AIEEE 2007 Practice Test 2

Q1.          Two holes of unequal diameters d1 and d2 (d1 > d2) are cut in a metal sheet. If the sheet is heated,
                                              
                (a) both d1 and d2 will decrease
                (b) both d1 and d2 will increase
                (c) d1 will increase, d2 will decrease
                (d) d1 will decrease, d2 will increase

Q2.          In the previous question, the distance between the holes will
                (a) increase
                (b) decrease.
                (c) remain constant
                (d) may either increase or decrease depending on the positions of the holes on the sheet and on the                  ratio d1/d2

Q3.          A metal wire of length l and area of cross-section A is fixed between rigid supports at negligible                 tension. If this is cooled, the tension in the wire will be
                (a) proportional to l
                (b) inversely proportional to l
                (c) independent of l
                (d) independent of A

Q4.          Two metal rods of the same length and area of cross-section are fixed end to end between rigid                supports. The material of the rods have Yong modulii Y1 and Y2, and coefficients of linear expansion                a1 and a2. The junction between the rods does not shift if the rods are cooled.
                (a) Y1a1 = Y2a2
                (b) Y1a2 = Y2a1
                 (c) Y1a12 = Y2a22
                 (d) Y12a1 = Y22a2

Q5.          Three rods of equal length are joined to form an equilateral triangle ABC. D is the midpoint of AB.                 The coefficient of linear expansion is a1 for AB, and a2 for AC and BC. If the distance DC remains                 constant for small changes in temperature,
                                             
                (a) a1 = a2
                (b) a1 = 2a2
                (c) a1 = 4a2
                 (d) a1 =a2

Q6.          When the temperature of a body increases from t to t + Dt, its moment of inertia increases from I to I                + DI. The coefficient of linear expansion of the body is a. The ratio  is equal to
                (a)
                (b)
                (c) aDt
                (d) 2aDt
Q7.          A horizontal tube, open at both ends, contains a column of liquid. The length of this liquid column                does not change with temperature. Let g = coefficient of volume expansion of the liquid and a =                coefficient of linear expansion of the material of the tube.
                (a) g = a
                (b) g = 2a
                (c) g = 3a
                (d) g = 0

Q8.          In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures, t1 and                 t2. The liquid columns in the two arms have height l1 and l2 respectively. The coefficient of volume                 expansion of the liquid is equal to
                                                                           
                (a)
                (b)
                 (c)
                  (d)

Q9.          A solid whose volume does not change with temperature floats in a liquid. For two different                temperatures t1 and t2 of the liquid, fractions f1 and f2 of the volume of the solid remain submerged in                the liquid. The coefficient of volume expansion of the liquid is equal to
                (a)
                 (b)
                (c)
                (d)

Q10.        A solid with coefficient of linear expansion a just float in a liquid whose coefficient of volume                expansion is g. If the system is heated, the solid will
                (a) sink in all cases
                (b) continue to float in all cases

                (c) sink if g > 3a
                (d) sink if g < 3a

Q11.        A gas at absolute temperature 300 K has pressure = 4 x 10–1 N/m2.
                Boltzmann constant = k = 1.38 x 10–23 J/K. The number of molecules per cm3 is of the order of
                (a) 100
                (b) 105
                (c) 108
               (d) 1011

Q12.        The root-mean-square (rms) speed of oxygen molecules (O2) at a certain absolute temperature is v.                If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the rms speed                would be
                (a) v
               (b)
                (c) 2 v
                (d)

Q13.        The average translational kinetic energy of O2 (molar mass 32) at a particular temperature is 0.048                eV. The average translational kinetic energy of N2 (molar mass 28) molecules in eV at the same                temperature is
                (a) 0.0015
                (b) 0.003
                 (c) 0.048
                 (d) 0.768

Q14.        A gas has volume V and pressure p. The total translational kinetic energy of all the molecules of the                gas is
                (a) pV only if the gas is monatomic
               (b) pV only if the gas is diatomic
                (c) >pV only if the gas is diatomic
                (d) pV in all cases

Q15.        A closed vessel is maintained at a constant temperature. It is first evacuated and then vapour is                injected into it continuously. The pressure of the vapour in the vessel
                (a) increases continuously
                (b) first increases and then remains constant
                (c) first increases and then decreases
                (d) none of the above

Q16.        When an air bubble rises from the bottom to the surface of a lake, its radius becomes double. Find                the depth of the lake, given that the atmospheric pressure is equal to the pressure due to a column of                water 10 m high. Assume constant temperature and disregard surface tension
                (a) 30 m
                (b) 40 m
               (c) 70 m
               (d) 80 m

Q17.        Two containers of equal volume contain the same gas at pressures p1 and p2 and absolute                temperatures T1 and T2 respectively. On joining the vessels, the gas reaches a common pressure p                and a common temperature T. The ratio p/T is equal to
                (a)
                (b)
                (c)
                (d)
Q18.        Two identical containers joined by a small pipe initially contain the same gas at pressure p0 and                absolute temperature T0. One container is now maintained at the same temperature while the other is                heated to 2T0. The common pressure of the gases will be
                (a)
                (b)
               (c)
                (d) 2p0

Q19.        In the pressure question, let V0 be the volume of each container. All other details remain the same.                The number of moles of gas in the container at temperature 2T0 will be
                (a)
                (b)
                (c)
               (d)

Q20.        A horizontal cylinder has two sections of unequal cross-sections in which two pistons can move                freely. The pistons are joined by a string. Some gas is trapped between the pistons. If this gas is                heated, the pistons will               

(a) mole to the left
(b) move to the right
 
               (c) remain stationary
               (d) either (a) or (b) depending on the initial pressure of the gas

Q21         A particle of mass 1 kg is moving in SHM with an amplitude 0.02 and a frequency of 60 Hz. The                maximum force acting on the particle is  
                (a) 144 p2
                (b) 188 p2
                (c) 288 p2
                (d) None of these
               
Q22         An instantaneous displacement of a simple harmonic oscillator is x = A cos (wt + p/4). Its speed will                be maximum at time
                (a) p/4 w
                (b) p/2w
                (c) p/w   
                (d) 2 p/w
               
Q23         Velocity of sound waves in air is 330 m/s. For a particular sound wave in air, a path difference of 40                cm. is equivalent to phase difference of 1.6 p. The frequency of this wave
                (a) 165 Hz
                (b) 150 Hz
                (c) 660 Hz
                (d) 330 Hz
               
Q24         The velocity of sound in air is 330 m/s. The rms velocity of air molecules (g = 1.4) is approximately                equal to
                (a) 400 m/s
                (b) 471.4 m/s
                (c) 231 m/s
               (d) 462 m/s
               
Q25         Sound waves of length l traveling with velocity v in a medium enter into another medium in which their                velocity is 4 v. The wavelength in 2nd medium is
                (a) 4 l
                (b) l
                (c) l/4
               (d) 16 l
               
Q26         The velocity of sound in a container of air at − 73 °C is 300 m/s. Its temp. of container were raised                 to 127 °C. What would be the velocity of sound ?
                (a) 300 m/s
                (b) 300  m/s
                (c) 300 /  m/s
               (d) 600 m/s
               
Q27         If the intensities of two interfering waves be I1 and I2, the contrast between maximum and minimum                intensity is maximum, when   
                (a) I1 >> I2
                (b) I1 << I2
                (c) I1 = I2
                (d) Either I1 or  I2   is zero
               
Q28         Two periodic waves of intensities I1 and I2  pass through a region at the same time in the same                direction. The sum of the maximum and minimum intensities is                
                (a) 2(I1 + I2)
                (b) I1 + I2
                (c)
                 (d)
               
Q29         If two tuning forks A and B are sounded together, they produce 4 beats per sec. A is then slightly                loaded with wax and same no. of beats / sec are produced again. If frequency of A is 256, the                frequency of B would be 
                (a) 250
               (b) 262
                (c) 252
                (d) 260
               
Q30         If the ratio of maximum to minimum intensity in beats is 49, then the ratio of amplitudes of two                 progressive wave trains is
                (a) 7 : 1
                (b) 4 : 3
                (c) 49 : 1
                (d) 16 : 9
               
Q31         A uniform wire of length 20 m and weighing 5 kg hangs vertically. If g = 10 m/s2, then the speed of                transverse waves in the middle of the wire is
                (a) 10 m/s
                (b) 10  m/s&
                 (c) 4 m/s
                (d) 0
               
Q32         If there are six loops for 1 m length in transverse mode of Melde’s experiment., the no. of loops in                longitudinal mode under otherwise identical conditions would be
                (a) 3
                (b) 6
                (c) 12
                (d) 8
               
Q33         The fundamental frequency of an open organ pipe is 300 hz. The first overtone of this pipe has same                frequency as first overtone of a closed pipe. If speed of sound is 330 m/s, then the length of closed                organ pipe is   
                (a) 41 cm
               (b) 37 cm
                (c) 31 cm
                (d) 80 cm
               
Q34         Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio                of fundamental frequency of tube A and B is 
                (a) 1 : 2  
                (b) 1: 4
                (c) 2 : 1
                (d) 4 : 1
               
Q35         When temperature increases, the frequency of a tuning fork
                (a) increases
                (b) decreases
                (c) remains same
                (d) increases or decreases depending upon the material
               
Q36         Two waves of wavelengths 99 cm and 100 cm both traveling with velocity 396 m/s are made to                 interfere. The number of beats produced by them per second are
                (a) 1
                (b) 2
                (c) 4
                (d) 8
Q37         y = 2 (cm) sin , what is the maximum acceleration of the particle doing the SHM
                (a)
                  (b)
                 (c)
                 (d)

Q38         A cylindrical tube open at both the ends, has a fundamental frequency ‘f’ in air. The tube is dipped                vertically in air. The tube is dipped vertically in water so that half of it is in water. The fundamental                frequency of the air column in now    
                (a) f/2
                (b) 3 f/4
                (c) f
                (d) 2f
               
Q39         A wave is represented by the equation y = a cos (kx − wt) is superimposed with another wave to                form a stationary wave such that point x = 0 is a node. The equation for the other wave is
                (a) a sin (kx + wt)
                (b) − a cos (kx − wt)
                (c)  − a cos (kx + wt)
               (d)  − a sin (kx − wt)             

Q40         An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe                open at both ends and vibrating in third harmonic. The ratio of length of two pipes is  
                (a) 1 : 2
               (b) 4 : 1
                (c) 8 : 3
                (d) 3 : 8

[ Chemistry ]

Q41.        In the reaction, H2(g) + I2(g)  2HI(g) the concentration of H2, I2 and HI at equilibrium are                8.0 , 3.0 and 28.0 moles are litres respectively. What will be the equilibrium constant ‑
               (a) 30.61
               (b) 32.66
               (c) 29.40
              (d) 20.90
               
Q42.        For a gas reaction, 3H2(g) + N2(g)  2NH3(g), the partial pressures of H2 and N2 are 0.4                and 0.8 atmosphere, respectively. The total pressure of the entire system is 2.8atmosphere. What will                be the value   of Kp if all the concentration are given in atmosphere ?
               (a) 32 atm‑2
                (b) 20 atm‑2
                (c) 50 atm‑2
                (d) 80 atm‑2

Q43         One mole of nitrogen and three moles of hydrogen are mixed in a 4 litre container. If 0.25 percent of                nitrogen is coverd to ammonia by the following reaction N2(g) + 3H2(g)  2NH3(g). What                will be the equilibrium constant (Kc) in concentration units ? What will be the value of K for the                following equilibrium ‑
                               N2(g) + H2(g)  NH3(g).
               (a) 1.49 x 10‑5 lit mol‑1
               (b) 2.22 x 10‑10 lit2 mol-2
               (c) 3.86 x 10‑3 lit mol‑1
                (d) Question is incomplete
               
Q44         When ethanol and acetic acid were mixed together in equilimolecular proportion 66.6% are                converted into ethyl acetate. Calculate Kc . Also calculate quantity of ester produced if one mole of                acetic acid is treated with 0.5 mole and 4 mole of alcohol respectively.
               (a) 4, 0.93, 0.43
                (b) 0.93, 4, 0.43
                (c) 0.43, 0.93, 4
                (d) 4, 0.43, 0.93
Q45         One mole of ammonium carbonate dissociate as shown below at 500 K.
                                NH2COONH4(s)  2NH3(g) + CO2(g)
                If the pressure exerted by the released gases is 3.0 atm, the value of Kp is.­
                (a) 7 atm
                (b) 3 atm
                (c) 4 atm
                (d) 8 atm

Q46         Iron filling and water were placed in a 5 litre tank and sealed The tank was heated to 1273 K. Upon                analysis the tank was found to contain 1.10 gram of hydrogen and 42.5 gm of water vapour. If the                reaction in the tank is represented by
                                                3Fe(s) + 4H2O(g)  Fe3O4 (s) + 4H2(g)
               the equilibrium constant will be ‑
               (a) 2.949 x 103
                (b) 6.490 x 103
               (c) 4.940 x 103
                (d) 3.200 x 103

Q47         At 700 K, the equilibrium constant KP, for the reaction
                                2SO3(g)  2SO2(g) + O2(g) is 1.8 x 10‑3 kPa.
               What is the numerical value of Kc for this reaction at the same temperature
                (a) 3.09 x 10‑7mole litre‑1
                (b) 9.03 x I 0‑7mole litre‑1         
               (c) 5.05 x 10‑9 mole litre‑1
                (d) 5.05 x 10‑5mole litre‑1

Q48         The value of KC for the reaction N2(g) + 3H2(g)  2NH3(g) is 0.50 at 400 °C. What will                be the value of KP at 400 °C when concentration are expressed in mole litre‑1 and pressure in                atmosphere ‑
               (a) 1.64 x 10‑4
                (b) 2.80 x 10‑6
                (c) 2.80 x 10‑4
                (d) 1.64 x 10‑6

Q49         The equilibrium constant for the reaction H2(g) + S(s)  H2S(g) ; is 18.5 at 935 K and 9.25                at 1000 K respectively. The enthalpy of the reaction will be ‑
               (a) ‑ 68000.05 J mol‑1
               (b) ‑71080.57 J mol‑1
              (c) ‑80071.75 J mol‑1
              (d) 57080.75 J mol‑1

Q50         Inhibitor is ‑
               (a) An activator
               (b) Negative catalyst
               (c) Catalyst for a catalyst   
               (d) Promoter

Q51         KP for the reaction A(g) + 2B(g) 3C(g) + D(g) ; is 0.05 atm. What will be its KC at 1000                K in terms of R ‑
                (a)
                 (b)
                (c)  R
                (d) none of these
Q52         The vapour density of N2O4 at a certain temperature is 30. The percentage dissociation of N2O4 at                this temperature is
               (a) 55.5 %
                (b) 60 %
                (c) 70 %
                (d) 53.3 %

Q53         If PCl5 is 80 % dissociation at 523 K. Calculate the vapour density of the equilibrium mixture at 523                 K­
               (a) 75.9
               (b) 57.9
               (c) 97.5
               (d) 95.7

Q54         Ammonium carbamate when heated to 200 °C gives a mixture of vapours
                (NH2COONH4  2NH3 + CO2)
                with a density 13.0. What is the degree of dissociation of ammonium carbamate ‑
                (a) 1
                 (b) 2
                 (c) 3
                (d) 4       

Q55         The volume of a closed reaction vessel in which the equilibrium
                                2SO2(g) + O2(g)  2SO3(g) sets is halved, Now‑
                (a)           The rates of forward and backwards reactions will remain the same.
                (b)           The equilibrium will not shift.
                (c)           The equilibrium will shift to the right.
                (d)           The rate of forward reaction will become double that of reverse reaction and the                 equilibrium will shift to the right.

Q56         H2(g) + I2(g)  2HI(g)
                When 46g of I2 and 1g of H2 are heated at equilibrium at 450 °C, the equilibrium mixture contained                 1.9 g of I2. How many moles of I2 and HI are present at equilibrium ‑
                (a) 0.0075 & 0.147 moles
                (b) 0.0050 & 0.147 moles
                (c) 0.0075 & 0.347 moles
                (d) 0.0052 & 0.347 moles
               
Q57         A two litre flask contains 1.4 gm nitrogen and 1.0 gm hydrogen. The ratio of active mass of nitrogen                 and hydrogen would be
                (a) 1 : 3
                (b) 1 : 5
                (c) 1.4: 1
                 (d) 1 : 10
Q58         In the reaction
                                 A + B  C + D
                The initial concentration of A is double the initial concentration of B. At equilibrium the concentration                 of B was found to be one third of the concentration of C. The value of equilibrium constant is
                (a) 1.8
                (b) 1.008
                (c) 0.0028
                (d) 0.08

Q59         The value of KC for the reaction :
                                A + 3B  2C at 400 °C . Calculate the value of KP
                (a) 1.64 x 10‑4
                (b) 1.6 x 10‑6
                (c) 1.6 x 10‑5
                (d) 1.6 x 10‑3

Q60         Two moles of ammonia was introduced in an evacuated vessel of 1litre capacity. At high temperature                 the gas undergoes partial dissociation according to the equation
                                2NH3(g)  N2(g) + 3H2(g)
                At equilibrium the concentration of ammonia was found to be 1 mole. What is the value of ‘K’ ?
                (a) 3/4 = 0.75 mol2
                (b) 3/2 = 1.5 mol2
                (c) 27/16 = 1.7 mol2
                (d) 27/64  = 0.42 mol2

Q61.        Which sodium salt will be heated with soda lime to obtain propane –
                (a) CH3 – CH2 – C – OΘNaÅ                                                 (b) CH3 – CH2 – CH2 – C – OΘNaÅ
             ||                                                                                            || 
                                         O                                                                                              O
                (c) CH3 – CH –  C – OΘNaÅ                                                 (d) 2nd and 3rd both
             ||                                                   
                                         O                                                   
               
Q62         Which of the following compounds cannot be prepared by Wurtz reaction ‑
                (a) CH3CH3
                (b) CH3CH – CH
                               |
                              
                              CH3
                   (c) (CH3)2CHCH3
                   (d) CH3CH2CH2CH3

                   (a) a, b
                   (b) b, c
                   (c) c, d
                   (d) none of these

Q63         Which of the following compounds liberate methane when treated with excess of methyl magnesium                    iodide in dry ether
                   (a) CH3 ‑ CH2 ‑ CH2OH
                   (b) H3C ‑ CH2 ‑ C ≡ CH
                   (c) H3C ‑ CH2 ‑ CO2H
                   (d) H3C ‑ CH2 ‑ CHO
                   (a) a, b
                   (b) b, c
                   (c) a, b, c
                   (d) All above

Q64         Raney Nickel is a suitable catalyst for: ‑
                (a) Bromination
                (b) Dehydration
                (c) Hydrogenation
                (d) Alkylation

Q65.        Correct order of boiling point is ‑
                (a) n‑Pentane < neohexane < isohexane < 3‑methyl pentane
                (b) neohexane < n‑pentane < isohexane < 3‑methyl pentane
                (c) 3‑methyl pentane < neohexane < n‑pentane < isohexane
                (d) n‑pentane < isohexane < 3‑methyl pentane < neohexane

Q66         In the complete combustion of Cn H2n + 2 , the number of oxygen rmoles required is
                (a) n / 2O2
                (b) O2
                 (c) O2
                  (d) O2
Q67         What is X in the following sequence of reaction:
                                  X  Z  CH4 ­
                   (a) Methane
                   (b) Ethanoic acid
                   (c) Propane
                   (d) None of the above

Q68.        The number of isomers of C6H14 are:
                   (a) 4
                   (b) 5
                   (c) 6
                   (d) 7

Q69.        Which of the following reaction pairs constitutes the chain propagation step in chlorination of methyl                   chloride?

(a)	·CH3 + Cl2 ® CH3Cl + ·Cl CH3Cl + ·Cl ® CH2Cl2 + ·H	(b)	CH3Cl + ·Cl ® CH2Cl + HCl ·CH2Cl + Cl2 ®     CH2Cl2 + ·Cl
(c)	CH3Cl + ·CI ® ·CH2Cl + HCl ·CH2Cl + ·CH2Cl ® CH2Cl + CH2Cl	(d)	·CH2Cl + Cl2 ® CH2Cl2 + ·Cl ·CH2Cl + ·Cl ® CH2Cl2

Q70         Kolbe's reaction is convenient for the preparation of:
                (a) Methane
                (b) Alkanes containing even number of carbon atoms
                (c) Alkanes containing even as well as odd number of carbon atoms
                (d) Alkanes containing odd number of carbon atoms

Q71.        For the formation of 27 gm of water, what volume of neopentane is required for the complete                  combustion:
                (a) 5.6 lit.
                (b) 11.2 lit.
                (c) 33.6 lit
                (d) 2.24 lit.

Q72.        Acetylene and ethylene reacts with alk. KMnO4 to give ‑
                   (a) Oxalic acid and formic acid
                   (b) Acetic acid and ethylene glycol
                   (c) Ethyl alcohol and ethylene glycol
                   (d) None

Q73.        Chloroform when heated with silver powder gives an alkyne. For the substitution of hydrogen atom                  by chlorine the reaction must be carried out with ‑
                 (a) Cl2 at 0°C in the presence of ultra violet light
                 (b) NaOCl at 0°C in the presence of light and air
                 (c) Cl2 at 0°C in dark
                 (d) None of the above

Q74.        Acetylene on passing into excess of HOCl solution forms ‑
                (a) Ethylene chlorohydrin
                (b) Acetaldehyde
                (c) Dichloroacetaldehyde
                (d) Methyl Chloride

Q75.        10 ml of a certain hydrocarbon require 25 ml of oxygen for complete combustion and the volume of                   CO2 produced is 20 ml. What is the formula of hydrocarbon ‑
                   (a) C2H2
                   (b) C2H4
                   (c) CH4
                   (d) C2H6

Q76.        Lindlar's catalyst consists of ‑
                   (a) Metallic nickel + nickel boride,
                   (b) Metallic platinum
                   (c) Metallic palladium deposited on calcium carbonate containing lead acetate and quinoline
                   (d) Sodium borohydride in ethanol.

Q77.        2‑Butyne and 1‑Butene show resemblance in all except ‑
                (a) Both decolourise alkaline KMnO4
                (b) Both turn bromine water colourless
                (c) Both undergo addition reaction
                (d) Both from white precipitate with Tollen's reagent

Q78.        Acetylene reacts with formaldehyde in the presence of sodium alkoxide to form mainly ‑
                   (a) CH2 = CH – CH2OH
                   (b) CH2OH – CH = CH2
                   (c)
                   (d)

Q79.        Acetylene reacts with 42% H2SO4 containing 1% HgSO4 to give:
                (a) C2H5HSO4
                (b) CH3CHO
                 (c) HCHO
                 (d) CH2 == CH2

Q80.        The alkene which on ozonolysis yields acetone is:
                (a) CH2 == CH2
                 (b) CH3 –– CH == CH2
                 (c) (CH3)2C == C(CH3)2
                 (d) CH3 –– CH == CH – CH3

[ Mathematics ]

Q81         A car is parked by a driver amongst 25 cars in a row, not at either end. When he returns he finds                 that 10 places are empty. The probability that both the neighboring places of driver’s car are vacant                  is   
                (a)
                 (b)
                 (c)
                 (d)

Q82         A is one of the six race horses which is to be ridden by one of the two jockeys B or C. It is 2 :1 that                  B rides A in which case all the horses are equally likely to win but if C rides, then A’s chances of                  wining are trebled.  The odds against his winning are
                 (a) 13 : 5
                 (b) 5 : 13
                 (c) 8 : 5
                 (d) 5 : 8

Q83         A and B play by throwing a pair of dice alternately. A wins if he throws 6 before B throws 7. If A                  starts the game their chances of wining  the game are in the ratio
                (a) 28 : 33
                 (b) 29 : 32
                 (c) 30 : 31
                 (d) none
Q84         Five coins whose faces are marked 2,  3, ….  Are thrown. The probability of obtaining a total of 12                  is
                (a)
                 (b)
                 (c)
                 (d)
Q85         The probability that a teacher will give an unannounced test during any class meeting is . If a                  student is absent twice, the probability that he will miss at least one test is 
                (a)
                 (b)
                 (c)
                 (d)

Q86         Two cards are randomly selected from a deck of 52 playing cards. The probability that both the                  cards are greater than 3 and less than 8 is  
                (a)
                 (b)
                 (c)
                 (d)

Q87         Probabilities of teams A, B and C wining are  respectively. Probability that one of these                  teams will win is
                (a)
                 (b)
                 (c)
                 (d) none

Q88         If two squares are chosen at random on a chess board, the probability that they have a side in                  common is
                (a)
                 (b)
                 (c)
                 (d) none

Q89         A single letter is selected at random from the word PROBABILITY . The probability that it is a                  vowel is
                (a)
                 (b)
                 (c)
                 (d) none

Q90         if P(A Ç B) = , P(Ç) = , P(A) = p, P(B) = 2p, then the value of p is given by
                 (a)
                 (b)
                 (c)
                 (d)

Q91         The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays is
                (a)
                 (b)
                 (c)
                 (d)

Q92         A bag contains 50 tickets numbered 1, 2, 3 , ……., 50 of which five are drawn at random and                  arranged in ascending order of magnitude (). The probability that x3 = 30 is
                 (a)
                 (b)
                 (c)
                 (d) none

Q93         A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of                  them is found to be good, the probability that the other is also good is 
                (a)
                 (b)
                 (c)
                 (d)

Q94         Three letters, to each of which corresponds an envelope, are placed in the envelopes at random. The                  probability that all the letters are not placed in the right envelope is 
                (a) 1/6
                 (b) 5/6
                 (c) 1/3
                 (d) 2/3

Q95         Two athletes A and B participate in a race along with other athletes. If the chance of A wining the                  race is 1/6 and that of B wining the same race is 1/8, then the chance that neither wins the race is
                (a) 1/4
                 (b) 7/24
                 (c) 17/24
                 (d) 35/38

Q96         Six coins are tossed simultaneously. The probability of getting at least 4 heads is
                (a) 11/64
                 (b) 11/32
                 (c) 15/44
                 (d) 21/32

Q97         Dialing a telephone number an old man forgets the last two digits remembering that these are different                 dialed at random. The probability that the number is dialed correctly is
                (a) 1/45
                 (b) 1/90
                 (c) 1/100
                 (d) none

Q98         If A and B are two independent events, the probability that both A and B occur is 1/8 and the                  probability that neither of them occur is 3/8. The probability of the occurrence of A is
                (a) 1/2
                 (b) 1/3
                 (c) 1/4
                 (d) 1/5

Q99         If three vertices of a regular hexagon are chosen at random, then the chance that they form an                  equilateral triangle is
                (a) 1/3
                 (b) 1/5
                 (c) 1/10
                 (d) 1/2

Q100       10 apples are distributed at random among 6 persons. The probability  that at least one of them will                  receive none is
                (a)
                 (b)
                 (c)
                 (d) none
Q101.      If (tan–1 x)2 + (cot–1 x)2 = , then x equals
                (a) – 1
                 (b) 1
                 (c) 0
                 (d) none of these

Q102.      cos–1 [cos (2 cot–1 ())] is equal to
                (a)
                 (b)
                 (c) p/4
                 (d) 3p/4

Q103.      The equation  has
                (a) no solution
                 (b) unique solution
                (c) infinite number of solution
                 (d) None of these

Q104.      Two angles of a triangle are cot–1 2 and cot–1 3. Then the third angle
                (a) p/4
                 (b) 3p/4
                 (c) p/6
                 (d) p/3

Q105.      Complete set of values of x satisfying [tan–1 x] + [cot–1 x] = 2, where [.] denotes the greatest                  integer function, is
                (a) (cot 3, cot 2]
                (b) (cot 3, – tan 1]
                 (c) (cot 3, 0)
                 (d) None of these

Q106.      Complete solution set of the equation [cot–1 x] + 2[tan–1 x] = 0, where [.] denotes the greatest                  integer function, is equal to
                (a) (0, cot 1)
                 (b) (0, tan 1)
                 (c) (tan 1, ¥)
                 (d) (cot 1, tan 1)

Q107.      The trigonometric equation sin–1 x = 2 sin–1 a, has a solution                  for:                                                              
                (a)
                (b) all real values of a
                 (c)
                 (d)

Q108.      , then sin x is equal
                (a)
                 (b)
                 (c) tan a
                 (d)

Q109.       is equal to:                     
                (a)
                  (b)
                  (c)
                  (d)

Q110.      The value of is:
                (a)
                 (b)
                 (c)
                 (d) none of these

Q111.      The number of real solutions of  is:                                     
                (a) 0
                 (b) 1
                 (c) 2
                 (d) infinite

Q112.      If  for 0 < |x| <, then x equals:
                (a) 1/2
                 (b) 1
                 (c) – 1/2
                 (d) – 1

Q113.      The value of x for which sin (cot–1 (1 + x)) = cos (tan–1 x) is                                                         
                (a) 1/2
                 (b) 1
                 (c) 0
                 (d) – 1/2

Q114.      The principal value of  is                                                                         
                (a) –
                 (b)
                 (c)
                 (d)
                  (e) none of these

Q115.      The period of the function f(x) = sin4 x + cos4 x is                                         
                (a) p
                 (b)
                 (c) 2p
                 (d) none of these

Q116.      The value of  is                                                                                              
                (a) 1
                 (b)
                 (c)
                 (d) 2

Q117.      If  then sin q is
                (a) but not
               (b) or
                (c) but not
               (d) none of these

Q118.      If sin (a + b) = 1, sin (a – b) = , then tan (a + 2b) tan (2a + b) is equal to:
                (a) 1
                 (b) – 1
                 (c) zero
                 (d) none of these

Q119.      Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2p] is&
                (a) 0
                 (b) 1
                 (c) 2
                 (d) 3

Q120.      In a triangle PQR, ÐR = p/2. If tan (P/2) and tan (Q/2) are the roots of the equation ax2 + bx + c =                  0 (a ¹ 0) then
                (a) a + b = c
                 (b) b + c = a
                 (c) a + c = b
                 (d) b = c