CHEMISTRY

1. IUPAC name of

CH3

CH CH2 3 is

(a) 1-methyl-3 ethyl cyclohexane(b) 1-ethyl-3 methyl benzene(c) 1-ethyl-3 methyl cyclo hexane(d) Cyclo hexane-1-ethyl-3-methyl

2. Which of the following resonance structure is lowest inenergy?

A.

B|C|H

H C||

: :O

O

:: HH

B.Q

B|C|H

H C||

: :O

O: H

:

+H

C.+

B|C|H

H C

: :O

O

:

: HH

|Q

:

(a) A (b) B(c) C (d) All have same energy

3. The hybridization of atomic orbitals of nitrogen in+2NO ,

-2NO and

+4NH are

(a) sp2, sp3 and sp2 respectively(b) sp, sp2 and sp3 respectively(c) sp2, sp and sp3 respectively(d) sp2, sp3 and sp respectivley

4. In a compound AOH, electronegativity of A is 2.1, thecompound would be(a) Acidic(b) Neutral towards acid & base(c) Basic(d) Amphoteric

5. Which of the following orders is wrong?(a) Electron affinity N < O < F < Cl(b) Ist ionisation potential Be < B < N < O(c) Basic property MgO < CaO < FeO < Fe2O3(d) ReactivityBe < Li < K < Cs

6. The dipole moment of chlorobenzene

Cl

is 1.5 D. The

dipole moment of Cl

Cl

Cl Cl is

(a) 2.86D (b) 2.25D(c) 1.5D (d) 0D

7. Following substances are in solid state :(A) Methane (B) Cesium chloride

INSTRUCTIONS

Chemistry (120 marks) : Question No. 1 to 30 are of 4 marks each.

Physics (120 marks) : Question No. 31 to 60 are of 4 marks each.

Mathematics (120 marks) : Question No. 61 to 90 are of 4 marks each.

Negative Marking : One fourth () marks will be deducted for indicating incorrect response of each question.. . . Best of Luck

Time : 3 hrs. Max. Marks : 360

MOCK TEST - 1

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ABOUT DISHA PUBLICATION

2

(C) Ice (D) LithiumWhich non-conductive solid when melts converts intoconductive liquid?(a) C, D (b) Only C(c) Only B (d) A, B and C

8. On applying pressure to the equilibriumice water, which phenomenon will happen(a) More ice will be formed(b) More water will be formed(c) Equilibrium will not be disturbed(d) Water will evaporate

9. The energy levels for )1Z(ZA-+ can be given by

(a) En for A(+Z1) = Z2 En for H

(b) En for A(+Z1) = Z En for H

(c) En for A(+Z1) = 2Z

1 En for H

(d) En for A(+Z1) =

Z1 En for H

10. Given, 3K

2 FOHOHHF a +++ ;

bK2

OHHFOHF + + .Which relation is correct

(a) Kb = Kw (b)w

b K1K =

(c) Ka Kb = Kw (d) wb

a KKK

=

11. In an amino acid, the carboxyl group ionises at 1apK = 2.34

and ammonium ion at 2apK = 9.60. The isoelectric point ofthe amino acid is at pH(a) 5.97 (b) 2.34(c) 9.60 (d) 6.97

12. AB, A2 and B2 are diatomic molecules. If the bond enthalpiesof A2, AB and B2 are in the ratio 1:1 :0.5 and enthalpy offormation of AB from A2 and B2 is 100 kJ mol

1 . What isthe bond energy of A2 :(a) 200 kJ mol1 (b) 100 kJ mol1(c) 300 kJ mol1 (d) 400 kJ mol1

13. Equal volume of 0.1 M urea and 0.1 M glucose are mixed.The mixture will have(a) Lower osmotic pressure(b) Same osmotic pressure(c) Higher osmotic pressure(d) None of these

14. If the following half cells have the E values as23 FeeFe ++ + ; E = + 0.77V and Fee2Fe 2 + -+ ;

E = 0.44V. The E of the half cell Fee3Fe 3 ++ will be(a) 0.33 V (b) 1.21 V(c) 0.04 V (d) 0.605 V

15. The oxidation states of sulphur in the anions--- 2

62242

23 OSandOS,SO follow the order

(a) ---

3

a white precipitate with NH4OH. This was soluble in excessof NH4OH. On passing H2S through this solution a whiteppt. is formed. The metal M in the salt is(a) Ca (b) Ba(c) Al (d) Zn

23. A laboratory reagent imparts green colour to the flame. Onheating with solid K2Cr2O7 and conc. H2SO4 it evolves a redgas. Identify the reagent(a) CaCl2 (b) BaCl2(c) CuCl2 (d) None of these

24. Which of the following compound can not used inpreparation of iodoform?(a) CH3CHO (b) CH3COCH3(c) HCHO (d) 2-propanol

25. The correct priorities for the substituents shown below,according to the E-Z sequence rule is

I. CN II. CBr 23 )CH(

III. COOH IV. 3

O||

2 OCHCCH --

V. HC

O||

-

(a) II, III, V, I, IV (b) V, II, I, IV, III(c) III, IV, I, II, V (d) II, V, I, IV, III

26. Identify X in the sequence given :

NH2

Cl

CHCl3KOH

(Y)HCl

(300 K)X + methanoic acid

(a) NH2 Cl (b) NC Cl

(c) N C Cl (d) ClCH NH3

27. Select the rate law that corresponds to the data shown forthe following reaction CBA +Expt. No. (1) (2) Initial Rate 1 0.012 0.035 0.10 2 0.024 0.070 0.80 3 0.024 0.035 0.10 4 0.012 0.070 0.80(a) Rate = K[B]3 (b) Rate = K [B]4

(c) Rate = K [A] [B]3 (d) Rate = K [A]2 [B]2

28. An alkene upon ozonolysis yieldCHO CH2 CH2 CH2 CHO only. The alkene is

(a) CH2= CH CH2 CH2 CH2 CH2 CH3

(b)

(c)

(d)

29. 1 mol of 2N and 3 mol of 2H are placed in a closed containerat a pressure of 4 atm. The pressure falls to 3 atm at the sametemperature when the following equilibrium is attained

)g(H3)g(N 22 + 2 )g(NH3 .

The pK for the dissociation of 3NH is

(a) 23 atm)5.1(5.0

33 -

(b) 23atm)5.1(5.0

(c) 23atm

33)5.1(5.0

(d) 2

3atm

5.0)5.1( -

30. 0.5 g mixture of K2Cr2O7 and KMnO4 was treated with excessof KI in acidic medium. I2 liberated required 100 cm

3 of 0.15N.Na2S2O3 solution for titration. The percentage amount ofK2Cr2O7 in the mixture is(a) 85.36 % (b) 14.64 %(c) 58.63 % (d) 26.14 %

PHYSICS31. A d.c. supply of 120V is connected to a large resistance X. A

voltmeter of resistance 10kW placed in series in the circuitreads 4V. What is the value of X?

(a) 190 kW (b) 90 kW

(c) 290 kW (d) 390 kW

32. An insect trapped in a circular groove of radius 12 cm. movesalong the groove steadily and completes 7 revolutions in100 sec. What is the linear speed of the motion

(a) 2.3 cm/sec. (b) 5.3 cm/sec.

(c) 0.44 cm/sec. (d) None of these33. The period of the satellite of the earth orbiting very near to

the surface of the earth is T0. What is the period of thegeostationary satellite in terms of T0

(a) 7T0

(B) 0T7

(c) 7T0 (d) 0T77

4

34. In Al and Si. If temperature is changed from normaltemperature to 70 K then(a) The resistance of Al will increase and that of Si will

decrease(b) The resistance of Al will decrease and that of Si will

increase(c) Resistance of both decrease(d) Resistnance of both increase

35. For Dopplers effect, which of the following is a correctstatement(I) During observer motion both frequency and

wavelength will change(II) During source motion both frequency and wavelength

will change(III) During source motion only frequency will change(IV) During observer motion only frequency will change(a) I, II (b) I, II(c) II, III (d) II, IV

36. When white light passes through a dispersive medium, itbreaks up into various colours. Which of the followingstatements is true?(a) Velocity of light for violet is greater than the velocity of

light for red colour.(b) Velocity of light for violet is less than the velocity of

light for red.(c) Velocity of light is the same for all colours(d) Velocity of light for differnet colours has nothing to do

with the phenomenon of dispersion37. An engine has an efficiency of 1/6. When the temperature

of sink is reduced by 62C, its efficiency is doubled.Temperatures of source and sink are(a) 99C, 37C (b) 124C, 62C(c) 37C, 99C (d) 62C, 124C

38. Two isothermals are shown in figure at temperatures T1 andT2. Which of the following relations is correct?

T1T2

P

V

(a) T1 > T2 (b) T1 < T2

(c) T1 = T2 (d) T1 = 21T2

39. During the experiment to determine the resistivity of a wireby a metre bridge, the jockey is moved gently along the wirefrom left to right to(a) find a deflection in the galvanometer towards left(b) find a deflection in the galvanometer towards right

(c) find no deflection in the galvanometer(d) find a maximum deflection in the galvanometer

40. The radius of curvature of a thin plano-convex lens is 10 cm(of curved surface) and the refractive index is 1.5. If theplane surface is silvered, then it behaves like a concavemirror of focal length(a) 10 cm (b) 15 cm(c) 20 cm (d) 5 cm

41. The circular head of a screw gauge is divided into 200divisions and move 1 mm ahead in one revolution. If thesame instrument has a zero error of 0.05 mm and the readingon the main scale in measuring diameter of a wire is 6 mmand that on circular scale is 45. The diameter of the wire is(a) 6.275 mm (b) 6.375 mm(c) 5.75 mm (d) 5.50 mm

42. Ammeter and voltmeter readings were recorded as 0.25 Aand 0.5 V during the experiment to determine the resistanceof a given wire using Ohm's law. The correct value of theresistance is(a) 0.125 W (b) 2 W(c) 0.75 W (d) 0.25 W

43. A wheel is rotating at 900 r.p.m. about its axis. When poweris cut off it comes to rest in 1 minute. The angular retardationin rad/s2 is(a) p/2 (b) p/4(c) p/6 (d) p/8

44. Choose the wrong statement from the following(a) a metre bridge can be used to determine the emf of a

primary cell(b) a metre bridge works on the principle of Wheatstone

bridge(c) a potentiometer is used to compare the emfs of two

primary cells(d) a multimeter can be used as an ohmmeter

45. The adjacent figure shows the position graph of onedimensional motion of a particle of mass 4 kg. The impulseat t =0 s and t = 4 is given respectively as:

3

0 4 t(s)

x(m)

(a) 0,0(b) 0, 3 kg ms 1

(c) + 3 kg ms1, 0(d) + 3 kg ms 1, 3 kg. ms1

46. In case of a p-n junction diode at high value of reverse bias,the current rises sharply. The value of reverse bias is knownas

5

(a) cut off voltage (b) zener voltage(c) inverse voltage (d) critical voltage

47. The following observations were taken while comparingthe e.m.f.s of two primary cells using a potentiometer.Balance point when E1 (Leclanche cell) in the circuit(l1 in cm) = 350Balance point when E2 (Daniel cell) is the circuit (l2 in cm)= 275The ratio (E1/E2) of emfs is approximately(a) 1.30 (b) 1.17(c) 1.27 (d) 1.5

48. A photon materializes into an electron-positron pair. Thekinetic energy of the electron is found to be 0.19 MeV. Whatwas the energy of the photon?(a) 0.38 MeV (b) 0.70 MeV(c) 1.40 MeV (d) None

49. If 10% of a radioactive material decays in 5 days, then theamount of the original material left after 20 days isapproximately(a) 60% (b) 65% (c) 70% (d) 75%

50. Lights of two different frequencies, whose photons haveenergies 1 eV and 2.5 eV respectively, successively illuminatea metal whose work function is 0.5 eV. The ratio of themaximum speeds of the emitted electrons will be(a) 1 : 5 (b) 1 : 4 (c) 1 : 2 (d) 1 : 1

DIRECTIONS (Qs. 51 and 52) : Read the following passageand answer the questions that follows :

A block of mass 15 kg is placed over a frictionless horizontalsurface. Another block of mass 10 kg is placed over it, that isconnected with a light string passing over two pulleys fastenedto the 15 kg block. A force F = 80N is applied horizontally to thefree end of the string. Friction coefficient between two blocks is0.6. The portion of the string between 10 kg block and the upperpulley is horizontal. Pulley, string and connecting rods aremassless. (Take g = 10 m/s)

10kg

15 kg

=0.6

Smooth

F = 80N

51. The magnitude of acceleration of the 10 kg block is(a) 3.2 m/s (b) 2.0 m/s(c) 1.6 m/s (d) 0.8 m/s

52. If applied force F = 120 N, then magnitude of acceleration of15 kg block will be (a) 8 m/s (b) 4 m/s(c) 3.2 m/s (d) 4.8 m/s

ASSERTION & REASON DIRECTIONS (Qs. 53 and 54) : Each of these questionscontains two statements: Statement-1(Assertion) andStatement-2 (Reason). Choose the correct answer (ONLYONE option is correct) from the following -(a) Statement-1 is false, Statement-2 is true.(b) Statement-1 is true, Statement-2 is true; Statement-2

is a correct explanation for Statement-1.(c) Statement-1 is true, Statement-2 is true; Statement-2

is not a correct explanation for Statement-1.(d) Statement-1 is true, Statement-2 is false.

53. Statement-1 : When two semiconductor of p and n type arebrought in contact, they form p-n junction which act like arectifier.Statement-2 : A rectifier is used to convert alternating currentinto direct current.

54. Statement 1 : A nucleus at rest splits into two nuclear partshaving radii in the ratio 1 : 2. Their velocities will be in theratio 8 : 1.Statement 2 : The radius of a nucleus is proportional to thecube root of its mass number.

55. A plate of mass (M) is placed on a horizontal frictionlesssurface and a body of mass (m) is placed on this plate. Thecoefficient of dynamic friction between this body and theplate is m. If a force 3mmg is applied to the body of mass (m)along the horizontal, the acceleration of the plate will be

(a) gMmm

(b)mM

mg+

m

(c)Mmg3m

(d)mM

mg+

2m

56. Two rods of length d1 and d2 and coefficients of thermalconductivities K1 and K2 are kept touching each other. Bothhave the same area of cross-section the equivalent of thermalconductivity is(a) K1 + K2 (b) K1d1 + K2d2

(c)21

2211ddKdKd

++

(d) )K/dK/d(dd

2211

21++

57. Two masses A and B of 10 kg and 5 kg respectively areconnected with a string passing over a frictionless pulleyfixed at the corner of a table (as shown in figure). Thecoefficient of friction between the table and the block is 0.2.The minimum mass of C that may be placed on A to preventit from moving is equal to

6

A

C

B

(a) 15 kg (b) 10 kg(c) 5 kg (d) 0 kg

58. A particle starts S.H.M. from the mean position. Its amplitudeis a and total energy E. At one instant5 its kinetic energy is3 E/4, its displacement at this instant is

(a)2ay = (b)

2ay =

(c)2/3

ay = (d) y = a

59. Two long parallel wires P and Q are both perpendicular tothe plane of the paper with distance of 5 m between them. IfP and Q carry current of 2.5 amp and 5 amp respectively inthe same direction, then the magnetic field at a point half-way between the wires is

(a)p

m23 0 (b)

pm0

(c)pm

23 0 (d)

pm20

60. In a circuit L, C and R are connected in series with analternating voltage source of frequency f. The current leadsthe voltage by 45. The value of C is

(a)1

2p pf fL R( )- (b)1

2 2p pf fL R( )-

(c)1

2p pf fL R( )+ (d)1

2 2p pf fL R( )+

MATHEMATICS

61. Area of triangle formed by the vertices (0, 0), (6, 0), (4, 3) is(a) 6 (b) 9(c) 18 (d) 24

62. In a box containing 100 bulbs, 10 are faulty. The probabilitythat from a sample of 5 bulbs none are defective.

(a)5

101

(b)5

109

(c) 5109

(d)51

63. If 2 sec 2a = tan b + cot b then one of the values of (a + b) =

(a) p (b) 2p

(c)4p

(d) None

64. The probability of getting the sum more than 7 when a pairof dice is tossed is

(a) 91

(b)41

(c)127

(d)125

65. The value of == -

5

1r 1rn

rn

CC

r

(a) 5 (n 3) (b) 5 (n 2)(c) 5n (d) 5 (2n 9)

66. =+=

-3

1i6

i177

14 CC

(a) 716C (b) 7

17C

(c) 817C (d) 8

61 C

67. If y = A sin wt then =55

dtyd

(a)

p-ww

2tcosA 5 (b)

p-ww

2tsinA 5

(c)

p+ww

2tcosA 5 (d)

p+ww

2tsinA 5

68. l for which l-

=-

=-- 8z

74y

32x and

6-

=--

=l- 3z

32y1x

are perpendicular equals(a) 5 (b) 6 (c) 7 (d) 8

69. The angle between the two lines 14z

23y

21x

--

=+

=+

&

21z

24y

14x +

=+

=- is

(a)

-94cos 1 (b)

-93cos 1

(c)

-92cos 1 (d)

-91cos 1

70. The contrapositive of (p q) r is

(a) r (p q) (b) ~ r (p q)

(c) ~ r ~ p ~ q (d) p (q r)

7

71. If (2, 3, 5) are ends of the diameter of a spherex2 + y2 + z2 6x 12y 2z + 20 = 0. Then coordinates of theother end are(a) (4, 9, 3) (b) (4, 3, 5)(c) (4, 3, 3) (d) (4, 3, 9)

72. Three persons A, B, C throw a die in succession. The onegetting 'six' wins. If A starts then the probability of B winningis

(a) 9136

(b) 9125

(c) 9141

(d) 9130

73. The eccentricity of the ellipse represented by25x2 + 16y2 150x 175 = 0 is

(a) 52

(b) 53

(c) 54

(d) 51

74. If f(x) = | x 2| and g(x) = f (f(x)) then for x > 10, g'(x) equal(a) 1 (b) 0(c) 1 (d) 2x 4

75. If a, b, c are in A.P., b, c, d are in G.P. and c, d, e are in H.P. thena, c, e are in(a) A.P. (b) G.P.(c) H.P. (d) None

76. The coefficient of x10 in the expansion of 15

22

x1x3

- is

(a)103

!5!10!15

(b) 103!5!10!15

(c)!5!103!15 5

- (d)83

!8!7!15

77. The mean of discrete observations y1, y2, y3,...,yn is givenby

(a)n

y in

1i=S

(b)i

y

n

1i

in

1i

=

=

S

S

(c)n

fy iin

1i=S

(d)i

n

1i

iin

1i

f

fy

=

=

S

S

78.( ) -ba-b- x)x()x(

dx is

(a) cxx2

+-b

a-b-a (b)

c)x()x(2 +-ba-b-a

(c) x)x(2

-ba-b-a

(d) none of these.

79. The spheres 01zyxzyx 222 =-+++++ and

05zyxzyx 222 =-+++++(a) intersect in a plane(b) intersect in five points(c) do not intersect(d) None of these

ASSERTION & REASON DIRECTIONS (Qs. 80 - 84) : Each of these questionscontains two statements: Statement-1(Assertion) andStatement-2 (Reason). Choose the correct answer(ONLY ONE option is correct) from the following -(a) Statement-1 is false, Statement-2 is true.(b) Statement-1 is true, Statement-2 is true; Statement-2

is a correct explanation for Statement-1.(c) Statement-1 is true, Statement-2 is true; Statement-2

is not a correct explanation for Statement-1.(d) Statement-1 is true, Statement-2 is false.

80. Let In = ( )e

n

1

nx l dx, n N

Statement-1 : I1, I2, I3 . . . is an increasing sequence.Statement-2 : ln x is an increasing function.

81. Statement1 : Range of f(x) = 24 x- is [0, 2]

Statement2 : f(x) is increasing for 0 x 2 and decreasingfor 2 x 0.

82. Let x, y, z are three integers lying between 1 and 9 such thatx 51, y 41 and z 31 are three digit numbers.Statement-1 : The value of the determinant

5 4 3x51 y41 z31x y z

is zero.

Statement-2 : The value of a determinant is zero if the entriesin any two rows (or columns) of the determinant arecorrespondingly proportional.

83. Statement-1 : Slope of tangents drawn from (4, 10) to

parabola y2 = 9x are 49,

41

Statement-2 : Every parabola is symmetric about its directrix84. Statement-1 : If x2 + x + 1 = 0 then the value of

2 222 27

2 271 1 1....x x xx x x

+ + + + + + is 54.

Statement-2 : w, w2 are the roots of given equation and

8

2x1x,1

x1x,1

x1x 3

32

2 =+-=+-=+

85. If AB = 0, then for the matrices

A =

qqqqqq

2

2

sinsincossincoscos and

B =

ffffff

2

2

sinsincossincoscos , q f is

(a) an odd number of 2p

(b) an odd multiple of p

(c) an even multiple of 2p

(d) 086. If f'(x) = (x 1) (x 2) (x 3) then f(x) in monotonically

increasing in(a) x < 1 (b) x > 3, x < 1(c) x > 3, 1 < x < 2 (d) x < 1, 2 < x < 3

87. The area enclosed by the curve y = x5, the x-axis and theordinates x = 1, x = 1 is

(a) 0 (b) 31

(c) 61

(d) None

88. An inverted cone is 10 cm in diameter and 10 cm deep. Wateris poured into it at the rate of 4cm3/min. When the depth ofwater level is 6 cm, then it is rising at the rate

(a) .min/cm49 3p

(b) .min/cm41 3p

(c) .min/cm91 3p

(d) .min/cm94 3p

89. The equation of tangent to 4x2 9y2 = 36 which areperpendicular to straight line 5x + 2y 10 = 0 are

(a) 5 (y3) =

-

2117x2

(b) 2y 5x + 10 182 = 0

(c) 2y 5x 10 182 = 0

(d) None of these

90. dxe31sece

log

2logx22x2

p

p

is equal to :

(a) 3 (b) 31

(c)233

(d) 321

9

1. (d)

CH3

CH CH2 3123

Ethyl group comes first in alphab-

atical order but IUPAC name of

C H52

CH3

Br

321 , 2-bromo-

4-ethyl-1-methyl cyclohexane. It follows lowest sumrule(i.e., lowest set of locant is preferred.)Lowest sum of locant is = 1 + 2+ 3 = 6

2. (a) The order of stability of resonating structures carryingno charge > carrying minimum charge and each atomhaving octet complete.

3. (b) +2NO = 12 [5 + 0 + 0 1] = 2 sp;

NO2 = 12 [5 + 0 + 1 0]= 3 sp2;

+4NH = 12[5 + 4 + 0 1] = 4 sp3

4. (b) In A O H, if EN of A is 2.1 then it will be neutral,as XA X0 = X0 XH. (where X is EN)

5. (b) Correct order is B < Be < O < N.

6. (c)

ClCl

ClCl

123

45

6120

Dipole moments of 2Cl and 5Cl

are vectorically cancelled.

It is due 1 Cl and 3 Cl 2m

= 2 21 2 1 22 cosm + m + m m q

= 120cos5.15.12)5.1()5.1( 22 ++ \ m = 1.5 D

7. (c) CsCl is ionic solid.8. (b) Volume of ice > volume of water & thus increase in

pressure favours forward reaction showing decreasein volume.

9. (a) EHe+ = EH 22; ELi

2+ = EH 32 ..... up to Z

10. (c)]OH][HF[]F][OH[

K2

3

a

+= and

]OH][F[

]OH][HF[K2

b = .

Therefore, Ka Kb = [H3O+] [OH] = Kw.

11. (a) Isoelectric point (pH)

= 97.52

60.934.22pKpK 21 aa =+=

+

12. (d) Let bond energy of A2 be x then bond energy of AB isalso x and bond energy of B2 is x/2.Enthalpy of formation of AB is 100 KJ/mole:

1 (d) 16 (d) 31 (c) 46 (b) 61 (b) 76 (b)2 (a) 17 (c) 32 (b) 47 (d) 62 (b) 77 (d)3 (b) 18 (c) 33 (d) 48 (c) 63 (c) 78 (a)4 (b) 19 (a) 34 (b) 49 (b) 64 (d) 79 (c)5 (b) 20 (b) 35 (d) 50 (c) 65 (b) 80 (a)6 (c) 21 (d) 36 (b) 51 (a) 66 (b) 81 (d)7 (c) 22 (d) 37 (a) 52 (b) 67 (d) 82 (d)8 (b) 23 (b) 38 (a) 53 (c) 68 (c) 83 (d)9 (a) 24 (c) 39 (c) 54 (a) 69 (a) 84 (b)

10 (c) 25 (a) 40 (c) 55 (a) 70 (c) 85 (a)11 (a) 26 (a) 41 (a) 56 (d) 71 (a) 86 (c)12 (d) 27 (a) 42 (b) 57 (a) 72 (d) 87 (b)13 (b) 28 (b) 43 (a) 58 (b) 73 (b) 88 (d)14 (c) 29 (b) 44 (a) 59 (a) 74 (c) 89 (d)15 (d) 30 (b) 45 (d) 60 (d) 75 (b) 90 (a)

ANSWER KEY

HINTS AND EXPLANATIONS

10

2 2 2 21 1A B 2AB; A B AB; 100KJ2 2

x x 2x x 4xor 100 x 100 x 400KJ

2 4 4

+ + D = -

+ - - = + - \- = \ =

13. (b) stvv

)nn(M

21

21total +

+= ,

n1 = n2 = 0.1, V1 = V2 = 1litre M1.0M total =

14. (c) 0 0.77 2( 0.44)E3

+ -=

0.77 0.883-

=0.113

= -

0.04 -15. (d) The chemical bond method gives the O.N.

O

O

S = O+4 +3 +5

O S S O

O S S O

O O

O

O O

O

: :

16. (d) CH = CH Cl2 CH CH = Cl

2 Vinyl chloride

d+ d +

17. (c) o-Nitrophenol is not sufficiently strong acid so as toreact with NaHCO3.

18. (c) Because the layer of Al2O3 (oxide) is inert, insolubleand impervious.

19. (a) Au, the gold is not attacked by acids and alkalis. Itforms AuCl3.AuCl3 further reacts with HCl to formH[Au(Cl)4] which is used in photography.

Complex3 4AuCl HCl H[Au(Cl) ]+

20. (b) 22 IKCl2ClKI2 ++

ColourVioletCClI 42 +Note: The excess of Cl2 should be avoided. The layermay become colorless due to conversion of

32 HIOtoI

HCl10HIO2OH6Cl5I 3222 +++In case of Br2 :

HCl2HBrO2ClOH2Br 222 +++21. (d) To convert covalent compounds into ionic compounds

such as NaCN, Na2S, NaX, etc.

22. (d)White ppt.

Soluble

White ppt.

24 2 4

2 4 4 2 2 2

4 2 2 2 4

Zn 2NH OH Zn(OH) 2NH

Zn(OH) 2NH OH (NH ) ZnO 2H O

(NH ) ZnO H S ZnS 2NH OH

+ ++ +

+ +

+ +

23. (b) The reagent is BaCl2 which imparts green colour toflame. BaCl2 forms chromyl chloride (which is red incolour), when treated with K2Cr2O7 and conc. H2SO4.

2 2 2 7 2 42BaCl K Cr O 3H SO+ +

2 4 4 2 2 2

Chromyl chloride(red gas)

K SO 2BaSO 2CrO Cl 3H O + + +

24. (c) Formaldehyde can not produce iodoform, as only those

compound which contains either 3|

CH CH

OH

- - group

or 3||

CH CH

O

- - group on reaction with potassium

iodide and sod. hypochlorite yield iodoform.

25. (a) (i)

CN||NC||CN

-- , (ii)

Br|

CHC|CH

3

3

-- ,

(iii)

CO||OC

|OH

-- , (iv)

OH||

OCHCC||

COH

3---

-

,

(v) H|

OC||CO

--

-

Arrange (NNN), (BrCC), (OOO), (CHH), (OOH) inincreasing atomic number. The order is ii, iii, v, i, iv.

26. (a) ClCHCl3KOH

NC [Y]300 KHCl

Cl

Cl + HCOOH

[X]27. (a) Let the rate law be r = [A]x[B]y

Divide (3) by (1) yxyx

]035.0[]012.0[]035.0[]024.0[

10.010.0

=

\ 1 = [2]x, x = 0

Divide (2) by (3) yxyx

]035.0[]024.0[]070.0[]024.0[

10.080.0

=

\ 8 = (2)y , y = 3Hence rate equation, R = K[A]0[B]3 =K[B]3

11

28. (b)

CH2 C H

CH C H2

CH2O

O

CH CH2

CH CH2

CH2Ozonolysis

29. (b) )g(H3)g(N 22 + 2 )g(NH31 x 3 3x 2x at equilibriumTotal moles,1 x + 3 3x + 2x = 4 2x = 3 (given)(Since, 4 moles = 4 atm given)\ x = 0.5

pK for dissociation of =3NH 3

22

NH2

H3

N

p

pp

= 2

3

335.02

33

5.03333

5.01

-

-

= 0.5 3)5.1( 2atm

30. (b) Let the amount of the 722 OCrK in the mixture be x g,

then amount of 4KMnO will be (0.5 x) g

\

-+

6.31x5.0

49x

= 100015.0100

where 49 is Eq. wt. of 722 OCrK and 31.6 is Eq. wt. of

4KMnO .On solving, we get x = 0.073 g

% age of 722 OCrK = %64.145.01000732.0

=

31. (c) Given (10 kW) I = 4V OR 10 kW . V4k10XV120

=W+

OR 300

kW = X + 10 kW;X = 290 kW.

X120V

10kWV

32. (b) This of example of uniform circular motion.

w = .sec/rad44.010072n2

T2

=p=p=p

;

V = Rw = 0.44 12 = 5.3 cm/sec.

33. (d) 2 3T r law; 2 30T R & 2 3sT ( 7R) > ;

32

0

s 7TT

=

; 0s T77T =

34. (b) )K70toK300(T

metalT R R semi - conductor (Al) (Si)

35. (d) (Source) motion l, n both change, (Observer) motiononly n change.

36. (b) As mv > mr therefore, vv < vr.

37. (a) From h = h-=- 1TT

,TT

11

2

1

2 = 65

611 =- ...(i)

In 2nd case : 32

621'1

T62T

1

2 =-=h-=-

.....(ii)

Using (i), T2 62 = 221 T54T

56

32T

32

==

or ,62T51

2 = T2 = 310 K = 310 273 = 37C

C99273372K37231056T

56T 21 =-====

38. (a) As isothermal at T1 is farther from the origin than theisothermal at T2, therefore, T1 > T2

39. (c) The jockey is moved so as to get the null point (i.e., nodeflection in the galvanometer).

40. (c) The silvered plano convex lens behaves as a concavemirror; whose focal length is given by

m1 f1

f2

F1

+=

If plane surface is silvered

=

==22

Rf 2m

1 1 2

1 1 1( 1) f R R

\ = m

1 1 1( 1) R R

m = m =

1 2( 1) 1 2( 1)F R R

m m\ = + =

)1(2RF

m=

Here R = 20 cm, m = 1.5

20F 20cm2(1.5 1)

\ = =

12

41. (a) Pitch = 1 mmNumber of divisions on circular scale = 200

L.C = Pitch

Number of divisions on circular scale

= 1 mm200 = 0.005 mm = 0.0005 cmDiameter of the wire = (Main scale reading + Circularscale reading L.C.) zero error= 6 mm + 45 0.005 ( 0.05)= 6 mm + 0.225 mm + 0.05 mm = 6.275 mm

42. (b) V 0.5R 2 .I 0.25

= = = W

43. (a) Angular retardation,22 1 2 12 (n n ) 2 (0 900 / 60) rad / s .

t t 60 2w - w p - p - p

a = = = =

44. (a) A metre bridge is used to determine the resistance of agiven wire and not to determine the emf of a cell.

45. (d) t < 0, vi = 0 and t > 0, vf = 3m / s

4

\ Impulse = m (vf vi) 3

4 04

= - = 3 kg ms 1

Little before 4 second 3

v m / s,4

= little after 4 second,

velocity becomes zeroTherefore, Impulse

1f i

3m(v v ) 4 0 3kgms

4- = - = - = -

46. (b) In reverse bias on p-n junction when high voltage isapplied, electric break down of junction takes place,resulting large increase in reverse current. This highvoltage applied is called zener voltage.

47. (d) 10c mf 9 N 9 9 10= =

62.7 10 Hz 2.7 MHz= =48. (c) Conservation of Energy,

energyeePhoton ++ -+

.E.KEEErereP

++= -+ of both +- + ee

We know that rest mass energy of -+ + ee is .5 MeVHence 219.5.5.EP ++= = 1.40MeV

49. (b) Let initial amount be 100 gm. disintegrated Left

100 gm 100

10100days5 10 90

90 1001090days5Next 9 81

81 1001081days5Next 8.1 73

73 100

1073days5Next 7.3 65

50. (c) Einstein equation KEmax = E Work function;

21 mv E W2

= -

Using this concept,

5.5.25.1

maxV21

maxmV21

22

21

--

=41

= or 21

maxVmaxV

2

1 =

51. (a) First, let us check upto what value of F, both blocksmove together. Till friction becomes limiting, they willbe moving together. Using the FBDs

15 kg

F

fFF

F

a2

a1f

10 kg block will not slip over the 15 kg block tillacceleration of 15 kg block becomes maximum as it iscreated only by friction force exerted by 10 kg block onit.

1 2(max)a a>

F f f10 15-

= for limiting condition as f maximum is 60N.

F = 100 NTherefore, for F = 80N, both will move together.Their combined acceleration, by applying NLM usingboth as system, F = 25a

280a 3.2 m / s25

= =

52. (b) If F = 120N, then there will be slipping, so using FBDsof both (friction will be 60 N)For 10 kg block, 120 60 = 10a a = 6 m/s.For 15 kg block, 60 = 50a a = 4 m/s.

53. (c) Study of junction diode characteristics shows that thejunction diode offers a low resistance path, whenforward biased and high resistance path when reversebiased. This feature of the junction diode enables it tobe used as a rectifier.

54. (a) ,6da =

a 3,=l

d ?=l ; a dd a 1 =

l

l

d 16 13

=l

dd

3 1 ; 26 2

= = =ll

13

If C be the critical angle, then

Sin C = 21

1

=

C = 45. As angle of incidence < 45, it will not beinternally reflected. So statement 1 is false statement 2is true.

55. (a) a = Mmgm

M plate

mBody

3 mgmfr

fr

fr = mg = Mam

56. (d) When two rods are connected in series

K/)dd(t)TT(A

Kd

Kd

t)TT(AQ

21

21

1

2

1

1

21+

-=

+

-=

2

2

1

121Kd

Kd

Kdd

+=+

\ ;

2

2

1

1

21

Kd

Kd

)dd(K

+

+=\

57. (a) Let T be the tension in the string; f = frictional forcebetween block A and table; m = minimum mass of C.For the just motion of block A on table

g)'m10(2.0g)'mm(RfT +=+m=m== ....(i)

For the just motion of block B, T = 5g ....(ii)From (i) and (ii), 5g = 0.2 (10 + m)g

or 5 = 2 + 0.2m or m = kg152.025

=-

58. (b) Total energy, E = 22am21

w ;

K.E. = )ya(m21

4E3 222 -w= .

So, 222

a

ya43 -

= or 4ay2

2 = or 2ay = .

59. (a) When current flow in both wire in same direction thenmagnetic field at half way due to P wire.

0 1 0 1 0P

I IB .5 52

2

m m m= = =

p pp

uur

(where I1= 5Amp)

The direction of Bp is downward

5 m

5 Amp 2.5 Amp

P

C

Q

Magnetic field at half way due to Q wire

pm

=p

m=

2252

IB 020Q [upward ]

[where .Amp5.2I2 = ]Net magnetic field at half way

QP BBB += =p

m=

pm

+p

m23

2000 (downward )

Hence net magnetic field at midpoint p

m=

23 0

60. (d) From figure,

tan 45 =

1w

wC

L

R

-

1w

wC

L- = R 1

ww

CR L= +

C = 1

w w( )R + = 1

2 2p pf R fL( )+

61. (b) (4, 3)

(6, 0)(0, 0) (4, 0)

Area = 21 b h = 2mt936

21

=

62. (b)109q

101p ==

\ Probability that none are defective 5

109

=

14

63. (c)bb

=b+b

=a cossin

1tan

1tan2cos2 2

sin2b = cos2a = sin (90-2a) a + b = 4p

64. (d) Sum of 7 can be obtained when (2,6), (3,5) (3, 6), (4, 4),(4,5), (4, 6)(5, 3)(5, 4) (5, 5)(5, 6)(6, 2)(6, 3)(6, 4)(6,5)(6, 6)

\ Probability of sum > 7 1536

= = 125

65. (b)n

rn

r 1

C r. n r 1. n r 1 n r 1.r. n r n n rC -

- - + - += =

- -

n r 1n r 1

n r- +

= = - +-

)2n(510n5

)4n()3n()2n()1n(n5

1r-=-=

-+-+-+-+=\=

66. (b)

717

616

716

616

615

715

616

615

614

714

3

1i6

i177

14

CCCCCC

CCCCCC

=+=++=

+++=+=

-

67. (d) y = A sinwt. dy

A cos tdx

\ = w w

22

2d y A sin tdx

= - w w

33

3d y A cos tdx

= - w w

44

4d y A sin tdx

= + w w

55 5

5d y

A cos t A sin t2dxp \ = w w = w w +

68. (c) For perpendicularity 3l 21 + 6l = 0 l = 7.69. (a) a1 = 2, b1 = 2,c1 = 1 and a2 = 1, b2 = 2, c2 = 2

1 2 1 2 1 22 2 2 2 2 21 1 1 2 2 2

a a b b c ccos

a b c a b c

+ +q =

+ + + +

2 4 2 494 4 1 1 4 4

+ -= =

+ + + +.

70. (c) Contrapositive of p q is ~ q ~ p

\ contrapositive of (p q) r is

~ r ~ (p q) i.e. ~ r (~ p ~ q)

71. (a) Let the co-ordiante of other ends are (x, y, z).The centre of sphere is C(3, 6, 1)

Therefore, x 2

3 x 42+

= =

y 3 6 y 92+

= = and z 5 1 z 32+

= = -

72. (d)4 8

3

P(E E) P(E E E E E )

5 1 5 1 5 1 ...6 6 6 6 6 6

5 5 301 ......36 6 91

+

= + +

= + =

73. (b) The ellipse

53ee1

25161

25y

16)3x( 222 =-=\=+- .

74. (c) For x > 10, f (x) = x 2.Therefore, g(x) = x 2 2 = x 4\ g(x) = 1.

75. (b) a, b, c in A.P. a + c = 2b; b, c, d in G.P..

bd = c2; c, d, e in H.P. d = ec

ce2+

2 2a c 2ce c (a c)e (c e)c c ae.2 c e+

\ = + = + =+

Therefore, in G.P.

76. (b)15

22

x1x3

-

r2r230rr15r

15

r

2r152

r15

1r

x)1(3Cx1)x3(CT

---

-+

-=

-=

Therefore, 30 4r = 10 r = 5.

Therefore, 1010515

6 3!5!10!153CT -=-= .

77. (d) Lf '(0) 0h0hLt

h)0(f)h0(fLt

2

0h0h=

--=

-+=

--

& 0hhLt

h)0(f)h0(fLt)0('Rf

2

0h0h=

+=

-+=

++

\ Lf (0) = Rf (0) ,Hence, f(x) is differentiable at x = 0

15

78. (a) I = -ba-b- )x)(x()x(dx

Put x = qb+qa 22 cossin[see the standard substitutions]

dx = qqqb-a dcossin)(2

Also, qa-b=a- 2cos)()x(

qb-a=b- 2sin)()x(

qqa-bqb-aqqqb-a=\cossin)(sin)(

dcossin)(2I 2

qqa-b=qq

a-b= deccos2

sind2 22

Ccot2C)cot(2 +qb-a

=+q-a-b

=

Now , x = qb+qa 22 cossin

qb+a=q 22 coteccosx

qb+a=q+ 22 cot)cot1(x

xxcot

-ba-

=q\ ; Cxx2I +

-ba-

b-a=\

79. (c) As the given spheres both have same cenre anddifferent radii therefore they are concentric and theydo not have any point in common. Hence they do notintersect.

80. (a) Statement II is true, as if f (x) = ln x, then

1f (x) 0x

= > (as x > 0, so that f (x) is defined)

Statement I is not true as 0 < ln x < 1, " x (1, e) andhence (ln x)n decreases as n is increasing. So that In isa decreasing sequence.

81. (d) 2

xf (x)

4 x

-=

-

\ f (x) is increasing for 2 x 0 and decreasing for0 x 2.

82. (d)5 4 3x51 y41 z31x y z

D =

5 4 3100x 51 100y 41 100z 31

x y z= + + +

5 4 31 1 1x y z

= [R2 R2 100R3 10R1]

which is zero provided x, y, z are in A.P.

83. (d)mamxy +=

09m40m16m4/91m410 2 =+--=

1 240 5

m m16 2

+ = = ; m1m2 = 169

49m,

41m 21 ==

every parabola is symmetric about its axis onlyStatement 1 is true.

84. (b) 2 21 1x 1, x 1,x x

+ = - + = -

3 43 41 1 1x 2, x x ,

xx x+ = + = +

5 65 61 1x 1, x 2x x

+ = - + = , etc.

2 3 22 3

2 31 1 1x x xx x x

+ + + + +

2 24 5

4 51 1x xx x

+ + + +

2 26 7

6 71 1x xx x

+ + + +

+........+ 2

9393

)x(1)x(

+

= (1 + 1 + 4) + (1 + 1 + 4) + (1 + 1 + 4) + ......... 9 times= 6 9 = 54.

85. (a) We have,

ffffff

qqqqqq= 2

2

2

2

sinsincossincoscos

sinsincossincoscosAB

fq+fqfqfqq+ffq

ffq+fqqfqfq+fq=

22

22

22

22

sinsinsinsincoscossinsincossincoscos

sincossincossincossinsincoscoscoscos

fqfqfqfq

f-q=sinsincossinsincoscoscos

)cos(

Since, AB = 0, 0)cos( =f-q\

f-q\ is an odd multiple of 2p

16

86. (c) When x > 3, f '(x) > 0; when 2 < x < 3, f '(x) < 0; when 1