iit jee - mains model test paper -1 (physics, chemistry, maths) - solutions

7/24/2019 IIT JEE - Mains Model Test Paper -1 (Physics, Chemistry, Maths) - Solutions

1/10

Max Marks:36

KEY & HINTS

PHYSICS

1 2 3 4 5 6 7 8 9 10

C C B B B A A D B B

11 12 13 14 15 16 17 18 19 20

A B A D B B A A B C

21 22 23 24 25 26 27 28 29 30

C A A A C B D B C A

MATHS

31 32 33 34 35 36 37 38 39 40

A D C B D B D B A C

41 42 43 44 45 46 47 48 49 50

B C D C B C C D B C

51 52 53 54 55 56 57 58 59 60

B B B B B A C B D D

CHEMISTRY

61 62 63 64 65 66 67 68 69 70

C D A D B B A A C B

71 72 73 74 75 76 77 78 79 80

A B D B D B C C B B

81 82 83 84 85 86 87 88 89 90

D D A A A B C D B D

PHYSICS SOLUTIONS

1. Conceputal

2. Conceputal

3. Conceputal

4.


2/10

Page 2

5. L-conservation 2

2 12 2 6cm cm

L ML MvL LMv v v

P-conservation 22 2 6

cm

L L Lv v v

3v

L

6. v vnRTPdV nC dT dV nC dTV

32

dV dT V T

2 3V CT , where C is a constant.

7. Induced electric field will have lines of force in the form of concentric circles and every segment has

their own enduced emf by Faraday law of electromagnetic induction.

8. Conceptual

9. Conserving moment of system along rod.

By work energy theorem :

10. Let v be the velocity of the engine and V be the velocity of sound. The frequency of the sound heard

as the engine approaches the observer is given by

The frequency of the sound heard as the engine recedes from the observer is given by

It is given that

The difference in the frequencies of the sound heard is

11. Conceptual

12. Conceptual

13. Conceptual

14. for wire of radius b is


3/10

Page 3

15. 2r

r ( )2

ll

2r l

2r

l

16.

17. If there will be no current in G. As the potential difference across resistance equal to then

18. FBD of cylinder and block are as shown by Newtons laws

402Tfs= 8a (1)

Tfs= 4a/2 (2)

Subtracting equation (2) from equation (1)

403T = 6a

T = (406a)/3Also, by = I, we get

T R + fsR =3a

I2R


4/10

Page 4

T + fs= 3Ia/2R2

(406a)/3 + (4012a)/3 = 3Ia/2R2 a = 80/(18 + 9I/2R

2)

As = I= I (3a/2R)

= I= I (3a/2R)

2

3I 80

9I2R18

2R

3 80 80

N m18 9 9

19. Conceptual

20. mv2/r = GMm/r2

mvr = nh/2

= h/mv

min= h2/2GMm

2

21. For V = 0, x = amplitude

AmplitudeE

A

For x = 0, V = Vmax

maxEVB

Vmax= A

E

AB

BE

A

BT 2

A

Dimensions of Ax2

= dimensions of BV2

Dimensional formula for1 2

2

2

A [LT ][T ]

B [L ]

.

22. Current 0 0 0V V sin t V cos t

iR

0 0

V V 2 sin( t 45 )

R

T2

0 0rms T

0

i dt V 2i

Rdt

.

23. i + eA = 60

i + e = 120

and i 30 = ei = 75, e = 45

i = 45, e = 75.

24. When the oil is poured and fraction of ice in the water decreases. Volume of ice melted into water >

volume of water displaced by ice So water level rises Overall volume of ice will decrease as it melts.

So oil's upper level falls.

25. Velocity of efflux is 2g

2

y y

1s u t gt

2 ; x xs u t

26. ForF

a =M + m

no slipping between m and M


5/10

Page 5

For no toppling of m

27. Conceptual

28. To get for curved surface

Use west d=3cm


6/10

Page 6

29. Energy stored in the inductor = heat produced

=

=

Hence (C) is the correct answer.

30.

Magnitude of induced emf

= constant

So, it a case of charging of a capacitor in C R circuit. Hence of

Where


7/10

Page 7

MATHS SOLUTIONS31) Two persons between A and B be filled in 6.5 ways. A,B be rearranged in 2 ways. Now taking these

4 members as a group the 5 persons can be rearranged in 120 ways

32) Let the ratio of roots be :1, then

2 2 21 p l

q m

33)

Cos= -4/5, then sin= 3/5

34) Use l-hospital rule

35)

0

2

lim

,2

y

f x y f xf x kx

y

f x kx

xf x k Find k and

36)

2 22 2

2 2 1 1 5 5a a a

37) Put tan2

xt

38) 2 2cos cos sin

axax ee bx dx a bx b bx

a b

39) Given integral =1 2

2

0 1

x dx xdx

40) 0.08dy f x x

41) B is the image of (5, 7) in the line x+3y=16

42)

Clearly 1 2 1 2 1 20, 0c c a a b b , hence obtuse angle bisector is2 7 1

2 5 2

x y x y

43) Req area = 11r S for the point C

44) Tangent with slope 1 is 2x2y +1 =0, hence the point of contact is (1/2, 1)

45)21 4

2c m

m

46) External angle bisector is the tangent at /4

47) Conceptual

48) Use the formula of cos(A+B+C)

49) Eliminate r from the given equations

50)

1 11 1cos cos2 2

x x

51)

b=5 and 2 2 2b a c and c-a = 1


8/10

Page 8

52) length of the altitude = 1 2

1 2

2r r

r r

53) 21 2, 2 , 2x w w

54)

Use1

1

1z

z

2

2

25z

z

55) The given lines are concurrent implies k = 1

56)

P = 2 1 2

3,1, 1 15 , ,3 3 3

57) Conceptual

58) 1 6 111

35 25

gof g

59)

x x is satisfied by all integers and negative real numbers

60)

Replace x by x+99


9/10

Page 9

CHEMISTRY SOLUTIONS

61. Conceptual

62. Conceptual

63. 4 45HIO 5HIO 2Glu cos e 5HCOOH HCHO; Fructose 3HCOOH 2HCHO CO

64. Conceptual

65.

OHCONaClHClCONagmgm

225.36210 6

32 22

Eq.wt of Na2CO3= 106/2 = 53 gm

66. For adiabatic changes dq = 0 hance 0Tdq

S

67. Conceptual

68.

HInI

PP nKinH

log

During colour change HInIn . So PH= 5

69. Conceptual

70. As C2has max. bond order = 2, hence max. B.E & min. bond length.

71. Lets total no. of moles of the gas be n, of which n1are in the larges sphere & n2in the smaller sphere

after the stop cock is opened

N = n1+ n2& pV = nRT

RT

Vp

RT

Vp

RT

pV

2

|

1

|

1 2

12

2|

2

2

TT

pTp

72. Lattice energy of hydrides of alkalimeter decrease down the gp, hence stability of hydrides &reactivity of GPIA elements with H2decreases.

73. RTEiiieAK

where i = 1,2,3..

(1)RTEaAeK

(2)

Putting 1 toRTE

RTERTE

eA

eAeA

K

KKK

2

31

22

2

3

33

1

2

2

3

3

1

.

....3.3

321 231

2

2

3

3

1 ...3 EEE

RTeA

AA

(3)

Now comparison 2 with 3 we get the ans.

74.

OHBaSOClCrOSOKSOHOCrKBaClAd

24Re

2242427222 32232


10/10

Page 10

OHNaClCrONaNaOHClCrO

BYellowC24222 224

COONaCHPbCrOCrONaPbCOOCHCYellow

344223 2

75.M

E C tw

316

500 2 160 10 1600.1 J KJ

(minus sign is used as heat is evolved)

76. Due to the absence of d-orbitals, F2does not combine with F-to from

3F ion.

77. Conceptual

78. Conceptual

79. Conceptual

80. Conceptual

81. Conceptual

82. Conceptual

83. Conceptual

84. Conceptual

85. Conceptual

86. Conceptual

87. Conceptual

88. Conceptual

89. Conceptual

90. Conceptual

iit jee - mains model test paper -1 (physics, chemistry, maths) - solutions

Documents