix .....

mis-

dis-

none-

37. One who is presented everywhere is ........

omnipresent

omniscient

theist

omnipotent

38. Fear of food is called as ........

Sitophobia

ergophobia

Panthophobia

Hyctophobia

39. A funeral bell is called

call

knell

replica

invitation

40. People ....... a large number of computer now, because prices are getting low

must buy

must have brought

must be buying

must buying

41. Although they are similar, chipmunks are ...... most other ground squirrels.

Alike

like as

like to

42. She ........ the whole day long

has been working

works

had worked

worked

43. Now a days shyam is ....... busy to take care of his health

very

extremely

44. She demanded ...... her status

know

knowing

to know

to be known

45. The mail comes at ten'O clock everyday ........ saturday

but also

and

also

but

46. In my office, salary is paid by ..... month.

the

some

47. Every boy and every girl ......... very responsible

are

has

have

48. Which of the following is accepted

Some of rice is still left

Time and tide wait for none

She absent herself from the college today

None of the square was properly drawn

49. Which of the following is complete sentence

However, hard she worked, she failed in the exam

It rained heavily, however he came to school

In spite of heavy rain, he come to school

Neither she nor he will come

50. Which of the following is an adjective

Sympathize

Lighten

Perception

Moral

Physics

51. The dimension of (h/e) are same as that of

Magnetic field

Electric field

Magnetic flux

Electric flux

52. The number of significant figure in 0.0030 x 10¹¹m are

53. μk and μk are coefficent of static and kinetic friction between two bodies. Then

μs ≥ μk

μs < μk

μs = 0 and μk > 0

μk < 0 and μk < 0

54. When a torque acts on a body, the change in the angular momentum of the body is

Perpendicular to $\vec{L}$

Always zero

180° $\vec{L}$

55. The Poisson's ratio of material can't be

0.10

0.20

0.40

0.65

56. The depth of water at which air bubble of radius 0.4mm may remain in equilibrium (surface tension of water = 72 x 10^-3 N/m, g = 9.8 m/s² is given by

7.348 cm

0.918 cm

3.674 cm

1.837 cm

57. When a cylinder is heated, it's length increases by 2%, the area of its base will increase by:

0.5%

58. In a pressure cooker food is cooked usually at a pressure

One atmosphere

half atmosphere

two atmosphere

50 atmosphere

59. The mean free path of a gas varies with absolute temperature (T)

T⁴

1/T⁴

1/T

60. The efficiency of Carnot engine working between steam point and ice point is:

16.8%

26.8%

36.8%

46.8%

61. The bending of sound waves through the corners of the obstacle is called

Refraction

interference

beats

diffraction

62. When a tuning fork is vibrated its prongs have a phase difference of

π / 4

2π

63. The image of an object placed at the focus of conves mirror is ar a distance

∞

f/2

64. If sky is seen from moon's surface, it will appear

black

Blue

White

Red

65. A double convex air bubble in a glass sheet would behave as a

Convergent lengs

Concave mirror

Divergent Lens

Plane Mirror

66. When two prism are combined it gives

Reflection only

lateral shift

Dispersion and deviation both

Dispersion or deviation

67. Which property of electrons is used in an electron microscope?

negative charge

wave nature

spin

small size

68. A system of three charges may be in equilibrium . If they are placed

On a straight line

On corners of equilateral triangle

On three corners of rectangle

On the corners of a cube

69. The radius of Earth 6400 km. The capacitance is

6400 MF

6400 F

1 F

711 μF

70. Two wire of same material have lengths L and 2L and are cross reaction areas 4A and A respectively. The ratio of their specific resistance would be

1:1

1:8

8:1

1:2

71. The magnetic field induction inside a long solenoid is

zero

2μ₀ni

μ₀ni

μni

72. Electron in the atom are held due to

Nuclear forces

Coulomb forces

Van der Waals force

Gravitational forces

73. Which series of H atom lies in visible region?

Lyman

Bracket and Paschen

Balmer

Paschen

74. The half-life of a substance is 1600 years. The mean life is

1600 yrs

3200 yrs

800 yrs

2309 yrs

75. Rydberg constant is

Same for all element

Different for different element

A universal constant

Is diffrent for lighter element but same for heavier elements

Chemistry

76. How many orbitals are possible for principle quantum number 3?

77. The number of moles of water present in 18g of water is

1.8

180

78. The half-life of an radioisotope is 30 minutes. After how much time the amount of radioisotope left is 1/4^th of the original amount?

4 minutes

30 minutes

60 minutes

120 minutes

79. What is oxidation of chlorine is HOCL?

-1

80. Hemoglobin contains 0.33% of iron by weight. Molecular weight of hemoglobin is 67200. The number of iron atoms (At wt of Fe = 55.85) ion one molecule of hemoglobin is

81. The gas law which deals with the effect of pressure is a given volumn of gas constant temperature is known as

Boyle's Law

Charle's Law

Graham's Law

Dalton's Law

82. Electronic configuration of four element A,b,c,d are as follows, which will be most metallic?

A = 2,8,4

B = 2,8,8

C = 2,8,1

D = 2,8,1

83. In which of the following compound the molecular geometry cannot be predicted by the use of VSEPR theory

NaCl

H₂O

CH₄

NH₃

84. Consider the reaction 2A + B → C + D. If the concentration of the reactants are increase by three times, the rate of reaction will increase by

3 times

6 times

9 times

27 times

85. An aqueous solution of NaCl would be

Acidic

Basic

Neutral

could be acidic or basic depending upon temperature

86. THe pH of pure water at 50°C would be

7.0

> 7.0

< 7.0

cannot be predicted

87. which of the following metals generate H₂0 on treatment with dil.HNO3?

88. 1 M H₂SO₄ is equals to

1 NH₂SO₄

2 NH₂SO₄

0.5 NH₂SO₄

4NH₂SO₄

89. Hydrogen molecule which has parallel spin of two nuclei called

Ortho hydrogen

para hydrogen

heavy Hydrogen

nascent hydrogen

90. Ammonia is manufactured by the use of

Solvay's process

Haber's process

Ostwald's Process

Down's Process

91. Hematite is an ore of

92. Which of the following is not a nucleophile

BF₃

NH₃

H₂O

93. Anti-Markovnikoff addition of HBr is not observed in

Propane

1-Butane

2-Butane

Pent-2-one

94. When oxalic acid crystals and glycerol are mixed and heated to about 110°C, The compound obtained is

Chloroform

Diethylether

Acetone

Formic acid

95. Which of the following is meta directing group?

-NH₂

-OH

-COOH

-R

96. How many position isomers are possible for dichlorobenzene?

97. which one of the following is condensation polymer

polythene

terylene

PVC

Teflon

98. Penicillin is an example of

Antiseptic drug

Antipyretic drug

Antibiotic drug

Analgesis drug

99. Enzymes are

Carbohydrates

Proteins

Lipids

Nucleic acid

100. Which base is found only in the nucleotides of RNA?

Adenine

Guanine

Uracil

Cytosine

bcafamily

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