AIEEE 2007 Practice Test 1

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.        Match 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)