all india test series for iit-jee

7/29/2019 ALL INDIA TEST SERIES FOR IIT-JEE

1/16

CRASH COURSE

for

IIT-JEE / AIEEE / PMT

Course Feat ures

59 , Ni t i Khand 3 Ind i rapuram (GZB. ) con t . 991 08 17 866 , 999 049 59 52

Intensive Crash Course b IITians & NITians


2/16

AIEEE

FULL TEST - 1

Time: 3 hours Maximum marks: 432

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONS

A. General:

(i) The Test Booklet consists of 90 questions. The maximum marks are 432.

(ii) There are three sections in this paper consisting of Mathematics, Physics & Chemistry having 30 questions each.

Part A CHEMISTRY (144 marks) Question No. 4 to 9 and 13 to 30 consist of FOUR (4) marks each and QuestionNo. 1 to 3 and 10 to 12 consist of EIGHT (8) marks each for each correct response.

Part B PHYSICS (144 marks) Questions No.33 to 49 and 54 to 60 consist of FOUR (4) marks each and QuestionNo. 31 to 32 and 50 to 53 consist of EIGHT (8) marks each for each correct response.

Part C MATHEMATICS (144 marks) Question No. 61 to 69, 73 to 81 and 85 to 90 consist of FOUR (4) markseach and Question No. 70 to 72 and 82 to 84 consist of EIGHT (8) marks each for each correct response.

(iii) Candidates will be awarded marks as stated above in instruction No. (ii) for correct response of each question 1/4 (onefourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score willbe made if no response is indicated for an item in the answer sheet.

(iv) Mark only one correct answer out of four alternatives.

(v) Use Blue/Black Ball Point Pen only for writing particulars/ or any marking.

(vi) Use of calculator is not allowed.

(vii) Darken the circles in the space provided only.

(viii) Use of white fluid or any other material which damages the answer sheet, is not permitted.

B. Filling the OMR SHEET:

Please read carefully the instructions printed on the OMR SHEET before marking your response.

TEST ID 00030403


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AIEEE Full Test - 1

1

PART A: CHEMISTRY

1. The two particles A and B have de-Broglie wavelengths 1 nm and 5 nm respectively. If mass of Ais four times the mass of B, the ratio of kinetic energy of A and B would be(a) 5 : 1 (b) 25 : 4 (c) 20 : 1 (d) 1 : 5

2. For a radioactive element, a graph of0

Nlog

Nvs time has a slope equal to

(a) 2.303+ (b)2.303

(c)

2.303

+ (d) 2.303

3. n Butane reacts with 2Br at 130C to give mainly

(a) (b) H C3 CH2 CH2 CH2 Br

(c) H C3 C CH3

CH3

Br

(d) None of these

4. An oxide of nitrogen is reddish brown and paramagnetic at room temperature but it decolourisesand also loses its paramagnetism on freezing it. The oxide at room temperature is

(a) Pure 2NO (b) Pure 2 4N O

(c) equilibrium mixture of 2 4N O and 2NO (d) 2 5N O

5. The following data were obtained at a certain temperature for the decomposition of ammonia incontact with tungsten:

P (mm) 50 100 200

Relative 1/2t 3.64 1.82 0.91

The order of the reaction is?(a) 2 (b) 1 (c) 3 (d) zero

6. In sodium nitroprusside, the oxidation number, co-ordination number and EAN of iron arerespectively(a) + 3, 6, 36 (b) +3, 6, 35(c) +3, 3, 36 (d) +6, 3, 35

7. Which carbocation among the following is most stable?

(a) ( )6 5 2C H CH+ (b)

(c) ( )3 2CH CH+ (d) ( )3 2CCl CH

+

8. Consider the species 3 2NO , NO + and 2NO

. Pick up the correct statement

(a) The hybrid state of N in all the species is same.

(b) The shapes of both 2NO+ and 2NO

is bent while 3NO is planer.

(c) The hybrid state of N in 3NO and 2NO

is same.

(d) The hybrid state of N in 2NO+ is sp2.


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AIEEE Full Test - 1

2

9. Which of the following is not true about 2 6B H ?

(a) It contains two types of B H bonds (b) It contains on B B bond(c) It is an electron deficient molecule (d) It contains multicentre bonds

10. In the accompanied diagram indicating R TE ,E and PE as the energies of reactants, activatedcomplex and products respectively. Which of the following is correct?

(a) Forward reaction is slow (b) Backward reaction is fast(c) Reaction is exothermic (d) Reaction is endothermic

11. Given

( ) ( ) ( ) ( )3 1g 2 g 3 g gNH 3Cl NCl 3HCl ; H+ +

( ) ( ) ( ) 22 g 2 g 3 gN 3H 2NH ; H+ +

( ) ( ) ( ) 32 g 2 g gH Cl 2HCl ; H+

The heat of formation of ( )3 gNCl in the terms of 1 2H , H and 3H is ?

(a) 2f 1 3H 3

H H H2 2

= + (b) 2f 1 3

H 3H H H

2 2

= +

(c) 2

f 1 3

H 3H H H

2 2

= (d) None of these

12. The conductivity of the saturated solution of some bivalent salt XY is 6 1 13.06 10 ohm cm and its equivalent conductivity is -1 2 -11.53ohm cm equivalent . The value of spK of XY is ?

(a) -64 10 (b) 92.5 10

(c) 132.5 10 (d) 61 10 13. 3- Methyl -1- butene on oxymercuration demercuration yields as the major

product?(a) 3-Methyl-2-butanol (b) 2-Methyl 2- butanol(c) 3-methyl -1-butanol (d) 2-Methyl-1-butanol

14. Amongst the following, the compound that is both paramagnetic and coloured is?

(a) 2 2 7K Cr O (b) ( ) [ ]4 62NH TiCl

(c) 4VOSO (d) ( )4 6K Fe CN

15. The number of sigma and pi bonds in the structure given below are

(NC) C2 CN(CO)2C H2 5

(a) 17, 9 (b) 17, 7(c) 15, 6 (d) 17, 5


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AIEEE Full Test - 1

3

16. The major role of fluorspar 2CaF , which is added in small quantities in the electrolyticreduction of alumina dissolved in fused cryolite, is(a) to act as catalyst

(b) to make the fused electrolyte less conducting(c) to lower the temperature of melt(d) to decrease the rate of oxidation of carbon at the electrode

17. Which carbohydrate cannot be metabolized by human body?(a) Amylose (b) Cellulose(c) Maltose (d) Amylopectin

18. ( )10 500/T1X Y K 10 .e ; =

( )12 1000/T2X Z K 10 .e =

At what T both 1K and 2K are equal ?

(a) 500 K (b)500

K4.606

(c)4.606500

K (d)2.3035000

K

19. Which among the following is hydrolysed most easily?

(a) 3 2 5CH COOC H (b) 3 2CH CONH

(c) 3CH COCl (d) 3 2(CH CO) O

20. The correct order of acid strength is?

(a) 2 7 2 4 10Cl O SO P O> > (b) 2 2 5 3CO N O SO> >

(c) 2 2 3Na O MgO Al O> > (d) 2K O CaO MgO> >

21. A compound is made by mixing cobalt (III) nitrite and potassium nitrite solutions in the ratioof 1 : 3. The aqueous solution of the compound showed 4 particles per molecule whereasmolar conductivity reveals the presence of six electrical charges. The formula of thecompound is?

(a) ( )2 23Co NO .2KNO (b) ( )2 23Co NO .3KNO

(c) ( )3 2 6K Co NO (d) ( )2 4K Co NO

22. What is true about the gas that diffuses through the porous plug at1

th6

of the rate of diffusion of

dihydrogen gas?

(a) The molar mass of the gas is 72 kg mol1

(b) It is one of the structural isomer of 5 12C H (c) The V.D. of the gas is 72(d) The gas is lighter than dihydrogen

23. The most unlikely representation of resonance structures of p-nitrophenoxide ion is?

(a)

(b) (c)

(d)


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AIEEE Full Test - 1

4

24. A molecule of white phosphorus does not have(a) Six P P single bonds (b) Four P P single bonds(c) Four lone pair of electrons (d) PPP bond angle of 60

25. What electronic transition in Li++ produces the radiation of the same wavelength as the firstline in the lyman series of hydrogen?(a) n = 4 to n = 2 (b) n = 9 to n = 6(c) n = 9 to n = 3 (d) n = 6 to n = 3

26. The permissible values of ' ' for electron belonging to fourth energy level are

(a)1

0, , 22

(b) 1, 2, 3

(c) 0, 1, 2, 3 (d) 1, 2, 3, 4

27. 5.6 litres of an unknown gas at NTP requires 12.5 calories to raise its temperature by 10C atconstant volume. Then atomicity of the gas is ?(a) Monoatomic (b) Diatomic(c) Triatomic (d) None of these

28. Which of the following has highest value of vant Hoff factor?

(a) 2 4K SO (40% Ionised) (b) KBr (50% ionised)

(c) ( )4 6K Fe CN (20% ionised) (d) 3FeCl (30% ionized)

29. In the sequence of reactions,

,The product B is ?(a) Benzyl alcohol (b) 2-phanyl ethanol(c) 1-phenyl ethanol (d) Quinol

30. The maximum kinetic energy of photoelectron ejected from a metal is x when it is irradiatedwith radiation having frequency twice the threshold frequency.If the frequency of the incident radiation is doubled. The maximum K.E. of the photoelectronswould become(a)x (b) 2x (c) 3x (d) 4x

PART B: PHYSICS

31. A solid sphere of mass 2kg is resting inside a cube as shown in figure. The cube is moving with a

velocity v (ti 2tj)= +

m/s. The sphere is at rest with respect to cube. Total force exerted bysphere on the cube [g = 10 m/s2]

(a) 488 (b) 260 N

(c) 26 N (d) 580 N


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AIEEE Full Test -1

5

32. Three rods made of same material and having the same cross-section have been joined as shownin figure. Each rod is of the same length. The left and right ends are kept at 0C, 90C & 60C.The temperature of the junction of the rods will be

(a) 45C (b) 50C (c) 55C (d) 6033. A body is moving with a speed 1 m/s and a force F is needed to stop it in a distance x. If the

speed of the body is 3 m/s the force needed to stop it in the same distance x will be(a) 1.5 F (b) 3 F (c) 6 F (d) 9 F

34. Two perfect gases at absolute temperatures 1 2T & T are mixed. There is no loss of energy. The

temperature of the mixture if the masses of the molecules are 1 2m & m and the number of

molecules in the gases are 1 2n & n (both gases are of same nature)

(a) 1 2T TT

2+

= (b) 1 2T T T=

(c) 1 2 2 1

1 2

n T n T

n n+

+(d) none of these

35. An ideal gas is taken through the cycle A B C A as shown in figure. If the heatsupplied to the gas in the cycle is 5J. The work done by the gas in the process C A is

(a) 25 J (b) 10 J(c) 15 J (d) 20 J

36. Light from source consists of two wavelength 1 26500 & 3900 = = . If D = 2m andd = 6.5 mm. The minimum value of y where the minima of both the wave lengths coincide.(a) 0.1 mm (b) 0.2 mm (c) 0.3 mm (d) 0.4 mm

37. Figure shows on irregular block of material of refractive index 2 . A ray of light strikes the faceAB at an angle of 45 with normal. Where will the final image formed (AB = 3m)

(a) inside the slab (b) at 6 m from CD(c) data insufficient (d) at infinity

38. An isolated hydrogen atom emits a photon of 10.2 eV recoil speed of hydrogen atom(a) 3.25 m/s (b) 3 m/s (c) 6.2 m/s (d) 1 m/s

39. Thermal energy of a thermal neutron is order of(a) 105 J (b) 105 J (c) 1010 J (d) 1021 J


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AIEEE Full Test - 1

6

40. The ratio of time constant in charging and discharging in the circuit shown in figure is

(a) 1 : 1 (b) 3 : 16 (c) 4 : 3 (d) 3 : 4

41. In an A.C. current given by 0 1I I I cos t= + then its r.m.s. value will be

(a) 0 1I I

2

+(b) 0

I

2(c) 0 1

I I

2

(d)

22 10

II

2+

42. Reading of ammeter is 2A. The value R is

(a) 2 (b) 3 (c) 4 (d) 6

43. Positive charge in a one mole of Li+ ion

(a) 191.6 10 C+ (b) 429 10 C

(c) 194.8 10 C (d) None44. A motor drives a body along circle with constant speed. The power P developed by the motor

must vary with time t as

(a) (b)

(c) (d)

45. A particle of mass m is moving in a circular path of constant radius r such that its centripetal

acceleration Ca is proportional tont (where t is time). Then the power p is proportional to

(a) n 1t (b) t (c)n 2

nt+

(d)3n 12t

46. A uniform rod AB of mass m & length '2 ' is at rest on a smooth horizontal surface. An impulseP is applied to the end B. The time taken by the rod to turn through 180 is

(a)m

6P

(b)m

3P

(c)2m

3P

(d)m

12P

47. For what condition wave speed in sine wave is greater than the particle speed

(a) A2

(c) A

>

(d) A

i being identity function is(a) 81/7 (b) 5/3(c) 91/7 (d) none of these

62. Let 1z and 2z be two non zero complex numbers such that1 2

2 1

z z1

z z+ = , then the origin and

points represented by 1z and 2z

(a) lie on a straight line (b) form a right triangle(c) form an equilateral triangle (d) none of these

63. If

2 0 1

A 2 1 3 ,1 1 0

=

then 2A 5A 6I + is equal to

(a)

1 1 3

1 1 10

5 4 4

(b)

1 1 5

1 1 4

3 10 4

(c) 0 (d) I

64. If ( )7tan xdx f x= then

(a) ( )f x is a polynomial of degree 8 in tan x

(b) ( )f x is a polynomial of degree 5 in tan x

(c) ( ) 6 4 21 1 1

f x tan x tan x tan x log cos x C6 4 2

= + + +

(d) ( )f x is a polynomial of degree 6 in tan x

65. The curve satisfying the differential equation 2(1 x )y ' xy ax + = are

(a) ellipses and hyperbolas (b) ellipses and parabola

(c) ellipses and straight lines (d) circles and ellipses

66. The number of real solution of ( )1 1 2tan x x 1 sin x x 1 / 2 + + + + = is

(a) 0 (b) 1(c) 2 (d) infinite

67. If z 25i 15 , then |maximum arg (z) minimum arg (z)| equals

(a) ( )12cos 3 / 5 (b) ( )12cos 4 / 5

(c) ( )1/ 2 cos 3 / 5 + (d) ( ) ( )1 1sin 3 / 5 cos 3 / 5


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AIEEE Full Test - 1

10

68. If 1

b c a b a

c a b c b

a b c a c

+

= +

+

and 2

a b c

b c a

c a b

= , then 1 2 equal to

(a) 0 (b) 3abc

(c) 6abc (d) 3 3 32(a b c )+ +

69. The summ

i 0

10 20

i m i=

(where

p0

q

=

if p < q) is maximum where m is

(a) 5 (b) 10 (c) 15 (d) 2070. Let A be the set of all determinants of order 3 with entries 0 or 1 only, B be the subset of A

consisting of all determinants with value 1, and C be the subset consisting of all determinantswith value 1. Then if n (B) and n(C) denote the number of elements in B and C, respectively,we have

(a) C = (b) ( ) ( )n B n C= (c) A B C= (d) ( ) ( )n B 2n C=

71. The value of( )

( )

2

2x

1 cos ax bx clim

x

+ +

where and are the roots of 2ax bx c 0+ + = is

(a) ( )2

a b (b)( )

2

2

(c)( )

2a

2

(d) none of these

72. If ( ) 2 2f x x 2bx 2c= + + and ( ) 2 2g x x 2cx b= + are such that min ( ) ( )f x max g x> ,then relation between b and c, is(a) no relation (b) 0 < c < b/ 2

(c)b

c2

< (d) c 2 b>

73. The greatest value of the term independent of x, as varies over R, in the expansion of20

sinxcos

x

+

is

(a) 20C10 (b)20C15 (c)

20C19 (d) none of these

74. The number of rational terms in the expansion of ( )6

31 2 5+ + is

(a) 7 (b) 11 (c) 12 (d) none of these

75. Coefficient of 100x in the expression( ) ( )

2 3a bx a bxa bx

....1! 2! 3!

+ +++ + + + upto is

(a) a 100e b / 99! (b) ( )a 100e b / 100!

(c) a 98e b /100! (d) none of these


13/16

AIEEE Full Test -1

11

76. Let f be a function defined on R by ( ) [ ] [ ]f x x x x= + then

(a) f is not continuous at every x I (b) f is not continuous at every x R ~ I (c) f is a continuous function (d) none of these

77. Let 2h(x) min{x, x }= for x R . Then which of the following is not correct(a) h is continuous for all x (b) h is differentiable for all x(c) h '(x) 1= for all x 1= (d) h is not a differentiable function at least two points

78. The image of the interval [-1, 3] under ( ) 3f x 4x 12x= is

(a) [-2, 0] (b) [-8, 72](c) [- 8, 0] (d) [8, 72]

79. ( )2

dxfog x C

2 3x x= +

then

(a) ( ) ( )1 2x 3f x sin x,g x17

= = (b) ( ) ( )1 2x 3f x tan x,g x17

+= =

(c) ( ) ( )12x 3

f x sin x,g x17

+= = (d) none of these

80. The value of2x 12

0x dx

+ , where [x] is the greatest integer less than or equal to x is(a) 2 (b) 8/3(c) 4 (d) none of these

81. If algebraic sum of distance of a variable line from points (2, 0), (0, 2) and (-2, -2) is zero, then

the line passes through the fixed point(a) (-1, -1) (b) (0,0)(c) (1, 1) (d) (2, 2)

82. Let ( ) ( ) ( )( )n

k 1f x cos 2k 1 x i sin 2k 1 x

== + then ( )( ) ( )( )Ref x '' i Im f x ''+ is equal to

(a) ( )2n f x (b) ( )4n f x

(c) ( )2n f x (d) ( )4n f x

83. The maximum and minimum value of ( ) 2f x absin x b 1 a cos x c= + + lie in the interval

(assuming a 1,b 0< > )

(a) [ ]b c, b c + (b) ( )b c,b c +

(c) [ ]c b, b c + (d) none of these

84. The value of16 1

1tan x 1dx is

(a)16

2 33

+ (b)

42 3

3

(c)4

2 33

+ (d)16

2 33


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AIEEE Full Test - 1

12

85. Let 0 / 2< < be a fixed angle. If P (cos ,sin )= and Q (cos( ),sin( ))= then Qis obtained from P by(a) clockwise rotation around the origin through an angle

(b) anticlockwise rotation around the origin through an angle (c) reflection in the line through origin with slope tan(d) reflection in the line through the origin with slope tan(/2)

86. If two lines represented by the equation 3 2 2 3ax bx y cxy dy 0+ + + = are at right angles then2 2a d ac bd+ + + is equal to

(a) 1 (b) 0(c) 1 (d) ab + cd

87. An equation of the chord of the circle 2 2 2x y a+ = passing through the point (2,3) farthest fromthe centre is

(a) 2x 3y 13+ =

(b) 3x y 3 =

(c) x 2y 4 0 + = (d) x y 1 0 + =

88. Equation of the plane through three points A, B, C with position vectors 6i 3j 2k,3i 2 j 4k,5i 7 j 3k + + + + + is

(a) ( ) r. i j 7k 23 0 + + = (b) ( ) r. i j 7k 23+ + =

(c) ( ) r. i j 7k 23 0+ + = (d) ( ) r. i j 7k 23 = 89. If the two regression coefficients are positive then

(a) YX XY1/ b 1/ b 2 / r+ > (b) YX XY1/ b 1/ b 2 / r+ <

(c) YX XY1/ b 1/ b r / 2+ < (d) none of these90. The number of times a fair coin must be tossed so that the probability of getting at least one head

is at least 0.95.(a) 5 (b) 6(c) 7 (d) 12

***


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AIEEE Full Test - 1

1

TEST ID 00030403

A IEEE FULL TEST - 1

ANSWERS KEY

CHEMISTRY

1. (b)

2. (b)

3. (a)

4. (c)

5. (a)6. (b)

7. (b)

8. (c)

9. (b)

10. (c)

11. (a)

12. (d)

13. (a)

14. (c)

15. (a)16. (c)

17. (b)

18. (b)

19. (c)

20. (a)

21. (c)

22. (b)

23. (c)

24. (b)

25. (d)26. (c)

27. (b)

28. (d)

29. (b)

30. (c)

PHYSICS

31. (d)

32. (b)

33. (d)34. (c)

35. (a)

36. (c)

37. (d)

38. (a)

39. (d)

40. (c)

41. (d)

42. (d)

43. (b)44. (d)

45. (a)

46. (b)

47. (a)

48. (d)

49. (d)

50. (a)

51. (b)

52. (c)

53. (a)54. (a)

55. (c)

56. (d)

57. (d)

58. (b)

59. (a)

60. (a)

MATHEMATICS

61. (b)

62. (c)63. (a)

64. (c)

65. (a)

66. (c)

67. (b)

68. (a)

69. (c)

70. (b)

71. (c)

72. (d)73. (d)

74. (a)

75. (b)

76. (c)

77. (b)

78. (b)

79. (c)

80. (d)

81. (b)

82. (b)83. (c)

84. (d)

85. (a)

86. (b)

87. (a)

88. (a)

89. (a)

90. (a)


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all india test series for iit-jee

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