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All India Engineering Entrance Examination (AIEEE) 2007 1











AIEEE 2007 Practice Test 1

- Test duration is 2 hours.
 Instructions


1. All questions are compulsory.

2. Every question carries 3 marks.

3. Do not write anything on answer sheet except in the marked area.

4. Every incorrect answer carries -1(negative) mark

5. The paper is of 2 hours duration



Syllabus

Physics - Heat, SHM and waves

Chemistry - Gaseous state Amines

Mathematics - Permutation and Combination, Matrices, Binomial theorem, Exponential log series, sequence and series


 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)


 

 

 

 
  Electricity and Effect of Current      Chemical Kinetics      Centre of Mass      Chemical Equilibrium      AIEEE 2009 Solutions and Analysis      Chemical Bonding      Quadratic Equations      Progression And Series      dasda      Chemical Bonding      General Principles of Extraction of Metals      Ether and epoxides      Atomic Structure      Parabola      IIT-JEE Chemistry by M.K.Tiwri      Properties of Matter      Material Wave and Sound      Heat & Thermodynamics      Aldehydes and ketones      Disha - Path to Success Series     
 



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