class: sz2 jee-main model date: 07-06-2020 time: 3hrs …...jul 06, 2020 ·...

Corporate Office: 10th Floor, Melange Tower; No.80-84, Pathrika Nagar; Hitech-City, Madhapur, Hyderabad. Telangana - 500 081.

: 040-45009999(360/341) : [email protected] : http://www.narayanagroup.com

Class: SZ2 JEE-MAIN MODEL Date: 07-06-2020

Time: 3hrs WTM-13 Max. Marks: 300

IMPORTANT INSTRUCTIONS

PHYSICS Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks

Sec – I(Q.N : 1 – 20) Questions with Single Answer Type 4 -1 20 80

Sec – II(Q.N : 21 – 25) Questions with Numerical Answer Type

(+/ - Decimal Numbers) 4 0 5 20

Total 25 100

CHEMISTRY Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks




Total 25 100

MATHEMATICS Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks




Total 25 100

mailto:[email protected]://www.narayanagroup.com/

SZ2_JEE-MAIN_WTM-13_QP_Exam.Dt.07-06-2020

Narayana CO Schools

2

–:SZ2 Jee-Main Exam Syllabus (07-06-20):–

TOPICS

PHYSICS

PRESENT WEEK 50%:

Force on submerged surfaces, horizontal surface, vertical surface,

Inclined surface, curved surface, stability of roller, gate submerged in

liquid, Applications.

PREVIOUS WEEK 50%:

Force of buoyancy in accelerating fluids, horizontal, vertical& rotating

fluids, level rise or fall of a liquid when a floating ice block melts, level

rise or fall when a loaded boat floating in liquid is unloaded,

Applications.

TOPICS

CHEMISTRY

PRESENT WEEK 50%:

Depression of freezing point, Osmosis and Osmatic pressure, Vant' Hoff's

theory of dilute solutions, Abnormal molar mass.

PREVIOUS WEEK 50%:

Vapour pressure, Boiling point, Lower vapour pressure, Raoult's law,

Limitations, Ideal, non - ideal solutions, Azeotropic mixtures, Elevation of

boiling points.

TOPICS

MATHS

PRESENT WEEK 50%:

RELATIONS: Relations, Definitions, Terminology, Types of Relations From

A To B, Types of Relations (Symmetric) From A To A, Composition of

Relation, Partial of Order Relations, Congruency of Numbers, No. of

Relations.

PREVIOUS WEEK 50%:

Trigonometric Inequations, Trigonometric Inequation Of Sinx>K, Sinx≤K,

Trigonometric Inequation Like F(X)>G(X), F(X)≤G(X), Trigonometric

Inequation |F(X)+G(X)|=|F(X)|+|G(X)|, Related Problems.


Narayana CO Schools

3

SECTION-I (1 TO 20)

(Single Answer Type)

This section contains 20 multiple choice questions. Each question has 4 options

(1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

01. An ice cube is floating in water above which a layer of lighter oil is

poured. As the ice melts completely, the level of interface and the

upper most level of oil will respectively

A) The level of interface is rise B) The upper most level falls

C) The upper most level rise D) The level of interface falls

Then choose correct options.

1) AC 2) AB 3) BC 4) AD

02. A cube of ice floats partly in water and partly in K.oil. The ratio of

the volume of ice immersed in water to that in K.oil is (Specific

gravity of K.oil is 0.8 and that of ice is 0.9.)

1) 9:8 2) 3:4 3) 1:3 4) 1:1


Narayana CO Schools

4

03. A ball is made of a material of density , where oil < < water with

oil and water representing the densities of oil and water,

respectively. The oil and water are immiscible. If the above ball is

in equilibrium in a mixture of this oil and water, which of the

following picture represents its equilibrium position?

1)

2)

3)

4)

04. A piece of ice is floating in a glass vessel filled with water. When ice

completely melts

1) level of water does not change 2) level of water falls down

3) level of water rises 4) none of these

05. A piece of wood is floating in water kept in a bottle. The bottle is

connected to an air pump. Neglect the compressibility of water.

When more air is pushed into the bottle from the pump, the piece

of wood will float with

1) large part in the water 2) lesser part in the water

3) small part in the water 4) it will sink

06. A cubical box is to be constructed with iron sheets 1mm in

thickness. The minimum value of the external charge so that the

cube does not sink in water is ___ cm (nearly)

3 38000 / , 1000 /Iron waterD kg m D kg m = =

1) 6 2) 4.8 3) 5.4 4) 4.3

07. A 20N metal block is sustended by a spring balance, A beaker

containing some water is placed on a weighing machine which

reads 40N. The spring balance is now lowered so that the block gets

immersed in the water. The spring balance now reads 16N. The

reading of the weighing machine will be

1) 36N 2) 60 N 3) 44 N 4) 56 N


Narayana CO Schools

5

08. If a block of Ice, floating in a liquid of density greater than that of

water, melts, then the liquid level

1) decreases 2) unchanged 3) rises 4) all of these

09. When ice block with cork floating in water melts, the level of water

in the vessel remains (density of cork less than density of water)

1) increases 2) unchanged 3) decreases 4) all of these

10. A solid hemisphere of radius R is made to just sink in a liquid of

density . Then the vertical thrust on the curved surface is

1) 32

3 3

Rg

upwards 2)

3

3

Rg

upwards

3) 32

3 3

Rg

downwards 4)

3

3

Rg

downwards

11. A body floating in a stationary liquid will be in stable equilibrium if

1) its center of buoyancy is above center of gravity

2) its center of buoyancy is below center of gravity

3) Density of body is more than density of liquid

4) Density of body is less than density of liquid

12. An L shaped glass tube is kept inside a vehicle which is moving

with constant acceleration. The level of liquid in the left arm is 8cm

where as in right arm is 6cm. Assuming that the diameter of the

tube is much smaller than the level of liquid and neglecting the

effect of surface tension, acceleration of vehicle is

(g=9.8 2ms − )

1) 24.9ms− 2) 21.4ms− 3) 22.8ms− 4) 2

g


Narayana CO Schools

6

13. A solid cone of height H and base radius H/2 floats in a liquid of

density r . It is hanging from the ceiling with the help of a string.

The force by the fluid on the curved surface of the cone is (0P =

atmospheric pressure)

1) 2 04 3

P gHH

+

2) 2 0

4 6

P gHH +

3) 2

0

4 4

PHgH

+

4) ( )

2

04

HP gH

+

14. The tension in a string holding a solid block below the surface of a

liquid ( where liquid block ) as in shown in the figure is T when the

system is at rest. The tension in the string if the system has upward

acceleration a is

1) 1a

gT

−

2) 1a

gT

+

3) 1a

gT

−

4) aT

g

15. The force acting due to the liquid per unit width (width is measured

perpendicular to the plane of figure) on a plane wall inclined at an

angle q with the horizontal (see figure), if the density of liquid is r ,

is

1) 2

2sin

gH

2)

2

sin

gH

3)

22.

3 sin

gH

4)

2

2sin

gH


Narayana CO Schools

7

16. A solid sphere of mass m = 2 kg and specific gravity s = 0.5 is held

stationary relative to a tank filled with water as shown. The tank is

accelerating vertically upward with an acceleration a = 2ms-2.

Calculate tension in the thread connected between the sphere and

the bottom of the tank. (g=10m/s2 , water density

31000 / 1 /kg m gr cc = = )

1) 12N 2) 48N 3) 24N 4) 36N

17. A thin uniform cylindrical shell, closed at both ends, is partially

filled with water. It is floating vertically in water in half-submerged

state. If ρc is the relative density of the material of the shell with

respect to water, then the correct statement is that the shell is

1) More than half-filled if ρc is less than 0.5

2) More than half-filled ρc is more than 1.0

3) half-filled if ρc is more than 0.5

4) less than half-filled if ρc is less than 0.5

18. Two ice cubes, each of side 10 cm have cavity of volume 20 cm3 at

the centre of each cube. These cavities are filled with materials A

and B respectively in cube 1 and cube 2. The specific gravity of

material of cube A is 4.9 and specific gravity of material of cube B

is 1.9. Now, these cubes are placed in two different vessels of same

base area as shown in the figure. Before putting the blocks, the

water levels in vessels are same.

Assume that ice melts uniformly from all sides and with same

constant rate in both the vessels.

(Given, specific gravity of ice = 0.9)

Choose the correct statement(s).

1) A and B sink simultaneously

2) A and B sink only after complete melting of ice

3) A sinks prior to B 4) B sinks prior to A


Narayana CO Schools

8

19. Two ice cubes, each of side 10 cm have cavity of volume 20 cm3 at

the centre of each cube. These cavities are filled with materials A

and B respectively in cube 1 and cube 2. The specific gravity of

material of cube A is 4.9 and specific gravity of material of cube B

is 1.9. Now, these cubes are placed in two different vessels of same

base area as shown in the figure. Before putting the blocks, the

water levels in vessels are same.

Assume that ice melts uniformly from all sides and with same

constant rate in both the vessels. (Given, specific gravity of ice =

0.9)

Choose the correct graph showing the variation of heights of water

level in two vessels with time.

1) 2)

3) 4)


Narayana CO Schools

9

20. A bucket of water contains a wooden block floating in water with

4th

5

of its volume sub merged in the water. The bucket is placed

on the floor of a lift and the lift now starts moving down with

uniform acceleration. The block of wood now

1) Moves upwards 2) Moves downward

3) Remains at same place 4) Buoyancy

SECTION-II (21 TO 25)

(Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical

values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -

123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.

21. A dumbbell is placed in water. It is observed that by attaching a

point mass m (neglect its volume and neglect surface tension) to the

rod, at ‘l’ distance from the centre of sphere B, the dumbbell floats

with the rod horizontal on the surface of the water and each sphere

exactly half submerged, as shown. Take density of water , Volume

of each sphere is V .Mass of spheres are shown in the diagram. The

value of m is V kM− . Then the vale of k is

22. A block of mass 1 kg and density 30.8 / ,gr cm is held stationary with

the help of a string as shown in figure. The tank is accelerating

vertically upwards with an acceleration 21 / .a m s= Then the tension

in the string is __________ Newton. ( )2 3 310 / , 10 /waterg m s d kg m= =


Narayana CO Schools

10

23. A block of mass 1 kg and density 30.8 / ,gr cm is held stationary with

the help of a string as shown in figure. The tank is accelerating

vertically upwards with an acceleration 21 / .a m s= If the string is

now cut, then the acceleration of the block is ___ 2/ .m s

( )2 3 310 / , 10 /waterg m s d kg m= =

24. A cubical block is floating in a liquid with half of its volume

immersed in the liquid. When the whole system accelerates

upwards with a net acceleration of / 2g , the fraction of volume

immersed in the liquid will be P

Q. Then the value of P Q+ is

25. A rectangular bar of soap has density 3800 /kg m floats in water of

density 1000 3/kg m . Oil of density 300 3/kg m is slowly added,

forming a layer that does not mix with the water. When the top

surface of the oil is at the some level as the top surface of the soap.

The ratio of the oil layer thickness to the soap’s thickness ( )/x L is

.A

B Then the value of A B+ is


Narayana CO Schools

11

SECTION-I (26 TO 45)


This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be

correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

26. Considering the formation, breaking and strength of hydrogen

bond, predict which of the following mixtures will show a positive

deviation from Raoult’s law?

1) Methanol and acetone 2) Chloroform and acetone

3) Nitric acid and water 4) Phenol and aniline

27. Colligative properties depend on

1) the nature of the solute particles dissolved in solution

2) the number of solute particles in solution

3) the physical properties of the solute particles dissolved in

solution

4) the nature of solvent particles

28. Which of the following solutions have lowest freezing point?

1) 0.1 M NaCl 2) 0.01 M NaCl

3) 1M NaCl 4) 0.001 M NaCl

29. The use of common salts, e.g., NaCl or anhyd. CaCl2, is made to

clear snow onthe roads. This causes:

1) A lowering in the freezing point of water

2) A lowering in the melting point of ice

3) Ice melts at the temperature of atmosphere present at that time

4) All the above

30. Which of the following is correct for ideal solutions

1) mixH 0 2) mixH=0

3) mix 0V 4) All of these


Narayana CO Schools

12

31. Colligative properties are observed when

1) a non volatile solid is dissolved in a volatile liquid

2) a non volatile liquid is dissolved in another non volatile liquid

3) a gas is dissolved in non volatile liquid

4) a volatile liquid is dissolved in another volatile liquid

32. Relative lowering of vapour pressure is a colligative property

because

1) It does not depends on the concentration of a non electrolyte

solute in solution and does not depend on the nature of the

solute molecules

2) It depends on number of particles of electrolyte solute in

solution and does not depend on the nature of the solute

particles

3) It depends on the concentration of a non electrolyte solute in

solution as well as on the nature of the solute molecules

4) It depends on the concentration of an electrolyte or non

electrolyte solute in solution as well as on the nature of solute

molecules

33. Which one of the following statement is incorrect?

1) Greater the lowering of vapour pressure, greater is the boiling

point of the solution

2) Greater the lowering of vapour pressure, greater is the freezing

point of the solution

3) At the freezing point, the solute and the solvent have same

vapour pressure

4) The units of molal depression constant are Km-1

34. Isotonic solutions have

1) same boiling point 2) same vapour pressure

3) same melting point 4) same osmotic pressure


Narayana CO Schools

13

35. Which of the following 0.10 m aqueous solution will have the lower

freezing point?

1) ( )2 4 3Al SO 2) 6 12 6C H O 3) KI 4) 12 22 11C H O

36. What is the normal b.p of an aquoues solution whose freezing point

is −2.480 C?

( )1 86 0 512O Of bK . C.kg /mol,K . C.kg /mol= =

1) 100.7O C 2) 102.50 C 3) 109.00 C 4) 99.30 C

37. During depression of freezing point in a solution, the following are

in equilibrium

1) liquid solvent -solid solute 2) liquid solvent -solid solvent

3) liquid solute -solid solute 4) liquid solute -solid solvent

38. If BaCl2 ionizes to an extent of 80% aqueous solution, the value of

Van’t Hoff factor is

1) 0.8 2)0.4 3) 2.6 4)2.4

39. Which one of the following is an isotonic pair of solutions?

1) 0.15 M NaCl and 0.1 M Na2SO4

2) 0.2 M urea and 0.1 M sugar

3) 0.2 M BaCl2 and 0.2 M Urea

4) 0.2 M MgSO4 and 0.1 M NH4Cl

40. The boiling point of 6 6 3 6 5 2 6 5 2andC H ,CH OH, C H NH C H NO are

0 0 080 65 184C, C, C and 0212 C respectively. Which will show

highest vapour pressure at room temperature?

1) 6 6C H 2) 3CH OH 3) 6 5 2C H NH 4) 6 5 2C H NO

41. The vapour pressure of water depends upon

1) Surface area of container 2) Volume of container

3) Temperature 4)All of these

42. The vapour pressure in mm of Hg, of an aqueous solution obtained

by adding 18 g of glucose ( )6 12 6C H O to 180 g of water at 0100 C is

1)7.60 2)76.0 3)759 4)752.4


Narayana CO Schools

14

43. The vapour pressure of 10% aqueous glucose solution at 0100 C

1) 750 mm 2) 755.6 mm 3)751. 6 mm 4) 740 mm

44. Blood cells retain their normal shape in solution which are

1) isotonic to blood 2) hypotonic to blood

3) hypertonic to blood 4) equinormal to blood

45. A perfectly semi-permeable membrane when used to separate a

solution from its solvent permits through it the passage of

1) Solute only 2) Solvent only

3) Both (1) and (2) 4) Neither (1) nor (2)



This section contains 5 questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers (place value

ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -


46. The osmotic pressure of a solution at 300 K is 0.821 atm. Its

concentration will be

47. Calculate the molecular weight of a substance if the freezing point

of a solution containing 100g of benzene and 0.2g of the substance

is 0.17K below that of benzene. The cryoscope constant of benzerne

is 15 16 . K kg mol −

48. Number of phases present in a true solution is

49. The vapour pressure of methanol at certain temperature is 1 atm.

by adding a small amount of ethyl acetate the vapour pressure of

the solution is found to be 684 mm. The relative lowering of vapour

pressure is

50. The weight in grams of a non-volatile solute (M.wt=60) to be

dissolved in 90 g of water to produce relative lowering of vapour

pressure of 0.02 is


Narayana CO Schools

15

SECTION-I (51 TO 70)


This section contains 20 multiple choice questions. Each question has 4 options

(1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

51. Let 22sin 3sin 2 0x x+ − and 2 2 0x x− − (x is measured in radians).

Then x lies in the interval

1) 5

,6 6

2) 5

1,6

−

3) ( )1,2− 4) ,26

52. If 0 2x and cos sinx x , then

1) 0,4

x

2) ,24

x

3) 3

,4 4

x

4) 0,x

53. The number of values of x in 0, 2 satisfying the inequation

cos sin 2x x− , is

1) 0 2) 1 3) 2 4) 3

54. The set of all x in ( ),− satisfying the inequation 4sin 1 5x − is

given by

1) 3

,10 10

−

2) ,10

−

3) ( ),− 4)

3,10

−

55. tan sec tan sec , 0,2x x x x x+ = + if and only if x belongs to the interval

1) 0, 2) 0,2

−

3)

3,2

2

−

4) ( ,2

56. The solution to the inequality 1

cos2

x − is

1) 2 ,2 ,6 3

x n n n Z

+ +

2) 2 4

2 ,2 ,3 3

x n n n Z

+ +

3) 2 2

2 ,2 ,3 3

x n n n Z

− +

4) 2 ,2 ,4 3

x n n n Z

− +


Narayana CO Schools

16

57. The value of ( )0,2 for which the inequation 22sin 5sin 2 0− + is

valid, is

1) 5

0, ,26 6

2)

5,

8 6

3) 5

0, ,8 6 6

4)

41,

48

58. The solution set of the inequation cos2 sinx x in the interval ,2

−

is

1) 5

, ,6 6 6

x−

2) 0,3 4

x

−

3) 3

, ,6 4 4

x−

4)

59. The value of ( , − for which the inequation sin 3 cos 1+ is

valid, is

1) 6 2

2)

6 2

− 3)

2

4)

6

−

60. If the inequality 2 2sin cos 1 cosx a x a x+ + + holds for any x R , then the

largest negative integral value of ' 'a is

1) –4 2) –3 3) –2 4) –1

61. Let Q be the set of all rational numbers and R be the relation defined

as ( ) , :1 0, , .R x y xy x y Q= + Then relation R is

1) Symmetric and transitive 2) Reflexive and transitive

3) An equivalence relation 4) Reflexive and symmetric

62. Consider the following relations ( ) , / ,R x y x y= are real numbers

and x wy= for some rational number ;w

, / , , and areintegers such that , 0 and ,m p

S m n p q n q qm pnn q

= =

then

1) neither R or S is an equivalence relation

2) S is an equivalence relation but R is not an equivalence relation

3) R and S both are equivalence relations

4) R is an equivalence relation but S is not an equivalence relation


Narayana CO Schools

17

63. Consider the following relations

( ) 1 , : and areintegers and or for some integerR x y x y x ay y ax a= = =

( ) 2 , : and areintegers and 1for some integer , .R x y x y ax by a b= + = Then

1) 1 2,R R are not equivalence relations

2) 1 2,R R are equivalence relations

3) 1R is an equivalence relation but 2R is not

4) 2R is an equivalence relation but 1R is not

64. Let ( ) ( ) ( ) ( ) ( ) 1,3 , 4,2 , 2,4 , 2,3 , 3,1R = be a relation on the set

1,2,3,4 .A = The relation R is

1) not symmetric 2) transitive

3) a function 4) reflection

65. Let I be the set of integers for , ,a b I aRb if and only if 1,a b− then

1) R is not reflexive 2) R is not symmetric

3) ( ) , :R a a a I= 4) R is not an equivalence relation

66. Let A and B be two sets containing 2 elements and 4 elements

respectively. The number of non empty relations from A to B is

1) 255 2) 256 3) 220 4) 219

67. Let P be the relation defined on the set of all real numbers such

that ( ) 2 2, : sec sec 1 .P a b a b= − = Then P is

1) Reflexive and symmetric but not transitive

2) Reflexive and transitive but not symmetric

3) Symmetric and transitive but not reflexive

4) An equivalence relation

68. Let ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) 3,3 , 6,6 , 9,9 , 12,12 , 6,12 , 3,9 , 3,12 3,6R = be a relation

on the set 3,6,9,12 .A = Then relation is

1) Reflexive and symmetric only 2) an equivalence relation

3) Reflexive only 4) Reflexive and transitive only


Narayana CO Schools

18

69. Let L be the set of all lines in a plane and R be a reflection on L

defined by 1 2l R l if and only if 1 2 ,l l⊥ then R is

1) Reflexive 2) Symmetric

3) Transive 4) an equivalence relation

70. If the relation : ,R A B→ where 1,2,3,4A = and 1,3,5B = is defined

by ( ) , : , , ,R x y x y x A y B= then 1ROR− is

1) ( ) ( ) ( ) ( ) ( ) ( ) 1,3 , 1,5 , 2,3 , 2,5 , 3,5 , 4,5 2) ( ) ( ) ( ) ( ) ( ) 3,1 , 5,1 , 5,2 , 5,3 , 5,4

3) ( ) ( ) ( ) ( ) 3,3 , 3,5 , 5,3 , 5,5 4) ( ) ( ) ( ) ( ) 3,3 , 3,1 , 5,3 , 5,1



This section contains 5 questions. The answer to each question is a Numerical

values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -


71. If ( ) 2sin 2 2x x b − + for all the real values of 1x and

0, , ,2 2

then the least positive integral value of b is

72. If sin sin cos cosx y x x R+ , then sin cosy + is equal to

73. If the number of relations on a finite set A having ' 'n elements is

812 , then n is equal to

74. If ( ) ( ) ( ) 1,2,3 , 1,2 , 1,1 , 1,3 .A R= = Then minimum of elements may be

adjoined with the elements of R so that it may become transitive is

equal to

75. The number of reflexive relations on a set of cardinality 3 is

"We always feel that the life of others is better than us! But, we always

forget that we are also 'others' for someone else"

class: sz2 jee-main model date: 07-06-2020 time: 3hrs …...jul 06, 2020 ·...

Documents