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# CSIT Entrance 2075

### Mathematics

1. a/b,a,b ∈ R, is equal to zero if

a ≠ 0, b ≠ 0

a = 0, b = 0

a = 0, b ≠ 0

a ≠ 0, b ≠ 0

2. If x ≥ 5, then x may be

-5

6

0

3. If |x - 2| = 5 then the value of x is

{5}

{-2,5}

{-2,-5}

{-3,7}

4. The range of relation R = {(1,2),(2,3),(3,4)} is

{1,2,3}

{1,2,3,4}

{2,3,4}

R

5. If y = ax is the exponential function passing through (4,81) then the base a is

4

3

81

a

6. If tan2x = 1 then x is

nπ ± π/4

nπ + π4

nπ - π/4

± π/4

7. Sin(2sin-1x) =

$\sqrt{1-{x}^{2}}$

$2x\sqrt{1-{x}^{2}}$

$2x\left(1-{x}^{2}\right)$

$\sqrt{2x\left(1-{x}^{2}\right)}$

8. The sum to infinity of the G.P : 1/4, -1/16 ...... is

5

-5

-1/5

1/5

9. The value of a so that 8a + 4, 6a - 2, 3a + 7 will form an A.P is

15

2

9

10

10. the value of $|\begin{array}{ccc}2& 3& 4\\ 5& 6& 7\\ 10& 12& 14\end{array}|$ is

10

15

0

20

11. If A = (1,2,3) and b = $\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$ then AB is

4

14

0

15

12. The inverse of the matrix $|\begin{array}{cc}-1& 1\\ 1& -3\end{array}|$ is

$|\begin{array}{cc}-3& 1\\ 1& -1\end{array}|$

$\frac{1}{2}$ $|\begin{array}{cc}-3& -1\\ -1& -1\end{array}|$

$|\begin{array}{cc}-3& -1\\ 1& 1\end{array}|$

$\frac{1}{2}$ $|\begin{array}{cc}-1& 1\\ 1& -3\end{array}|$

13. If ω is the cube root of unity the (1 - ω + ω2)3 =

0

-8

1

8

14. $|\frac{1}{1+i}|$ =

$\frac{1}{2}$

$\sqrt{2}$

$\frac{1}{\sqrt{2}}$

$2$

15. The quadratic equation whose roots are 3 and 4 is

x2 - 7x - 12 = 0

x2 - 7x + 12 = 0

x2 + 7x + 12 = 0

x2 + 7x - 12 = 0

16. The perpendicular distance from (-1,-2) to the line 3x + 4y + 12 = 0 is

-1

1

2

3

17. If the lines represented by ky2 + (2 - k)2xy - 3x2 = 0 are perpendicular if k =

-3

3

0

1

18. The equation of the tangent to the circle x2 + y 2 = 5 at (2,1) is

2x + y = 5

x + y = 5

2x - y = 5

x - y = 5

19. $\underset{x\to \mathrm{\infty }}{lim}\frac{x\left(x+1\right)}{{x}^{2}}=$

1

0

2

20. $\underset{x\to \frac{\pi }{4}}{lim}\frac{se{c}^{2}x-2}{tanx-1}=$

0

1

2

-2

21. $\frac{dy}{dx}$ of $t={x}^{2},y=\frac{1}{t}$ is

1

-2/x2

2/x2

2/x3

22. The derivative of x2 with respect to -x2 is

0

1

2x

-1

23. ${\int }_{0}^{1}\frac{2x}{1+{x}^{2}}dx$

0

log2

2

1

24. $\int \frac{dx}{x\left(1+lnx{\right)}^{2}}=$

$-\frac{1}{1+lnx}+c$

$\frac{1}{1+lnx}+c$

$\frac{1}{lnx}+c$

$\frac{1}{x\left(1+lnx\right)}+c$

25. Area bounded by the x-axis and the curve y = 4x2 and the ordinate x = 1 and x = 4 is

64

84

16

-84

### English

26. I promise that I won’t ............ to anyone.

Let up

Let off

Let on

Let down

27.Henry ............. because of the heat and stuffy atmosphere.

pass on

pass out

pass off

pass over

28. I don’t want you to feel ............. By my presence-please go out whenever you like

tie down

tie in with

tie up

thrown out

29.Jenny is unpredictable, she always .......... When you least expect her.

show off

callby

callon

call up

30.Don’t go out. Mahesh is .......... This evening.

call for

call by

call on

call up

31.Select the right synonym to the word “Languid”.

vigorous

grave

weak

Cnaste

32. Select the right synonym to the word “magniloquent”.

dismal

hazy

precept

inflated

33.Give the opposite meaning of “ mendacious”

false

veracious

obstinate

venal

34. Give the opposite meaning of “vivacious”.

gay

offence

depressed

faint

35.One who remains silent while others talk continuously is ..........

taciturn

tarnish

blemish

hot

36. There is no cause .......... anxiety but you should take care ........ your health.

for, in

for, of

of, after

of,in

37. have no sympathy .......... the musicians as I have no taste ...... music

to , for

for , in

with, for

for , to

38. The boy acted contrary ......... my order and he had deaf ear............ my suggestions.

to ,on

for , to

by, to

to , to

39. Most of street children are addicted .......... Drugs and are not anxious ...... their future.

to ,for

to , to

for , for

on, at

40. A poet touches ..........a subject and turn it ....... A poem.

at ,to

upon, into

on, to

at , in

41. An abnormal dread of being shut up in a small room.

zoophobia

hydrophobia

claustrophobia

podophobia

42. Correct meaning of “magnum opus” is

Precious

a great work

miraculous

significant

43. The killing of one’s wife is called:

uxoricide

homicide

filicide

sorricide

44. Bees are kept in ................ Whereas fishes are kept in..........

aviary, zoo

apiary, aquarium

cemetery, depot

dispensary, garage

45. Swear like a trooper

swear sometimes

speak very fast

use swear words frequently

use harsh words

46. As right as rain

one in best emotional and physical condition

secure and stable

quick and intelligent

reserved and shy

47. do serve time

be in prison/serve a prison sentence

present time service

pleasant time

48. Call it a night

go out for entertainment

sleep well

stop some activity , work etc. to go to bed

drink before night

49.Play it by ear

ignore unwelcome things

listen attentively

play an instrument from memory

Act according to the situation

50.Be in the red

important occasion

have no money is one’s bank account, owe money to the bank

a sign of welcome

very angry

### Physics

51. The rate of tension and surface tension has dimension of

[M0L0t0]

[L]

[L-1]

[LT-1]

52. A force of 5N acts on a body of weight 10N the acceleration of body is

50 m/s2

2 m/s2

5 m/s2

0.5 m/s2

53.The depth from surface of earth at which value of acceleration due to gravity become half of on the surface of earth is

$R$

$\sqrt{2}R$

$\frac{R}{2}$

$\frac{R}{4}$

54. Spokes in a bicycle wheel is used to

Increase mass

Give better mass

Increase moment inertia

Drive Easily

55. If length of wire is doubled keeping the diameter constant, it’s Young's modulus will

increases

decrease

remains same

depend upon nature of matter

56.A rain drop of radius 0.3mm has terminal velocity Im/s in air.The viscosity of air is 18 x 10-5 poise, then viscous force is

1.01 x 10-7N

1.01 x 10-8N

1.6 x 10-9N

1.6 x 10 -8

57. The material of least linear expansivity is

Aluminum

Invar

Steel

Nickel

58.A glass vessel contains air at 27°C the temperature to which it must be heated so that one-fourth of air is expelled from it at constant pressure is

47°C

77°C

102°C

127°C

59.The efficiency of heat engine will be 100% if the temperature of sink is

0K

0°C

equal to source

none of above

60. A cylinder of 0.6 m long and 6mm radius is rated at 1.5 kW.the temperature of filament if Stefan’s constant is 6 x 10-8 Wm -2K -4

920K

1125K

1025K

1320K

61. Light of wavelength 550 nm falls normally on a slit of width 22 x 10-7m, the angular position of second minima from central maxima will be

14.5°

30°

42°

62°

62. Two lens of power 5D and -7.5D are placed in contact.The equivalent focal length of combination will be

-40cm

+40cm

-25cm

+25cm

63. The length of the microscope is 14 cm and magnifying power is 25 for relaxed eye the focal length of the eyepiece is 5 cm then a distance of object from objective is

2.4cm

2.1cm

1.5cm

1.8cm

64. A sound wave has frequency 500Hz and velocity 360m/s. What is the distance between 2 particles having phase difference 60°

0.7cm

1.2cm

70cm

12cm

65. In bringing an electron towards another electron electrostatic potential the energy of the system

decreased

increases

remains same

zero

66.n-equal capacitors are first connected in series and then in parallel. The the ratio of maximum to minimum capacitance

n2

1/n2

n

1/n

67.A wire of resistance 12Ω is bent to form a circle.The effective resistance between the two points on any diameter of circle is

12Ω

9Ω

6Ω

3Ω

68. The resistance of an ideal ammeter is

0

low

high

infinite

69. A 10 eV electron is circulating in a plane at right angles to a uniform field of magnetic induction 10-4, the orbital radius of the electron is

18cm

16cm

11cm

9cm

70. Whenever the magnetic flux linked with a coil changes,there is emf induced in the circuit the emf last

For a short time

For a long time

Forever

so long as the change in flux takes place

71. The property of retentivity of material is useful in the construction of

Permanent magnet

Electro magnet

Transformer

none of Above

72. The color of the positive columns in a gas discharge tube depends on

Type of glass

Glass used for the tube

the gas in the tube

pressure inside the tube

73. The kinetic energy carried by emitted electron depends on

frequency

intensity

work function

momentum

74. A nucleus reactor has a power of 16 kW if the energy per fission is 200 MeV then number of fissions per second is

5 x 1017

5 x 1016

5 x 1015

5 x 1014

75. To obtain p-type silicon semiconductor, pure silicon may be doped with

Aluminum

Oxygen

phosphorous

copper

### Chemistry

76.The mass of one atom hydrogen is approximately

1.0g

0.5g

1.6 x 10-24

3.2 x 10-24

77. Which property of an element is always a whole number

atomic weight

equivalent weight

atomic volume

atomic number

78.The azimuthal quantum number specifies

size of the orbital

the shape of the orbital

energy of orbitals

the orientation of orbital in spaces

79. Which of the following statement is correct for pure water? With increase in temperature

pH increases but pOH decrease

pH decreases but pOH increase

both pH and pOH increase

both pH and pOH decrease .

80. Which has the highest first ionization potential?

Ne

Mg

Cl

Na

81.The aqueous solution of which of the following salt be neutral?

Na2SO4

(NH4)SO4

FeSO4

ZnSO4

82.A first order reaction is 50% completed in 50 minutes, when will 75% of the reaction be completed?

75minutes

100 minutes

200 minutes

300 minutes

83. Malachite is an ore of

Fe

Zn

Cu

Hg

84. In the extraction of iron from hematite using blast furnace, iron oxide is reduced by

Silica

Coal

Limestone

CO

85. An equal volume of 1.0M HCL and 1.0M NaOH are mixed together. The concentration of the NaCl produced would be

1.0M

0.5 M

2.0M

0.1 M

86. The catalyst used in the oxidation of SO, to SO3 in the manufacture of sulfuric acid by contact process is

Fe powder

Nipowder

ZnO

V2O5

87. In a reaction 2A + B ⟶ C + D the molecularity of the reaction is

1.0

0.0

2.0

3.0

88. Heavy water is

Deuterium oxide (D2O)

Water in which heavier salts are dissolved

H3O

Water formed by the combination of hydrogen and heavier isotopes of oxygen

89. Coating of Zn on iron for the prevention of rusting is known as

Surface coating

Electroplating

Shearding

Galvanizing

90. The pair of compounds which cannot exist together in solution is

NaHCO, and NaOH

Na2CO3 and NaHCO,

NaHCO3 and NaOH

NaHCO, and NaCl

91. In which of the following reaction hydrogen acts as an oxidizing agent

2H2 + O 2 ⟶ 2H2O

H2 + Cl2 ⟶ 2HCl

N2 + 3H2 ⟶ 2NH3

2K + H2 ⟶ 2KH

92. In benzene all the C-C bonds have same length because of

Tautumerism

Inductive Effect

Metamerism

Resonance

93. The organic acid which does not contain -COOH group is

ethanoic acid

Oxalic acid

Lactic acid

Picric acid

94. The action of NaHO2/HCl on primary amine gives

alcohol

alkyl nitride

secondary anime

nitro alkane

95. In which of the following reactions, both oxidized nd reduced forms of the same compounds are obtained

Wurtz reaction

Riemer-Tiemann reaction

Cannizzaro reaction

Aldol condensation

96. Nitrating of benzene by the use of nitrating mixture is an example of

Electrophile substitution

Nucleophile substitution

97. Antiseptic action of Dettol is mainly due to

Ampicillin

Acetyl salicylic acid

Paracetamol

chloroxylenol

98. D.D.T is a

insecticide

dye

synthetic polymer

antiseptic drug

99. An example of Zwitter ion is

Glucose

DNA

Soap

Glycine Hydrochloride

100. Fructose is an example of

Aldose

Ketose

Pentose

Hexose

I there is