all india engineering entrance exam 2007 question paper with solution

8/7/2019 All India Engineering Entrance Exam 2007 Question Paper With Solution

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1. In a geometric progression consisting ofpositive terms, each term equals the sum of thenext two terms. Then the common ratio of thisprogression equals:C a ) .!(1- /5)2(c) .Js

(b) !-Is2(d) !.Js - 1)2

2. Ifsin-l(-~) + cosec-l(~) =~, then a value ofxis ;(a) 1(c) 4

(b) 3C d ) 5

3. In'the binomial expansion of (a - bt, n ~5, theasum of 5th and 6th terms is zero, then bequals:5 6(a) -~. ~. (b) ~.n-4 n-5

n-5 n--4(c) ~ C d ) - -6 , 54. The set S: ={l, 2, 3 , , I2} is to be

partitioned into three sets A, B, C of equal size.Thus, AuB uC "".5, A nB""BnC '" A nC '" $. The number of ways topartition S is ;(a) 121/3! (4!i (b) 121/3!(3!/ec ) 121/(4!i (d) 121/(3!)4

5. The largest interval lying in (- -~, ~) for whichthe function '[ ' f e x ) ' " 4 _x 2 + cos -i( 1 - 1) + lo g ( co s X ) ]is defined, is :(a) [0, T e lec ) [ - % , ~ )

6. A body weighing 13 kg is suspended by twostrings 5 m and 12 m long, their other endsbeing fastened to the extremities of a rod 13mlong. If the rod be so held that the body hangsimmediately below the middle point. Thetensions in the strings arc :(a) 12 kg and 13 kg (b) 5 kg and 5 kg(e) 5 kg and 12 kg (d) 5 kg and 13 kg

7. A pair of fair dice is thrown independentlythree times. The probability of gening a scoreof exactly 9 twice is :(a) 1/729 (b) 8/9(e) 8/729 (d) 8/243

8. Consider a family of circles which are passingthrough the point (-1, 1) and are tangent tox-axis. 1f (h, .k) are the coordinates of the centreof the circles, then the set of values of k is givenby the interval :C a ) 0


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~ b(a) tan l_acI b e(c) tan" -.-a(e - a)

(b) 45. -1 be(d) tan -a

27. The average marks of boys ina class is 52 andthat of girls is 42. The average maries of boysand girls combined is 50. The percentage ofboys in the class is :(a) 40 (b) 20(c) 80 (d) 60

28. The equation of a tangent to the parabolay2 := 8x is y '" x + 2. The point on this linefrom which the other tangent to the parabola isperpendicular to the given tangent is:(a) (-1,1) (b) (0, 2)

.. {e) (2,4) (d) (-2,0)29. If (2, 3, 5) is' one end of a diameter of the

sphere x2 + y2 -t - z2 - 6x :"'12y - 2z + 20", 0,then the coordinates of the other end of thediameter are:(a) (4,9, - 3)(e) (4,3,5)

(b) (4, -3, 3)(d) (4,3,-3)

30. Let and...." ".~ ->e '"x i+ e x - 2)j - K. If the vector e lies in the

". ~ ~")-plane of a and b, then x equals: '(a) 0 . (b) 1(e) - 4 (d) - 2

31. LetA(h, k), B(l, 1)and C(2, 1)be the vertices ofa right angled triangle with AC as itshypotenuse. If the area of the triangle is 1, thenthe set of values whieh 'k' can take is given by:(a) {l,3} (b) {O,2}(c) {-I, 3} (d) {-3,-2}

32. Let P '" (-1, O)~Q = = (0, 0) and R = = (3, 3.J3) bethree poin ts,Theequation of the bisector of theangle PQR is :(a) .f3x + y '" 0(c) .fjx + y =02

. J 3(b) x +~. y =0. 2(d) x+ J3y==O

33. Hone of the lines ofmy2 + (1 - m 2)zy - mx2 '" 0 is a bisector of theangle between the lines xy '" 0, then m is :(a) -!. (b) -22ec) 1 (d) 2

34. Let F(x) '" fex) + f ( ~ ) .logt .-~ dt. Then Fee ) equals:1+ t '

wherefex) = J ; "

1(a) ' 2(c) 1

(b) 0(d) 2

35. Let f :.R -+ R be a function defined byf (x) '" min {x + 1, j x] + 1}.Then which of the, following is true?(a) fex) 2: 1for all x E R(b) fex) is not differentiable at x =1(c) fex) is differentiable everywhere(d) fex) is not differentiable at x =0

36. The function j :R/{O} -+ Rgiven byf(x) " ' . ! . 2_x ell:_l

can be made continuous at x '" 0 by defining!CO) as :C a ) 2(e) 0 '(b) -l-Cd) 1

37. The solution for x of the equationr . . .r .=1f/2iS:.fi tJt2-1(a) 2 (b) 1 fec ) J3J2 (d) 2 - 1 2

38. J . dxr: . equals:, cos x + - v 3 sin x(a) !.Jog tan ( . : < . : + ~) + c2 2 12(b) ~ log tan (~- 1 1 ( 2 ) + cC ~ ) log tan (~+i~)+c(d) log tan (~-~) + c2 12

39. The area enclosed between the curves y2 =xand y el xj is :2C a ) -31(c) ~6

(b) 1(d) !.3

40. If the difference between' the roots of theequation x2 + ax ...:1 = 0 is less than J ' S , thenthe set of possible values of a is: .(a) (-3, 3) (b) (-3, oo(e ) (3, co (d) ( - ( -0 , - 3)


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41. The displacement of -an object attached to aspring and executing simple harmonic motionis given-by x 0= 2 x 10~2 cos 1t t metre. The timeat which the maximum speed first occurs is :(8) 0.5S (b) 0.75 s_(c) 0.125 s (d) 0.25 s

42. In an AC circuit the .voltage applied' isE ""E o sin rot. The resulting current in thecircuit is 1= [0 sin (rot -~} The powerconsumption in the circuit is given by :(a) P = - E o Q . (b) P ""zeroJ2( c ) p '" Eo lq . C d ) P = - J " 2 Eolo2

43. An electric charge lO-J!-lC. is placed at theorigin (0, 0) of X -V coordinate system. Twopoints A and B are situated at (../2, - J 2 ) and(2, 0) respectively. The potential differencebetween the points A and B will be :(a) 9 V (b) zero .

_(c) 2 V Cd) 4.5 V44_ A battery is used to charge a parallel platecapacitor till the potential difference betweenthe plates becomes equal to the electromotive

force of the battery. The ratio of the energystored in the capacitor and the work done bythe battery will be :(a) 1 Eb)- 2(c) _ ! , (d)!'4 2

45. An ideal coil of IOI-I is connected in series witha resistance of sn and a battery of 5 v . 2 s afterthe connection is made, the current flowing (inampere) in the circuit is :(a) (I-e) (byee e ) e-1 Cd) (1 - e-1)

46. Along straight Wire of radius a carries a steadycurrent i.The current is uniformly distributedacross its cross-section. The ratio of themagnetic field at ~ and 2a is :2. 1(a) - (b) 44(c) 1 n . ! .2

47. A current I flows along the length o f aninfinitely long, straight, thin walled pipe.'Then :.(a) the magnetic field is zero only on the axisof tne pipe .(b) the magnetic field is different at differentpoints inside the pipe _(c) the magnetic field at any point inside thepipe is zero. (d) the magnetic field at all points inside thepipe is the same, but not zero

48. If M" is the mass of an oxygen isotope $017"M f' and Mil ate the masse s of a,proton and aneutron, respectively, the nuclear bindingenergy-of the isotope is :(a) (M" - 8M p )C 2(b) eM " - 8M p - 9M~)C2(c) Moc2(d) (M" -17Mn)c2

49. I n . gamma ray emiss ion from a nucleus:(a) both the neutron number and the protonnumber change(b) there is no change in the proton numberand the neutron number(c) only the neutron number changes(d) only the.proton number changes

50. If in a p-n junction diode, a square input signa!of 10 V is applied as shown:5V

-5VThen the output signal across RL will be:

(a) J O n ( b ) l i .-lOV+5 V

{d) TLc) II-5vL_j


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51. Photon of frequency v has a momentumassociated with it. If c is the velocity of light, themomentum is :(a) vic(c) hv/c2

(b) hvc(d) hv/c

52. The velocity of a particle is v = = "o + gt + ft 2. Ifits position is x = = 0 at. t '" 0, then itsdisplacement after unit time (t =1) is :(a ) V o + 2g +3/ (b) V o + g/2+ 1/3(c) V o + g + - / (d) V o + g/2+ /

53.. For the given uniform square lamina ABCD ,whose centre is 0 :

"

54.

A ,,-,,_.----::.41-------' BE:(a) .J2IA c = [ F _ p , (b) lA D;: 3 IfJ l(c) ' [Ac=:IEF Cd) IAc=- .J2~EFA point mass .oscillates along the x-axisaccording to the law x = Xo cos {rot - n/4} Ifthe acceleration of the particle i s written as, :a = A cos {rot + 0), then:(a) A = xo , 0 = - x/ 4(b) A = = XO(02: a =: 1 1 : / 4(e) A==XO(i)2, &""-n/4(d) A;: XOO)2, 1 ) =3n/4

55. Charges are placed onthe vertices of a square ,as shown. Let E be theelectric field and V thepotential at th ~centre. ,I f the charges on A andB are interchangedwith those on 0 and Crespectively, then :(a) E remains unchanged, V changes(b) both E and V change(c) E and V remain unchangedCd) E changes, V remains unchanged

c

q.-----"-_....,...., qA 8

D-q

56. The half-life period of a radioactive element Xis same as the mean life time of anotherradioactive element Y. Initially they have thesame number of atoms. Then :'

(a) X will decay faster than Y(b) Ywill decay faster than Xec) Y and X have same decay rate initially(d) X and Y decay at-same rate always

57. A Carnot engine, having an efficiency of11" 1/10 as heat engine, is used as arefrigerator. If the work done on the system is10 J, the amount of energy absorbed from thereservoir at lower temperature is :. (a) 99 J (b) 90 J(c) 1J (d) 100 J

58. Carbon, silicon and germanium have tourvalence electrons each. At room temperaturewhich one of the following statements is mostappropriate?Cal The number of free conduction electrons issignificant in C but small in Si and Ge(b) The number of free conduction, electrons isnegligibly small in ail the three(c) The number of free electrons forconduction is significant in all the three(d) The number of free electrons forconduction is signiflcant only in Si and Gebut small in C

59. A charged particle with charge q enters aregion of constant,uniform and mutuallyorthogonal fields E and B with a velocity vperpendicular to both ind : 8 , and comes outwithout any change in magnitude or direction~ ,;'~fv. Then:~i .... ;t ... 2(a) V"" r; x B/ B

(c) v';'E:B/E2(b) ~ = = ih E/B2(d) :;=BxE/E2

60. The potential at a point x (measured in urn)due to some charges situated on the xaxis isgiven by: Vex) = 20/ (x? - 4)voltThe electric field E at x ""4 ~m is given by :(a) ~ V/~Im and in the -ve x direction3 . '(b) ~V/Ilmand in-the +ve x direction3 ,(c) 10 V/pm and in the -ve x direction9(d) 10 V/~ m and in the + ve x direction9 '

61. Which of the following transitions in hydrogenatoms emit photons of highest frequency?(


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62. A block of mass m isconnected to another blockof mass M by a spring (massless) of springconstant k. The blocks are kept on a smoothhorizontal plane. Initially the blocks are at restand the spring is unstretched. Then a constantforce F statts acting on the block of mass M top t i u it. Find the force on the block of mass m.(a) mF (b) eM + m)F

M .mmF MF(c) ,_,_- (d)---(m +M) (m +M)

63. Two lenses of power -150 and +50 are incontact with each other. The focal length of thecombination is :(a) -20 em (b) -10 cm(c) +20cm (d) +lOcm

64. One end of a thermally insulated rod is kept ata temperature T} and the other at T2' The rod iscomposed of twa sections of lengths II and /zand thermal conductivities Kl, and K2respectively. The temperature at the interfaceof the two sections is

T, I , '2 T 2I 71.K, K2

(a) (K 212T1 + KIIITz)/(KIII + K2h )(b) (K2/jT1 + K1lzT2)/(K2i, + K112)(c) (Kj12T1 + K211Tz)/(Kl lz + K24 )(d) (KIltTl+ Kzbh)/(K,ll + K212 )

65. A sound absorber attenuates the sound level D Y20 dB. The intensity decreases by a factor of:(a) 1000 (b) 10000ec ) 10 (d) 100

66. If C p and C v 'denote the specific heats of'nitrogen per unit mass at constant pressure andconstant volume respectively, then:(a) Cp -Cv =R/28 (b) Cp -Cv =R/14(c) Cp -Cv =R (d) Cp - Cv ""28R

67. A charged particle moves through a magneticfield perpendicular to its direction. Then: .(a) the momentum changes but the kineticenergy is constant(b) both momentum and kinetic energy of theparticle are not constant(c) both momentum and kinetic energy of thepanicle are constant(d) kinetic energy changes but the momentumis constant

68. Two identical conducting wires AOB and CODare placed at right angles to each other. Thewire AOB carries an electric current I. and CODcarries a cnrrentJy. The magnetic field on apoint lying at a distance dfrom 0, in a direction, perpendicular to the plane of the wires AOBand COD, will be given by:(a) IJ 0 ( 1 1 + 1 2 ) 1 1 2 (b) J : : _ Q _ (1 2 + [ 2 i n

2n d 2rrd 1 2(c) h([I ) Cd) ' J : : _ Q _ (1 2 + 12)2 1 t d 1 2 2 : r r d 1 2 .

69. The resistance of a wire is 50 at 50C and 60at 100"


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74. Angular momentum of the particle rotatingwith a central force is constant due to :(a) constant force(b) constant linear momentum(c) zero torque(d) constant torque

75. A 2 kg block slides on a horizontal floor with aspeed of 4 m/s, It strikes a uncompressedspring, and compresses it till the block ismotionless. The kinetic friction force is 15 Nand spring constant is 10,000 N/m. The-springcompresses by :(a) 5.5 em(c ) 1'1.0 em

(b) 2.5 emCd) 8.5 em

76. A particle is projected at 60" to the horizontalwith a kinetic energy K. The kinetic energy atthe highest point is :(a) K (b) zeroee) K I4 C d) K /2

77. In a' Young's double slit experiment theintensity at a point where the path difference is~ C } . being the wavei.ength of the light used)' isI. If 1 .0 denotes the maximum intensity, II1 0 isequal to :(a) .L (b) J3J2 2(c) ~ Cd) !

78. Two springs, of force constants kl and k2' areconnected to a mass m as shown. Thefrequency of oscillation of the mass isj, -Ifbothkl and k2 are made four times their originalvalues, the frequency of oscillation becomes:

m

(a) jl2(c) 4f

(b) "114(d) 2f

79. When a system is taken from state ito state falong the path iaj, it is found that Q = = 50 caland W = 20 cal, Along the path ib f Q '" 36 cal.W along the path ib f is:a .-- ~ ~~~~~--.,

(a) 6 cal(c) 66 cal (b) 16 cal(d) 14 cal80. A particle o f m ass m executes simple harmonicmotion with amplitude a and frequency v.Theaverage kinetic energy during Its motion fromthe position of equilibrium to the end is :

(a ) 1[2ma2y2 (b) . ! . ma\.24( c) 41t2 ma~ 2 (d) 2n:2ma2y2_ _ , . , . . - - - - - - - - - - - - - - - - - - - -1. The energies of activation for forward andreverse reactions for A2 + B2 -=-'" 2AB are180 kJ mol" and 200 kJ mol"! respectively.The presence of a catalyst lowers the activationenergy of both (forward and reverse) reactionsby 100 kJ mor '. The enthalpy change of the.reaction CA z + Bl -4 2 AB ) in the presence of .catalyst will be (in kJ mol ") :(a) 300 (b) 120ec ) 280 Cd) 20

82. The cell, Zn 1 2n 2+(1M) I I Cu2+-(lM) \eu(E O cen "" 1.10V), was allowed to be completelydischarged at 298 K. The relative concentrationof2n2+ to cU 2+ ( [ Z ' D . 2+1 )iS :lC U 2 ~ ]

(a) antilog (24.GB) (b) 37.3(c) 1037.3 Cd) 9.65)(104

83. The pKa ofa weak acid (HA)is 4.5. The pOH ofan aqueous buffered solution of HA in which50% of the acid ionised is :(a) 4.5 (b) 2.5(c) 9.5 Cd) 7.0

84. Consider the reaction,2A.,+ B -+ products

When concentration of B alone was doubJed,the half-life did not change. When theconcentration ofA alone was doubled, the rateincreased by two times. The unit of rateconstant for this reaction is :


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(a) Lmol~ls-lec) mol L-1s-1 (b) no unitC d) 5-1

85. Identify the incorrect statement among thefollowing:(a) d-bloek clements show irregular' and

erratic chemical properties amongthemselves

(b ) La and Lu have partially filled d orbitalsand no other partially filled orbitals(c) The chemistry of various lanthanoids isvery similar .(d) 4f and Sf orbitals are equally shielded

Whieh one of the following has a square planargeometry t(a) [CoCI4J 2- (b) (FeCI4]2-(e) fNiCl~f- (d) [PtCI4)2-(At. no. Co =27, Ni :: 28, F e : : 2?, Pt = = 78)Which of the following molecules is expectedto rotate the plane of plane-polarised light?

CHO(a) HO+H ,CH20H

86.

87.

(b)~SH

H~~JHNH2(O ! H"'I I"'H (d)

.Ph Ph88. The secondary structure of a protein refers to :(a) a-helical backbone

(b) hydrophobic interactions(c) sequence of a-amino acids(d) fixed configuration of the polypeptide

backboneWhich of the following reactions will yield,2, 2-dibromopropane ?(a) CH3-C~CH+ 2HBr----+(b) qbCH --:CHBr+ HBr----+(c) CH~H + 2HBr----+(d) CHJ-CH =CH2 + HBr----+In the chemical reaction, "CHJCH2NH2 + CHCl3 + 3KOH ~(A) + (B) + 3HzO, the compounds C A ) and(B) are respectively:(a) C2HsCN and 3KCl(b) CH3CH2CONHi and 3KCIec) C2HSNC and K2C03(d) C2HsNC and 3KCl

91. The reaction of toluene with Cl2 in presence ofFeCI) give s predominantly:(a) benzoyl chloride(b)" benzyl chloride(c) a-and p-chlorotoluene(d) m-chlorotoluene

92. Presence of a nitro 'group in a benzene ring:(a) activates the ring "towards electrophilic .substitution(b) renders the ring basic(c) deactivates the ring towards nucleophilic

substitution(d) deactivates the ring towards electrophilicsubstitution .93. In which of the following ionisation processes,the bond order has increased and the magneticbehaviour h as changed?

(a) C2 ----+ C; (b) NO ----+ NO+(c) 2 ----+ o~ (d) N2 ----+ N~

94. The actinoids exhibit more' number ofoxidation states in general than theIantha no ids. This is because:(a) the Sf orbitals are more buried than the 4f

orbitals ,(b) there is a similarity between 4/ and 5/orbitals in their angular pan of the wavefunction(c) the actinoids are more reactive than theIanthanoids '(d) the S f orbitals extend further hom thenucleus than the 4f orbitals

Equal masses of methane and oxygen aremixed in an empty container at 25'C. Thefraction of the total pressure exerted by oxyge n

95.

is : 2(a) -3T(c) '-:3

(b) . ! . x 2733 298'1"-C d ) -289.

90.

96. A 5.25% solution of a substance is isotonic with"a 1.5% solution of urea {molar mass e60 gmol-l J in the same 'solvent If the densities ofboth the solutions are assumed to be equal toLOg cm-3, molar m.asS of the substance will be:(a) 90.0 g mol-tO (b) 115.0 g mol"!.Cc), 105.0 g mol-l (d) 210 ..0 g mol-lAssuming that water vapour is an ideal g 3 s , th einternal energy change (AU) when.!" mole ofwater is vapourised at 1 bar pressure and100"C, (Given: molar enthalpy of vaporisationof water at 1 bar and 373 K '" 41 kJ moFl and-R '" 8.3~ moJ-IK-1)wi l l be:

97.


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(a) 4.100 kJ mol-l (b) 3.7904 kJ mol"(c) 37.904 kJ mo\-l (d) 41.00 kJ mol-1

98. In a saturated solution of the sparingly solublestrong electrolyte AgIO 3 (Molecular mass= = 283) the equilibrium which sets in is

AgIOj(s) Ag ' (aq) + 10 i{aq)if the solubility product constant K.p of AgIO Jat a given temperature is 1.0 x 10-8, what is themass of AgI03 contained in 100 mL of itssaturated solution?(a) 28.3 x 10-2 g(c) 1.0 X 10-7 g

(b) 2.83 x 10-3 g(d) 1.0 x 10-4g,

99. A radioactive element gets spilled over thefloor of a room. Its half-life period is 30 days. Ifthe initial activity is ten times the permissiblevalue, after how many days will it be safe toenter the room 1(a) 1000 days (b) 300 days(c) 10 days (d) 100days.

100. Which one of the following conformations ofcyclohexane is chiral?(a) Twist boat (b) Rigid(c) Chair (d) Boat'101. Which of the following is the correct order ofdecreasing SN 2 reactivity ?

(a) RCH2X > RFX > R2CH X(b) RCH 2X >R2CHX > RJC X(c) R3CX > R 2CHX > RCH 2 XC d ) R 2C HX > R 3CX > RC H 2 X(X = a halogen)

102. In the following sequence Of reactions,CH3CH20H ~ A ~ B HCHO. etherC~D

the compound 'D ' is :(a) butanal (b) n-butyl alcohol(c) a-propyl alcohol .(d) propanal

103. Which of the following sets of quantumnumbers represents the highest energy of anatom?(a) n=3,1=1,m=1,s;;o+1!2(b) n",3,1=2, m=.l,'S-+ 1/2(c) n ""4, I...0, m "" 0, S:: + 1/2(d) n:=3,1",,0,m=O,s=+1/2

104. Which of the following hydrogen bonds is thestrongest?(a) O-H N (b) F-H F(c) O-H O (d) O:.......H F

105. In the reaction,2Al(s) + 6HCl(aq)--..) 2AI3+{aq)

+ 6Cnaq) + 3H2(g}(a) 6 LHCl(aq)is consumed for every 3L H2(g)produced(b) 33.6 1. H2 (g) is produced regardless of

temperature and pressure for every moleAI that reacts(c) 67.2 LH2(g) at STP is produced for every.mole A 1 that reacts(d) 11.2 LH2(g) at STP is produced for everymole HCl(aq) consumed

106. Regular use o(which of the following fertilisersincreases the acidity of.soil ?(a) Potassium nitrate(b) Urea(c) Superphosphate of limeC d ) Ammonium sulphate

107. Identify the correct statement regarding aspontaneous process:(a) For a spontaneous process iii an isolatedsystem, the change in entropy is positive(b) Endothermic processes are neverspontaneous(c) Exothermic processes are alwaysspontaneousC d ) Lowering of energy in the reaction processis the only criterion for spontaneity108. Which of the following nuclear reactions willgenerate an isotope?

(a) Neutron-particle emission(b) Positron emission. (c) a-particle emission(d) J3-particle emission

109. The equivalent conductances of two strongelectrolytes at infinite dilution inHp (whereions move freely through a solution) at 2S"Care given below:

/\oCH]COONa'" 91.0 S cm2/equiv .A\ICI '" 426.25 cm2/ equiv

What additional information/quantity one.need s to calculate A 0 of an aqueous solution ofacetic acid ?(a) /\oofNaCI(b) /\oofCH:lCOOK(c) The limiting equivalent conductance' ofW(AOW )(d) N of chloroacetic add (ClCH2COOH)

110. Which 'one of the following is the strongestbase in aqueous solution?


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(a) Trimethylamine (b) Aniline(e) Dimethylamine (d) Methylamine

111. The compound formed as a result of oxidationof ethyl benzene by KMnO", is :(a) benzophenone (b) acetophenone(c) benzoic acid (d) benzyl alcohol

.112. The IUPACname Of) is: ..(a) 1, t-diethyl-z, 2dimethytpentane(b) 4, 4-dimethyl-S, 5-diethylpentane(c) 5 , 5-diethyl-4; 4-dimethylpentan~(d) 3-ethyl-4,4-dimethylheptane

113. Which of the following species exhibits thediamagnetic behaviour?(a) O~- (b) 0;(e) O2 (d) NO

114_ The stability of dihalides of Si, Ge, Sn and Pbincreases steadily in the sequence :(a) GeXz < SiKz < snXz < PbX2(b) six,


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'. PHYSICS41. (a) 42. (b) 43. (b) 44. (d) 45.' (d)- 46. ( e ) 47. ( c ) 48. (b)49. (b) 50. ( d) 51. (d) 52. (6) 53. ( e ) 54. (d ) 55. (d ) 56. (b)57. (b) 5B. ( d) 59. (a) 60. (d) 61. (e) 62. ( e ) 63. (b) 64. (c)65. (d) 66. (a) 67. (a) 68. (b) 69. (el 70. (d) 71. (a) 7 2 . (a)73. (a) 74. e e ) 75. (a) 76. ( e ) 7 7 . (d) 7B. (d) 79. (a) 80. (a)

'. CHEMISTRYBl. ( d) 82. ( c ) 83. (c) 84. (al 85. ( d) 86. (d) 87. (a) 88. (a)89. (a) 90. (d) 91. ee) 92. (d) 93. eb) 94. (d) 95. eel 96. ( d)97. ( e ) 98. (b) 99. ( d) 100. (c) 101. (b) 102. (c) 103. (6) 104. (b)

105. (d) 106. ( d) 107. (a) 108. (a) 109. (al 110. ec) 111. (e) 112. ( d)113. (a) 114. ee l 115. ( d) 116. ee) 117. (e) 118. (c) 119. (al 120. (d)

H IN T S S O L U T IO N S

1r+ r2 2~ ~ r+r-l=O. J 5 -1 ( - . - - ~ - 1 )r",-- r*~--2 2 5.

4. Required number of ways'" 12C 4 x Sc 4 X 4C 412! 8! 1=--x--x8!x4!!x4!12 1(4!i'

4-x2 is defined for (- ~, ~).cos"! ( 1 - 1 ) is defined if -1:::; 1 - 1 s 1. .

1. Since, each term is equal to the sum of twopreceeding terms.arn-I = nr" + ar"+1

2. ; sin " (~) + cosec':' (~);; ~ -I ( x ) . -1 ( 4 ) 7t~ sin 5 + sm " 5 "" 2. -I ( x ) . 7t -1 ( 4 )~ sin 5 ;;2-510 " 5

~ sin-l(~)=cos-l(~)~ sin." (~);; sin " G )~ x=3 .

3. Since, in binomial expansion of (a - bt ,n 2: 5 ,the sum of fifth and sixth term is equal to zero.:. "C4 a" -4 (-bt + 'Cs a"-5(-bi ;;0

O :;;E:S2 ~ O :Sx:S42and log (cosx) is defined, if cos x > 0

7t 1 1 :--


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B

~ - - ~ - - - - - - ~ ~ ~ - - - - - - ~T,cos91 3 1 < g

Also Tl s in e + Tz cos e '" 13::::) T2 ( 5 ,~+ 12) ""1312 13 13= = > ' T2 ( 169 ) '"13. 1213= = > ,T2 '" 12 kg and T} "" 5 kg.

7. Probability of getting score 9 in a single throw-4 1==-=-36 9Probability of getting score 9 exactly twice

' " 3 C 2 X ( ~ r x % ~ 2 : 3 '8. Equation of circle which touches z-axls andcoordinates of c entre are (It, k), is

(x~hf + (y-ki:: k2.. ,' It is passing through (- 1, 1), then

(-1- hl + (l-kl = k2 ,h 2+ 2h - 2k + 2", 0D~O

2k-l~O => k 'Ot!. .29. Ifdirection cosines of L be I,m, n, then

21+3m+n=Oand' l+3m+2n"'OOn solving eqs, (i) and (li), we getl r 7 t n

...(i).. ,(Ii)

.~ .-3 31 _ ( 1 ) I ': m: n = = h: - .J 3 :. .[31 1l = ; . J 3 = = > cos ex"" - J 3 ' '

10. General equation of all such circles which passthrougb -the origin and whose centre lie onx-axis, isXl + y2 + 2gx.= O.

On ditferentiating w.r.t, x, we getd y2x+2y-+2"=0dx2g '" - ( 2 x + 2y :)

...(i)

1 1 .

On putting .the value of 28 in eq. (i), we get. , . '( d ) .x2 + y2 + _ 2x - 2y!-'"0

d lY 'x2 + y2 _ 2x_2.., 2 .: c y _ '" " 0.. dxy2 = = x2 + 2l;y dydxWhich is required equatioJl.

U s ing AM ~ GM - ': .:- , i l + cf--2:pq2 1pqs-

-~(p+ q)2='l +l + Zpq(p + q)2 =1+.2pq(p+q)z~l+l

,p't q..",[2.

. . : : : : >

Now

12 . Let h be th e height of atower, , LAOB """600.:, AOM is equilateral ... GA ee 08 "" AB :; a c

- . - h I h.Now in ADAe, tan 30",,- =>""7'::=-a .....3 aa~ . :h=:rs'

13. Weknow that{l ~ . lOe lOe . lOe' 10. + X J . = 0 + IX + ... + loX. +

- 2Q 20.. + (;20Xo n putting x :; -1in above expansion, we g e t- lUC we - - 20e 20c 2(Ic0:; 0- 1+ ,,- 9 + ~O- '11 +

... + 2OCZO '


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~ 0 = = 20CO - 20C] + ... - 20C9 + 20C}020C 20e9+':'+ 0

=> 0:: 2eoCo - 20C1 + '..... - 20C9)+ 20C1O .. = > 20c]0 = = 2 (2OCo :- 20C} + ... + 20C1O)=>

14. Equation of normal Is Y - Y '" _dx (X'_ x)dy=> G = ( X + Y k ' O )According to question! x + y : I = 1 2 x 1

dy , el y=> y~""x or y-=-3xd x - d x=> ydy = = xdx or ydy =-3xdxy2 x2 . or y2 3x2= > -=-+c -=--+c2 2 2 2= > x2 _ y2 ""_ 2c or 3xz +y2 = = 2c,

15. From the Argarid diagram maximum value ofIz+ljis6.

(-7,0)

y

Aliter:Iz+ll =lz+4-31 ~1z+41 + 1-31~,6T hus m ax im um value of']z + 11is 6 .

16. 72=p2+3'-+2x3.xPcos9 (1 )-~""~-'-'~''~''''''''''''''-i-P------_

33and (.ff9l = = p2 : + (-3i + 2)- 3)(P rose

~.(ii)On adding eqs. (i) and (ii), we get

68=2P2+18 => p=s.

11. The desired probability"" (0.7) (0.2) + (0.7) (O.8) (0,7) (0.2) +

(0.7) (0.8) (0.7) (0.8) (0.7) (0.2) + .....'"0.14(1 + (0.56)+ (0. s6f +....1'"O.14[ 1 '] =0,14 = = 2_ = 0.32.1-0.56 0.44 22From above it is clear that no option is correct.

I 1 1 ID= 1 l+x 1 II

1 1 1+y18.

On applying C, -4 C2 -~Cl and C3 ~C3 -C\100=lxO=xy.l Oy

Hence, D is divisible by both x and y.19. The given equation af hyperbola is

x2 y2-- - -- '" 1. Here, rt '"cos2 (J. andcor (J. sin2 ub2=::sinzaCoordinates of foci are. (.:!: ae, 0).. e = H .

s in 2 (J. I 2e~ 1+-~2-= ....+tan (J.cos a .= >~ e= sec a.Hence, abscissae of foci remain constant whena varies.

20. Since, a line makes an angle of ~ with positive. 4'direction of each of x-axis and y-axis, therefore

21.

:I t 1ta = 4 , 1 3 " " " 4we know that cos2 !l+ 00521 3 + cos2 y '" 1= > cos"2 ~ + co s 2 ~ + cos2 y '" 14 4

1 1 2= > -+-+cos y = = l2 2=> cos 2 y = = 0 :::;. y =900'U s in g m ea n value theorem.. f'(c)", /(3)- f (1)

3-1!'"og 3-log 1c 2 .2c= -- '" 210g3 e.log, 3


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22. -: f (x) = tan -1 (sin x + cos x):-f'(x)= 1 , 2 (cos x-sin x)1+ (sin x-s ccsx)

~ c o s ( x + ~ )1+ (sin x + cos xl

23.

f ( j is i " f 1< 1< 11X is mcreasmg i " " ' 2 < x + 4 < " 231< 1t---


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31. .: A(h, k), B(l, 1)and c(2, 1) are the vertices ofa right angled triangle ABC.Y A(h, k)

_ B(1L..,-1-)----....>..C(2, 1)o X

Now, AB = = ~i + (1- kior BC = ~(2:- Ii + (1 - Ii = 1or 0\ ==~(h - 2l + (k -IfNow, Pythagorus theorem

AC2 '" AB2 +BC24+ h2 - 4h + k2 +1- 2k"" h2 + 1 - 2h +e+ 1 - 2k + 15-4h=3-2.1I

h=1Now, given that area of the triangle is 1.1 .Then, area (MBC) =- x AB )(BC2

... (i)

1 ~ - 2 k21'"-)( (1- h) + (1- - ) )(122"'-.J(i - hl + (1 - kl ... (ii)

Putting h = = 1 from Eq. (i),we get2==~(k -Ii

Squaring-both the sides, we get4", k2 +1-2k

or k2 - 2k - 3 ' " 0or (k - 3) (k + 1) = = 0So, k = = -1,3Thus the set of values of k is {-I, 3}.

32. Slope of the line QM = = tan 2rr = = -.,f33y R(3,3I3)

pQ(O,O) x

Hence equation is line QM isy = = - . J 3 xor . J 3 x + y = = o.

33. Equation ofbisectors of lines .xy = = 0 are y := xput y = = x in my2 + (1- m 2 ) x : y - mx2 = 0, weget~

mx2 + (1_ m2) Xl - mx2 = = 0(1_m2)x2 =0 ~ m= 1.fex)= 1 log t dt

1 l+tFee ) = = f (e)+ f G )nd

35.

e I 1/,I= > Fee ) = = f og t dt + f og t dt11+t - 1 1+t'" logt dt + } log t de11+t It(1+1)

= = r iog t dt = [(lOgC)2l:-+0 (e2x -1)+ Zxe2x 4e2x= lim _.. . =1x -+0 4e2x + 4xe2x:.f (x) is continuous at x"" 0, thenlim f(x)= f(O )x ....0

= > 1= !CO).j dt =~. J 2 C ~t 2 -1 2[sec'" t]x = ~. J 2 2

37.

= >


16/23

~ sec"! x - 2 ! = , 2 !4 2"'" sec'" x ""3 1


17/23

Now, L 10'C"'~""-",2sR 5After 2s, i.e., at t '" 2sRise of current I = = (1 - e:-I)A

46. Current density J'"~ltaFrom Ampere's circuital lawf B . dl ee !to . iendo,edFor I" < a B x 2 1 1 : 1 " = = 1 1 0 x JX 1 { , I . 2

For r > aB x 2 1 1 : 1 " '" 1 1 0 i = :> B '" 1 1 0 i

2 1 1 : rB _ M o i~-4ltaB I =1B 2So;

rb\ .E7

:~

47. Using Ampere's circuital law the magnetic fieldat any point inside the pipe is zero.48. Binding energy

BE '" (M nucleus - M nucleon,) c2= = (Mu - 8M p - 9Mn)c2

49. in gamma ray emission the energy is releasedfrom nucleus, so that nucleus get stabilised.50. For V i < 0

the diode is reverse biased and hence offerinfinite resistance, so circuit would be like asshown in Fig. (2) and V o '" O.5V

fr Fig. (2)

1 1Vi RL v ,

! 1Fig. (1)iiV o Vi! !Fig. (3)

51.

For V i > 0, the diode is forward biased andcircuit would be as shown in Fig. (3) andV o = = V i,Hence, the opitcal (d) is correct.The momentum of the photon

h hP=J:=-Zv = = Vo + gt + ft 2

dxor - = = v + gf + ft 2dt 0= :> dx = = (v o + gt + ft2)dtSo, f ; dx ""f : (v o + gr + ft2)dt= :> x=vo+g/2+J/3Let the each side of square lamina is d.So, Iu: =lcH (due to symmetry)and lAC ee ISD (due to symmetry)Now, according to theorem of perpendicular

52.

53.

axis, or-__ ~F__ ...........".

E...,._---d----"

IAc+lBD=[O= :> 2/1 1 c = = [0and IFy + Icn = = 10;::? 2 1 p F " " I oFrom Eqs, (0 and (ii), we get I I IC " ' . I E I '

md 2lA D =1M +-4

...(i)... (ii)

So,

md2md2'-"--+-_12 4md 2I AI) '" -- = = 4 1 1 ' 1 '3

54. x = = Xo cos C U l t -It/4)d2xAcceleration, a =-idt

= -oo2xo cos(oot - rc/4)= 002 Xo cos (Olt + 3n/4)

So, A = oo2xoand S ""3n/4


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55. Direction of - e reverses while magnituderemains same and V remains unchanged.56. Tl/2(X) = 1 : (Y)0.693 1--::-l x Ay

t.y=~0.693=:} x, > Ax

So, Y will decay faster than X.57. For Camet engine using as refrigerator

W = Q 2 G : - 1 J1 .. 1t IS givenT l =~10

T[ 10SO , Q 2 = 90 J (as W = 10J)58. The number of free electrons for conduction issignificant only in Si and Ge but small in C, as Cis an impurity.

59. Asvof charged particle is remaining constant,it means force acting on charged particle iszero.So, ~ -) ;q(vx B)=qE

- - - + - - ) _ ,vxB=E

60.

and is along positive x-direction,61. Emission spectrum would be when electron.makes a jump from higher energy level tolower energy level.

, Frequency of emitted photon is proportional tochange in energy of two enery levels, i.e.,v'" RCZ 2(].- _ J_2 2nl "2

62. Acceleration of system, a=_F_m+M, k~F//

So , force acting on mass m = mamFm+M

63. Power of a lens is reciprocal of its focal length.Power of combined lens is

P =P1 + P 2=-15+ 5=-10D

1 100f =-=_..-emP -10f = -10 em

64. Let temperature at the interface is T.For part AB,

For panEe, Q 2 c r -T2)K2~~o.: -t 1 2At equilibrium, Q 1 "" g ; : _t t(fl - T)K1 = (T - T2)Kz

~T = T1K]IZ + T~~~ll

K]12 + K 2 1 165. Let intensity of sound be J and 1'.

Loudness of sound initially( I )~l = 1010g l I o

~2 =1010gU JGiven, ~2 - ~l = 20

20 = 10 log ( f )I' ""1001

Later,

66. According to Mayer's relation,R HCp -Cv =-=-m 28


19/23

67. In case of motion of a charged particleperpendicular to the motion, i .e. ,displacement, the work doneW ~ f F ' . I s '" J Fill case", 0 (as 9 = =9 0)and by work-energy theorem, W = =AKE , thekinetic energy and hence speed v remains'

- - - >constant. But v changes, so, momentumchanges,68. The magnetic field induction at a point P, at adistance d from 0 in a direction perpendicularto the plane ABCD due to currents through

AOB and COD are perpendicular to each other,is

A p

"c---~O+----+--- 01 2

BHence,

69. From R f '" RoC l +at)5"" RoC l + 500:)6", RoC l + 10Cla)5 1 + S O c x-6 1 + 1000:

,..(i)... (ii)nd 1

;=}(:( ==- -200Putting value of (:(in Eq (i), we get

5==RoO + 50 x 1/200)Ro ==4Q

70. On introduction and removal and again onintroduction, the capacity and potential remainsame. So, net work done by the system in thisprocess

w==u/-u,'" ~C V2 -~C V 22 2",0

71. According to Millikan's oil drop experiment,electronic charge is given by,

6 7Cllr (Yj + Y2)q= Ewhich is independent of g.So, electronic charge on ~hemoon ee ]

electronic charge on the earth72. In this question distance of centre of mass ofnew disc [rom the centre of mass of remaining

disc is aR,Mass of remaining disc",M -M/4= 3Mj43M M:. - -.- a R + - R '" 04 4

0. '" 1/3Note; In Q. No, 72, the given' distance must be uR forreal approac h tot he solution

73. Assuming that no energy is used up againstfriction, the loss in potential energy is equal tothe total gain in the kinetic energy.

vMgh = . ! J (v2j R Z) + . ! . My2-2 . 2

~ y2 e M + I1R2)=Mgh2y2 2Mgh ::: 2gh

M+ I/R2 1+ IIMR2If s be the distance covered along the plane,then

Thus,oror

74.

h '" s sin a2 2gs sin ey '" .1+ I/MR2y2 =.2as2as '" 2gs sinS

1+l!MR2g sinea= --'=-------,,-1+ I/MR2

According to the principle of conservation ofangular momentum, in the absence of externaltorque, the total angular momentum of thesystem is constant.

a=: .F k " "1 5 ,, ,,7 .5m !s2m 2

Now,

or

75.


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76.

Now maoo . ! . kx2, 2or 2X7.5==.!.x10000xx22or x2 = 3x 10-3or X =0.055m~ xo o 5.5cmKinetic energy at highest point

(KE)H= .!.mv2 cos2 e2ooK cos1eooK(cos 600iK= -- 4

phase difference = - 2J r x path differenceA2J r A -r.e ., < jl= Tx'6rt

77.

As,3

1 ==max cos2($/2)_1_ = co s 2 (


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Half-life is independent of change in cone.of reactant ~ First orderFirst order W.Lt. to B[A ] is doubled, rate increased by two times= : > First order w.r.t AHence, net order of reaction = = 1+ 1'"2Unit for the rate constant = cone. (I - n) t-1'" (mol. L-1ri, S-1

=: Lmol-1s-185. 4f and S f belongs to different shell, experiencedifferent amount of shielding.86. CI- is a weak ligand butCI- cause the pairing ofelectron with large Pt2+ and consequently give

dsp2 hybridisation and square planar geometry.87. The molecule, which is optically active, haschiral centre, is expected to rotate the plane of

polarised light.

CH20HOne chiral centre = : > optically active

H2N NH;z

Ph Ph

88.Two chiral centres, but plane of symmetrywithin molecule = :> optically inactivePrimary structure involves sequence ofo-amino acids polypeptide chain.Secondary structure involves a-helical and~-pleated sheet like structures.CH3-C==CH+ HBr-4 CHJ-I=CH2

Br

1 H s r89.

BrICH3-C-CH3IBr - +~CH3-C~CH3I ~

Br2 , 2 - d i b r o m o p r o p a n e m o r e s ta b l ecarbocaticn . .f - - ' R e : . . : . : .; . ; a ! T : . . ; , ;M ; : _ , , , ,g e _ m . . .; e n : . . ; , ;t _3C-iH-CH2

Br

CH3-CH=CHBr H8r CH)-CH2-CHBr2CH==CH~ CH3CHBr2CH3-CH =CH2 ~ CH3-CHBr-CH3

90. CH3CH2NH2 +CHC13+ KOH-4 A + B + 3H20CHCl3 + KOH ----7 :CG12+ KCl+ HP

~CH3CH2NH2 + :CCI2 ~ CH3CH2NC + 2HClcarbylamine91. VCH3 C I2FeC I3(~l+)I chlorinationto uene electrophlltc

substitution

j J ' C H 'Clp-chloro toluene

+ P'YCH3~Cl

o-chloro toluene

92.~+/0C J N ' - O

-N02 group withdraw electron from the ring,shows -M effect makes ring electron deficient,thus, deactivates ring for electrophlllcsubstitution.NO__,. NO+3.

+(NO) Totai e: = 140'1S20' " 15202520' 2S21t2p~ + 1 '" 2p~,+la2P:DiamagneticBond order ""10 - 4 = = 32(NO) Total e = = 15als2(J }520"2s,20 25 2, 02P: rt 2p; 1- 1 1t 2P~+ I1t * 2p; = n2pyParamagnetic

10 - 5Bond order = = _ ' - = = 2.52Electron is taken away from non-bondingmolecular orbital, that's why bond orderincreases.

94. The actinoid (Sf-elements) exhibits motenumber of oxidation states in general than thelanthanoid because Sf orbitals extend fartherfrom the nucleus than the 4f orbitals.


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95. Suppose the equal mass of methane andoxygen e IV = 1gM I f ., f w/32o e racnon or oxygen", -----.-.. w/32+ w/16

1=_J.Z_ " ' . ! .3/32 3

Let the total pressure =PPressure exerted by oxygen (partial pressure)1=XOz X PlOt"l := P X --3

96. Solution is isotonic.=> GIRT =GzRT

C1 =C2Density of both the solutions are assumed to beequal to 1.0 g cm-3 = > molality = molarity5.25%in 100 g 5.25 g of substance in 1000 g 52.5 g ofsubstance

52.5 15Hence - ..=~.'M 60'M = = molecular mass of the substance

M = 52.5x 60 = 21015

97. H20 (I) ~ HzO(g)8n=1-0=1till = = Ali - LlnRT

= 41 -1 x 8.3 x 373 x lO-j (R :=8.3 x 10-3)'" 37.9 kJ mol-l

9S. AgI03(s) ~ Ag" (aq)+ IO;Caq)Let solubility of AgIO 3 be S

K,p = [Ag+][IOiJ1.0 x 10-8 '" 52 or S = 1X 10-4 moVL

In 1000 mL mol of AgIOj dissolved=1 x 10-4 mol

In 100 mL of mole of AgIO 3 dissolved'" 1 x 10-5 mol

Mass of AgIO) in 100 mL ;" 1 )I: 10-5 x 283:= 2.83x 10-3

99. Activity ee N ~=(! rNo 2or 110= ( ~ ror 10", 2n

Taking log on both sideslog 10", nlog 2

1n=-- =3.320.301time = n x half-life

'" 3.32 x 30 = = 99.6 days100. \XjChair form is unsymmetrical and absence ofany element of symmetry.101. Sill2 reactions are greatly controlled by stericfactor.

R-CH~-X R2CH-X J.{3C-X1" 2 :ll)

SN 2 reactivity decreases as bulkyness of alkylgroup increases.

'C' 'B'ORICH3CH2CHz+ Mg(OH)I'D'n-propyl alcohol103. n + 1 "" 5 maximum.104. Hydrogen bond is strongest in HF due to higherelectronegatlvity of F.lOS. 2Al(s) + 6HCI(aq) --t 2AIJ+ (aq) + 6Cnaq)

lmol

+106. (NH4)2S04 ------t- 2NJ-I4 + SO~-acidic

107. In an isolated system where either mass andenergy are not exchanged with surrounding forthe spontaneous process, the change in entropyis positive.lOS. : . X ~ :-1 X + onl

Isotopes ar-e species having Same number ofproton, but different number of neutron.109. We know from Kohlrausch's law

' ) . , 0 CH3COOH = ;" 0 CH3COONa + ' ).,HCI- '),_NaCl110. In aqueous solution, basicity order:

Dimethylarnine > methylamine20 1

> trimethylamine> aniline3"


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111. Any aliphatic carbon with hydrogen attachedto it, in combination with benzene ring, will beoxidised to benzoic acid by KMnO 4/ H+ .

6 2112. 7

3-ethyl-diethylheptane113. The correct option is O~-. This species has 18

electrons, which are filled in such a way that allmolecular orbitals are fully fil1~d, sodiamagnetic.crls20'*1s2, a2s2cr' 252 a2p;, 'lt2p; = = 1C2p;,

'It' 2p; =0 1t' 2p;114_ Due to inert pair effect, the stability of +2

oxidation state increases a s we move down thisgroup... SiXz < GeX2 < 5nX2 < PbX2

115. BiZ reacts with hot and strong NaOH to giveNaBr, NaBr03 and Hp.

116. Higher the charge/size ratio, more is thepolarising power.

. . K+ < Ca2+ < Mg2+ < Be2+Molarity =10 ~ densi~_:._wt. of s5:I~te

mol. wt. of the soluted . 3.60 x 98 21enslty = = . - - - - = = J.10 x 29

K = = k j X k2=: 1.0 x 10-5 X S.OX 10-10=5x 10-15

119. According to Raoult's law:

117.

118.

P =poAXA + pOIJ XB290 = 200 x 0.4 + p O B x 0.6pOB = 350

M/120.68==-TllS = = 160.2J/KilH=179.1X 103 J I molT = = 179.1X 1 9 3 J I mo~

160.2J/K=1117.97 K",,1118K

all india engineering entrance exam 2007 question paper with solution

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