# CSIT Entrance 2072

### Mathematical

1. If a,b ∈ R , a/b is indeterminate, if

a = 0, b ≠ 0

a = 0, b = 0

a ≠ 0, b ≠ 0

a ≠ 0, b = 0

2. (-∞, ∞)

{x: -∞ ≤ x ≤ ∞}

{x: -∞ < x < 0}

{x: -∞ < x < ∞}

{x:x ≥ 0}

3. The statement is

Bagmati is a River

x > 0

How old are you?

y > 0

4. If (2x -1, -3) = (3, y + 3), then

x = 1, y = 0

x = -1, y = -3

x = 2, y = -6

x = 0, y = -1

5. If f: R ⟶ R is defined by f(x) = x and g: R ⟶ R is defined by g(x) = x then (fog)(x) is

x

x_{2}

1/x_{2}

1/x

6. If sin^{2}x = 1, then x is

π/2

± 1

- π / 2

nπ ± π/2

7. The value of sin(tan^{-1}x) is

$x$

$\frac{1}{1+{x}^{2}}$

$\frac{1}{\sqrt{1+{x}^{2}}}$

$\frac{x}{\sqrt{1+{x}^{2}}}$

8.If 2p, p + 8, 3p + 1 are in A.P. Then p is

5

3

7

-5

9. A,G and H are arithmetic mean, geometric mean and harmonic means respectively then

A^{2}-GH

h^{2} - AG

G - AH

G^{2} - AH

10. If A = $\left(\begin{array}{ccc}-1& 0& 2\end{array}\right)$ and B = $\left(\begin{array}{c}2\\ 3\\ 4\end{array}\right)$, then AB is

6

0

(-2 0 8)

(2 0 -4)

11. The value of the determinant $\left[\begin{array}{ccc}1& 2& 0\\ 2& 4& 1\\ 3& 6& 2\end{array}\right]$ is

1

3

0

4

12. The adjoint of the matrix abcd is

$\left(\begin{array}{cc}a& d\\ b& c\end{array}\right)$

$\left(\begin{array}{cc}a& b\\ d& c\end{array}\right)$

$\left(\begin{array}{cc}a& d\\ c& b\end{array}\right)$

$\left(\begin{array}{cc}d& \mathrm{-b}\\ \mathrm{-c}& a\end{array}\right)$

13. The real part of $\frac{(1+i{)}^{2}}{2-1}$ is

-2/5

2/5

1/5

1

14. If (1 + ω + ω^{2})( 1 + ω - ω^{2}) =

0

2

4

15. The value of k for which the equation x^{2} + 2(k + 2)x + 9k = 0 has equal roots are

4,1

-4,-1

-4,1

4,-1

16. The distance between the point (1,2) and the line 3x + 4y - 7 = 0 is

4

5

4/5

-4/5

17. The two line represented by ax^{2} + 2hxy + by^{2} = 0 are coincident if

h^{2} = ab

h^{2} >

h^{2} < ab

h^{2} > 0

18. The equation of tangent to the circle x^{2} + y^{2} = 4 at (2,1) is

x + y = 4

x - y = 4

2x + y = 4

x + 2y = 4

19. $\underset{x\to 0}{lim}\frac{x-2}{\sqrt{{x}^{2}-4}}$

0/0

0

1

4

20. $\underset{x\to 0}{lim}\frac{1-2co{s}^{2}ax}{{x}^{2}}$

0

a^{2}

2a^{2}

2

21. The value of x for which the function y = x^{} - x^{2} has $\frac{\text{}dy}{dx}$ = 0

0,2/

2/3

0

-2

22. the point of inflection for y = x^{2} - 2x

0

does not exist

2

1

${\int}_{0}^{1}\frac{2xdx}{\sqrt{1-{x}^{2}}}$

1/2

1

0

2

24. $\int xsinxdx=$

Sinx - xCosx + C

Sinx + xCosx + C

Cosx + xSinx + C

-Sinx + xCosx + C

25. Area bounded by the x-axis and the curve y = 3x^{2} and the ordinate of x = 2 and x = 4 is

27

8

19

0

### English

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

pair, tear

hut, but

seat, sit

salt, mark

27. The sentence " I saw a black bird" has a tone.

rising

falling

fall-rise

fall-fall

28. The word "joy" has the same initial consonant sound as the word

Zoo

gig

gesture

game

29. How many syllables does the word "pleasurable" have?

three

two

four

one

30. One who knows everything is

omnipresent

omnipatent

fatalist

omniscient

31. Select the right synonym to the word "aspiration"

apathy

yearning

haughty

soothe

32. Give the opposite meaning of "hypocrisy"

majority

jolly

sincerity

praise

33. He died ........ neglect but she died ..... a train accident.

through, in

in, through

of, of

of, is

34. Who did you go ...... ?

to

with

at

for

35. Insert the missing vowel : defin_te, po_gnant, exist_nce

e-i-e

a-i-e

i-e-a

e-e-e

36. The plane flew ....... my head

under

through

on

over

37. You and ...... I working

are

is

am

has

38. Choose the correct meaning to the underlined expression. He has turned the table on his enemy.

hit

joy

Change the possible defeat into a victory

run

39. Opposed to great or sudden change is called

static

conservative

evolutionary

revolutionary

40. Greed is terrible

sin

crime

vice

mistake

41. The gun ....... by mistake

went off

gave off

gave out

hit on

42. She has ....... down for ........ a rest

laid

lied

lay

lain

43. The work "brother" takes the suffix.

-ish

-ly

-some

-y

44. The word "desirable" takes the -prefix

un-

mis-

dis-

non-

45. English teacher makes her class interesting. It is

Adjunct

Complement

Direct Object

Indirect Object

46. Which is the correct expression?

today afternoon

this evening

the backside of a building

a worth seeing sight

47. She beckoned to enter the room. It means she

told

said

signalled

advised

48. The fear of blood is called

chirophobia

ergophobia

monomania

hemophobia

49. He has _______ friends because of his short temperament

few

a few

lot of

a lot of

50. Which of the following is a passive sentence

I like people loving me.

I found him driving my car

I hate having my hair style criticised

I don't mind people criticising my work

### Physics

51. A force F = $\overrightarrow{\mathrm{2i}}+\overrightarrow{\mathrm{3j}}-\overrightarrow{\mathrm{4k}}$ newton acts on a body. In 5 seconds the force displaces the body through a displacement S = $\overrightarrow{\mathrm{3i}}+\overrightarrow{j}-\overrightarrow{\mathrm{2k}}$ meter. The power (in watt) of the force is

4.3

3.4

5.4

6.3

52. Two simple harmonic waves are represented respectively by y1 = A1 sin ωt and y2 = A2 cos ωt. The phase difference between the two wave is

3π / 2

π

π/2

π/4

53. A river is flowing west to east at a speed of 5 m/min. A man on the south bank of the river, capable of swimming at 10m/min in still water, wants to swim across the river by the shortest path. He should swim in the direction

due north

30° East of North

60° East of North

30° West of North

54. Dimension of surface energy is

[M^{1}L^{0}T^{-2}]

[M^{1}L^{1}t^{-1}]

[M^{0}L^{1}T^{-2}]

[M^{2}L^{0}T^{-2}]

55. The terminal velocity of a small sized spherical body of radius r falling vertically in a viscous liquid is given as one of the following proportionality with radius.

r^{-2}

r^{-1}

r

r^{2}

56. A constant torque acting on a uniform circular wheel changes its angular momentum from L_{0} to 4L_{0} in 4 second. The magnitude of this torque is

(3/4)L_{o}

L_{o}

4_{o}

12L_{o}

57. At what temperature the rms velocity of a hydrogen molecule be equal to that of oxygen at 47°C

-273°C

273K

20K

20°C

58. Dimension of change in entropy is

[M^{1}L^{2}T^{2}K^{-1}]

[M^{1}L^{1}T^{2}K^{-2}]

[M^{1}L^{2}T^{-2}]

[M^{0}L^{2}T^{-2}K^{-1}]

59. A square plate of side 2 units is heated through 10°C. If the linear exansivity of the material is x, increase in the surface area of the plate is

480x

80x

240x

240x^{2}

60. A black body radiates heat energy at the rate of 2 x 10 Js''m' at a temperature of 127°C. The temperature of the black body at which the rate of heat radiation is 32 x 10^{5} is

327°

927°

527°

727°

61. A ray of light in air enters a glass slab. Its

wave length decrease

wave length increases

speed increases

frequency decreases

62. By using white light in double slit interference experiment the central fringe is white. What color of fringe can be seen nearest to the central fringe?

blue

green

red

violet

63. A convex lens is immersed in water. Compared to its power in air, the power in water will

increase for red and decrease for blue

decrease for all colors

be same for all colors

increase for all colors

64. Two vehicles are approaching each other with a speed of 10ms^{-1}. If A emits a note of 1000 vibrations, what will be the frequency of the note of 1000 vibration, what will be the frequency of the note as heard by a person sitting in B if the velocity of sound is 330 ms^{-1}?

950Hz

1000 Hz

1062.5 Hz

1215.5 Hz

65. An open pipe and a closed pipe resonate to the same tuning fork. The ratio of their lengths is

1:1

2:1

1:2

4:1

66. The radius of a copper wire carrying a current is doubled, the drift velocity of electrons will

remains the same

increases four times

decreases four times

increases first and then decreases

67. A 25W, 120V lamp and 100W, 120V lamp are connected in series across a 120V line. Which lamp will burn more brightly

25W, 120V

100W, 120V

Both will have same brightness

Alternatively both may be bright, one at a time.

68. A Spherical condenser of 1 Farad will have the dimension of

a small metallic ball of radius 0.04m

a big metallic ball of radius 100m

radius of earth whose radius is 6.4 x 106 m

A sphere having radius of more than that of earth

69. The ratio of induced emf in a coil having 50 turns and rotating with 50 Hz to that of induced emf in a coil having 100 turns and rotating with 150 Hz in the same magnetic field is

1:2

2:3

1:6

3:2

70. A 0 - 100mA resistance 1ft is to be converted to an ammeter in the range of 0-1A. We have to use shunt

1Ω

0.1Ω

0.111Ω

0.055Ω

71. The ratio of specific charge of proton to that of an alpha particle is

1:4

1:2

4:1

2:1

72. The angular momentum of electron in the hydrogen atom in the ground state is

h/2π

h/4π

h2

2h

73. The approximate radius of aluminum nucleus is

1.5 Fermi

2.5 Fermi

4.5 Fermi

13.5 Fermi

74. The kinetic energy of a particle is doubled, de Broglie wavelength becomes

2 times

4 times

2 times

1/2 times

75. Half life and mean life of a radioactive element are related. Choose correct answer from the following

Half life is less than the mean life

Half life is more than the mean life

mean life and the half life are the same

mean life is exactly two times the half life

### Chemistry

76. The number of moles present in 90g of water is

1.0

90.0

5.0

9.0

77. 1.0g of HCL reacts with 1.0g of CaCO_{3}, the volume of CO_{2} produced at NTP would be equal to

1.0 litres

0.224 litres

2.24 litres

22.4 litres

78. Magnetic quantum number specifies

orientation of orbitals

size of orbitals

shape of orbitals

magnetic properties of orbitals

79. A cooking gas cylinder can withstand a pressure of 20 atmosphere. At 27°C the pressure of the containing gas is 10 atmosphere. On raising the temperature, the cylinder will burst when the temperature exceeds

273°C

327°C

300°C

127°C

80. Which of the following: methods of expressing concentration is independent of temperature.

Molality

Molarity

Normality

Grams per liter

81. An aqueous solution of Na_{2}CO_{3} would be

acidic

basic

neutral

either acidic or basic

82. Which one of the-following is not a lewis base?

HO

NH_{3}

OH^{-1}

BF_{3}

83. In alkaline condition, KMnO^{4} reacts as follow

2KMnO_{4} + 2KOH ⟶ 2K_{2}MnO_{4} + H_{2}O + O, the Equation weight of KMnO_{4} is

M/1

M/2

M/5

M/6

84. The molecular geometry of which compound cannot be predicted by the application of VSEPR theory

CH_{4}

PCl_{5}

SF_{6}

MgCl_{2}

85. Which of the following is an amphoteric oxide

ZnO

MgO

SiO_{2}

H_{2}O

86. Ammonia is manufactured by the use of

Downs Process

Solroy's Process

Haber's Process

Ostwald's Process

87. Dry ice is

ice which is dried by treating with dehydrating agent

ice which is super cooled

Solid CO_{2}

ice mixed with some organic solvents

88. Number of atoms in one molecule of sulfur is

8

4

2

1

89. Which of the following noble gas is not present in atmosphere?

He

Ar

Ne

Rn

90. Chalcopyrite is an ore of

Fe

Cu

Zn

Hg

91. The substance used as flux in the extraction of iron from hamatite in blast furnace is

Calcium phosphate

Silica

Limestone

Calciu Silicate

92. The formula of bleaching powder is

Ca(OCl)Cl

CaSO_{4}.2H_{2}O

2CaSO_{4}.H_{2}O

MgSO_{4}.7H_{2}O

93. The members of a homologous series have

different general formula

different molecular weight

different chemical properties

Diffrent method of preparation

94. Which of the following reagent cannot be used to distinguish between acetaldehyde and acetone

Tollen's Reagent

Fehling's Solution

Schiff's Reagent

Br_{2} in CCl_{4}

95. Reduction of nitrobenzene in acidic medium gives

aniline

azoxybenzene

azobenzene

Hydrazobenzene

96. When formaldehyde reacts with ammonia, it gives

aldehyde ammonia

formic acid

urotropine

methyl amine

97. Dettol is an example of

analgesic drug

antipyretic drug

antibiotic drug

antiseptic drug

98. BHC is an example of

Condensation polymer

addition polymer

azo Dye

Pesticide

99. Protein is a compound having

ether linkage

ester linkage

peptide linkage

arhine linkage

100. Which one of the following is present as sugar unit in DNA

Glucose

Sucrose

Deoxyribosed

Ribose