Narayana IIT Academy 10-01-15_Sr.IIT-Z (IZ) CO-SPARK_JEE MAIN_CTM-6

NARAYANA IIT ACADEMYINDIASec: Sr.IIT-Z (IZ) CO-SPARK

JEE MAIN

Dt: 10-01-15Time : 3 Hours

CTM-6

Max Marks : 360

KEY SHEET

PHYSICS

1)2)3)4)5)6)7)8)9)10)

2212342432

11)12)13)14)15)16)17)18)19)20)

3443314221

21)22)23)24)25)26)27)28)29)30)

4424424323

MATHS

31)32)33)34)35)36)37)38)39)40)

2211241122

41)42)43)44)45)46)47)48)49)50)

1111131112

51)52)53)54)55)56)57)58)59)60)

4312312211

CHEMISTRY

61)62)63)64)65)66)67)68)69)70)

2321442213

71)72)73)74)75)76)77)78)79)80)

2441313431

81)82)83)84)85)86)87)88)89)90

2234322441

PHYSICS SOLUTIONS

1.(B) Let initial pressure, volume, temperature be P0, V0, T0 indicated by state A in PV diagram. The gas is then inochorically taken to state B (2P0, V0, 2T0 ) and then taken from state B to state C (2P0, 2V0, 4T0) isobarically.

Total heat absorbed by 1 mole of gas

= Cv (2T0 T0) + Cp (4T0 2T0)

= R T0 + R 2T0 = RT0

Total change in temperature from state A to C is

= 3T0

Molar heat capacity = = = R.

2.(B) As AB is common and O1B = BI

AO, BA and BAI are congruent

By symmetry AI is perpendicular to O1 to O2

and

BAI = 45

and

3.A (CONEAPTUAL)

4.C (CONEAPTUAL)

5.(C) for M1 : V = 60, m1 = 2

for M2 : u = + 20. f = 10 v = 20

M2 = M = M1 M2 = +2

6.D (CONEAPTUAL)

9.(C) = =

For Y = 50X = 1375.0oX

11.(C) Energy of photon is given by mc2 now the maximum energy of photon is equal to the maximum energy of electron = eV.

hence mc2 = evm = = 3.2 1032 kg

12.(D) =

Clearly

13.(D)BC is isochoric. VB > VA , VB = VC , VD > VC

14.(C) Energy released = (B. E. of product BE of reactant)

= (80 7 + 120 8 200 6.5) = 220 MeV.

15.(C) Just before opening the switch, the current in the inductor is /R, Energy stored in it =

This energy will dissipate in the resistor R1 and R2 in the ratio

16.(A) BH = Bv cot = B cot

Hence the induced e.m.f. in the rod is B v cot

17.(D) The electron ejected with maximum speed Vmax are stopped by electric field E=4N/C after

travelling a distance d = 1 m

\

= eEd = 4eV

The energy of incident photon == 6.2 eV

From equation of photo electric effect

= hu f0

f0 = 6.2 4 = 2.2 eV.

18.B (CONCEPTUAL)

19.(A) E = =Bbv = B 2 102 20 = 0.40 B

t = = 5 104 sec = 500 sec

t = = 3 103 sec = 3000 sec

20.(A) When switch K1 is opended and K2 is closed it becomes LC circuit so applying energy conservation :

= Li2; Q0 = Ceq V =V = (20 106)

= (0.2 103) i2 i = 1 A

21.(D) Heat absorbed by gas in three processes is given by

QACB = + WACBQADB = ; QAEB = + WAEB

The change in internal energy in all the three cases is same. And WACB is +ve, WAEB is ve.

Hence QACB > QADB > QAEB

22.(D) The image is erect hence, mirror must be between object & image. Virtual image of real object is diminshed, hence mirror is convex.

23.(B)

24.(D) Shift of fringe pattern = (m 1)

\

25.(A) (Z 1) =

=

Z = 27

26.(B) Time constant = = 50 msec

so i = 0.633 imax = 0.633 E =

27. (D) From the rating of the bulb, the resistance of the bulb can be calculated.

R = = 100

For the bulb to be operated at its rated value the rms current through it should be 1A

Also Irms =

1 =

L =

28. (C) XL = XC at resonance, = 1, for both circuit

29.(B) P = VI

For secondary:

V2 = = = 40 volts

For an ideal transformer (100%5555 efficient)

Pinput = Poutput V1 I1 = V2I2

I1 == 2.5 A.

30.(B) will increase to 3 due to decrease in the energy of bombarding electrons. Hence, no characteristics x-rays will be visible, only continuous X-ray will be produced.

MATHS SOLUTIONS31.Use

32.

33.

is the only solution of the equation

34.L.H.S = .

35. for

for

36.

.

37.

38.From

39.Conceptual

40.Conceptual

41.

42.Conceptual

43.Conceptual

44.We have

odd factors of the form are neither multiples of 2 nor multiples of 3. So the factors may be if which just 5 and 35 are of the form . Their sum is 40.

45.For ; is divisible by 240. Thus, when x is divided by 240, the remainder is .

46.

47.We can choose one denoination in ways, then 3 cards of this denomination can be chosen in ways and one remaining card can be chosen in ways. Thus, the total number of choices is

.

48.The total number of cases is .

number of favourable ways .

Thus, probability of the required event .

49.

50.Total number of ways of choosing four cards out of 52 is . The number of ways of choosing one card from each suit is

Thus , probability of the required event is

51.Conceptual52.

53.

54.Let d be the common difference of the A.P. , then

Thus, minimum possible value of b is , that is the case when d = 0.

55.We have upto

upto

56.Conceptual

57.The discriminant D of the quadratic equation is given by

As a, b, c are real ,

Also, as

Thus, .

Therefore, the equation has real and unequal roots

58.The discriminant D of the equation is given by

If , then both the roots of are real.

Also, since ,.

Therefore, in this case both the roots and are negative

If , the both the roots of are imaginary and are given k by

Both these roots have negative real parts.

59.Conceptual

60.Conceptual

CHEMISTRY SOLUTIONS

61.Syn addition of H2 takes place. Hence (b) is only optically active

62.Addition of HCl in presence of H2O2 is marconicoffs addition only

63.Kolbeys Electrolysis

64.Marconicoffs addition of water

65.Electron donating capacity is NH2>OH>CH366.Freidal crafts alkylation

67.Anti elimination requires Cl and H atoms must be frans to each other

68.Stability of carbocation Aromatic > non aromatic > Anti aromatic

69.

70.Conjugation is preferred & Benzyl carbanion is stable

71.Phenyl-Oxygen bond is not cleaved only benzyl-oxygen bond is cleaved

72.Conceptual

73.

74.Aldol condensation

75.Condensation reaction

76. The +M effect of NH2 reduces the electrophilicity of carbonyl carbon also is a poor leaving group

77.Electron with drawing groups increases reactivity but electron donating groups decreases reactivity

78.

-Keto acids undergo decarbonfication

79.Acyl-oxygen eleavage bimolecular mechanism

80.In basic medium is stronger donar than

81.Conceptual

82.R-NH2 stronger base than

83.Acidic amino acids will have low Isoelectric points. at pH=7 it exists as anion

84.Conceptual

85.

86.Conceptual

87.Polyester

88.Conceptual

89.Conceptual

90.Conceptual

12Sr.IIT-Z (IZ)_JEE-MAIN_Solutions Page 10

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