physics chemistry mathematics · 2021. 2. 1. · 17. the pressure at the bottom of a lake, due to...

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Class: SZ2-A JEE-MAIN MODEL Date: 02-01-2021

Time: 3hrs WTM-16 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

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SZ2-A_JEE-MAIN_WTM-16_QP_Exam.Dt.02-01-2021

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2

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. The Poisson’s ratio should satisfy the relation (theoretical)

1) − 1 0.5 2) − 0.5 1.0

3) 0.5 1.0 4) − −10 0.5

02. The strain-stress curves of three wires of different materials are

shown in the figure. P, Q and R are the elastic limits of the wires.

The figure shows that

1) Elasticity of wire ‘P’ is maximum

2) Elasticity of wire ‘Q’ is maximum

3) Tensile strength of ‘R’ is maximum

4) Elasticity P, Q & R are same

03. A uniform bar of length ' 'L and cross sectional area ' 'A is

subjected to a tensile load ' 'F . ' 'Y be the Young’s modulus and ' '

be the Poisson’s ratio then volumetric strain is

1) ( )− 1F

AY 2) ( )−2

F

AY 3) ( )− 1 2

F

AY 4) .

F

AY

04. A copper wire of cross-sectional area 20.01cm is under a tension of

20 .N Find the decrease in the cross-sectional area. Young modulus

of copper = 11 21.1 10 N m− and Poisson’s ratio 0.32.=

1) − 2 21.164 10 cm 2) − 6 21.164 10 cm

3) − 3 21.164 10 cm 4) − 1 21.164 10 cm


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05. A heavy uniform rod is hanging vertically from a fixed support. It is

stretched by its own weight. The diameter of the rod is

1) smallest at the top and gradually increases down the rod

2) largest at the top and gradually decreases down the rod

3) uniform everywhere

4) maximum in the middle

06. , ,Y K represent the Young’s modulus, bulk modulus and rigidity

modulus of a body respectively. If rigidity modulus is twice the bulk

modulus, then

1) = 5 /18Y K 2) = 5 /9Y 3) = 9 /5Y K 4) = 18 /5Y K

07. Figure shows water filled in a symmetrical container. Four pistons

of equal area A are used at the four openings to keep the water in

equilibrium. Now an additional force F is applied at each piston.

The increases in the pressure at the centre of the container due to

this addition is

1) F

A 2)

2F

A 3)

4F

A 4) 0

08. A beaker of circular cross section of radius 4cm is filled with

mercury up to a height of 10cm. Find the force exerted by the

mercury on the bottom of the beaker. The atmospheric pressure

5 210 .Nm−= Density of mercury 313600 .kgm−= Take

210 .g ms−=

1) 571N 2) 578 N 3) 584 N 4)all of these

09. If S is stress and Y is Young's modulus of material of a wire, then

the energy stored in the wire per unit volume is

1) 22S Y 2)

2

2

S

Y 3)

2

2Y

S 4)

2

S

Y


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10. A steel wire of length 2m is stretched through 2mm. The cross-

sectional area of the wire is 24mm . Calculate the elastic potential

energy stored in the wire in the stretched condition. Young’s

modulus of steel 11 22.0 10 /N m=

1) 0.2J 2) 0.4J 3) 0.6J 4) 0.8J

11. When equal volumes of two metals are mixed together, the specific

gravity of alloy is 4. When equal masses of the same two metals are

mixed together, the specific gravity of the alloy now becomes 3.

Find the specific gravity of each metal.

1) 3, 4 2) 2, 6 3) 6, 4 4) 6, 8

12. The figure shows a hydraulic press with the larger piston of

diameter 35cm at a height of 1.5m relative to the smaller piston of

diameter 10cm. The mass on the smaller piston is 20kg. What is

the force exerted on the load by the larger piston? The density of

oil in the press is 750 kg/m3. (Take g=9.8m/s2)

1) 1340.8 N 2) 31.3 10 N 3) 310 N 4) 41.5 10 N

13. A hydraulic automobile lift is designed to lift cars with a maximum

mass of 3000kg. The area of cross section of the piston carrying

the load is 425 cm2. What maximum pressure would the smaller

piston have to bear? (g = 9.8 m/s2)

1)56.8 10 N/m2 2) 56.917 10 N/m2

3) 57 10 N/m2 4) 57.2 10 N/m2

14. A wire fixed at the upper end stretches by length l by applying a

force F. The work done in stretching is

1) 2

F

l 2) Fl 3) 2Fl 4)

2

Fl


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15. The area of cross section of the wider tube shown in figure is 900

cm2. If the boy standing on the piston weighs 45 kg, find the

difference in the levels of water in the two tubes

1) 100 cm 2) 30 cm 3) 50 cm 4) 25 cm

16. In a hydraulic lift, used at a service station the radius of the large

and small piston are in the ratio of 20:1. What weight placed on

the small piston will be sufficient to lift a car of a mass 1500 kg?

[take g=10m/s2]

1) 3.75 kg 2) 37.5 kg 3) 7.5 kg 4) 75 kg

17. The pressure at the bottom of a lake, due to water is

6 24.9 10 /N m . What is the depth of the lake?(g=9.8m/sec2)

1) 500m 2) 400 m 3) 300 m 4) 200m

18. Two liquids which do not react chemically are placed in a bent tube

as shown in figure. The heights of the liquids above their surface

of separation are

1) directly proportional to their densities

2) inversely proportional to their densities

3) directly proportional to square of their densities

4) equal

19. A swimmer goes from the surface of water to a depth of 20m, the

change in the pressure on his body is nearly be [take g=10m/s2

1atm=105 N/m2]

1) 3 atmospheres 2) 1 atmosphere

3) 2 atmospheres 4) Zero


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20. The three vessels shown in figure have same base area. Equal

volumes of a liquid are poured in the three vessels. The force on

the base will be maximum in

1) A 2) B 3) C 4) equal in all

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. For a given material 10 26.6 10 /Y N m= and bulk modulus

10 211 10 /K N m= , then its Poisson’s ratio is

22. If the Poisson’s ratio of a solid is 2

5, then the ratio of its young’s

modulus t o the rigidity modulus is

23. A hydraulic automobile lift has input and output pistons with

diameters 10 cm and 30 cm. The lift is used to hold up a car of

weight 41.44 10 .N The force on the input piston is

30.4 10P N .

Then the value of P is

24. A U-tube contains water and oil separated by mercury. The mercury

columns in the two arms are at the same level with 10cm of water

in one arm and 12.5 cm of oil in the other as shown.

25. A wire suspended vertically from one of its ends is stretched by

attaching a weight of 200 N to the lower end. The weight stretches

the wire by 1 mm. Then, the elastic energy stored in the wire is

_______J.


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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. Which of the following are not used in the preparation of 2 2H O

1) Acidifying barium peroxide

2) Peroxodisulphate

3) Auto oxidation of 2-alkylanthraquinols

4) Synthetic resin method

27. 2 2 2 22 2H O H O O→ +

The above decomposition represents

1) Oxidation of 2 2H O 2) Reduction of 2 2H O

3) Disproportionation 4) Acidic nature 2 2H O

28. What is the volume strength of a molar solution of 2 2H O ?

1) 5.6 Vol. 2) 11.2 Vol.

3) 2.8 Vol. 4) 22.4 Vol.

29. 2 2H O can oxidise

1) 2 3Na SO 2) KI 3) PbS 4) 3O

30. For the decolourisation of one mole of acidified 4KMnO , the number

of moles of 2 2H O required is

1) 1/2 2) 5/2 3) 3/2 4) 7/2

31. Which of the following statement regarding 2 2H O is false?

1) It is decomposed by 2MnO

2) It behaves as a reducing agent towards acidified 4KMnO

3) It is more stable in a basic solution

4) It is a strong oxidising as well as a reducing agent in both acidic

and basic mediums


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32. The bleaching properties of 2 2H O are due to its

1) Reducing properties 2) Oxidising properties

3) Unstable nature 4) Acidic nature

33. In alkaline medium, 2 2H O reacts with 3Fe + and 2Mn + ions

separately to give

1) 4 4,Fe Mn+ + 2) 2 4Fe and Mn+ +

3) 2 3,Fe Mn+ + 4) 4 3Fe and Mn+ +

34. Heavy water is manufactured

1) By combination of hydrogen and heavier isotope of oxygen

2) By electrolysis of water containing dissolved heavy hydrogen

3) By repeated electrolysis of water containing little NaOH

4) By repeated electrolysis of water containing little HCl

35. Identify (X) and (Y) respectively in given reaction:

( )+ →3 2 4SO X D SO

2 22Y X C D Z+ ⎯⎯→ +

1) 2 2,D O CaC 2) 2 4 3,H O Al C

3) 2 2,D O Be C 4) 2 2,D CO

36. Which of the following is/are correct

1) melting point of 2 2H O D O 2) density of 2 2H O D O

3) dielectric constant 2 2H O D O 4) Boiling point of 2 2H O D O

37. The melting points of most of the solid substances increase with an

increase of pressure. However, ice melts at a temperature lower

than its usual melting point when the pressure is increased. This

is because

1) Ice is less denser than water 2) Pressure generates heat

3) The chemical bonds break under pressure

4) Ice is not a true solid


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38. Point out the incorrect statements

1) Hardness of water depends upon its soap consuming power

2) Temporary hardness is due to bicarbonates of calcium and

magnesium

3) Permanent hardness is due to soluble sulphates, chlorides of Ca

and Mg

4) Permanent hardness can be removes by boiling water

39. Heavy hydrogen is used:

1) In filling the balloons

2) In studying reaction mechanism

3) In calculating heat of formation

4) As oxidant

40. Zeolites are extensive used in:

1) Softening of water 2) Preparing heavy water

3) Increasing the hardness of water

4) Preparing hydrogen peroxide

41. The O O H− − bond angle in 2 2H O is ( in gas phase)

1) 0106 2) 0 1109 .28 3) 0120 4) 094.8

42. If water is boiled for sometime it becomes free from

1) Permanent hardness 2) Temporary hardness

3) Suspended matter

4) Temporary hardness and dissolved gases

43. Permanent hardness of water is due to the presence of:

1) Bicarbonates of sodium and potassium

2) Chlorides and sulphates of sodium and potassium

3) Chlorides and sulphates of calcium and magnesium

4) Phosphates of sodium and potassium

44. When electric current is passed through an ionic hydride in molten

state:

1) Hydrogen is liberated at anode

2) Hydrogen is liberated at cathode

3) Hydride ion migrates towards cathode

4) Hydride ion remains in solution


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45. Which combination cannot be used for the preparation of hydrogen

gas in the laboratory?

i) Zinc and conc. 2 4H SO

ii) Zinc and dilute 3HNO

iii) Granular zinc and dilute HCl

iv) Pure zinc and dilute 2 4H SO

1) i and iii 2) i, ii and iv

3) iii and iv 4) i, ii and iii



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.

46. What is the molarity of a commercial sample of 33.6 volume

hydrogen peroxide solution?

47. How much hydrogen will be obtained from a mixture containing 9

grams of LiH and 21 grams of 2CaH ?

48. There are three sample labelled as 10 Vol., 15 Vol. and 20 Vol. Half

litre of each sample are mixed and then diluted with equal volume

of water. What is the volume strength of the resulting solution?

49. 2

2

O /

2 2/

2-ethylanthraquinal air

H pdH O⎯⎯⎯→ +⎯⎯⎯ oxidised product in this case how

much percentage of 2 2H O is formed

50. Mass percentage of deuterium in heavy water is:


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11

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 f(x) and g(x) are two functions defined on (-a,a) such that f (x)

and g(x) are both odd functions. Then which one of the following is

correct?

1) fog is an even function 2) gof is an even function

3) ( ) ( )f x .g x is an odd function 4) ( )fof x is an odd function

52. If ‘ f ’ is a real valued function NOT identically zero satisfying

( ) ( ) ( ) ( )2f x y f x y f x .f y+ + − = x,y R then ( )f x is _____

1) odd 2) Even

3) Neither even nor odd 4) both even and odd

53. If ( )f x is an even function and satisfies the relation

( ) ( )21

2x f x f g xx

− =

Where ( )g x is an odd function then ( )10f

=________

1) 0 2) 50

79 3)

49

75 4) 1

54. Let 10 10f : , R− → Where ( )2x

f x sinxa

= +

Where [.] is G.I.F be

an odd function then a

1) ( )10 10 0, { }− − 2) ( )0 10, 3) 100[ , ) 4) 100( , )

55. If ( ) ( ) ( ).f x y f x f y+ = for all real ,x y and ( )0 0f then the

function ( )( )

( ) 2

1

f xg x

f x=

+

1) even function 2) odd function

3) odd if ( ) 0f x 4) neither even nor odd


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56. Let f(x) be a function satisfying ( ) ( ) ( )4 4f x f x f x+ + − = . For all

real ‘x’. If f(x) is periodic . Then the period of f(x) is

1) 12 2) 42 3) 24 4) 21

57. If ( ) ( ) ( ) ( )2f x f x a f x a ..... f x na+ + + + + + + = constant x R

and a > O and f (x) is periodic. Then the period of f(x) is ___________

1) ( )1n a+ 2) ( )1n a

e+

3) na 4) ena

58. Period of ( )( )1

x xf x sin cos

n ! n!

= +

−

1) n! 2) 2 (n!) 3) 2(n-1)! 4) 2(n+1)!

59. The period of the function ( )sin cos

sin cos

x xf x

x x

−=

+ is __________

1) 2

2) 2 3) 4) 4

60. The period of ( ) ( )( )f x sin cosx x= + is _______________,

1) does not exist 2)

3) 2

4) 2

61. If ( ) ( )1 1

= +

f x .f f x fx x

. 0x R − where ( )f x be a

polynomial function of degree n N . Then f(x) = ________________

1) 1nx 2) 2

nx

3) nx 4) 1

nx−


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62. For x R , the function f(x) satisfies ( ) ( ) 22 1f x f x x+ − = . Then

( )4f =_______

1) 13

3 2)

43

3 3)

23

3 4)

3

23

63. Let ( )f x be a function satisfying ( )1

21

f x f xx

+ =

− . Then ( )3 2f

=________

1) 1 2) 3 3) 2 4) -1

64. If ( )f x satisfies the functional equation ( ) ( )2 41 2x f x f x x x+ − = −

then 1

3f

=

______

1) 1

3 2)

1

9 3)

8

9 4)

10

9

65. For x R the function ( )f x satisfies ( ) ( ) 22 1+ − =f x f x x . Then

f(x) = ______

1) 2 2 1

3

x x+ − 2)

2 2 1

3

x x+ +

3) 2 2 1

3

x x− − 4) none of these

66. If f is a function such that

( ) ( ) ( ) ( ) ( )0 2 1 3 2 2 1f ,f ,f x f x f x= = + = − + For all x R . Then

( )5f =__________

1) 7 2) 13 3) 1 4) 5

67. A function ‘ f ‘ well defined x,y R is such that ( ) ( )1 2 2 8f ,f= =

and ( ) ( ) 22f x y Kxy f x y+ − = + where K is some constant. Then

( )f x is ____________

1) x2 2) 3x2 3) 2x2 4) 4x2


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68. The maximum value of the expression

2 2

1

3 5sin sin cos cos + + is

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

69. The difference of the maximum and minimum values of the

function.5 3 83

cos x cos x

+ + +

over R is ______

1) 16 2) 14 3) 15 4) 7

70. If ( ) ( ) ( )3 33 4= + + +f x sinx sin x cos x cos x 21

2 52

sin x+ + . Then

the sum of extreme values of ( )f x is

1) 9 2) 10 3) 11 4) 12



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.

71. If ( )f x satisfies the relation ( ) ( ) ( ) ( )+ + − = 2 .f x y f x y f x f y for all

, ,x y R and ( )0 0;f then ( ) ( )10 10f f− − =_____________

72. If ( )f x is a function such that ( ) ( ) ( )f xy f x f y= + ,

( ) ( )= =2 1, logkf f x x then K =________

73. The minimum value of ( ) ( )3 3 0 3120 105 120cos x cos x x+ + + − is K

Then 4k = _______________


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74. If f is an even function defined on the interval (–5, 5) then the total

number of real values of x satisfying the equations ( )1

2

xf x f

x

+ =

+

are _____

75. If ( )f x is an odd periodic function with period 2 then ( )4f = ____

physics chemistry mathematics · 2021. 2. 1. · 17. the pressure at the bottom of a lake, due to...

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