Q1. The temperature of an ideal gas is increased from 27 °C to 927 °C. The root mean square speed of its molecules becomes

(a) twice

(b) half

(c) four times

(d) one fourth

Q2. At a given volume and temperature, the pressure of a gas

(a) varies inversely as its mass

(b) varies inversely as the square of its mass

(c) varies linearly as its mass

(d) is independent of its mass

Q3. A monatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If L1 and L2 are the lengths of the gas column before and after expansion respectively, then T1 / T2 is given by

(a) (L1 / L2 )2/3

(b) (L1 / L2)

(c) (L2 / L1 )

(d) (L2 / L1 )2/3

Q4 .A cycle tyre bursts suddenly. This represents an

(a) isothermal process

(b) isobaric process

(c) isochoric process

(d) adiabatic process

Q5. The slope of isothermal and adiabatic curves are related as

(a) isothermal curve slope = adiabatic curve slope

(b) isothermal curve slope = g (adiabatic curve slope)

(c) adiabatic curve slope = g (isothermal curve slope)

(d) adiabatic curve slope = (1/2) (isothermal curve slope)

Q6. A box contains n molecules of gas. How will the pressure of the gas be affected if the number of molecules is made 2n

(a) pressure will decrease

(b) pressure will remain unchanged

(c) pressure will be doubled

(d) pressure will become three times

Q7. The pressures P of an ideal gas and its mean kinetic energy per unit volume are related as

(a) P =

(b) P = E

(c) P =

(d) P =

Q8. If a gas has f degrees of freedom, the ratio of the specific heats g the gas is

(a)

(b)

(c) 1 +

(d)

Q9.The temperature of gas is produced by

(a) the potential energy of its molecules

(b) the kinetic energy of its Molecules

(c) the attractive force between its molecules

(d) the repulsive force between its molecules

Q10. A polyatomic gas with f degrees of freedom has a mean energy per molecules given by

(a)

(b)

(c)

(d) None of these

Q11. The number of translational degrees of freedom for a diatomic gas is

(a) 2

(b) 3

(c) 5

(d) 6

Q12 . The internal energy U is a unique function of any state because change in U

(a) does not depend upon path

(b) depends upon path

(c) corresponds to an adiabatic process

(d) corresponds to an isothermal process

Q13. A cube of side 5 cm made of iron, and having a mass of 1500 gm, is heated from 25° C to 400° C. The specific heat for iron is 0.12 cal/gm °C and the coefficient of volume expansion is 3.5 x 10–5 / °C. The change in internal energy of the cube is (atmospheric pressure = 105 N/m2):

(a) 320 kJ

(b) 282 kJ

(c) 141 kJ

(d) 423 kJ

Q14. One end of a copper rod of length 1.0 m and area of cross-section 10–3 m2 is immersed in boiling water and other end in ice. If the coefficient of thermal conductivity of copper is 92 cal/ms C° and the latent heat of ice is 8 x 104 cal/kg., then the amount of ice which melt in one minute is:

(a) 9.2 x 10–3 kg

(b) 8 x 103 kg

(c) 6.9 x 10–3 kg

(d) 5.4 x 10–3 kg

Q15. A tap supplies water at 10 °C and another tap at 100 °C. How much hot water must be taken so that we get 20 kg water at 25°C?

(a) 7.2 kg

(b) 10 kg

(c) 5.6 kg

(d) 14.4 kg

Q16. The average kinetic energy per mole of hydrogen at a given temperature is:

(a) equal to that of helium

(b) 3/5 times that of helium

(c) 5/3 times that of helium

(d) times that of helium

Q17. A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is:

(a) same everywhere

(b) lower in the front side

(c) lower in the rear side

(d) lower in the upper side

Q18. The volume of air increases by 5 % in its adiabatic expansion. The percentage decrease in its pressure will be:

(a) 5 %

(b) 6 %

(c) 7 %

(d) 8 %

Q19. Two spherical vessels of equal volume are connected by a narrow tube. The apparatus contains an ideal gas at one atmosphere and 300 K. Now if one vessel is sphere and 300 K. Now if one vessel is immersed in a bath of constant temperature 600 K and the other in a bath of constant temperature 300 K, then the common pressure will be:

(a) 1 atm

(b) atm

(c) atm

(d) atm

Q20. A wall has two layers A and B, each made of different material. Both the layers have same thickness. The thermal conductivity of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is 36 °C. The temperature difference across the layer A is:

(a) 24 °C

(b) 18 °C

(c) 12 °C

(d) 6 °C

Q21. Which of the following quantities are always zero in a simple harmonic motion ?

(a)

(b)

(c)

(d) all of these

Q22. Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel. the motion of the particle is

(a) Simple harmonic

(b) Parabolic

(c) Oscillatory

(d) non − Periodic

Q23 .The motion of a particle is given by x = A sin wt + B cos wt. The motion of the particle is

(a) Not simple harmonic

(b) Simple harmonic with amplitude

(c) Simple harmonic with amplitude (A+ B)/2

(d) Simple harmonic with amplitude

Q24. When a sound wave goes from one medium to the quantity that remains unchanged is

(a) Frequency

(b) Amplitude

(c) Wavelength

(d) Speed

Q25 . The differential equation of a wave is

(a) d2y/dt2 = v2d2y/dx2

(b) d2y/dx2 = v2d2y/dt2

(c) d2y/dx2 = d2y/dt2

(d) d2y/dx2 = − vd2y/dt2

Q26. The relation between velocity of sound in a gas (v) and r.m.s. velocity of molecules of gas (Vrms.) is

(a) v = Vrms (g/3)1/2

(b) Vrms = v(2/3)1/2

(c) v = vrms

(d) v = Vr.m.s. (3/g)1/2

Q27. When a wave is reflected from a denser medium, the change in phase is

(a) 0

(b) p

(c) 2 p

(d) 3 p

Q28 .A closed pipe has certain frequency. Now its length is halved. Considering the end correction, its frequency will now become

(a) Double

(b) More than double

(c) Less than double

(d) Four times

Q29 .The fundamental frequency of a closed end organ pipe is n. Its length is doubled and radius is halved. Its frequency will become nearly

(a) n/2

(b) n/3

(c) n

(d) 2n

Q30. The equation of a plane progressive wave is y = 0.9 sin 4 p when it is reflected at a rigid support, its amplitude becomes of its previous value. The equation of the reflected wave is

(a) y = 0.6 sin 4p

(b) y = − 0.6 sin 4p

(c) y = − 0.9 sin 8p

(d) y = − 0.6 sin 8p

Q31.Three transverse waves are represented by

y1 = A cos (kx ? wt)

y2 = A cos (kx + wt)

y3 = A cos (ky ? wt)

The combination of waves which can produce stationary waves is

(a) y1 and y2

(b) y2 and y3

(c) y1 and y3

(d) yl, y2 and y3

Q32 . If two waves of same frequency and same amplitude, on superposition, produce a resultant disturbance of the same amplitude, the wave differ in phase by

(a) p

(b) 2 p/3

(c) Zero

(d) p/3

Q33 .A body of mass 5 gram is executing S.H.M. A point O. with an amplitude of 10 cm, its maximum is 100 cm/s. Its velocity will be 50 cm s−1 at a distance (in cm)

(a) 5

(b) 5

(c) 5

(d) 10

Q34. The potential energy of a particle (Ux) executing SHM is given by

(a) Ux =

(b) Ux = K1x + K2x2 + K3x3

(c) Ux = Ae −bx

(d) Ux = a cosntant

Q35 . A second's pendulum is placed in a space laboratory orbiting around the earth at a height 3 R from the earth's surface where R is earth's radius. The time period of the pendulum will be

(a) Zero

(b) 2

(c) 4 sec

(d) Infinite

Q36 .The threshold intensity of sound is 10−12 W m−2. What is the intensity level of sound whose intensity is 10−8 W m−2 ?

(a) 40 dB

(b) 8 dB

(c) 12 dB

(d) 20 dB

Q37.Two sinusoidal plane waves of same frequency having intensities I0 and 4 I0. are traveling in the same direction, the resultant intensity at a point at which waves meet with a phase difference of zero radian is

(a) I0

(b) 5 I0

(c) 9 I0

(d) 3 I0

Q38 . A child swinging on a swing in sitting position, stands up, then the time period of the swing will

(a) increase

(b) decrease

(c) remains same

(d) increases of the child is long and decreases if the child is short

Q39 .The displacement y of a wave traveling x ?direction is given by

y =10−4 sin metres

where x is expressed in metres and t in seconds. The speed of the wave ? motion in ms−1 is

(a) 300

(b) 600

(c) 1200

(d) 200

Q40 . The displacement of a particle varies according to the relation x = 4 (cos pt + sin pt ). The amplitude of the particle is

(a) − 4

(b) 4

(c) 4

(d) 8

**[ Chemistry ]**

Q41. A gas will approach ideal behavior at

(a) Low temperature and low pressure

(b) Low temperature and high pressure

(c) High temperature and low pressure

(d) High temperature and high pressure

Q42. Which of the following has maximum root mean square velocity at the same temperature?

(a) SO2

(b) CO2

(c) O2

(d) H2

Q43. The total kinetic energy of 2 moles of an ideal gas at 127°C is (R = 8.3 JK?1 mol?1)

(a) 9.96 kJ

(b) 19.92 kJ

(c) 3.32 kJ

(d) 39.84 kJ

Q44. The vapour density of a gas is 11.2. The volume occupied by 11.2 gm of this gas NTP is:

(a) 1 L

(b) 11.2 L

(c) 22.4 L

(d) 20 L

Q45.The unit of van der Waal's constant ‘a’ is

(a) litre

(b) atmosphere

(c) atmosphere litre2 mole-1

(d) atmosphere (litre)2 (mole)?2

Q46. The value of gas constant per mole is approximately?

(a) 1 cal

(b) 2 cal

(c) 3 cal

(d) 4 cal

Q47 Dalton's law of partial pressure is not applicable to

(a) H2 and N2 mixture

(b) H2 and C12 mixture

(c) H2 and CO2 mixture

(d) None

Q48. The total pressure of a mixture of two gases is?

(a) The sum of partial pressures of each gas

(b) The difference in partial pressures

(c) The product of partial pressures

(d) The ratio of partial pressures.

Q49. While He is allowed to expand through a, small jet under adiabatic condition heating effect is observed. This is due to the fact that ?

(a) Helium is an inert gas

(b) Helium is a noble gas

(c) Helium is an ideal gas

(d) The inversion temp. of helium is very low

Q50 .The increasing order of effusion among the gases, H2 , O2 , NH3 and CO2 is -

(a) H2 , CO2, NH3 , O2

(b) H2 , NH3 , O2 , CO2

(c) H2, O2, NH3 , CO2

(d) CO2 , O2 , NH3 , H2

Q51. In which of the following pairs the gaseous species diffuse through a porous plug with the same rate of diffusion

(a) NO, CO

(b) NO, CO2

(c) NH3 , PH3

(d) NO , C2H6

Q52 .Solubility of a gas in water ?

(a) Increases with temperature

(b) Decreases with pressure

(c) Decreases with temperature

(d) None

Q53 . Which is not correct in terms of kinetic theory of gases

(a) Gases are made up of small particles called molecules

(b) The molecules are in constant motion

(c) When molecules collide, they lose energy

(d) When the gas is heated, the molecules moves faster

Q54 . Which one of the following gases would have the highest R.M.S. velocity at 25°C ?

(a) Oxygen

(b) Carbon dioxide

(c) Sulphur dioxide

(d) Carbon monoxide.

Q55 . At S.T.P. the order of mean square velocity of molecules H2, N2 , O2 and HBr is ?

(a) H2 >N2 > O2 >HBr

(b) HBr > O2 > N2 > H2

(c) HBr > H2 > O2 >N2

(d) N2 > O2 > H2 > HBr

Q56 . Most probable velocity average velocity and root mean square velocity are related as ?

(a) 1 : 1. 128 : 1.224

(b) 1 : 1.128 : 1.424

(c) 1 : 2.128 : 1.224

(d) 1 : 1.428 : 1.442

Q57. Which of the following gases is adsorbed strongly by charcoal ?

(a) CO

(b) N2

(c) H2

(d) NH3

Q58. V versus T curves at constant pressure P1 and P2 for an ideal gas are shown in the figure Which is correct -

(a) P1 > P2

(b) P1 < P2

(c) P1 = P2

(d) All

Q59. Figure shows graphs of pressure versus density for an ideal gas at two temperatures T1 and T2 . Which is correct

(a) T1 > T2

(b) T1 = T2

(c) T1 < T2

(d) None of the above

Q60. I, II, III are three isotherms respectively at T1, T2 and T3. Temperature will be in order

(a) T1 = T2 = T3

(b) T1 < T2 < T3

(c) T1 > T2 > T3

** **(d) T1 > T2 = T3

Q61.Tilden's reagent is?

(a) C6H5SO2Cl

(b) NOCI

(c) ClNH2

(d) (C2H5)2Zn

Q62 . Which of the following compound gives the smell of mustard oil?

(a) Alkyl isocyanate

(b) Alkyl isothiocyanate

(c) Alkyl isocyanide

(d) Alkyl isonitrile

Q63 . In the reaction CH3NH2 X Y Z the final product Z is moist

(a) (CH3)3N

(b) (CH3)4N+ Cl?

(c) (CH3)4N+OH?

(d) (CH3)2NH

Q64 .Suitable explanation for the order of basic character (CH3)3N < (CH3)2NH is?

(a) Steric hindrance by bulky methyl group

(b) Higher volatility of 30 amine

(c) Decreased capacity for H? bond formation with H2O

(d) Decreased electron ? density at N atom

Q65. Ethylamine can be prepared by the all except -

(a) Curtius reaction

(b) Hofmann reaction

(c) Mendius reaction

(d) Reduction of formaldoxime

Q66. atch list I with list II and then select the correct answer from the codes given below the lists

List I List II

(A) Rapid heating of urea (a) Urethane

(B) Slow and gentle heating of urea (b) Sodium carbonate

(C) Refluxing of urea with alkanol (c) Cyanuric acid

(D) Heating of urea with aqueous NaOH solution (d) Biuret

Codes

(a) Ac, Bd, Cb, Da

(b) Ac, Ba, Cb, Dd

(c) Ac, Bd, Ca, Db

(d) Ac, Bb, Cd, Da

Q67. Urea reacts with formaldehyde to form a plastic known as

(a) Bakelite

(b) Teflon

(c) Urea – formaldehyde resin

(d) Methyluracil

Q68. The compounds A, B and C in the reaction sequence,

are given by the set ?

(a) Phosphine, PCl3, CH3CONH2

(b) Urea, NH2 ? NH2, CH3CONHCONH2

(c) O = CH ? NH2 , NH2 ? NH2, CH3 ? NH ? CO ? NH2

(d) Urea, N2, acetylurea

Q69 . Which reaction sequence would be best to prepare 3 - chloroaniline from benzene ?

(a) Chlorination, nitration, reduction

(b) Nitration, chlorination, reduction

(c) Nitration, reduction, chlorination

(d) Nitration, reduction, acetylation, chlorination, hydrolysis

Q70 .C6H6 + A C6H5CONH2

A in the above reaction is ?

(a) NH2 CONH2

(b) ClCONH2

(c) CH3CONH2

(d) CH2(Cl)CONH2

Q71.The species responsible for nitration and sulphonation by nitric acid, conc. H2SO4 and fuming H2SO4 are?

(a) NO2 and SO3

(b) NO2+ and SO3

(c) NO+ and SO2

(d) NO2 and SO2

Q72. Nitrobenzene on reduction in acidic medium gives ?

(a) Aniline

(b) Nitrosobenzene

(c) Azobenzene

(d) Phenyl hydroxyl amine

Q73 .Match list I with list II and then select the correct answer from the codes given below the lists ?

List I List II

(A) Nitrobenzene (a) Used as explosive

(B) Trinitrotoluene (b) Used as powerful reducing agent

(C) Azobenzene (c) Used in preparation of dyes

(D) Phenyl hydroxylamine (d) Used as cheap scent

Codes:

(a) Aa, Bc, Cd, Db

(b) Ab, Bc, Cd, Da

(c) Ad, Ba, Cc, Db

(d) Ad, Ba, Cb, Dc

Q74 .Which of the following statements is untrue for pheny1hyroxylamine ?

(a) It reduces Tollen's reagent

(b) It is prepared by reducing nirtrobenzene with zinc dust and aqueous ammonium chloride

(c) It absorbs oxygen from air to form nitrobenzene

(d) It absorbs oxygen from air to form nitrosobenzene

Q75 . Nitrobenzene on reduction in alkaline medium gives ?

(a) Aniline

(b) Nitrosobenzene

(c) Hydrazobenzene

(d) Phenylhydroxyl amine

Q76. The major product (70?80%) of the react between m – dinitrobenzene with NH4HS is

(a)

(b)

(c)

(d)

Q77. A f–CHO B

A and B respectively are ?

(a) Benzoyl chloride, benzonitrile

(b) Benzyl chloride, benzylnitrile

(c) Benzal chloride, benzonitrile

(d) Benzotrichloride, benzonitrile

Q78 . Benzaldehyde is heated with a conc. solution of KOH to form ?

(a) C6H5CH2OH

(b) C6H5COOH

(c) C6H5COOK

(d) C6H5COOK + C6H5CH2OH

Q79. Hydrobenzamide is formed in the reaction ?

(a) C6H5COOH + NH3

(b) C6H5CHO + NH3

(c) HCHO + NH3

(d) CH3COCH3 +NH3

Q80. HCHO and C6H5CHO can be distinguished by ?

(a) Fehling solution

(b) Tollen's reagent

(c) KMnO4

(d) All of these

**[ Mathematics ]**

Q81.The maximum number of points into which 4 circles and 4 straight lines intersect is

(A) 26

(B) 50

(C) 56

(D) 72

Q82 .The number of products that can be formed with 10 prime numbers taken two or more at a time is

(A) 210

(B) 210 − 1

(C) 210 − 11

(D) 210 − 10

Q83 .The number of rectangles in the following figure is

(a) 5 x 5

(b) 5P2 x 5P2

(c) 5C2 x 5C2

(d) None of these

Q84 . If n(B) = 2 and the number of mappings from A to B which are onto is 30, then number of elements in A is

(A) 4

(B) 5

(C) 6

(D) None of these

Q85 .The number of ways in which 6 red roses and 3 white roses can form a garland so that all the white roses come together is

(A) 2170

(B) 2165

(C) 2160

(D) 2155

Q86 . We are required to form different words the help of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then is equal to

(A) 42

(B) 30

(C) 6

(D)

Q87 . The number of divisors of 3630, which have a remainder of 1 when divided by 4, is

(A) 12

(B) 6

(C) 4

(D) None of these

Q88 . The sum of divisors of 25 . 37 . 53. 72 is

(a) 26 . 38 54 73

(b) 26 . 38 . 54 . 73 − 2 . 3 . 5 . 7

(C) 26 . 38 . 54 . 74 − 1

(D)

Q89 . If in a chess tournament each contestant plays once against each of the others and in all 45 games are played, then the number of participants is

(A) 9

(B) 10

(C) 15

(D) None of these

Q90 .The number of ways of choosing 10 balls from infinite white, red, blue and green balls is

(A) 70

(B) 84

(C) 286

(D) 86

Q91. Number of positive unequal integral solutions of the equation x + y + z = 6 is

(A) 4!

(B) 3!

(C) 5!

(D) 2 x 4!

Q92. 20 people are to travel by a double decker bus which can carry 9 in the lower deck and 11 in the upper deck. In how many ways can the party be seated if 4 keep themselves in the lower deck and 5 keep in the upper deck ?

(A) (11!)2 x 9!

(B) 11P5 . 6P6

(C) (11!)2

(D) None of these

Q93. The number of all possible selections of one 10 or more questions from 10 given questions, each question having an alternative is

(A) 310

(B) 210 − 1

(C) 310 − 1

(D) 210

Q94 . There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is

(A) 6

(B) 11

(C) 13

(D) None of these

Q95 . There are 4 parcels and 5 post offices. In how many ways can 4 parcels be got registered?

(A) 20

(B) 45

(C) 54

(D) 54 − 45

Q96. Six X have to be placed in the squares of adjoining figure such that each row contains at least one X. In how many different ways can this be done ?

(A) 28

(B) 27

(C) 26

(D) 25

Q97. On a railway there are 10 stations. The number of types of tickets required in order that it may be possible to book a passenger from every station to every other is

(A)

(B) 10!2!

(C)

(D)

Q98 .How many words can be formed by taking 4 letters at a time out of letters of the word MATHEMATICS?

(A) 2500

(B) 2550

(C) 2454

(D) 3000

Q99 .There are 10 cages for keeping 10 animals in circus in which 4 cages are so small that 5 animals out of 10 can not enter into them. In how many ways can 10 animals be kept in 10 cages ?

(A) 66400

(B) 86400

(C) 96400

(D) 96000

Q100. A letter lock contains 5 rings each marked with four different letters. The number of all possible unsuccessful attempts to open the lock is

(A) 625

(B) 1024

(C) 624

(D) 1023

Q101 . If , y , be in AP then x, , z will be in

(a) AP

(b) GP

(c) HP

(d) None of these

Q102 If a, b, c be in AP ., b, c, d are in GP ., and c, d, e are in HP , then a, c, e will be in

(a) AP

(b) GP

(c) HP

(d) None of these

Q103 Three non − zero real numbers form an AP and the squares of these numbers taken in the same order form a GP then the number of all possible common ratios of the GP is

(a) 1

(b) 2

(c) 3

(d) None of these

Q104 If pth , qth, rth and sth terms of an AP are in GP then q − q, q − r, r − s are in

(a) AP

(b) GP

(c) HP

(d) None of these

Q105 The nth term of the series 4, 14, 30, 52, 80, 114 ………. is

(a) n2 + n + 2

(b) 3n2 + n

(c) 3n2 − 5n + 2

(d) (n + 1)2

Q106 If in the expansion of (1 + x), the coefficients of (2r + 3)th and (r − 1)th terms are equal, then the value of r is

(a) 5

(b) 6

(c) 4

(d) 3

Q107 The coefficient of x17 in the expansion of (x − 1) (x − 2) (x − 3) ….. (x − 18) is

(a) 342

(b)

(c) − 171

(d) 684

Q108 The middle term in the expansion of is

(a) 251

(b) 252

(c) 250

(d) None of these

Q109 If in the expansion of occurs in the rth term, then

(a) r =10

(b) r = 11

(c) r = 12

(d) r = 13

Q110 The value of upto three decimal places is

(a) 9.949

(b) 9.958

(c) 9.948

(d) None of these

Q111 is equal to

(a)

(b)

(c) log (2x +1)

(d) log

Q112 The sum of the series log 4 2 − log 8 2 + log 16 2 − …, is

(a) e2

(b) log e 2 + 1

(c) log e 3 − 2

(d) 1 − log e 2

Q113 2 log x − log (x + 1) − log (x − 1) is equal to

(a)

(b)

(c) −

(d) None of these

Q114 . The coefficient of xn , where n is a multiple of , in the expansion of log (1 + x + x2) is

(a) −

(b)

(c)

(d) None of these

Q115 The sum of the series is equal to

(a) log e x

(b) 2 log e x

(c) − log e (x + 1)

(d) None of these

Q116. If the system of equations x – ky – z = 0, kx – y – z = 0, x + y – z = 0 has a non-zero solution, then the possible values of k are:

(a) – 1, 2

(b) 1, 2

(c) 0, 1

(d) – 1, 1

Q117. If A = and B =, then value of a for which A2 = B is:

(a) 1

(b) – 1

(c) 4

(d) no real values

Q118. If A = and | A3 | = 125 then the value of a is:

(a) ± 1

(b) ±2

(c) ± 3

(d) ± 5

Q119. If A = and I = and A–1 = , then the value of c and d are:

(a) (– 6, – 11)

(b) (6, 11)

(c) (– 6, 11)

(d) (6, – 11)

Q120. If P = and A = and Q = PAPT and x = PTQ2005P then x is equal to:

(a)

(b)

(c)

(d)

** **