# CSIT Entrance 2070

### Mathematics

1. If A and B are any two sets, then A-(A-B) is equal to A

B - A

A ^ B

A ∪ B

∅

2. The range of the functio y = $\sqrt{{a}^{2}-{x}^{2}},a>0$ is equal to

[-a,a]

(-a,a)

[0,a]

(0,a)

3. what is the value of $lo{g}_{a}\sqrt{{a}^{3}\sqrt{{a}^{2}}}$

4

3

2

1

4. If A = $\left(\begin{array}{cc}a& b\\ \text{}c& d\end{array}\right)$, then A^{100} is equal to

1

0

-1

None

5. If a^{x} = b^{y} = c^{z} and a,b,c are in G.P then x,y,z are in

G.P

A.P

H.P

None

6. $\underset{x\to \mathrm{0}}{lim}\frac{{a}^{x}-{b}^{x}}{x}$ is equal to

0

log(ab)

log(a/b)

log(b/a)

7. The derivative of y = 5x with respect to x is equal to

5xloge5

5x

loge5

5loge5

8. The function f(x) = x - 1 / x2, x ∈ R, x ≠ 0 is

(-∞,0) ∪ (0,∞)

(-∞,0)&cup[0,∞)

[-1,1]

(-∞,∞)

9. The integral $\int \frac{dx}{({e}^{x}-{e}^{-x}{)}^{2}}$ is equal to

$\frac{-1}{2|{e}^{2}+1|}+c$

$\frac{-1}{|{e}^{2x}+1|}+c$

$\frac{-1}{2|{e}^{x}+{e}^{-x}|}+c$

$\frac{-1}{2|{e}^{2x}+1|}+c$

10. For what value of k will the equation 5x^{2} - kx + 45 = 0 have equal roots?

0

± 3

± 30

± 33

11. The quadratic equation whose one root is $2+\sqrt{3}$

x^{2}+4x+1 = 0

x^{2}-4x + 1 = 0

x^{2} - 4x - 1 = 0

-x^{2} - 4x - 1 = 0

12. The distance between the parallel lines y - 2x = 4 and 6x - y = 5 is

$\frac{1}{\sqrt{45}}$

$\frac{7}{\sqrt{45}}$

$\frac{17}{\sqrt{45}}$

$\frac{17}{2\sqrt{45}}$

13. Radius of the circle ${x}^{2}+{y}^{2}+2y-x-\frac{3}{4}$ is

2

1

4

3

14. The absolute value of the complex number (1+i)-1 is

1

$\sqrt{2}$

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

2

15. If z = cosθ + isinθ then z^{n} + 1 / z ^{n} is equal to

-2cosnθ

2cosnθ

2sinnθ

-2sinnθ

16. The nth term of the series: 2 + 4 + 6 + 12 + 20 + ..... is

n(n+1)

(n+1)(n+2)

n(n-1)

n

17. If |x| < 1 and y=x + x^{2} + x^{4} + ....... + ∞ , then x is equal to

$\frac{y}{1-y}$

$\frac{y}{y-1}$

$\frac{y+1}{y}$

$\frac{y}{1+y}$

18. If a = 2, b = $\sqrt{6}$ and A = 65° , then c is equal to

$\sqrt{2}\pm 1$

$1\pm \sqrt{2}$

$\sqrt{3}\pm 1$

$1\pm \sqrt{3}$

19. 3cos-1x is equal to

3x-4x^{2}

4x^{3}-3x

4x-3x^{3}

3x^{3} - 4x

20. Solution of tanax- cotbx is

$\frac{2n+1}{a+b}\frac{\pi}{4}$

$\frac{2n-1}{a-b}\frac{\pi}{2}$

$\frac{2n+1}{a+b}\frac{\pi}{2}$

$\frac{\pi}{2}$

21. What is the value of $\left[\begin{array}{ccc}1& \omega & {\omega}^{2}\\ \omega & {\omega}^{2}& 1\\ {\omega}^{2}& 1& \omega \end{array}\right]$, Where ω is an imaginary cube of unity.

1

0

3

2

22. The single equation representing the pairs of lines y = x and y = -x is

y^{2} - x^{2} = 0

y - x = 0

x - y = 0

x^{2} - y^{2} = 0

23. Let A = [-3,2] and B = [-2,3] then A - B is equal to

[-3,3)

[-3,2]

(-2,2)

(-2,1)

24. If $\underset{x\to 0}{lim}f(x)\ne \underset{x\to 0}{lim}f(x)$ then f(x) is said to be an

Infinite discontinuity

Removal Discontinuity

Jump Discontinuity

None

25. Which one of the following is the area enclosed by curve y = 3x, the x-axis and the ordinate x = 0, x = 4?

12

16

20

24

### English

26. Inscription on a tomb is called _________

Epitaph

cemetery

Morgue

Demagogue

27. After he finished the exam, he ............ to the teacher.

Handed over it

handed it over

handed it out

handed out it

28. Every week she ............. her sister in her village to talk to her.

Calls over

calls on

calls out

calls up

29. He has a coat .................. five pockets.

of

about

with

in

30.To hit below the belt means:

to use force

to use unfair means

to use energy

to use leather

31. I disapprove ........his cheating on the exam.

of

at

in

off

32.The lights were............... because the room was bright.

put off

take off

left off

switched off

33. Which of the following is a noun?

thicken

impoverish

mercantile

mercy

34. Which of the underlined word is an adjective?

Swimming is good for health.

Students are walking on the lawn.

Many people like smoking.

She is taking knitting classes.

35. Which of the following is an active voice?

This work will be finished.

The suspect was seen.

I know him.

The letter was posted.

36. The memorandum ..............approved

have been

has been

was

is

37. Which of the following takes a singular verb?

police

furniture

families

committees

38. Neither her nor they..........going to the college.

is

are

has

was

39. Which expression is incorrect?

A pile of books

A-herd of cattle

A herd of sheep

A pack. of wolve

40. They daren’t go............?

did they

do they

hasn't they

dare they

41.l am hungry and ..................

She is too

they are so

So aren’t they

they are too

42. 'Which-word has the stress on the first syllable?

Likelihood

religious

fantastic

oxthography

43. How many syllables does the word ‘economical’ have?

five

four

three

six

44.The pair.......has the same pronunciation.

Pot, Port

so, sow

pull, Pool

did, dead

45. The word ‘they’ has the same initial consonant bound as the word.......... a

Day

date

thief

that

46. A professional horse rider is called

Jockey

rider

coach

Horse courser

47. Give the opposite meaning of "appropriate"

Inevitable

likely

unsuitable

suitable

48. Select the right synonym to the word ‘sporadic’. -

Occasional

frequently

continuously

never ending

49. Which of the following is incorrect punctuated?

The teacher said, "Honesty is the best policy”.

He said to me, "When did she come to the party"?

The man received a gift, the women, a book.

The man, whom he met, had excellent speech skills

50. The word “father” takes the suffix:

......is

....... some

....... ly

...... y

### Physics

51. The dimensional formula for potential difference is

[ML2T-3I-1]

[ML2T-3I]

[ML2TI-1]

[ML2T-2I-2]

52. A stone is thrown vertically upward with a speed u from the top of a tower reaches the ground with a speed of 3u. The height of the tower iS...............

3u^{2}/g

4u^{2}/g

6u^{2}/g

9u^{2}/g

53. The acceleration of a particle in SHM is ..........

Always zero

always constant

Maximum at extreme position

Maximum at the equilibrium position

54. An iron ball is heated. The percentage increase will be largest in .............

volume

density

diameter

surface area

55. Two wires A and B are of the same material. Their lengths are in the ratio of 1:2 and diameters are in the ratio of 2:1. If they are pulled by the same force, their increase in length will be in the ratio.

2:1

1:4

1:8

8:1

56. Water is flowing through a tube of the non-uniform cross-section. If the radius of the tube at the entrance and the exit is 3:2, then the ratio of the velocity of liquid entering and leaving the tube is:

8:27

4:9

9:4

1:1

57. The thermodynamic process in which the pressure of the system remains constant is called...............

isothermal

adiabatic

isochoric

isobaric

58. 50g of ice at -6°C is dropped into the water at 0°C. how many grams of water freeze? Sp. Heat capacity of ice=2000JKg^{-1}C^{-1}.

1.785 g

4.25 g

3.16 g

9.33 g

59. The image of an object placed at the focus of a concave mirror is at

f

Infinity

2f

f/2

60. The temperature of source and sink of carnot engine are 400k and 300k respectively. What is it's efficiency?

100%

75%

33.33%

25%

61. The refractive index of air with respect to glass is 2/3. The refractive index of diamond with respect to air is 12/5. Then the refractive index of glass with respect to diamond will be.

5/8

8/9

5/18

18/5

62. The focal length of a double conves lens for which radius of curvature of each surface is R will be ....( µ = 1.5)

R/2

R

2R

4R

63. Light of wave length 7200 Å in air has wave length in glass equal to ......... (given Refractive index of glass with respect to air = 1.5)

7200 Å

4800 Å

1080 Å

10800 Å

64. Three capacitor of capacitance 3µF, 9µF and 18µF are connected first in series and then I parallel. the ratio of C equivalent capacitance in two cases (CI/CP) will be

1:15

15:1

1:1

1:3

65. Three equal registers each of resistance 'r' are connected to form a triangle. The equivalent resistance across any two comes of the triangle is.....

2r

r/3

2r/3

3r

66. The resistance of two lamp are in ratio of 1:2. Their wattage will be in the ratio of

1:2

2:1

4:1

1:4

67. The energy stored in 50mH inductor carrying a current of 4A is .......

0.1 J

0.4 J

0.3 J

0.01 J

68. The alternating current in an LCR circuit is maximum when

XL = 0

XC = 0

XL = XC

$\sqrt{X{{}_{L}}^{2}+X{{}_{C}}^{2}}$

## Check It

69. A particle of mass 10^{-31} kg is moving with a speed of 10^{5}m/s. The De-Broglie wavelength of the particle is ......

6.63 x 10^{-8} m

6.63 Å

66.3 Å

6.63 x 10^{-7}m

70. Two waves of the same wavelength and amplitude interfere to give a minimum when their phase difference is

π

π/2

3π/2

0

71. Hard X-rays are compared to soft X-rays have

Higher Intensity

Lower frequency

Higher Frequency

Higher Speed

72. The mass of α-particle is

Equal to the mass of four protons

Equal to the mass of four neutrons

Equal to the masses of 2 protons and 2 neutrons

Less than the sum of masses of 2 protons and 2 neutrons

73. A common emitter transistor amplifier has a current fain of 50. If the load resistance is 4 kΩ and the input resistance is 500 Ω. The voltage gain on the amplifier is .......

400

6.2

500

300

74. A tube closed at one end has a resonating length 1 meter. The air column in the pipe can resonate for sound of frequency ..... (V = 320ms^{-1})

166 Hz

249 Hz

575 Hz

80 Hz

75. A displacement wave is represented by y = 0.025 sin(5006 - 0.0025x), where y,t and x are in cm, second and meter respectively. The wave length of wave is .......

20π m

40 π m

60 π m

80 π m

### Chemistry

76. The gas obtained by adding water on aluminum carbide is

Ethyne

Ethane

Methane

Ethane

77. The mixture of HCL and ZnCl2 is known as

Tollen's Reagent

Baeyer's Reagent

Lucas Reagent

Nessler's Reagent

78. The IUPAC name of n-valeric acid is

Pentanoic Acid

Butanoic Acid

Propanoic Acid

Ethanoic Acid

79. A blood red coloration of ferric sulphocyanide obtained by addition of ferric chloride in sodium extract confirms the presence of

Sulfur

Nitrogen

Both A and B

Halogens

80. Which of the following compounds has highest boiling point?

CH4

CH3Cl

CH3Br

CH3OH

81. The compound that undergoes Cannizzaro reaction is

CH_{3}COOH

C_{2}HSCHO

HCHO

CH_{3}OCH_{3}

82. Benzene is converted to toluene by

Friedel Craft Reaction

Grignard Reaction

Wutrz Reaction

Perkin Reaction

83. The compound that gives positive carbylamines reaction is

(CH3)2NH

(CH3)3N

(CH3)4N

(CH3)NH2

84. Hematite is an ore of

Sliver

iron

mercury

copper

85. Na2O is a

Neutral oxide

acidic oxide

Basic Oxide

Amphoteric oxide

86. Which of the following element has highest electro-negativity?

Bromine

Iodine

Chlorine

Fluorine

87. Zinc Sulphate (ZnSO_{4}.7H_{2}0) is also called

White Vitriol

Green Vitriol

Blue Vitriol

Corrosive Sublimate

88. Brass is an alloy of

Copper and Zinc

Copper and nickel

Copper and tin

Copper and lead

89. The formula of dolomite is

CaCO3

CaCO3.MgCO3

CaSO4.2H2O

CaF2

90. The general Electronic configuration of zinc is

[Ar]4s23d10

[Ar]4s13d10

[Ar]4s23d8

[Ar]4s23d7

91. Equivalent weight of KMnO4 in neutral medium is

52.6

158.0

31.6

63.0

92. Bohr's model was modified by

Rutherford

Sommerfeld

Dalton

Pauli

93. How many oxygen atoms are there in 8.0g of oxygen atoms

3.011 x 1023 atoms

3.011 x 1022 atoms

3.011 x 1020 atoms

3.011 x 1019 atoms

94. What is the pH of 0.001 M HCL

2.0

3.0

4.0

5.0

95. The rate of reaction is independent of

Temperature

Concentration

Particle size of reactant

Molecularity

96. The CGS unit of specific conductance is

Siemen cm^{-1}

ohm^{-1}cm^{2}equiv^{-1}

Siemen

ohm^{-1}

97. Hess's Law deals with

Total change in heat of reaction

Rate of reaction

Equilibrium constant of reaction

Influence on pressure of volume of gas

98. The degree of dissociation of an electrolyte

Decreases with dilution

Increases with dilution

May increase or decrease with dilution

Is not affected by dilution

99. The weight of 100 ml of NH3 gas at NTP

0.0759g

0.0579g

0.0459g

0.0359g

100. The law of multiple proportions was given by

Richter

John Dalton

Albert Einstein

Gay Lussac