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TTHHEERRMMAALL PPRROOPPEERRTTIIEESS OOFF MMAATTTTEERR,, TTHHEERRMMOODDYYNNAAMMIICCSS && KKIINNEETTIICC TTHHEEOORRYY OOFF GGAASSEESS ,, OOSSCCIILLLLAATTIIOONN ,, WWAAVVEESS,, BBAASSIICC

CCOONNCCEEPPTTSS IINN CCHHEEMMIISSTTRRYY,, SSTTAATTEESS OOFF MMAATTTTEERR,, TTHHEERRMMOODDYYNNAAMMIICCSS,, EEQQUUIILLIIBBRRIIUUMM,, AATTOOMMIICC SSTTRRUUCCTTUURREE,, CCHHEEMMIICCAALL

BBOONNDDIINNGG && MMOOLLEECCUULLAARR SSTTRRUUCCTTUURREE ,, TTRRIIGGOONNOOMMEETTRRYY,,IINNVVEERRSSEE TTRRIIGGOONNOOMMEETTRRYY,,SSEEQQUUEENNCCEE AANNDD

SSEERRIIEESS,,SSEETTSS,,RREELLAATTIIOONNSS AANNDD FFUUNNCCTTIIOONNSS

1. The readings of a constant volume gas thermometer at 00C and 1000C are 40cm and 60cm of mercury respectively. If its reading at an unknown temperature is 100 cm of mercury column, then the temperature is a) 1000C b) 500C c) 250C d) 3000C e) None of these

2. On heating , the temperature at which water has minimum volume is a) 00C b) 40C c) 4K d) 1000C e) -2730C

3. A lead bullet strikes against a steel plate with a velocity 200 m/s. If the impact is perfectly inelastic and the heat produced is equally shared between the bullet and the target , then the rise in temperature of the bullet is (specific heat capacity of lead= 125 Jkg -1 K-1 ) a) 800C b) 600C c) 400C d) 1200C e) 1200C

4. Three rods made of same material and having same cross –section are joined as shown in the figure . Each rod is of same length. The temperature at the junction of the three rods is

a) 450C b) 900C c) 300C d) 200C e) 600C

5. The plots of intensity of radiation versus wavelength of three black bodies at temperatures T1,T2 and T3 are shown .Then

a) T3>T2>T1 b) T1>T2>T3 c) T2>T3>T1 d) T1>T3>T2 e) T3>T1>T2

6. The surface area of a black body is 5×10-4 m2 and temperature is 7270C . The energy radiated by per min is (σ=5.67 ×10-8 Jm -2 –s-1K-4) a) 1.7 ×103J b) 2.5 ×102J c) 8 ×103 J d) 3 ×104 J e) None of the above

7. The thermodynamics process in which no work is done on or by the gas is a) isothermal process b) adiabatic process c) cyclic process d) isobaric process e) isochoric process

8. 100g of water is heated from 300C to 500C . Ignoring the slight expansion of water, the change in its internal energy is a) 8.4 kJ b) 84 kJ c) 2.1 kJ d) 4.2 kJ e) 3.2 kJ

9. In the given p-V diagram, I is the initial state and F is the final state. The gas goes from I to F by The gas goes from I to F by I) IAF II)IBF III)ICF

The heat absorbed by gas is a) the same in all three processes b) the same in I and II c) greater in I than in II d) greater in III than in II e) Greater in III than in II

10. The change in internal energy of a given mass of gas, when its volume changes from V to 2V at a constant pressure p is

p

v

C=γ, universal gas constant=R

C

a) pV

γ b)

(2 1)

pV

γ −

c) 2( 1)

pV

γ − d)

( 1)

R

γ −

e) ( 1)

pV

γ − 11. A carnot engine operating between temperature Ti

and T2 has efficiency 0.2. When T2 is reduced by 50K, its efficiency is to 0.4 .Then T1 and T2 are respectively a) 200 K, 150K b) 250K , 200 K c) 300K,250K d) 300K,200K e) 300K, 150K

Time : 2½ Hours 1133..0033..1199

VVeerrssiioonn CCooddee:: AA

12. In a carnot engine , the temperature of reservoir is 9270C and that of sink is 270C. If the work done by the engine when it transfers heat from reservoir to sink is 12.6 ×106J, the quantity of heat absorbed by the engine from the reservoir is a) 16.8 ×106J b) 4×106J c) 7.6×106J d) 4.25×106J e) 20.8×106J

13. A diatomic ideal gas is compressed adiabatically to 1

32of its initial volume. If the initial temperature of

the gas is Ti (in kelvin)and the final temperature is Tf= aTi, the value of a is a) 4 b) 6 c) 5 d) 9 e) 2

14. Which of the following is true in the case of an adiabatic process, where , γ=Cp/Cv? a) p1-γ T γ= constant b) pγ T 1-γ= constant c) p Tγ= constant d) pγ T = constant e) None of these

15. A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at as pressure p and temperature T. Whereas the other part is completely evacuated. If the valve is suddenly opened, then the pressure and temperature of the gas will be

a) ,2

pT b) ,

2 2

p T

c) p,T d) ,2

Tp

e)

,22

pT

16. Real gas behaves like an ideal gas, if its

a) pressure and temperature are both high b) pressure and temperature are both low c) pressure is high and temperature is low d) pressure is low and temperature is high e) None of these

17. If L of oxygen at a pressure of 1 atm and 2L of nitrogen at a pressure of 0.5 atm are introduced into a vessel of volume 1L .If there is no change in temperature , the final pressure of the mixture of gas (in atm ) is a) 1.5 b) 2.5 c) 2 d) 4 e) 3

18. In a certain region of space, there are only 5 molecules per cm2 on an average and temperature is 3K. The pressure of this dilute gas is (k=1.38 ×10-23 JK -1) a) 20.7 ×10-17 Nm-2 b) 15.3×10-15 Nm-1 c) 2.3× 10-10 Nm-1 d) 5.3 ×10-5 Nm-1 e) 3.5 ×10-8 Nm-1

19. If m represents the mass of each molecule of a gas and T its absolute temperature , then the root mean square velocity of the gaseous molecule is proportional to a) mT b) m1/2T1/2 c) m-1/2 T d) m -1/2 T1/2 e) m-1T

20. According to Maxwell`s law of distribution of velocities of molecules , the most probable velocity is

a) Greater than the mean velocity b) equal to the mean velocity c) equal to the root mean square velocity d) less than the root mean square velocity e) Greater than the root mean square velocity

21. A molecule of a gas has six degrees of freedom. Then, the molar specific heat of the gas at constant volume is

a) 2

R b)

2

R

c) 3

2

R d) 3R e) 5R

22. Two moles of oxygen is mixed with eight moles of helium. The effective specific heat of the mixture at constant volume is a) 1.3R b) 1.4 R c) 1.7R d) 1.9R e) 1.5 R

23. A particle executes simple harmonic motion with a time period of 16s. At time t =2s ,the particle crosses the mean position while at t=4s , velocity is 4 ms-1. The amplitude of motion in metre is a) 2π b) 16 2π

c) 2 4 2π d) 4

π e)

32 2

π 24. Two simple harmonic motions are represented by the

equations , y1=0.1 sin 1003

tπ π +

and y2=0.1 cos

πt. The phase difference of the velocity of particle 1, with respect to the velocity of particle 2 is

a)6

−π b)

3

π

c) 3

−π d)

6

π

e)

2

π

25. The total energy of a simple harmonic oscillator is proportional to a) square root of displacement b) velocity c) frequency d) amplitude e) square of the amplitude

26. A body of mass 4 kg hangs from a spring and oscillates with a period of 0.5 s. On the removal of the body, the spring is shortened by a) 6.2 cm b) 0.63cm c) 6.25cm d) 6.3 cm e) 0.625cm

27. The period of a simple pendulum inside a stationary lift is T. The lift accelerates upwards with an acceleration of g/3 .The time period of pendulum will be

a) 2T b) 2

T

c)3

2T

d) 3

T e)

2

3T

28. A simple pendulum is released from A , as shown in the figure. If m and l represent the mass of the bob and length of the pendulum , the gain kinetic energy at B is

a) 2

mgl b)

2

mgl c)

3

2mgl d)

2

3mgl e) mgl

29. For a simple pendulum, the graph between T2and L is a) a straight line passing through the origin b) parabola c) circle d) ellipse e) hyperbola

30. A simple pendulum has a time period T 1 when on the earth`s surface and T2 when taken to a height 2R above the earth`s surface , where R is the radius of the earth. The value of (T1/T2 ) is

a) 1/9 b) 1/3 c)1

3 d) 9 e) 3

31. The amplitude of a damped becomes 1/3rd in 2s. If its amplitude after 6s is 1/n times the original amplitude , the value of n is a) 32 b) 3√2 c) 3√3 d) 23 e) 33

32. The speed of sound in gas of density ρ at a pressure p is proportional to

a)

2p

ρ b)

3/2p

ρ c)

p

ρ

d) p

ρ e)

2

p

ρ

33. Transverse wave is described by the equation,

0 sin 2x

y y ft = π − λ

. The maximum particle

velocity is equal to four times the wave velocity, if

a) 0

4

yπλ = b) 0

2

yπλ =

c) 0yλ = π d) 02 yλ = π

e) 02

3

yπλ =

34. In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.14s . The frequency of the wave is a) 0.42Hz b) 2.75 Hz c) 1.79Hz d) 0.56Hz e) 3.5 Hz

35. The instantaneous displacement of a simple harmonic oscillator is given by ,

y=a cos 4

tπ ω +

. Its speed will be maximum at

the time

a) 2πω

b) 2

ωπ

c) ωπ

d) 4

πω

e) πω

36. A progressive wave y=a sin (kx –ωt)is reflected by a rigid wall at x=0. Then, the reflected wave can be represented by, a) y= sin(kx +ωt) b) y= a cos (kx +ωt) c) y= -a sin(kx -ωt) d) y= -a sin(kx +ωt) e) y= a cos (kx -ωt)

37. Tube A has both ends open while tube B has one end closed. Otherwise they are identical. Their fundamental frequencies are in the ratio a) 4:1 b) 2:1 c) 1:4 d) 1:2 e) 2:3

38. A sonometer wire 100 cm long has a fundamental frequency of 330 Hz. The velocity of propagation of transverse waves on the wire is a) 330 ms-1 b) 660 ms-1 c) 990ms-1 d) 115ms-1 e) 550 ms-1

39. A glass of length 1.0 m is completely filled with water. A vibrating turning fork of frequency 500 Hz is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is 330 ms-1 , then the total number of resonances, that occur will be a) 2 b) 3 c) 1 d) 5 e) 4

40. An observer is approaching a stationary source with a velocity 1/4 th of the velocity of sound . Then the ratio of the apparent frequency to actual frequency of source is a ) 4:5 b) 5:4 c) 2:3 d) 3:2 e) 2:5

41. If 1021 molecules are removed from 200 mg of CO2, then the number of moles of CO2 left are a) 2.88×10-3 b) 1.66 ×10-3 c) 4.54 ×10-3 d) 1.66 ×10-2

e) 2.88×103 42. The ratio between the root mean square velocity of

H2 at 50 K and that of O2 at 800 K is a) 4 b) 2 c) 1 d) ¼ e) 10

43. If ∆H is the change in enthalpy and ∆E is change in internal energy accompanying a gaseous reaction, then a) ∆H is always greater than ∆E b) ∆H < ∆E only if the number of moles of the products is greater than the number of moles of the reactants c) ∆H is always less than ∆E d) ∆H < ∆E only if the number of moles of the products is less than the number of moles of the reactants e) None of these

44. 28 g of N2 and 6.0 g of H2in a closed 1 L flask at 450mixture required 500 ml of 1.0 M Hnaturalization. The value of KN2(g) + 3 H2(g) ��⇀↽�� 2NH3(g)

a) 1.69 mol2 L-2 c) 0.59 mol -2 L2

e) 1.33 mol-2 L2 45. The solubility product of an electrolyte AB

2.7 ×10-19 (mol L-1)4. The molarity of its saturated solution is a) 3.0 ×10-5 c) 271/4 ×10-5

46. Rearrange the following (I to IV) in the order of increasing masses and choose the correct answer from (a) (b) (c) and (d). Atomic masses: N =14, O = 16, Cu = 63) I. 1 molecule of oxygen II. 1 atom of nitrogen III. 1 ×1010 g molecular weight of oxygen IV. 1 ×10-18 g atomic weight of copper a) II < I < III < IV c) II < III < I < IV e) I < II < IV < III

47. If the collision frequency of a gas at 1 atm pressure is Z, then its collision frequency at 0.5 atm is a) 0.25 Z b) 0.50 Z c) Z

48. For the formation of 3.65 g of hydrogen chloride gas, what volumes of hydrogenrequired at N.T.P conditions?a) 1.12 lit, 1.12 lit b) 1.12 lit, 2.24 litc) 3.65 lit, 1.83 lit d) 1 lit. 1 lit

49. If w1,w2,w3 and w4 for an ideal gas are magnitude of work done in isothermal , adiabatic, isobisochoric reversible expansion processes, the correct order will be: a) w1 > w2 >w3> w4

c) w3 > w2 >w4> w1

e) w4 > w1 >w2> w3 50. Which of the following is false?

a) 0.1 M Fe2+ + 0.1 M NHFe(OH)2 b) 0.1 M Mg2+ + 0.1 M NH

No precipitation of Mg(OH)c) 0.01 M Ag+ + 0.1 M NHAgOH d) 0.01 M Ag+ + 0.1 M NHof AgOH

51. 50 ml 10 N H2SO4, 25 ml 12 N HCl and 40 ml 5N HNO3 were mixed together and the volume of the mixture was made 1000 ml by adding water. The normality of the resultant solution will be: a) 1 N b) 2N c) 3 N

52. One mole of calcium phexcess of water gives a) one mole of phosphine b) two moles of phosphoric acid c) two moles of phosphine d) one mole of phosphorus pentoxide.e) One mole of phosphoric acid

2 are heated over a catalyst ask at 450oC. The entire equilibrium

mixture required 500 ml of 1.0 M H2SO4 for naturalization. The value of KC for the reaction :

3(g) is b) 0.03 mol2 L-2 d) 0.06 mol -2 L2

The solubility product of an electrolyte AB3 type is . The molarity of its saturated

b) 1.0 ×10-5 d) 3.0 ×10-4

Rearrange the following (I to IV) in the order of increasing masses and choose the correct answer from (a) (b) (c) and (d). Atomic masses: N =14,

g molecular weight of oxygen g atomic weight of copper

b) IV < III < II < I d) III < IV< I< II

If the collision frequency of a gas at 1 atm pressure is Z, then its collision frequency at 0.5 atm is

c) Z d) 2Z e) 1.5Z For the formation of 3.65 g of hydrogen chloride gas, what volumes of hydrogen gas and chlorine gas are required at N.T.P conditions?

b) 1.12 lit, 2.24 lit d) 1 lit. 1 lit e) None of these

for an ideal gas are magnitude of work done in isothermal , adiabatic, isobaric and isochoric reversible expansion processes, the correct

b) w3 > w2 >w4> w1 d) w3 > w1 >w2> w4

Which of the following is false? + 0.1 M NH3 → Precipitation of

+ 0.1 M NH3 + 0.1 M NH4+ →

No precipitation of Mg(OH)2 + 0.1 M NH3 → Precipitation of

+ 0.1 M NH3 → No precipitation

, 25 ml 12 N HCl and 40 ml 5N were mixed together and the volume of the

mixture was made 1000 ml by adding water. The normality of the resultant solution will be:

3 N d) 4 N e) 5 N hosphide on reaction with

b) two moles of phosphoric acid c) two moles of phosphine d) one mole of phosphorus pentoxide. e) One mole of phosphoric acid

53. A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends, the white ammonium chloride ring first formed will be a) at the centre of the tubeb) near the hydrogen chloride bottlec) near the ammonia bottled) throughout the length of the tube

54. Which of the following volume (V) plots represents the behaviour of one mole of an ideal gas at one atmospheric pressure?

55. As the temperature is raised average kinetic energy of neon atoms changes by a factor of which of the following?a) ½c) 313/293

56. What is the pressure of 2 mole of NHits volume is 5 litre(a = 4.17, b = 0.03711)a) 10.33 atmc) 9.74 atm

57. ∆Hof

mol are respectively ∆H in kJ of the following reaction: 2NOa) 836

58. When 110 g of manganese (At. Mass =55) dissolves in dilute HNOthe work done in the a) 2494.2 Jc) –

59. When an electron of Hlower energy state, thena) its potential energy increasesb) its kinetic energy increasesc) itsd) wavelength of de Broglie wave associated with the electron increasee) its kinetic energy decreases

60. An electron in the ground state of hydrogen was excited to a higher energy level using monochromatic radiations of wawave length that appears in the resulting spectrum is due to transition from :

a) n n

c) n n

A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends, the white ammonium chloride ring first formed will be a) at the centre of the tube b) near the hydrogen chloride bottle

near the ammonia bottle d) throughout the length of the tube e) None of these Which of the following volume (V) – temperature (T) plots represents the behaviour of one mole of an ideal gas at one atmospheric pressure?

As the temperature is raised from 20oC to 40oC, the average kinetic energy of neon atoms changes by a factor of which of the following? a) ½ b) 313 / 293 c) 313/293 d) 2 e) 293/313 What is the pressure of 2 mole of NH3 at 27oC when its volume is 5 litre in van der Waals equation? (a = 4.17, b = 0.03711) a) 10.33 atm b) 9.33 atm c) 9.74 atm d) 9.2 atm e) 10 atm

f of CO2(g), CO(g), N2O(g) and NO2(g) in kJ/ mol are respectively -393, -110, 81 and 34. Calculate

H in kJ of the following reaction: 2NO2(g) + 3CO(g) → N2O(g) + 3CO2(g) a) 836 b) 1460 c) -836 d) -1460 e) 810When 110 g of manganese (At. Mass =55) dissolves in dilute HNO3 at 27oC under atmospheric pressure, the work done in the process is: a) 2494.2 J b) – 2494.2 J

4988.4 J d) 4988.4 J e) 249.42 J When an electron of H- atom jumps from a higher to lower energy state, then a) its potential energy increases b) its kinetic energy increases c) its angular momentum remains unchanged d) wavelength of de Broglie wave associated with the electron increase e) its kinetic energy decreases An electron in the ground state of hydrogen was excited to a higher energy level using monochromatic radiations of wave length (λ ) 975 Å. The longest wave length that appears in the resulting spectrum is due to transition from :

4 1n n→ b) 4 3n n→

5 4n n→ d) 5 1n n→

A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends, the white ammonium

e) None of these temperature (T)

plots represents the behaviour of one mole of an ideal

C, the average kinetic energy of neon atoms changes by a

C when in van der Waals equation?

(g) in kJ/

110, 81 and 34. Calculate

e) 810 When 110 g of manganese (At. Mass =55) dissolves

C under atmospheric pressure,

atom jumps from a higher to

d) wavelength of de Broglie wave associated with the

An electron in the ground state of hydrogen was excited to a higher energy level using monochromatic

) 975 Å. The longest wave length that appears in the resulting spectrum is

61. The percentage of Se in peroxidase anhydrous enzyme is 0.5% by weight (atomic weight = 78.4). Then minimum molecular weight of peroxidase anhydrous enzyme is a) 1.568 × 104 b) 1.568 × 103 c) 15.68 d) 3.136× 104

e) 15.68 × 102 62. Densities of two gases are in the ratio 1:2 and their

temperatures are in the ratio 2:1, then the ratio of their respective pressures is a) 1:1 b) 1:2 c) 2:1 d) 4:1

63. The molar heat capacity (Cp) of CD2O is 10cals at 1000 K. The change in entropy associated with cooling of 32 g of CD2Ovapour from 1000K to 100K at constant pressure will be: (D = deuterium, atomic mass = 2u) a) 23.03 cal deg-1 b) –23.03 cal deg-1 c) 2.303 cal deg-1 d) –2.303 cal deg-1

e) 23.3 cal deg-1 64. The pH of 0.1 M solution of the following salts

increases in the order: a) NaCl < NH4Cl < NaCN < HCl b) HCl < NH4Cl < NaCl < NaCN c) NaCN < NH4Cl < NaCl < HCl d) HCl < NaCl < NaCN < NH4Cl e) NH4Cl < HCl < NaCN < NaCl

65. In HS-, I-, RNH2 and NH3, order of proton accepting tendency will be a) I- > NH3> RNH2 > HS- b) HS- > RNH2 > NH3 > I- c) RNH2 > NH3 > HS- > I- d) NH3 > RNH2 > HS- > I-

e) RNH2 > HS- > NH3> I- 66. The pH at the equivalence point of titration of 0.2 M

NH3 with 0.2 M HCl is : pKb of NH3 = 4.74) a) 9.72 b) 9.87 c) 5.13 d) 4.98 e) 10.26

67. A beam of specific kind of particles of velocity 2.1 ×107 m/s is scattered by a gold (Z =79) nuclei. Find out specific charge (charge/ mass) of this particle if the distance of closest approach is 2.5×10-14 m. a) 4.84 ×107 C/kg b) 4.84 ×10 -7 C/kg c) 2.42 ×107 C/kg d) 3 ×10-12 C/kg

68. Which statement (s) are correct? 1) A 3s sub- shell has a maximum of 8 electrons. 2) An element with configuration of 1s22s23p63s2 would be in the same group as beryllium 3) The general electronic configuration of the group containing N2 is ns2np5 4) A strontium atom has a filled outer shell if it loses two electrons. a) 1, 2 and 3 b) 1 and 3 c) 2 and 4 d) Only 4 e) Only 2

69. In a multi – electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields? A) n = 1, =0, m = 0 B) n = 2, ℓ =0, m = 0 C) n = 2, ℓ =1, m = 1 D) n = 3, ℓ =2, m = 1 E) n = 3, ℓ =2, m = 0 a) D and E b) C and D

c) B and C d) A and B e) D and B

70. On the basis of figure given below which of the following statement (s) is/are correct?

i) At point B, when only electric field is applied ii) At point C, when both electric and magnetic field is applied. iii) At point, B, when both electric and magnetic fields are balanced iv) At point C, when only magnetic field is applied Which of the following is/are correct? a) i and ii b) only iii c) iii and iv d) i and iii e) iii and ii

71. Which among the following is the heaviest? a) One mole of oxygen b) One molecule of sulphur trioxide c) 100 amu of uranium d) 44 g of carbon dioxide

72. Molar heat capacity of CD2O (deuterated form of formaldehyde) at constant pressure is 14 cal mol-1 K-1 at 1000 K. The entropy change associated with cooling of 3.2 g of CD2O vapour from 1000 to 900 K is a) – 0.1 cal K-1 b) – 0.25 cal K-1 c) – 0.4 cal K-1 d) – 0.15 cal K-1

e) – 0.015 cal K-1 73. Consider the following equilibria at 25oC,

2NO(g) ��⇀↽�� N2(g) + O2(g) ; K1 = 4 ×1030 and NO(g) +1/2 Br2(g) ��⇀↽�� NOBr(g) ; K2 = 1.4 mol-1/2 L1/2. The value of KC for the reaction (at the same temperature ) ½ N2(g) + ½ O2(g) + ½ Br2(g) ��⇀↽�� NOBr(g) is: a) 3.5 ×10-31 b) 2.8 ×1015 c) 7.0×10-16 d) 5.6×1030

e) 7.0 ×1016 74. Four diatomic species are listed below in different

sequences. Which of these presents the correct order of their increasing bond order? a) O2

− < NO < C22

− < He 2+

b) NO < C22

− < O 2− < He 2

+

c) C22

− < He 2+ < NO < O2

−

d) He2+ < O 2

− < NO < C22

−

e) NO < O2

− < He 2+ < C2

2−

ℓ

75. Arrange the following ions in the order of decreasing X – O bond length, where X is the central atom in a) ClO 4

− , SO24

− , PO34

− , SiO 4−

b) SiO44

− , PO34

− , SO24

− , ClO 4−

c) SiO44

− , PO34

− , ClO 4− , SO2

4−

d) SiO44

− , SO24

− , PO34

− , ClO 4−

e) PO3

4− , SiO4

4− , SO2

4− , ClO 4

−

76. In which of the following molecules/ ions are all the bonds not equal? a) XeF4 b) BF 4

− c) SF4 d) SiF4

77. In which case hydrogen bond will not be observed

a) H3O 2− b) H2O c) H5O 2

+ d) H3O+

78. The relative stabilities of CN, CN+ and CN- are in the order a) CN > CN+ > CN- b) CN- > CN > CN+ c) CN- > CN+ > CN d) CN+ > CN > CN-

79. The hybridization of P in PO34− is the same as of

a) S in SO3 b) N in NO-3 c) I in ICl+2 d) I in ICl4

- 80. Which of the following has dipole moment ?

a) 1- 4- dichlorobenzene b) [Ni(CN)4]2-

c) H2S d) trans -2,3- dichlorobutene e) None of these

81. Let A = {x : x is a digit in the number 3591}, B = {x : x ∈ N, x < 10}. Which of the following is false ? a) A ∩ B= { 1, 3, 5 9} b) A - B = φ c) B – A = {2, 4, 6, 7, 8} d) A ∪B = {1,2,3,5,9}

82. A class has 175 students. The following data shows the number of students opting one or more subjects. Math 100, Physics 70, Chemistry 40, Math and Physics 30, Math and Chemistry 38 Physics and Chemistry 23, Math, Physics and Chemistry 18. How many have opted for math alone ? a) 35 b) 48 c) 50 d) 22 e) 30

83. Consider the following relations : (i) A – B = A – (A ∩ B) (ii) A = (A ∩ B) ∪ (A – B) (iii) A – (B ∪ C) = (A – B) ∪(A – C) Which of these is/are true ? a) (i), (iii) b) (ii) c) (ii) , (iii) d) (i), (ii)

84. In the set N of natural numbers, the binary operation ‘*’ is defined as follows : m * n =

,mn

pwhere p is a fixed number, then the

identity elements of * is a) a prime number b) p + m + n c) p – 1 d) p

85. In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then the persons travelling by car or bus is a) 80% b) 40% c) 60% d) 70% e) 30%

86. If A ={x : x 2 – 5x + 6 = 0},B = {2, 4} C = {4, 5}, then A × (B ∩ C) is a) {(2, 4), (3, 4)} b) {(4, 2), (4,3)} c) {(2,4), (3,4) (4,4)} d) {(2,2),(3,3), (4,4), (5,5)}

87. Let A = {2, 3, 4, 5,…,16, 17,18}. Let ≈ be the equivalence relation on A × A, the cartesian product of A and A, defined by (a,b) ≈ (c,d) if ad = bc. Then the number of ordered pairs in the equivalence class of (3,2) is a) 4 b) 5 c) 6 d) 7

88. Let S be the set of all real numbers. Then the relation R = {(a,b) : 1 + ab > 0} on S is a) reflexive and symmetric but not transitive b) reflexive and transitive but not symmetric c) symmetric and transitive but not reflexive d) reflexive, symmetric and transitive e) none of the above is true

89. Let R be the real line. Consider the following subsets of the plane R × R : S = {(x,y) : y = x + 1 and 0 < x < 2}, T = {(x,y): x – y is an integer} Which one of the following is true ? a) Neither S nor T is an equivalence relation on R b) Both S and T are equivalence relations on R c) S is an equivalence relation on R but T is not d) T is an equivalence relation on R but S is not

90. If f(x) = 1 - 1 1

,then f f isx x

a) 1

x b)

1

1 x+ c)

1

x

x − dd))

1

1x −

91. The domain of the function f (x) = | 3 |

3

x

x

++

is

equal to a) { - 3 } b) R – { - 3 } c) R – {3} d) none of these

92. The function f (x) = |sin x| has an inverse if its domain is a) [0,π] b) [0, π/2] c) [ - π/4, π/4] d) none of these

93. If the sum of the first n terms of a series be 5n2 + 2n, then its second term is a) 16 b) 17 c) 27/14 d) 56/15

94. If x , 2x + 2, 3x + 3, …..are in G.P., then the fourth term is a) 27 b) – 27 c) 13.5 d) - 13. 5

95. If a1, a2, …, an are A.M. between a and b, then

1

2n

ii

a=

=∑

a) ab b) n (a + b) c) ( )n a b

ab

+ d) a b

n

+

96. a,b,c are respectively , the pth , qth and rth terms

of an A.P., then 1

1

1

a p

b q

c r

=

a) 1 b) – 1 c) 0 d) pqr e) p + q + r 97. The sum of the series

2 2

1 1 1 1.....

1 2 2 3 3 4 1n n+ + + +

+ + + − +

is equal to

a) 2 1n

n

+ b)

1

1

n

n n

+

+ − c)

2

1

2

n n

n

+ − d) n – 1

98. If ax = by = cz and x, y, z are in H.P., then a, b, c are in a) A.P b) H.P. c) G.P. d) none of these

99. If 1, log9 (31-x + 2), log3 (4. 3x – 1 ) are in A.P.,

then x equals a) log3 4 b) 1- log4 3 c) 1 –log3 4 d) log4 3

100. The value of the sum 13

1

1

( ), 1,n n

n

i i where i+

=

+ = −∑ equals

a) i b) i – 1 c) – i d) 0

101. The principal value of sin – 1 2sin

3is

π

a) 2 π/3 b) - 2 π/3 c) π/3 d) 4 π/3 102. The value of sin (cot – 1x ) is

a) 2

1

1 x+ b)

2

1

1 x+ c)

21

x

x+ d)

21

x

x+

103. The value of cot – 1 1 sin 1 sin

1 sin 1 sin

x xis

x x

− + +

− − +

(0 < x < 2 π) a) π- x/2 b) 2 π – x c) x/2 d) 2 π – x/2

104. If x + 1

2,x

= the principal value of sin – 1 x is

a) 4

π b)

2

π c) π d)

3

2

π

105. If sin (cot -1 (x + 1)) = cos (tan – 1 x), then x =

a) 1

2− b)

1

2 c) 0 d)

9

4

106. The number of real solutions of

tan – 1 1 2( 1) sin 12

x x x xπ−+ + + + = is

a) zero b) one c) two d) infinite 107. cot -1 1( cos ) tan ( cos ) xα α−− = then sin x

a) tan2 2

α b) cot2

2

α

c) tan α d) cot2

α

108. If sec -1 x = cosec – 1 y then the value of

cos – 1 11 1cos

x y−+ =

a) 4

π b) -

2

π c) π d)

2

π

109. If sin θ + cos θ = 2 sin θ, then value of

sin θ - cos θ is

a) 2 cos θ b) - 2 sin θ

c) - 2 cos θ d) none of these

110. value of cos 400 cos 800 cos 1600 is

a) 1

8 b)

1

16 c)

1

8− d) -

1

16

111. Value of 2 0 4 0

4 0 2 0

sin 20 cos 20

sin 20 cos 20

++

is

a) 1 b) 2 c) 1

2 d) none of these

112. Minimum value of sin6 θ + cos6 θ is

a) 1

4 b)

1

2 c)

3

4 d) none of these

113. The range of log 5 [ 2 (sin x – cos x ) + 3] is a) [0,2] b) [1,2] c) [0,3] d) [1,3]

114. The number of real solutions of the equation cos (ex) = 2x + e – x is a) 1 b) 0 c) 2 d) infinite

115. The maximum value of 3 cos x + 4 sin x + 5 is a) 5 b) 9 c) 7 d) none of these

116. 3 5 7

1 cos 1 cos 1 cos 1 cos8 8 8 8

π π π π + + + + is equal to

a) 1

2 b) cos

8

π c)

1

8 d)

1 2

2 2

+

117. If sin B = 1

sin(2 ),5

A B then+ tan( )

tan

A B

A

+ is

equal to

a) 5

3 b)

2

3 c)

3

2 d)

3

5

118. The value of cos120 + cos 840 + cos 1560 + cos 1320 is

a) 1

2 b) 1 c)

1

2

− d)

1

8

119. The maximum value of

sin cos6 6

x xπ π + + +

in the interval 0,

2

π

is

attained at

a) 12

π b)

6

π c)

3

π d)

2

π

120. The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution is a) 4 b) 8 c) 10 d) 12

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1. On heating , the temperature at which water has minimum volume is a) 00C b) 40C c) 4K d) 1000C e) -2730C

2. A lead bullet strikes against a steel plate with a velocity 200 m/s. If the impact is perfectly inelastic and the heat produced is equally shared between the bullet and the target , then the rise in temperature of the bullet is (specific heat capacity of lead= 125 Jkg -1 K-1 ) a) 800C b) 600C c) 400C d) 1200C e) 1200C

3. Three rods made of same material and having same cross –section are joined as shown in the figure . Each rod is of same length. The temperature at the junction of the three rods is

a) 450C b) 900C c) 300C d) 200C e) 600C

4. The surface area of a black body is 5×10-4 m2 and temperature is 7270C . The energy radiated by per min is (σ=5.67 ×10-8 Jm -2 –s-1K-4) a) 1.7 ×103J b) 2.5 ×102J c) 8 ×103 J d) 3 ×104 J e) None of the above

5. The thermodynamics process in which no work is done on or by the gas is a) isothermal process b) adiabatic process c) cyclic process d) isobaric process e) isochoric process

6. 100g of water is heated from 300C to 500C . Ignoring the slight expansion of water, the change in its internal energy is a) 8.4 kJ b) 84 kJ c) 2.1 kJ d) 4.2 kJ e) 3.2 kJ

7. In the given p-V diagram, I is the initial state and F is the final state. The gas goes from I to F by The gas goes from I to F by I) IAF II)IBF III)ICF

The heat absorbed by gas is a) the same in all three processes b) the same in I and II c) greater in I than in II d) greater in III than in II e) Greater in III than in II

8. The change in internal energy of a given mass of gas, when its volume changes from V to 2V at a constant

pressure p is p

v

C=γ, universal gas constant=R

C

a) pV

γ b)

(2 1)

pV

γ −

c) 2( 1)

pV

γ − d)

( 1)

R

γ −

e) ( 1)

pV

γ − 9. In a carnot engine , the temperature of reservoir is

9270C and that of sink is 270C. If the work done by the engine when it transfers heat from reservoir to sink is 12.6 ×106J, the quantity of heat absorbed by the engine from the reservoir is a) 16.8 ×106J b) 4×106J c) 7.6×106J d) 4.25×106J e) 20.8×106J

10. A diatomic ideal gas is compressed adiabatically to 1

32of its initial volume. If the initial temperature of

the gas is Ti (in kelvin)and the final temperature is Tf= aTi, the value of a is a) 4 b) 6 c) 5 d) 9 e) 2

11. A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at as pressure p and temperature T. Whereas the other part is completely evacuated. If the valve is suddenly opened, then the pressure and temperature of the gas will be

a) ,2

pT b) ,

2 2

p T

c) p,T d) ,

2

Tp

e) , 2

2

pT

12. Real gas behaves like an ideal gas, if its

a) pressure and temperature are both high b) pressure and temperature are both low c) pressure is high and temperature is low d) pressure is low and temperature is high e) None of these

13. In a certain region of space, there are only 5 molecules per cm2 on an average and temperature is 3K. The pressure of this dilute gas is (k=1.38 ×10-23 JK -1) a) 20.7 ×10-17 Nm-2 b) 15.3×10-15 Nm-1 c) 2.3× 10-10 Nm-1 d) 5.3 ×10-5 Nm-1 e) 3.5 ×10-8 Nm-1

14. If m represents the mass of each molecule of a gas and T its absolute temperature , then the root mean square velocity of the gaseous molecule is proportional to a) mT b) m1/2T1/2 c) m-1/2 T d) m -1/2 T1/2 e) m-1T

Time : 2½ Hours 1133..0033..1199

VVeerrssiioonn CCooddee:: BB

15. According to Maxwell`s law of distribution of velocities of molecules , the most probable velocity is a) Greater than the mean velocity b) equal to the mean velocity c) equal to the root mean square velocity d) less than the root mean square velocity e) Greater than the root mean square velocity

16. A molecule of a gas has six degrees of freedom. Then, the molar specific heat of the gas at constant volume is

a) 2

R b)

2

R

c) 3

2

R d) 3R e) 5R

17. A particle executes simple harmonic motion with a time period of 16s. At time t =2s ,the particle crosses the mean position while at t=4s , velocity is 4 ms-1. The amplitude of motion in metre is

a) 2π b) 16 2π

c) 24 2π d) 4

π e)

32 2

π 18. Two simple harmonic motions are represented by the

equations , y1=0.1 sin 1003

tπ π +

and y2=0.1 cos

πt. The phase difference of the velocity of particle 1, with respect to the velocity of particle 2 is

a)6

−π b)

3

π

c) 3

−π d)

6

π

e)

2

π

19. A body of mass 4 kg hangs from a spring and oscillates with a period of 0.5 s. On the removal of the body, the spring is shortened by a) 6.2 cm b) 0.63cm c) 6.25cm d) 6.3 cm e) 0.625cm

20. The period of a simple pendulum inside a stationary lift is T. The lift accelerates upwards with an acceleration of g/3 .The time period of pendulum will be

a) 2T b) 2

T

c) 3

2T d)

3

T

e)

2

3T

21. A simple pendulum is released from A , as shown in

the figure. If m and l represent the mass of the bob and length of the pendulum , the gain kinetic energy at B is

a) 2

mgl b)

2

mgl c)

3

2mgl

d) 2

3mgl e) mgl

22. A simple pendulum has a time period T 1 when on the earth`s surface and T2 when taken to a height 2R above the earth`s surface , where R is the radius of the earth. The value of (T1/T2 ) is

a) 1/9 b) 1/3 c)1

3 d) 9 e) 3

23. The amplitude of a damped becomes 1/3rd in 2s. If its amplitude after 6s is 1/n times the original amplitude , the value of n is a) 32 b) 3√2 c) 3√3 d) 23 e) 33

24. Transverse wave is described by the equation,

0 sin 2x

y y ft = π − λ

. The maximum particle

velocity is equal to four times the wave velocity, if

a) 0

4

yπλ = b) 0

2

yπλ =

c) 0yλ = π d) 02 yλ = π

e) 02

3

yπλ =

25. The instantaneous displacement of a simple harmonic oscillator is given by ,

y=a cos 4

tπ ω +

. Its speed will be maximum at

the time

a) 2πω

b) 2

ωπ

c) ωπ

d) 4

πω

e) πω

26. Tube A has both ends open while tube B has one end closed. Otherwise they are identical. Their fundamental frequencies are in the ratio a) 4:1 b) 2:1 c) 1:4 d) 1:2 e) 2:3

27. A sonometer wire 100 cm long has a fundamental frequency of 330 Hz. The velocity of propagation of transverse waves on the wire is a) 330 ms-1 b) 660 ms-1 c) 990ms-1 d) 115ms-1 e) 550 ms-1

28. An observer is approaching a stationary source with a velocity 1/4 th of the velocity of sound . Then the ratio of the apparent frequency to actual frequency of source is a ) 4:5 b) 5:4 c) 2:3 d) 3:2 e) 2:5

29. The readings of a constant volume gas thermometer at 00C and 1000C are 40cm and 60cm of mercury respectively. If its reading at an unknown temperature is 100 cm of mercury column, then the temperature is a) 1000C b) 500C c) 250C d) 3000C e) None of these

30. The plots of intensity of radiation versus wavelength of three black bodies at temperatures T1,T2 and T3 are shown .Then

a) T3>T2>T1 b) T1>T2>T3 c) T2>T3>T1 d) T1>T3>T2 e) T3>T1>T2

31. A carnot engine operating between temperature Ti

and T2 has efficiency 0.2. When T2 is reduced by 50K, its efficiency is to 0.4 .Then T1 and T2 are respectively a) 200 K, 150K b) 250K , 200 K c) 300K,250K d) 300K,200K e) 300K, 150K

32. Which of the following is true in the case of an adiabatic process, where , γ=Cp/Cv? a) p1-γ T γ= constant b) pγ T 1-γ= constant c) p Tγ= constant d) pγ T = constant e) None of these

33. If L of oxygen at a pressure of 1 atm and 2L of nitrogen at a pressure of 0.5 atm are introduced into a vessel of volume 1L .If there is no change in temperature , the final pressure of the mixture of gas (in atm ) is a) 1.5 b) 2.5 c) 2 d) 4 e) 3

34. The total energy of a simple harmonic oscillator is proportional to a) square root of displacement b) velocity c) frequency d) amplitude e) square of the amplitude

35. Two moles of oxygen is mixed with eight moles of helium. The effective specific heat of the mixture at constant volume is a) 1.3R b) 1.4 R c) 1.7R d) 1.9R e) 1.5 R

36. For a simple pendulum, the graph between T2and L is a) a straight line passing through the origin b) parabola c) circle d) ellipse e) hyperbola

37. The speed of sound in gas of density ρ at a pressure p is proportional to

a)

2p

ρ b)

3/2p

ρ c)

p

ρ

d) p

ρ e)

2

p

ρ

38. In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.14s . The frequency of the wave is a) 0.42Hz b) 2.75 Hz c) 1.79Hz d) 0.56Hz e) 3.5 Hz

39. A progressive wave y=a sin (kx –ωt)is reflected by a rigid wall at x=0. Then, the reflected wave can be represented by, a) y= sin(kx +ωt) b) y= a cos (kx +ωt)

c) y= -a sin(kx -ωt) d) y= -a sin(kx +ωt) e) y= a cos (kx -ωt)

40. A glass of length 1.0 m is completely filled with water. A vibrating turning fork of frequency 500 Hz is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is 330 ms-1 , then the total number of resonances, that occur will be a) 2 b) 3 c) 1 d) 5 e) 4

41. The hybridization of P in PO34− is the same as of

a) S in SO3 b) N in NO-3

c) I in ICl+2 d) I in ICl4-

42. Molar heat capacity of CD2O (deuterated form of formaldehyde) at constant pressure is 14 cal mol-1 K-1 at 1000 K. The entropy change associated with cooling of 3.2 g of CD2O vapour from 1000 to 900 K is a) – 0.1 cal K-1 b) – 0.25 cal K-1 c) – 0.4 cal K-1 d) – 0.15 cal K-1

e) – 0.015 cal K-1 43. Four diatomic species are listed below in different

sequences. Which of these presents the correct order of their increasing bond order?

a) O2− < NO < C2

2− < He2

+

b) NO < C22

− < O2− < He2

+

c) C22

− < He2+ < NO < O2

−

d) He2+ < O2

− < NO < C22

−

e) NO < O2

− < He2+ < C2

2−

44. In a multi – electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields? A) n = 1, =0, m = 0 B) n = 2, ℓ =0, m = 0 C) n = 2, ℓ =1, m = 1 D) n = 3, ℓ =2, m = 1 E) n = 3, ℓ =2, m = 0 a) D and E b) C and D c) B and C d) A and B e) D and B

45. In which of the following molecules/ ions are all the bonds not equal?

a) XeF4 b) BF4− c) SF4 d) SiF4

46. An electron in the ground state of hydrogen was excited to a higher energy level using monochromatic radiations of wave length (λ ) 975 Å. The longest wave length that appears in the resulting spectrum is due to transition from :

a) 4 1n n→ b) 4 3n n→

c) 5 4n n→ d) 5 1n n→

47. A beam of specific kind of particles of velocity 2.1 ×107 m/s is scattered by a gold (Z =79 ) nuclei. Find out specific charge (charge/ mass) of this particle if the distance of closest approach is 2.5×10-14 m. a) 4.84 ×107 C/kg b) 4.84 ×10 -7 C/kg c) 2.42 ×107 C/kg d) 3 ×10-12 C/kg

ℓ

48. The pH of 0.1 M solution of the following salts increases in the order: a) NaCl < NH4Cl < NaCN < HCl b) HCl < NH4Cl < NaCl < NaCN c) NaCN < NH4Cl < NaCl < HCl d) HCl < NaCl < NaCN < NH4Cl e) NH4Cl < HCl < NaCN < NaCl

49. As the temperature is raised from 20oC to 40oC, the average kinetic energy of neon atoms changes by a factor of which of the following?

a) ½ b) 313 / 293 c) 313/293 d) 2 e) 293/313

50. Rearrange the following (I to IV) in the order of increasing masses and choose the correct answer from (a) (b) (c) and (d). Atomic masses: N =14, O = 16, Cu = 63) I. 1 molecule of oxygen II. 1 atom of nitrogen III. 1 ×1010 g molecular weight of oxygen IV. 1 ×10-18 g atomic weight of copper a) II < I < III < IV b) IV < III < II < I c) II < III < I < IV d) III < IV< I< II e) I < II < IV < III

51. Which of the following has dipole moment ? a) 1- 4- dichlorobenzene b) [Ni(CN)4]

2- c) H2S d) trans -2,3- dichlorobutene e) None of these

52. On the basis of figure given below which of the following statement (s) is/are correct?

i) At point B, when only electric field is applied ii) At point C, when both electric and magnetic field is applied. iii) At point, B, when both electric and magnetic fields are balanced iv) At point C, when only magnetic field is applied Which of the following is/are correct? a) i and ii b) only iii c) iii and iv d) i and iii e) iii and ii

53. When 110 g of manganese (At. Mass =55) dissolves in dilute HNO3 at 27oC under atmospheric pressure, the work done in the process is: a) 2494.2 J b) – 2494.2 J c) – 4988.4 J d) 4988.4 J e) 249.42 J

54. In HS-, I-, RNH2 and NH3, order of proton accepting tendency will be a) I- > NH3> RNH2 > HS- b) HS- > RNH2 > NH3 > I-

c) RNH2 > NH3 > HS- > I- d) NH3 > RNH2 > HS- > I-

e) RNH2 > HS- > NH3> I- 55. 28 g of N2 and 6.0 g of H2 are heated over a catalyst

in a closed 1 L flask at 450oC. The entire equilibrium mixture required 500 ml of 1.0 M H2SO4 for naturalization. The value of KC for the reaction :

N2(g) + 3 H2(g) ��⇀↽�� 2NH3(g) is a) 1.69 mol2 L-2 b) 0.03 mol2 L-2 c) 0.59 mol -2 L2 d) 0.06 mol -2 L2

e) 1.33 mol-2 L2 56. If w1,w2,w3 and w4 for an ideal gas are magnitude of

work done in isothermal , adiabatic, isobaric and isochoric reversible expansion processes, the correct order will be: a) w1 > w2 >w3> w4 b) w3 > w2 >w4> w1 c) w3 > w2 >w4> w1 d) w3 > w1 >w2> w4

e) w4 > w1 >w2> w3 57. If 1021 molecules are removed from 200 mg of CO2,

then the number of moles of CO2 left are a) 2.88×10-3 b) 1.66 ×10-3 c) 4.54 ×10-3 d) 1.66 ×10-2

e) 2.88×103 58. 50 ml 10 N H2SO4, 25 ml 12 N HCl and 40 ml 5N

HNO3 were mixed together and the volume of the mixture was made 1000 ml by adding water. The normality of the resultant solution will be: a) 1 N b) 2N c) 3 N d) 4 N e) 5 N

59. The molar heat capacity (Cp) of CD2O is 10cals at 1000 K. The change in entropy associated with cooling of 32 g of CD2O vapour from 1000K to 100K at constant pressure will be: (D = deuterium, atomic mass = 2u) a) 23.03 cal deg-1 b) –23.03 cal deg-1 c) 2.303 cal deg-1 d) –2.303 cal deg-1

e) 23.3 cal deg-1 60. The relative stabilities of CN, CN+ and CN- are in the

order a) CN > CN+ > CN- b) CN- > CN > CN+ c) CN- > CN+ > CN d) CN+ > CN > CN-

61. Consider the following equilibria at 25oC,

2NO(g) ��⇀↽��N2(g) + O2(g) ; K1 = 4 ×1030 and

NO(g) +1/2 Br2(g) ��⇀↽�� NOBr(g) ; K2 = 1.4 mol-1/2 L1/2. The value of KC for the reaction (at the same temperature )

½ N2(g) + ½ O2(g) + ½ Br2(g) ��⇀↽�� NOBr(g) is: a) 3.5 ×10-31 b) 2.8 ×1015 c) 7.0×10-16 d) 5.6×1030

e) 7.0 ×1016 62. Which statement (s) are correct?

1) A 3s sub- shell has a maximum of 8 electrons. 2) An element with configuration of 1s22s23p63s2 would be in the same group as beryllium 3) The general electronic configuration of the group containing N2 is ns2np5 4) A strontium atom has a filled outer shell if it loses two electrons. a) 1, 2 and 3 b) 1 and 3 c) 2 and 4 d) Only 4 e) Only 2

63. What is the pressure of 2 mole of NHits volume is 5 litre in van der Waal(a = 4.17, b = 0.03711) a) 10.33 atm b) 9.33 atmc) 9.74 atm d) 9.2 atm e) 10 atm

64. If the collision frequency of a gas at 1 atm pressure is Z, then its collision frequency at 0.5 atm is a) 0.25 Z b) 0.50 Zc) Z d) 2Z e) 1.5Z

65. A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends, the white ammonium chloride ring first formed will be a) at the centre of the tube b) near the hydrogen chloride bottlec) near the ammonia bottle d) throughout the length of the tubee) None of these

66. If ∆H is the change in enthalpy and internal energy accompanying a gaseous reaction, then a) ∆H is always greater than b) ∆H < ∆E only if the number of products is greater than the number of moles of the reactants c) ∆H is always less than ∆d) ∆H < ∆E only if the number of moles of the products is less than the number of moles of the reactants e) None of these

67. For the formation of 3.65 g ofwhat volumes of hydrogen gas and chlorine gas are required at N.T.P conditions?a) 1.12 lit, 1.12 lit c) 3.65 lit, 1.83 lit e) None of these

68. ∆Hof of CO2(g), CO(g), N

mol are respectively -393, -∆H in kJ of the following reaction: 2NO2(g) + 3CO(g) → N2O(g) + 3COa) 836 b) 1460 c)

69. The percentage of Se in peroxidase anhydrous enzyme is 0.5% by weight (atomic weight = 78.4). Then minimum molecular weight of peroxidase anhydrous enzyme is a) 1.568 ×104 b) 1.568 ×c) 15.68 d) 3.136×

70. In which case hydrogen bond will not be observed

a) H3O 2− b) H2O

71. Arrange the following ions in the order of decreasing X – O bond length, where X is the central atom in

a) ClO4− , SO2

4− , PO3

4− , SiO

b) SiO44

− , PO34− , SO2

4− , ClO

c) SiO44

− , PO34− , ClO4

− , SO

d) SiO44

− , SO24

− , PO34− , ClO

e) PO34− , SiO4

4− , SO2

4− , ClO

What is the pressure of 2 mole of NH3 at 27oC when its volume is 5 litre in van der Waals equation?

b) 9.33 atm d) 9.2 atm e) 10 atm

If the collision frequency of a gas at 1 atm pressure is Z, then its collision frequency at 0.5 atm is

b) 0.50 Z d) 2Z e) 1.5Z

A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends, the white ammonium chloride ring first formed will be

b) near the hydrogen chloride bottle

d) throughout the length of the tube

is the change in enthalpy and ∆E is change in internal energy accompanying a gaseous reaction,

is always greater than ∆E only if the number of moles of the

products is greater than the number of moles of the

∆E only if the number of moles of the

products is less than the number of moles of the

For the formation of 3.65 g of hydrogen chloride gas, what volumes of hydrogen gas and chlorine gas are required at N.T.P conditions?

b) 1.12 lit, 2.24 lit d) 1 lit. 1 lit

(g), CO(g), N2O(g) and NO2(g) in kJ/ -110, 81 and 34. Calculate

H in kJ of the following reaction: O(g) + 3CO2(g)

a) 836 b) 1460 c) -836 d) -1460 e) 810 The percentage of Se in peroxidase anhydrous

s 0.5% by weight (atomic weight = 78.4). Then minimum molecular weight of peroxidase

×103 ×104 e) 15.68 ×102

In which case hydrogen bond will not be observed

c) H5O 2+ d) H3O

+

Arrange the following ions in the order of decreasing O bond length, where X is the central atom in

, SiO4−

, ClO4−

, SO24

−

, ClO4−

, ClO4

−

72. The ratio between the root mean H2 at 50 K and that of Oa) 4

73. The solubility product of an electrolyte AB2.7 ×10solution is a) 3.0 ×10c) 27

74. Which of the following is false?

a) 0.1 M FeFe(OH)

b) 0.1 M Mg

precipitation of Mg(OH)

c) 0.01 M AgAgOH

d) 0.01 M Agof AgOH

75. One mole of calcium posphide on reaction with excess of water givesa) one mole of phosphineb) two moles of phosphoric acid c) two moles of phosphine d) one mole of phosphorus pentoxide.e) One mole of phosphoric acid

76. When an electron of Hlower energy state, thena) its potential energy increasesb) its kinetic energy increasesc) itsd) wavelength of de Broglie wave associated with the electron increasee) its kinetic energy decreases

77. Densities of two gases are in the ratio 1:2 and their temperatures are in the ratio 2:1, then the ratio of their respa) 1:1

78. The pH at the equivalence point of titration of 0.2 M NH3

a) 9.7279. Which among the following is the heaviest?

a) One mole of oxygen b) One molecule of sulphur trioxide c) 100 amu of uranium d) 44 g of carbon dioxide

80. Which of the following volume (V) plots represents the behaviour of one mole of an ideal gas at one atmospheric pressure?

The ratio between the root mean square velocity of at 50 K and that of O2 at 800 K is b) 2 c) 1 d) ¼ e) 10

The solubility product of an electrolyte AB3 type is 2.7 ×10-19 (mol L-1)4. The molarity of its saturated solution is a) 3.0 ×10-5 b) 1.0 ×10-5 c) 271/4 ×10-5 d) 3.0 ×10-4 Which of the following is false?

a) 0.1 M Fe2+ + 0.1 M NH3 → Precipitation of Fe(OH)2

b) 0.1 M Mg2+ + 0.1 M NH3 + 0.1 M NH4+ →

precipitation of Mg(OH)2

c) 0.01 M Ag+ + 0.1 M NH3 → Precipitation of AgOH

d) 0.01 M Ag+ + 0.1 M NH3 → No precipitation of AgOH One mole of calcium posphide on reaction with excess of water gives a) one mole of phosphine b) two moles of phosphoric acid

two moles of phosphine d) one mole of phosphorus pentoxide. e) One mole of phosphoric acid When an electron of H- atom jumps from a higher to lower energy state, then a) its potential energy increases b) its kinetic energy increases c) its angular momentum remains unchanged d) wavelength of de Broglie wave associated with the electron increase e) its kinetic energy decreases Densities of two gases are in the ratio 1:2 and their temperatures are in the ratio 2:1, then the ratio of their respective pressures is a) 1:1 b) 1:2 c) 2:1 d) 4:1 The pH at the equivalence point of titration of 0.2 M

3 with 0.2 M HCl is : pKb of NH3 = 4.74) a) 9.72 b) 9.87 c) 5.13 d) 4.98 e) 10.26Which among the following is the heaviest? a) One mole of oxygen b) One molecule of sulphur trioxide c) 100 amu of uranium d) 44 g of carbon dioxide Which of the following volume (V) – temperature (T) plots represents the behaviour of one mole of an ideal gas at one atmospheric pressure?

velocity of

d) ¼ e) 10 type is

. The molarity of its saturated

Precipitation of

→ No

Precipitation of

No precipitation

One mole of calcium posphide on reaction with

atom jumps from a higher to

d) wavelength of de Broglie wave associated with the

Densities of two gases are in the ratio 1:2 and their temperatures are in the ratio 2:1, then the ratio of

The pH at the equivalence point of titration of 0.2 M

e) 10.26

temperature (T) plots represents the behaviour of one mole of an ideal

81. The domain of the function f (x) = | 3 |

3

x

x

++

is

equal to a) { - 3 } b) R – { - 3 } c) R – {3} d) none of these

82. a,b,c are respectively , the pth , qth and rth terms

of an A.P., then 1

1

1

a p

b q

c r

=

a) 1 b) – 1 c) 0 d) pqr e) p + q + r 83. Let A = {2, 3, 4, 5,…,16, 17,18}. Let ≈ be the

equivalence relation on A × A, the cartesian product of A and A, defined by (a,b) ≈ (c,d) if ad = bc. Then the number of ordered pairs in the equivalence class of (3,2) is a) 4 b) 5 c) 6 d) 7

84. In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then the persons travelling by car or bus is a) 80% b) 40% c) 60% d) 70% e) 30%

85. Let A = {x : x is a digit in the number 3591}, B = {x : x ∈ N, x < 10}. Which of the following is false ? a) A ∩ B= { 1, 3, 5 9} b) A - B = φ c) B – A = {2, 4, 6, 7, 8} d) A ∪B = {1,2,3,5,9}

86. If the sum of the first n terms of a series be 5n2 + 2n, then its second term is a) 16 b) 17 c) 27/14 d) 56/15

87. If sin θ + cos θ = 2 sin θ, then value of

sin θ - cos θ is

a) 2 cos θ b) - 2 sin θ

c) - 2 cos θ d) none of these

88. If 1, log9 (31-x + 2), log3 (4. 3x – 1 ) are in A.P.,

then x equals a) log3 4 b) 1- log4 3 c) 1 –log3 4 `d) log4 3

89. The value of sin (cot – 1x ) is

a) 2

1

1 x+ b)

2

1

1 x+ c)

21

x

x+ d)

21

x

x+

90. If sin (cot -1 (x + 1)) = cos (tan – 1 x), then x =

a) 1

2− b)

1

2 c) 0 d)

9

4

91. If sec -1 x = cosec – 1 y then the value of

cos – 1 11 1cos

x y−+ =

a) 4

π b) -

2

π c) π d)

2

π

92. The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution is a) 4 b) 8 c) 10 d) 12

93. The value of cos120 + cos 840 + cos 1560 + cos 1320 is

a) 1

2 b) 1 c)

1

2

− d)

1

8

94. The maximum value of 3 cos x + 4 sin x + 5 is a) 5 b) 9 c) 7 d) none of these

95. Value of 2 0 4 0

4 0 2 0

sin 20 cos 20

sin 20 cos 20

++

is

a) 1 b) 2 c) 1

2 d) none of these

96. The sum of the series

2 2

1 1 1 1.....

1 2 2 3 3 4 1n n+ + + +

+ + + − +

is equal to

a) 2 1n

n

+ b)

1

1

n

n n

++ −

c) 2 1

2

n n

n

+ − d) n – 1

97. A class has 175 students. The following data shows the number of students opting one or more subjects. Math 100, Physics 70, Chemistry 40, Math and Physics 30, Math and Chemistry 38 Physics and Chemistry 23, Math, Physics and Chemistry 18. How many have opted for math alone ? a) 35 b) 48 c) 50 d) 22 e) 30

98. Consider the following relations : (i) A – B = A – (A ∩ B) (ii) A = (A ∩ B) ∪ (A – B) (iii) A – (B ∪ C) = (A – B) ∪(A – C) Which of these is/are true ? a) (i), (iii) b) (ii) c) (ii) , (iii) d) (i), (ii)

99. In the set N of natural numbers, the binary operation ‘*’ is defined as follows : m * n =

,mn

pwhere p is a fixed number, then the

identity elements of * is a) a prime number b) p + m + n c) p – 1 d) p

100. If A = {x : x 2 – 5x + 6 = 0}, B = {2, 4} C = {4, 5}, then A × (B ∩ C) is a) {(2, 4), (3, 4)} b) {(4, 2), (4,3)} c) {(2,4), (3,4) (4,4)} d) {(2,2),(3,3), (4,4), (5,5)}

101. Let S be the set of all real numbers. Then the

relation R = {(a,b) : 1 + ab > 0} on S is a) reflexive and symmetric but not transitive b) reflexive and transitive but not symmetric c) symmetric and transitive but not reflexive d) reflexive, symmetric and transitive e) none of the above is true

102. Let R be the real line. Consider the following subsets of the plane R × R : S = {(x,y) : y = x + 1 and 0 < x < 2}, T = {(x,y): x – y is an integer} Which one of the following is true ? a) Neither S nor T is an equivalence relation on R b) Both S and T are equivalence relations on R c) S is an equivalence relation on R but T is not d) T is an equivalence relation on R but S is not

103. If f(x) = 1 - 1 1

,then f f isx x

a) 1

x b)

1

1 x+ c)

1

x

x − dd))

1

1x −

104. The function f (x) = |sin x| has an inverse if its domain is a) [0,π] b) [0, π/2] c) [ - π/4, π/4] d) none of these

105. The number of real solutions of the equation cos (ex) = 2x + e – x is a) 1 b) 0 c) 2 d) infinite

106. If x , 2x + 2, 3x + 3, …..are in G.P., then the fourth term is a) 27 b) – 27 c) 13.5 d) - 13. 5

107. If a1, a2, …, an are A.M. between a and b, then

1

2n

ii

a=

=∑

a) ab b) n (a + b) c) ( )n a b

ab

+ d) a b

n

+

108. If ax = by = cz and x, y, z are in H.P., then a, b, c are in a) A.P b) H.P. c) G.P. d) none of these

109. The value of the sum 13

1

1

( ), 1,n n

n

i i where i+

=

+ = −∑ equals

a) i b) i – 1 c) – i d) 0

110. The principal value of sin – 1 2sin

3is

π

a) 2 π/3 b) - 2 π/3 c) π/3 d) 4 π/3

111. The value of cot – 1 1 sin 1 sin

1 sin 1 sin

x xis

x x

− + +

− − +

(0 < x < 2 π) a) π- x/2 b) 2 π – x

c) x/2 d) 2 π – x/2

112. If x + 1

2,x

= the principal value of sin – 1 x is

a) 4

π b)

2

π c) π d)

3

2

π

113. The number of real solutions of

tan – 1 1 2( 1) sin 12

x x x xπ−+ + + + = is

a) zero b) one c) two d) infinite

114. cot -1 1( cos ) tan ( cos ) xα α−− = then sin x

a) tan2 2

α b) cot2

2

α

c) tan α d) cot2

α

115. value of cos 400 cos 800 cos 1600 is

a) 1

8 b)

1

16

c) 1

8− d) -

1

16

116. Minimum value of sin6 θ + cos6 θ is

a) 1

4 b)

1

2 c)

3

4 d) none of these

117. The range of log 5 [ 2 (sin x – cos x ) + 3] is a) [0,2] b) [1,2] c) [0,3] d) [1,3]

118. 3 5 7

1 cos 1 cos 1 cos 1 cos8 8 8 8

π π π π + + + + is equal to

a) 1

2 b) cos

8

π

c) 1

8 d)

1 2

2 2

+

119. If sin B = 1

sin(2 ),5

A B then+ tan( )

tan

A B

A

+ is

equal to

a) 5

3 b)

2

3

c) 3

2 d)

3

5

120. The maximum value of

sin cos6 6

x xπ π + + +

in the interval 0,

2

π

is

attained at

a) 12

π b)

6

π

c) 3

π d)

2

π

KKEERRAALLAA MMOODDEELL EENNTTRRAANNCCEE EEXXAAMM

RREEPPEEAATTEERRSS –– EENNGGIINNEEEERRIINNGG ((MMOODDUULLEE –– IIVV))

AANNSSWWEERR KKEEYY VVEERRSSIIOONN CCOODDEE –– AA

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

D B A E D A E A A E B A A A A

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

D C A D D D C E A E A C C A B

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

E D B C D D B B B B A C D C B

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

A A A D B A C B C C B C C B B

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

A A B B C C A C A C D D C D B

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

C D B C C D C D D C A C A D D

91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

B B B D B C D C C B C B A B A

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

C A D A C A A A B D A C B A B

AANNSSWWEERR KKEEYY VVEERRSSIIOONN CCOODDEE –– BB

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B A E A E A A E A A A D A D D

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

D E A A A C B E B D B B B D D

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

B A C E C A D C D B C D D A C

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

B A B C A C C C C C D A A B B

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

C C B A B D A C A D B C B B C

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

B A C D C B C C C D B A C B A

91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

D B B D A D C D D A A D D B B

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

D B C B C A B C A C A A A C A

1133..0033..1199

AANNSSWWEERRSS AANNDD SSOOLLUUTTIIOONNSS

First No: Version code: A Second No: Version code: B

1. 29

2. 1

3. 2

4. 3

5. 30

6. 4

7. 5

8. 6

9. 7

10. 8

11. 31

12. 9

13. 10

14. 32

15. 11

16. 12

17. 33

18. 13

19. 14

20. 15

21. 16

22. 35

23. 17

24. 18

25. 34

26. 19

27. 20

28. 21

30. 22

31. 23

32. 37

33. 24

34. 38

36. 39

37. 26

38. 27

39. 40

40. 28

41. 57

42. 72

43. 66

44. 55

45. 73

47. 64

48. 67

49. 56

50. 74

51. 58

52. 75

53. 65

54. 80

55. 49

56. 63

57. 68

58. 53

59. 76

60. 46

61. 69

62. 77

63. 59

64. 48

65. 54

66. 78

67. 47

68. 62

69. 44

70. 52

71. 79

72. 42

73. 61

74. 43

75. 71

76. 45

77. 70

78. 60

79. 41

80. 51

81. 85

82. 97

83. 98

84. 99

85. 84

86. 100

87. 83

88. 101

89. 102

90. 103

91. 81

92. 104

93. 86

94. 106

95. 107

96. 82

97. 96

98. 108

99. 88

100. 109

101. 110

102. 89

103. 111

104. 112

105. 90

106. 113

107. 114

108. 91

109. 87

110. 115

111. 95

112. 116

113. 117

114. 105

115. 94

94

116. 118

117. 119

118. 93

119. 120

120. 92