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# CSIT Entrance 2074

### Mathematics

1. p/q ∈ R is defined if

p ≠ 0, q = 0

p = 0, q = 0

p ≠ 0, q ≠ 0

p = 0, q ≠ 0

2. [a,b] =

{x: ≤ x b}

{x : a < x < b}

{ x : a < x ≤ b}

{x : a ≤ x ≤ b}

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

undefined

$\sqrt{13}$

$i\sqrt{5}$

$-\sqrt{12}$

4. If |x| = 1 then x is

{1}

{-1}

{-1,1}

{-1,-1}

5. If log2(x - 7) = 1 then x is

unknown

8

6

9

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

4/5

3/5

5/4

5/3

7. If tan2x = 3 then x is

nπ + π/3

nπ - π/3

nπ ± π/3

5/3

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

-6

0

3

-3

Solutions
According to AP Property AP = first term+third term is equal to twice of second term that is
(k+2)+(3k−2)=2(4k−6)
⇒4k=8k−12
⇒4k−8k=−12
⇒−4k=−12
⇒4k=12
⇒k=12/4 =3
Hence k=3.

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

0

2/3

1/3

1

Solutions
First you must find r, the common ratio.
You find this with the following formula: r = t2/t1 ⇒ -(1/2) / 1 ⇒ -1/2
⇒s∞ = a/1-r
⇒s∞ = 1/ 1 - (-1/2)
⇒s∞ = 2/3

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

$\left(\begin{array}{cc}1& 49\end{array}\right)$

$\left(\begin{array}{cc}1& 4\end{array}\right)$

$0$

$\left(\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ 3& 6& 9\end{array}\right)$

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

10

1

0

-1

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

Diagonal

Symmetric

Skew Symmetric

unit

13. [2(cos15 + isin15)]6 =

64i

64

0

-64i

14. (1 + w + w2)3 + ( 1 + w - w2)3 =

16

16w

-16

16w2

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

x2 + x - 6 = 9

x2 + x + 6

x2 - x - 6 = 0

x2 - x + 6 = 0

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

-6/5

-6/5

3/5

-3/5

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

5

3

0

-5

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

x + y = 9

x - y = 9

2x + 2y = 9

-x - y = 9

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

2

3

5/7

1/2

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

a2/2

a2

2a2

4a2

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

tant

tan(t/2)

-tant

-tan(t/2)

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

-tanx

tanx

cotx

-cotx

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

12

-12

4

0

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

a + x + c

-a + x + c

tanx + c

tanx + c

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

π / 4

π / 2

0

tanx + c

### English

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

First

Second

Third

Fourth

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

nor

four

sew

for

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

Opens

is opened

has to be opened

be opened

29 . One who is fond of fighting is _______

bellicose

bigot

pacifist

fatalist

30. Select right synonym the word "analogus"

obvious

clear

equivocal

expressed

31. Give opposite meaning of "ominous"

rash

auspicious

folly

fictitious

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

of, from

from,of

of,at

on, at

33. Whom did you give it _______ ?

at

for

from

to

34. The dog sprang _______ a car

upon

on

at

from

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

e-i-o

i-e-o

o-i-e

e-e-e

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

are

has

is

am

37. There is a snag in it somewhere,

flow

insect

profit

garland

38. Custom of having many wives is called

bigamy

polygamy

monogamy

Matrimony

39. Choose the right word: Monkeys _______

growl

gibber

yelp

howl

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

Complement

direct object

indirect object

41. The car needs _____ hood repaired

Its

It's

itself

there

42. These are two photographers are ______ same.

an

a

the

nothing

43. The girls is versatile, means

chumey

unluckey

44. The word "aggresion" takes prefix

non

un

in

il

45. Fear of fire is called

sitophobia

pyrophobia

trihophobia

monomania

46. Which of the following is noun?

real

reality

none

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

fill

until

while

unless

48. One who travels from place to place

itinerant

mendicant

tramp

tourist

49. You're coming to the party ______ ?

aren't you

can't you

won't you

isn't you

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

rising and rising

rising and falling

rising

falling and falling

### Physics

51. Order of magnitude of radius of an atom is

10-7m

10-10m

10-12m

10-15m

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

45°

90°

120°

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

friction of air

gravity

mass

54. Powder cling to skin because of

compression

cohesion

capillarity

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

inertia

shearing sharing

transfer of momentum

surface tension

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 (αsteel = 11 × 10-6)

15.4 cm

15.9 cm

15.8 cm

10 cm

57. Internal Energy of perfect gas does not change during

isothermal process

isobaric process

Isochoric process

58. Efficiency of steam engine is of order of

10%

20%

60%

100%

59. A gas maximum works when it expands

isothermally

isobarically

isochorically

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

interference is constructive

Interference is destructive

Interference depends on type of water

All

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)

500 Hz

420 Hz

520 Hz

532 Hz

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

parallel to wave velocity

anti-parallel to wave velocity

perpendicular to wave velocity

a or b

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

10 lux

15 lux

25 lux

100 lux

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

lateral shift

dispersion only

deviation only

dispersion and deviation

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

2

0.5

1.5

2.5

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

6.25 x 1018

6.25 x 10-19

1.6 x 10-19

1.6 x 1018

67. On heating a liquid, the refractive index generally

does not change

decrease

increase

may increase or decrease depending upon the rate of heating

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

P/E

E/P

P.E

PE tanθ

69. Wheat stone bridge is used to measure

emf

potential

current

resistance

70. Magnetism of a magnet

is zero at absolute zero temperature

increase with temperature

is maximum at curie temperature

becomes practically zero above curie temperature

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

0.02 Wb

0.01 Wb

0.05 Wb

10 Wb

72. Positive rays are

electromagnetic waves

proton

ions

protons

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

3keV

4000 eV

3.1J

3.1eV

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

π / n

n2

n

1/n2

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

Semi Conductors

Conductors

Insulator

Dielectric

### Chemistry

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

1.505 x 1023

1.005 x 1023

1.205 x 1023

1.303 x 1023

77. Electronic Configuration of chromium is

[Ar]3d54s1

[Ar]3d64s2

[Ar]3d74s2

[Ar]3d4

78. Structure of CO2 molecule is

Linear

Tetrahedral

Angular

Polynomial

79. Which element has highest electronic affinity?

Linear

Tetrahedral

Angular

Polynomial

80. Oxidation number Fe in compound Fe2O4

1.33

4/3

+2/3

+5/3

81. MgO is an example of

basic oxide

amphoteric oxide

neutral oxide

acidic oxide

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

Sodium

Sodium Hydroxide

Sodium Carbonate

None

83. IUPAC name of C-(CH2)4 is

2-dimethyl propane

2 methyl butane

Pentane

2 methyl propane

84. Al4C3 reacts with water to give

CH4

C2H2

H2

C2H4

85. Protein is polymer of

clycol

glucose

α-amino acid

pthalic acid

86. Which carbohydrates gives Tollen's Test?

Glucose

Fructose

Galactose

Maltose

87. DDT is an example of

Insecticide

Herbicide

Fugicede

Rodenticede

88. Tranquilizers are substance used for treatment of

cancer

Mental Anxiety

Physical Disorder

Malaria

89. Each carbon atom in benzene is

SP2 Hybridized

SP Hybridized

SP3 hybridized

SP3d hybridized

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

Hoffman's Test

Fehlen's Solutions

Victor Mayer's Test

Beilstein's Test

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

Clemenson Reduction

Wolff-Kishner Reduction

Carnnizaro's

Perkin's Reduction

92. Which is most basic?

NH3

CH3NH2

(CH3)2NH

(CH=3)3N

93. Molecular formula of white vitrcol is

ZnSo4.7H2O

Zn(OH)2

ZnCO3

ZnO

94. Cinnabar is an ore of

Zinc

Copper

Mercury

Iron

95. PH of 0.04M HNO3

1.4

2

3

4

96. Unit of rte constant for first order reaction is

Mols-1

L mol-1s-1

s-1

Mols L-1s-1

97. Which is an intensive property?

Volume

Mass

Area

Concentration

98. Unit of cell constant is

Sm-1

M-1

Ohm-1am-1

Ohm

Curie

nik/L

Gauss

g/L

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

Sodium Nitroprusside

Prussian blue

Tollen's Reagent

Bayer's Reagent

I there is