JEE - Main - eenadupratibha.net€¦ · Page 1 JEE - Main Chapter wise Model Paper - II Time: 3 hrs Max

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JEE - Main

Chapter wise Model Paper - II Time: 3 hrs Max. Marks: 360 =============================================================================================== IMPORTANT INSTRUCTIONS : Physics : Question No. 1 to 30 consists FOUR (4) marks. Negative (-1)

Chemistry : Question No. 31 to 60 consists FOUR (4) marks. Negative (-1)

Maths : Question No. 61 to 90 consists FOUR (4) marks. Negative (-1) ============================================================================== Syllabus: Mathematics : Vectors, 3D and complex numbers Physics : Rotational dynamics, S.H.M., Gravitation. Chemistry : Solutions, Kinetics, Equilibrium, Chemical thermodynamics, Electro chemistry and

surface chemistry

PHYSICS 1 A rod of mass ‘m’, length ‘l’ pivoted at its centre is free to rotate in a vertical plane. The rod

is at rest and is in vertical position. A bullet of mass m/2 moving horizontally with speed ‘v’ strikes and sticks to one end of the rod. Angular velocity of system just after collision is

1. 2vl

2. 35vl

3. 5vl

4. 56vl

2 Each wheel of a bicycle has moment of inertia 210 .kg m . When the bicycle is moving

towards east, its wheels have angular velocity each 2 rad/s. Now it turns left by 090 and moves with same speed. The turning takes place in 20 s. The torque acting on the bicycle is

1. 2 J along S – W 2. 0 J

3. 2 J along N – E 4. 2 J along N – W


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3 The density of the core of planet is 1ρ and that of the outer shell is 2ρ . The radius of the core

and that of the planet are R and 2R respectively. Gravitational intensity at the surface of

the planet is same as at a depth R. Find the ratio 1

2

ρρ

, assuming them to be uniform

independently.

1. 1/3 2. 2/33 3. 5/3 4. 7/3

4 A uniform rod of mass m and length l is suspended by means of two light inextensible strings

as shown in figure. Tension in one string immediately after the other string is cut is

1.

2mg

2. 2mg 3. 4

mg 4. mg

5 A symmetric lamina of mass ‘M’ consists of a square shape with a semicircular section over

each of the edge of the square as shown in fig. The side of the square is 2a. The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is 1.6 2Ma . The moment of inertia of the lamina about the tangent AB in the plane of the lamina is

1. 4.8 2Ma 2. 3.2 2Ma 3. 6.4 2Ma 4. 1.6 2Ma


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6 The time period of an artificial satellite in a circular orbit of radius R is 2 days and its orbital velocity is 0v . If time period of another satellite in a circular orbit is 16 days then:

1. Its radius or orbit is 4R and orbit velocity is 0v

2. Its radius of orbit is 4R and orbital velocity is 0

2v

3. Its radius of orbit is 2R and orbital velocity is 0v

4. Its radius of orbit is 2R and orbital velocity is 0

2v

7 The kinetic energy of a simple harmonic oscillator of mass ‘m’ is given by 2

0 cosk k tω= . The

displacement equation is given by

1.

2

0

2 sin tmkω ω 2. 02 sink t

mω

ω

3. 02 sinmk tω

ω 4. 0

2

2 sink tm

ωω

8 V- t graph of a particle in SHM is as shown in figure. Choose the wrong option:

1. At A particle is at mean position and moving towards positive direction

2. At B acceleration of particle is zero

3. At C acceleration of particle is maximum and in positive direction

4. None of the above

9 A cubical block of side ‘a’ moving with velocity ‘v’ on a smooth horizontal plane as shown. It hits a rigid point ‘O’. The angular speed of the block after it hits ‘O’ is.


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1. 34

va

2. 32

va

3. 32

va

4. Zero

10 1T is time period of a simple pendulum when it is on the surface of the earth. 2T is its time

period when it is taken to a height R above the earth’s surface (R is radius of earth). Then 2

1

TT

=

1. 1 2. 2 3. 4 4. 2

11 A uniform rod AB of mass m and length L is at rest on a smooth horizontal surface. An impulse P is applied to the end B. The time taken by the rod to turn through a right angle is

1. 2 mLPπ 2. 2 P

mLπ 3.

12mLP

π 4. PmLπ

12 A disc of radius r is removed from the disc of radius R then

a) Minimum shift in center of mass is zero.

b) The maximum shift in centre of mass is 2

( )r

R r+.

c) Centre of mass must lie where mass exists.

d)the shift in centre of mass is 2

2 2

rR r−

1. a, b and d are correct 2. b and c are correct

3. a and b are correct 4. all are correct

13 A projectile is fired upward from the surface of the earth with a velocity eKV where eV is the

escape velocity (K < 1). If ‘r’ is the maximum distance from the centre of the earth to which it rises and R is the radius of the earth, then ‘r’ is

1. 2

RK

2. 2

21

RK−

3. 2

2RK

4. 21RK−

14 A sphere of radius R and mass M has a spherical cavity of radius R/2. The centre of the

cavity is at a distance R/2 from the centre of the sphere. The intensity of gravitational field at the centre of cavity is:

1. Zero 2. 2

GMR

3. 22GM

R 4. 2

32GMR


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15 Three masses each ‘m’ are placed at the vertices of an equilateral triangle of side ‘a’. The statement which is wrong is

1. the gravitational potential at the centroid of the triangle is 3 3 Gma

−

2. the gravitational force on one due to the other is 2

2

3Gma

3. the gravitational field at the centroid of the triangle is not zero.

4. if the bodies keep up their configuration while rotating round the centroid, the velocity of

each body is Gma

16 A smooth sphere A is moving on a frictionless horizontal plane with angular ω and centre of

mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision their angular speeds are Aω and

Bω respectively. Then

1. A Bω ω< 2. A Bω ω= 3. Aω ω= 4. Bω ω=

17 Two particles are in SHM along same line with same amplitude A and same time period T.

At time t = 0, particle 1 is at 2A

+ and moving towards positve x-axis. At the same time

particle 2 is at 2A

− and moving towards negative x-axis. Find the time when they will

collide:

1. 23T 2. 5

12T 3. 4

3T 4. 2

5T

18 A ring of mass m and radius R rolls on a horizontal rough surface without slipping due to an

applied force ‘F’. The friction force acting on ring is


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1. 3F 2. 2

3F 3.

4F

4. Zero

19 The torque τ on a body about a given point is found to be equal to A L× , where A is

constant vector and L is the angular momentum of the body about that point. From this it follows that:

1. dL

dt is perpendicular to L at all instants of time

2. the component of L n the direction of A does not change with time

3. the magnitude of does not change with time

4. all of the above

20 A particle performs uniform circular motion with an angular momentum L. If the frequency of particle motion is doubled and its KE is halved, the angular momentum becomes :

1. 2L 2. 4L 3. 2L 4.

4L

21 A ring of mass m and radius R is pivoted at O on its periphery. It is free to rotate about an

axis perpendicular to its plane. Then time period of the ring is

1. 2 RT

gπ= 2. 22 RT

gπ=

3. 2RTg

π= 4. 32 RTg

π=

22 The collision between both blocks shown in the figure is completely inelastic. The total

energy of oscillation after collision is

1. 2

2mV

2. 2

3mV

3. 2

4mV

4. 2

8mV

23 Average torque on a projectile of mass m, initial speed u and angle of projection


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θ between initial and final positions P and Q as shown about the point of projection is.

1. 2 sin 2

2mu θ

2. 2 cosmu θ 3. 2 sin 2mu θ

4. 2 cos2

mu θ

24 The total energy of an object of mass ‘m’ revolving in the earth’s orbit at a height of ‘h’

from the surface of earth of radius ‘R’ is ‘n’ times the total energy of an object of same mass on the surface of earth. Then the value of ‘h’ is.

1. 1 2

2n R

n−⎛ ⎞

⎜ ⎟⎝ ⎠

2. Rn

3. 22 1

n Rn

⎛ ⎞⎜ ⎟+⎝ ⎠

4. 21 2

n Rn

⎛ ⎞⎜ ⎟−⎝ ⎠

25 A particle of mass 2kg is moving with uniform velocity 13 .m s− in XOY plane along the

line 3 54

y x= + . The magnitude of its angular momentum about the origin is (X and Y are in

metre)

1. 30 J.s 2. 24 J.s 3. 22.5 J.s 4. 42 J.s

26 A cube of side ‘L’ and density r is attached to a spring of constant ‘k’ and partly submerged in a liquid of density σ as shown in fig. If the cube is slightly pressed and released then the frequency of oscillations is

1. 3

12

k gL L

σπ ρ ρ

+ 2. 31

2L Lk gρ ρ

π σ+

3. 12

kLgρ

π σ 4. 1

2g

kLσ

π

27 A uniform rod of length ‘L’ and weight ‘W’ is suspended horizontally by two vertical ropes as

shown. The first rope is attached to the left end of the rod while the second rope is attached at a distance L/4 from the right end. The tension in the second rope is :


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1.

2W 2.

4W 3.

3W 4. 2

3W

28 Consider a semicircular plate of radius R and mass M as shown in figure.

The M.I of the plate about an axis passing through ‘A’ and perpendicular to the plane of paper is

1. 2

2MR

2. 243

MR 3. 254

MR 4. 23MR

29 By applying a force F, the mass M is displaced vertically down by ‘y’ from equilibrium

position as shown in fig. Find the force ‘F’ in terms of the force constant ‘K’ of the spring and displacement ‘y’, for the two cases shown in the fig.

1. ,

4 4Ky Ky

2. 4Ky, 4Ky 3. , 44

Ky Ky 4. , 22

Ky Ky

30 The gravitational field in a region is 10( )ˆ1 ˆi j Nkg −− . The work done by gravitational force to

shift slowly a particle of mass 1kg from (1m, 1m) to or point (2m, –2m) is


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1. 10J 2. –10J 3. –40J 4. 40J

CHEMISTRY 31 One molal solution of a carboxylic acid in benzene shows the elevation of boiling point of 1.518

K. The degree of association of the acid in benzene is ( bK for benzene = 2.53 K 1kg mol− )

1. 60% 2. 70% 3. 75% 4. 80%

32 The rate constant of the reaction : 2A B→ , is 31.0 10−× mol 1 1minL− − . If the initial concentration of A is 1.0 mol 1L− . What would be the concentration of B after 100 minutes

1. 10.1mol L− 2. 10.2mol L− 3. 10.9mol L− 4. 11.8mol L−

33 E° for 2 2, (1 ) / / (1 ),Zn Zn M Cu M Cu+ + is +1.1 V, E° for , (1 )Ag Ag M+ 2/ / (1 ),Cu M Cu+ is – 046 V.

Then E° for 2, (1 ) / / (1 ),Zn Zn M Ag M Ag+ + is

1. +0.46V 2. -0.46V 3. +1.1V 4. +1.56V

34 Enthalpy of formation of acetylene and benzene are respectively 230 and 85 1kJ mol− . The heat of cyclic trimerisation of acetylene is

1. -605 kJ 2. -145 kJ 3. +145 kJ 4. +605 kJ

35 During electrolysis, the amount(g) of the liberated product is plotted against the electric charge (F) as x – axis. The correct graph is :


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1. 2.

3. 4.

36 One gram of activated charcoal absorbs 380 mL of 2SO , 16 ml L of 4CH and 8 ml of

2N separately. The increasing order of the critical temperature of these gases is

1. 2 4 2SO CH N< < 2. 2 4 2N CH SO< < 3. 2 2 4N SO CH< < 4. 4 2 2CH SO N< <

37 When a solution containing non – volatile solute freezes, which of the following equilibrium would exist?

1. Solid solvent liquid solvent 2. Solid solute solution

3. Solid solute liquid solvent 4. Solid solvent solution

38 The activation energies of two reactions are aE and 'aE , '

a aE E> . If the temperature of reaction

systems is increased from 1T to 2T , predict which of the following alteratives is correct? (k’s are

the rate constants)

1.

' '1 2

1 2

k kk k= 2.

' '1 2

1 2

k kk k< 3.

' '1 2

1 2

k kk k> 4.

' '1 2

1 2

2k kk k=

39 The progress of the reaction, A nB , with time, is presented in figure given below.


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The value of n and the equilibrium constant K are respectively

1. 1,2 2. 2,1.2 3. 2,2 4. 1,1.2

40 For the reaction 2( ) ( ) 2 ( )g s gH S H S+ , the equilibrium constant at 925K is 18.5 and at 1000K is

9.25. The enthalpy of the reaction is

1. 10.71KJ mol− 2. 17.1KJ mol− 3. 4.

41

2 ,0.34

Cu CuE V+

° = + . Molarity of aqueous 4CuSO at 25 C° in order to have zero potential of copper

electrode is

1. 93 10 M−× 2. 123 10 M−× 3. 153 10 M−× 4. 183 10 M−×

42 A curve denoting chemisorptions at constant pressure is

1. 2.

3. 4.


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43 At 17 C° , the osmotic pressure of sugar solution is 580 torr. The solution is diluted and the temperature is raised to 57 C° , when the osmotic pressure is found to be 165 torr. The extent of dilution I s

1. 2times 2. 3times 3. 4times 4. 5times

44 The concentration of R in the reaction R P→ was measured as a function of time and the following data is obtained.

[R](molar) 1.0 0.75 0.40 0.10 Time (min) 0.0 0.05 0.12 0.18

The order of reaction is

1. 3 2. 2 3. 1 4. 0

45 Which of the following is the correct order of strengths of the Lowry bases

1. 3 3CN CH COO ClO− − −> >

2. 3 3ClO CH COO CN− − −> >

3. 3 3CH COO CN ClO− − −> >

4. 3 3ClO CN CH COO− − −> >

46 An increase in temperature increases the rate of

A) exothermic reactions B) endothermic reactions

C) Spontaneous reactions D) non – spontaneous reactions

1. A,B,C,D 2. A and C only 3. A and B only 4. B and D only

47 Equivalent conductances of NaCl, HCl and 3CH COONa at infinite dilution are 126, 426 and 91 1 2 1ohm cm eq− − , respectively at 298 K. The equivalent conductance of 3CH COOH at infinite

dilution at 25 C° (in 1 2 1ohm cm eq− − ) is

1. 391 2. 486 3. 548 4. 693

48 Match the following


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Column I Column II

A. Clouds P. Emulsion

B. Blood Q. Gas in solid

C. Foam rubber R. Solid in gas

D. Milk S. Solid in liquid

T. Liquid in gas

1). A--> S B--> T C--> Q D--> P

2). A--> T B--> S C--> Q D--> R

3). A--> T B--> S C--> Q D--> P

4). A--> T B--> S C--> R D--> P

49 If P° is the vapour pressure of pure solvent and P is the vapour pressure of the solution, which of the following is independent on temperature

1. P° 2. P 3. P P° − 4. /P P°

50 At 25 C° for the reaction, R → products, the half – life of the reaction with decimolar R is 10 min and with semimolar R is 2 min. The kinetics of reaction is

1. Third order 2. Second order 3. First order 4. Zero order

51 For the process 2 ( )lH O (1bar, 373K) 2 ( )gH O→ (1bar, 373K), the correct set of thermodynamic parameters is

1. 0,G S ve∆ = ∆ = + 2. 0,G S ve∆ = ∆ = − 3. , 0G ve S∆ = + ∆ = 4. ,G ve S ve∆ = − ∆ = +


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52 4 ( ) 4( ) ( )aq aq aqNH OH NH OH+ −+ ; 52 10K −= × . If equimolar ammonium sulphate and ammonia

are present together as a mixture in solution, the pH is

1. 4.7 2. 5.0 3. 9.0 4. 9.3

53 Consider the following cell reaction:

2( ) 2( ) ( ) ( ) 2 ( )2 4 2 2s g aq aq lFe O H Fe H O+ ++ + → +

0 1.67E V=

At 2 3[ ] 10Fe M+ −= , 2( ) 0.1P O atm= and pH = 3, the cell potential at 25 C° is

1. 1.47V 2. 1.77V 3. 1.84V 4. 1.57V

54 Among the following, the intensive property is (properties are)

A) molar conductivity B) electromotive force

C) resistance D) heat capacity

1. A,B,C and D 2. Only A, B 3. Only C,D 4. A and C only

55 Molal elevation constant for water is 10.56Kkg mol− . When 6 grams of urea is present dissolved in 200 g of water, the boiling point of the solution at 1 atm is

1. 373.28 K 2. 373.82K 3. 375.8K 4. 376.6K

56 For a first order chemical reaction, if ‘log a/(a-x)’ is taken on y – axis and ‘t’ taken on x – axis, the slope of the straight line obtained is

1. 2.303K 2. - 2.303K 3. 0.4343K 4. - 0.4343K

57 One mole of each hydrogen and iodine are heated in a closed vessel at 420 C° . Equilibrium is attained when 80% of iodine is converted to hydrogen iodine. The numerical value of equilibrium constant for the reaction,

2 2 2H I HI+ is


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1. 16 2. 32 3. 64 4. 128

Paragraph: Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Application of colligative properties are very useful in day – to – day life. One of its example is the use of ethylene glycol and water mixture as anti freezing liquid in the radiator of automobiles.

A solution M is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is 0.9. Given:

Freezing point depression constant of water

1( ) 1.86waterfK K kg mol−=

Freezing point depression constant of ethanol

1( ) 2.0ethanolfK K kg mol−=

Boiling point elevation constant of water

1( ) 0.52waterbK K kg mol−=

Standard freezing point of water = 273 K

Standard freezing point of ethanol = 155.7 K

Standard boiling point of water = 373K

Standard boiling point of ethanol = 351.5 K

Vapour pressure of pure water = 32.8 mm Hg.

Vapour pressure of pure ethanol = 40 mm Hg.

Molecular weight of water = 118g mol−

Molecular weight of ethanol = 118g mol−

In answer the following questions, consider the solution to be ideal dilute solutions and solutes to be nonvolatile and non dissociative.


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58 The freezing point of the solution M is

1. 268.7K 2. 268.5K 3. 234.2K 4. 150.9K

59 The vapour pressure of the solution M is

1. 39.3 mm Hg 2. 36.0 mm Hg 3. 29.5 mm Hg 4. 28.8 mm Hg

60 Water is added to the solution M such that the mole fraction of water in the solution becomes 0.9. The boiling point of this solution is

1. 380.4K 2. 376.2K 3. 375.5K 4. 354.7K

MATHEMATICS

61 Let z and w be two non-zero complex numbers such that | | | |z w= and arg ( )z + arg ( )w π= . Then z equal

1. w 2. w− 3. w 4. w−

62 If the imaginary part of 2 1

1z

iz++

is 4− , then the locus of the point representing z in the

complex plane is

1. A straight line 2. A parabola 3. A circle 4. An ellipse

63 If a plane meets the co-ordinate axes in A, B, C such that the centroid of the triangle ABC is the point 2(1, , )r r , then equation of the plane is

1. 2 23x ry r z r+ + = 2. 2 23r x ry z r+ + = 3. 2 3x ry r z+ + = 4. 2 3r x ry z+ + =

64 The distance between a point P whose position vector is 5 3i j k+ + and the line (3 7 ) ( )r i j k t j k= + + + + is

1. 3 2. 4 3. 5 4. 6

65 If , , ,A B C D are four points in a space and | |AB CD BC AD CA BD λ× + × + × = (area of the triangle ABC). Then the value of λ is

1. 1 2. 2 3. 3 4. 4 66 If ( ) ( )1 2,A Z B Z and ( )3C Z are the vertices of triangle ABC, such

that 1 2 3| | | | | |Z Z Z= = and 1 2 1 2| | | |Z Z Z Z+ = − then C


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1. 2π 2.

4π 3.

3π 4.

6π

67 If , ,a b c are non-coplanar unit vectors such that

1( ) ( )2

a b c b c× × = + then the angle

between &a b is

1. 3 / 4π 2. / 4π 3. / 2π 4. π

68 Let , ,a b c be three non-coplanar vectors and d be a non-zero vector, which is perpendicular to .a b c+ + Now, if (sin )( ) (cos )( ) 2( )d x a b y b c c a= × + × + × then minimum value of 2 2x y+ is equal to

1. 2π 2.

2

2π

3. 2

4π

4. 25

4π

69 The number of values of z satisfying both the equations | 4 6 | | 2 2 | 5Z i Z i− − + − − = and | 3 4 | 6Z i− − = is

1. 0 2. 1 3. 3 4. 4 70 O is incentre of le ABC∆ lying in xy-plane. Given 3 , 2 .A i B i j= − = + Then the triangle ABC is

1. Equilateral 2. right angled 3. acute angled 4. obtuse angled

71 If ,p q are two non-collinear vectors such that ( ) ( ) ( ) 0b c p q c a p a b q− × + − + − = where a, b, c are lengths of sides of a triangle, then the triangle is

1. right angled 2. obtuse angled 3. Equilateral 4. Right angled isosceles triangle

72 If 1 2( ), ( )A Z B Z and 3( )C Z are vertices of an equilateral triangle then value of

Arg 2 3 1

3 2

2z z zz z

⎛ ⎞+ −=⎜ ⎟−⎝ ⎠

1. 4π 2.

2π 3.

3π 4.

6π

73 In the complex plane the points A & B represent 1 2 5z i= + and 2 5 11z i= + respectively; If p(z) moves in that plane such that 1 2| | 2 | | .z z z z− = − Then maximum area of triangle PAB (in square units) is


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1. 5 2. 14 3. 253

4. 15

74 The equation of a plane that passes through (1, 2, 3) and is at maximum distance from (–1, 1, 1) is

1. 2 2 6x y z− + = 2. 2 3x y z− + = 3. 2 2 10x y z+ + = 4. none of these

75 IfOA a= ,OB b= , 2 4OC a b= − then

1. C lies outside of OAB∆ but inside the OBA 2. C lies outside of OAB∆ but inside the OAB 3. C lies inside of OAB∆ 4. C lies outside of OAB∆

76 If 1 2,z z are two different points in the argand plane. If 1 2| | | |z zα β= (where , Rα β ∈ ) then the

point 1 2

2 1

z zz z

α ββ α

+ lies on

1. line segment joining –2, 2 on real axis 2. line segment joining –2, 2 on imaginary axis 3. unit circle | | 1z = 4. the line with arg z = tan–12

77 If 1 2 3, ,z z z are distinct non-zero complex numbers and , ,a b c R+∈ such

that1 2 2 3 3 1| | | | | |

a b cz z z z z z

= =− − −

then2 2 2

1 2 2 3 3 1

a b cz z z z z z

+ +− − −

is always equal to

1. 1 2 3Re( )z z z+ + 2. 1 2 3( )Im z z z+ + 3. Zero 4. None

78 A line passing through A=(1, 2, 3) and having direction ratios 3, 4, 5 meets a plane x+2y–3z = 5 at B, then length of AB is equal to

1. 94

2. 114 2

3. 134

4. 45 24

79 A parallelopiped is formed by planes drawn parallel to coordinate axes through the points A=(1, 2, 3) and B(9, 8, 5). The volume of that parallelopiped is equal to (in cubic units)

1. 192 2. 48 3. 32 4. 96

80 The square of the distance between the line 2 2 3 ( 5 )i j k i j kγ λ= − + + + + and the plane .( 4 ) 10,i j kγ − + = is _______

1. 12

2. 14

3. 2 4. 1

8

81 If ,a b are vectors perpendicular to each other and | | 2,| | 3, ,a b c a b= = × = then the least


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value of 2 | |c a− is _______.

1. 1 2. 2 3. 3 4. 4

82 If 1 21 , 1 ,z i z i= + = − Z and origin are four concyclic points in Argand plane then maximum value of | |Z is ____

1. 2 2. 4 3. 6 4. 8

83 If 1 1z

z+ = and 2005

2005

1a zz

= + and b is last digit of the number 22 1n

− when the integer n > 1,

and 2 2 13a b λ+ = thenλ =____________

1. 8 2. 4 3. 2 4. 0

84 The position vector of a point P moving in space is given by (3cos ) (4 cos ) ˆ(5sin ) .ˆ ˆOP R t i t j t k= = + + The time 't' when the point P crosses the plane 4x – 3y + 2z = 5 is

1. sec2π 2. sec

6π 3. sec

3π 4. sec

4π

85 If , ,m n are direction cosines of a line then maximum value of3 4 5m n+ − is

1. 5 2. 5 2 3. 37 4. 3

86 If the lines 2 3 4

1 1x y z

λ− − −

= = and 1 4 5 ( 0)2 1

x y z λλ− − −

= = ≠ intersect at a

point ( , , )α β γ then | |λ = ____________

1. 1 2. 2 3. 3 4. 4

87 The angle between the diagonal of a cube and edge of a cube is

1. 1 13

Cos− 2. 1 23

Cos− 3. 1 13

Cos− ⎛ ⎞⎜ ⎟⎝ ⎠

4. 1 32

Cos−⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

88 If[ ] 3a b c = then the value of

[2( ) 2( ) ( ) 2( ) ( ) 2( )( ) 2( ) 2( )]

a b b c c a a b b cc a a b b c c a

× + × + × × − ×− × × − × + ×

is

1. –27 2. 243 3. –343 4. –243

89 If 1

2

zz

is purely imaginary then 1 2

1 2

z zz z+−

is equal to :

1. 1 2. 2 3. 3 4. 0

90 In OAB∆ , M is the mid point of AB. C is a point on OM, such that 2OC = CM. X is a point on the side OB such that OX = 2 XB. The line XC is produced to meet OA is Y then OY:YA=

1. 2:7 2. 1:3 3. 3:2 4. 2:5


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KEY SHEET

PHYSICS :-

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

11) 3 12) 3 13) 4 14) 3 15) 3 16) 3 17) 2 18) 4 19) 4 20) 4

21) 2 22) 3 23) 1 24) 1 25) 2 26) 1 27) 4 28) 1 29) 3 30) 4

CHEMISTRY :-

31) 4 32) 2 33) 4 34) 1 35) 2 36) 2 37) 4 38) 3 39) 2 40) 3

41) 2 42) 3 43) 3 44) 4 45) 1 46) 1 47) 1 48) 3 49) 4 50) 2

51) 1 52) 3 53) 4 54) 2 55) 1 56) 3 57) 3 58) 4 59) 2 60) 2

MATHEMATICS :-

61) 4 62) 3 63) 2 64) 4 65) 4 66) 2 67) 1 68) 4 69) 1 70) 4

71) 3 72) 2 73) 4 74) 3 75) 1 76) 1 77) 3 78) 4 79) 4 80) 3

81) 3 82) 1 83) 3 84) 2 85) 2 86) 1 87) 3 88) 4 89) 1 90) 1

- Prepared By

Hyderabad.

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