Class: SZ1 JEE-MAIN MODEL Date: 11-04-2020 Time: 3hrs WTM ... · charged ring, Charged circular arc...

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: SZ1 JEE-MAIN MODEL Date: 11-04-2020

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

mailto:[email protected]

http://www.narayanagroup.com/

SZ1_JEE-MAIN_WTM-16_QP_Exam.Dt.11-04-2020

Narayana CO Schools

2

–:SZ1 Jee-Main Exam Syllabus (11-04-20):–

TOPICS

PHYSICS

PRESENT WEEK 50%:

Electric field strength due to a uniformly charged hollow hemispherical

cup, Uniformly charge sphere, Hollow conducting sphere, Non conducting

sphere, Electric field due to non-uniformly charged bodies: non-uniformly

charged rod, Ring, Radially charged solid non-conducting sphere, large

non-uniformly charged slab, (Excluding Electric field inside a cavity of

conducting and non-conducting charged body), Electric field due to non-

uniformly charged bodies: non-uniformly charged rod, Ring, Radially

charged solid non-conducting sphere, large non-uniformly charged slab,

(Excluding Electric field inside a cavity of conducting and non-conducting

charged body), Applications

PREVIOUS WEEK 50%:

Electric field, Intensity of electric field, Some properties about electric

lines of forces in electric field, Electric field due to a point charge, Vector

form of electric field due to a point charge, Electric filed due to a

uniformly charged rod, electric field strength at a general point due to

a uniformly charged rod, Electric field due to an infinitely long wire,

Electric field due to a semi-infinite uniformly charged wire, Uniformly

charged ring, Charged circular arc at its centre, Uniformly surface

charged disc, Large charged sheet, Charged disc as a limiting case of

large sheet, Applications

TOPICS

CHEMISTRY

PRESENT WEEK 50%:

Nernst Equation, E.M.F of cell, Equilibrium Constant from Nernst equation,

Gibbs free energy, Variation of E.M.F with temperature

PREVIOUS WEEK 50%:

Electro Chemistry: Introduction, Electrochemical Cell, Standard Hydrogen

Electrode, Determination of Electrode Potential, Electrochemical Series.

TOPICS

MATHS

PRESENT WEEK 50%:

Modulus and Amplitude of a Complex Number, Mod-Amp form,

Properties of Modulus and Amplitude, Related Problems, Triangular

Inequality, Parallelogram law, Geometrical Interpretation of Sum and

Difference of two Complex Numbers, Related Problems.

PREVIOUS WEEK 50%:

COMPLEX NUMBERS: Definition of a Complex Number, Algebra of

Complex Numbers, Related Problems, Square roots and Cube roots of

a+ib (excluding cube roots of unity), Conjugate of a Complex Number,

and its properties, 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. A ring of charge with radius 0.5 m has 0.002m gap. If the ring

carries a charge of +1 C, the electric field at the center is

1) 7 17.5 10 NC− 2)

7 17.2 10 NC−

3) 7 16.2 10 NC− 4)

7 16.5 10 NC−

02. A rod of length l with uniform charge per unit length is placed at

a distance d from origin along the x-axis, A similar rod is placed at

the same distance along y-axis. The magnitude of net electric field

intensity at the origin is

1) 0

2

( )

l

d d l

+ 2)

0

2

4 ( )

l

d d l

−

3) 0

2

8 ( )

l

d d l

+ 4)

0

2

4 ( )

l

d d l

+


Narayana CO Schools

4

03. A charged cork ball of mass 1 g is suspended on a light string in

the presence of a uniform electric field as shown. When

( ) 5 1ˆ ˆ3 5 10E i j NC−= + , the ball in equilibrium at 37= . Then the

tension ( )T in the string is (Take sin37 0.60 = and 210g ms−= )

1) 35.55 10− N 2) 36.75 10− N

3) 32.45 10− N 4) None

04. A few electric field lines for a system of two charges 1Q and 2Q fixed

at two different points on the x-axis are shown in the figure. With

the figure what information about charges and electric field we are

getting:

1) 1 2Q Q 2)

1 2Q Q

3) At a finite distance to the of 1Q the electric field is zero

4) At a time distance to the right of 2Q the electric field is zero

05. Electric field in an XY-plane produced by a charged particle is

( )7.2 4 3i j+ N/C at the point (3cm, 3cm) and is 100 i N/C at point

(2cm, 0). Then X coordinate of the charged particle is

1) 1 cm 2) –1 cm 3) 0 cm 4) None

06. Point charges q,-q, 2Q and Q are placed in order at the corners

A,B,C and D of a square of side 2b. If the field at the mid point CD

is zero then 5

2

q x

Q= . Then the value of x is

1) 5 2) 4 3) 3 4) 2


Narayana CO Schools

5

07. A ring of radius a contains a charge Q distributed uniformly over

its length. Find the electric field at a point on the axis of the ring at

a distance x from the centre.

1)

( )2/3

2 203

xQ

a x +

2)

( )1/2

2 202

xQ

a x +

3)

( )3/2

2 204

xQ

a x +

4)

( )3/2

2 20

4xQ

a x +

08. Find the electric field at a point P on the perpendicular bisector of

a uniformly charged rod. The length of the rod is L, the charge on

it is Q and the distance of P from the centre of the rod is a.

1) 2 2

02 4

Q

a L a +

2) 2 2

0 4

Q

a L a +

3) 2 2

04 2

Q

a L a −

4) 2 2

0 2

Q

a L a −

09. A small ball of mass m and charge q+ tied with a string of length

l , rotating in a vertical circle under gravity and a uniform

horizontal electric field E as shown. The tension in the string will

be minimum for

1) 1tanqE

mg

− =

2) =

3) 0 = 4) 1tanqE

mg

− = +


Narayana CO Schools

6

10. A proton and an electron are placed in a uniform electric field.

1) The electric forces acting on them will be equal

2) The magnitudes of the forces will be equal

3) Their accelerations will be equal

4) The magnitudes of their accelerations will be equal

11. Two charges 1q and 2q are kept on the x-axis, and the electric field

at different points on the x-axis is plotted against x. Choose the

correct statement about the nature and magnitude of 1q and 2q .

1) 1q is positive, 2q is negative; 1 2q q

2) 1q is positive, 2q is negative; 1 2q q

3) 1q is negative, 2q is positive; 1 2q q

4) 1q is negative, 2q is positive; 1 2q q

12. Calculate the electric field at the centre of a uniformly charged wire

in the form of an arc of radius r. The wire subtends an angle at

the centre.

1) ( )0

sin /22

Er

=

2)

02E

r

=

3) 0

sin2

Er

=

4)

0

sin

2E

=

13. The electric field intensity in a region of space is given by

ˆˆ ˆ8 4 4 .E xi yj jk= − − Determine the equation of the electric field lines in

the plane z = 0.

1) 3xy = 2) 4x

zy=

3) 2 tanxy cons t= 4) 2 tanx y cons t=


Narayana CO Schools

7

14. A few electric field lines for a system of two charges 1Q and

2Q fixed

at two different points on the x-axis are shown in the figure. With

the figure what information about charges and electric field we are

getting

1) 1

2

13

9

Q

Q= 2) 1

2

9

13

Q

Q= 3) 1

2

1

6

Q

Q= 4) 1

2

7

8

Q

Q=

15. In the given arrangement of a charged square frame the electric

field at centre is given by ( )

0

2 7i j

n

− +

. Then the value of n is___

(The linear charged density is as shown in figure).

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

16. A point charge q is placed at origin. Let .A B CE E and E be the electric

field at three points A (1, 2, 3), B (1,1, –1) and C (2, 2, 2) due to the

charge q. Then choose correct options.

A) A BE E⊥ B) A BE E

C) 4B CE E= D) 8B CE E=

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


Narayana CO Schools

8

17. A charged cork ball of mass 1 g is suspended on a light string in

the presence of a uniform electric field as shown. When

( ) 5 13 5 10 ,E i j NC−= + the ball in equilibrium at oθ 37 .= (Take

2sin 37 0.60 10o and g ms−= = ). Then the charge (q) on the ball is

(Approximately) is

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

18. A point charge is brought in an electric field. The electric field at

a nearby point may decrease if the charge is ____________

1) Negative 2) Positive

3) Neutron 4) All of these

19. A thin non conducting ring of radius R has linear charge density

verying as 0 cos = , 0 is a positive constant and is the

azimuthal angle. The magnitude of the electric field strength at

the centre of ring is

1) 0

02 R

2) 0

04 R

3) 0

0R

4) 0

05 R

20. A cube of side ' 'b has charge ( )q at earth of its vertices. The electric

field at the centre of the cube will be __________

1) Zero 2) 2

32q

b 3)

22

q

b 4)

2

q

b


Narayana CO Schools

9

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. Two charges Q+ each are placed on the two vertices of an

equilateral triangle of side(a). The intensity of electric field at the

third vertex is 2

0

1.

4

QN

a Then the value of N is

22. Three charges, each equal to ,q are placed at the three corners of a

square of side(a). The electric field at the fourth corner is

( ) 2

0

2 2 1 .q

N a+

Then the value of N is

23. Two charges 10 C and 10 C− are placed at points A and B

separated by a distance of 10cm. The electric field at a point(P) on

the perpendicular bisector of AB at a distance of 12cm from its

middle point is 6__________ 10 / .N C

24. A vertical electric field of magnitude 54 10 /N C just prevents a

water droplet of mass 410 kg− from falling. The charge the droplet is

9________ 10 .C− ( )29.8 /g m s=

25. A point charge produces an electric field of magnitude 5 N/C of a

distance of 40 cm from it. The magnitude of the charge is

13________ 10 C− .


Narayana CO Schools

10

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. The EMF of a galvanic cell is determined by using a

1) Voltmeter 2) potentiometer

3) Coulometer 4) Ammeter

27. Which metal pairs when coupled will get maximum EMF for a

voltaic cell

1) Fe and Cu 2) Pb and Cu

3) Cu and Au 4) Ca and Cu

28. Which of the following energy changes occurs in galvanic cell

1) Electrical energy → Chemical energy

2) Chemical energy → Electrical energy

3) Chemical energy → internal energy

4) Internal energy → Electrical energy

29. Pure water does not conduct electricity because it is

1) Neutral 2) Readily decomposed

3) Almost unionized 4) Completely ionised

30. In a Daniel cell when Cu and Zn electrodes are connected current

flows from

1) Cu to Zn within the cell 2) Cu to Zn outside the cell

3) Zn to Cu outside the cell 4) Zn to Cu inside the cell

31. If a spoon of copper metal is placed in a solution of ferrous sulphate

1) Cu will precipitate out 2) iron will precipitate

3) Cu and Fe will precipitate 4) no reaction will take place


Narayana CO Schools

11

32. In a galvanic cell

1) Chemical reaction produces electrical energy

2) Electrical energy produces chemical reaction

3) Reduction occurs at anode

4) Oxidation occurs at cathode

33. For the cell reaction to be spontaneous the EMF of the cell should

be

1) Negative

2) Positive

3) Zero

4) Sometimes positive and sometimes negative

34. Which of the following statements is true for the electrochemical

cell?

1) Electrons flow from copper electrode to zinc electrode.

2) Current flows from zinc electrode to copper electrode.

3) Cations moves toward copper electrode.

4) Cations moves toward zinc electrode

35. Salt bridge contains:

1) Calomel 2) corrosive sublimate

3) H2O 4) agar-agar paste

36. A standard hydrogen electrons has zero electrode potential because

1) Hydrogen is easier to oxidise

2) This electrode potential is assumed to be zero

3) Hydrogen atom has only one electron

4) Hydrogen is the lightest element.

37. The relationship between standard reduction potential of a cell and

equilibrium constant is

1) ocell

nE logKc

0.059= 2)

ocell

0.059E logKc

n=

3) ocellE 0.059n logKc= 4) o

celllogKc

En

=


Narayana CO Schools

12

38. Electrode potential data are given below.

( ) ( )3 2 0Fe aq e Fe aq ; E 0.77+ − ++ → = +

( ) ( )3 0Al aq 3e Al s ; E 1.66 V+ −+ → = −

( ) ( ) 02Br aq 2e 2Br aq ; E 1.08 V− −+ → = +

Based on the data given above, reducing power of Fe2+, Al and Br-

will increase in the order:

1) - 2Br Fe Al+ 2) 2 -Fe Al Br+

3) - 2Al Br Fe + 4) 2 -Al Fe Br+

39. The reduction potential of hydrogen half cell will be negative if (T =

298 K)

1)2

1=HP atm and [H+] = 1.0 M 2) 2

2=HP atm and [H+] = 2.0 M

3) 2

2=HP atm and [H+] = 1.0 M 4) 2

1=HP atm and [H+] = 2.0 M

40. The electrode potential becomes equal to standard electrode

potential when reactants and products concentration ratio is

1) equal to 1 2) greater than 1

3) less than 1 4) none of the above

41. Which of the following statements about the spontaneous reaction

occurring in a galvanic cell is always true?

1) cellEº 0, Gº 0, and Q Kc



4) o

cellE 0, G 0, and Q Kc

42. Adding powdered Pb and Fe to a solution containing 1.0 M is each

of Pb2+and Fe2+ ions would result into the formation of

1) More of Pb and 2Fe + ions 2) More of Fe and 2Pb + ions

3) More of Fe and Pb 4) More of 2Fe + and 2Pb + ions

43. ( ) ( ) ( ) ( )2 1 2 2Pt H P H 1M H 1M H P Pt+ + (where P1and P2 are

pressures) cell reaction will be spontaneous if:

1) P1= P2 2) P1> P2 3) P2 > P1 4) P1= 1 atm


Narayana CO Schools

13

44. The relationship between free energy and electrode potential is

1) G nFE =− 2) G nFE = 3) nFE

GR

= 4) H

GnFE

=

45. The Nernst equation giving dependence of electrode reduction

potential on concentration is

1) o

n

M2.303RTE E log

nF M += +

2)

n

oM2.303RT

E E lognF M

+

= +

3)

n

oM2.303RT

E E lognF M

+

= − 4) o n2.303RT

E E log MnF

+ = −



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. The potential of hydrogen electrode is -118 mv. The + H

concentration of the solution is 2X 10− . Then the value of X is

47. The Eo in the given figure is

48. oE for 2F 2e 2F− −+ → is 2.8 V, oE for 21/2F e F− −+ → is_____V

49. If the solution of the 4CuSO in which copper rod is immersed is

diluted to 10 times, the electrode potential decreased by 2X 10− .

Then the value of X is (take nearest integer)

50. The standard EMF of a cell having one electron change is found to

be 0.591 V at 250C. The equilibrium constant of the reaction is

10Y 10 . Then the value of Y is


Narayana CO Schools

14

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. The value of ( )

( )( ) ( )

2

6 6

2

121 1

21

nnn n

n n

ii i

i

++ + + + −

+ when n is odd integer

, is and 1i = −

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

52. The value of ( )4 1

2 3 4

1

mk k k k

k

i i i i+

=

+ + + = ( 1i = − )

1) 4 1m− 2) 4 1m+ 3) 4m 4) 0

53. The value of 4

4 3 20 4 3 20i i + + − =

____________

where ( )a ib x iy+ = + +

1) 625 2) 256 3) 81 4) 1296

54. If ( ) ( )1 2 2 3

,3 3

i x i i y ii

i i

+ − + + + =

+ − where ,x y R then the value of

( )19 x y+ is equal to

1) 10 2) 15 3) 20 4) 17

55. If ( )2 2

2 2

1 31

2 16

x y x yA iB

y x i y x

+ + + + = +

where ,A B R , then

1) The minimum value of A is 2 for all 0, 0x y

2) 4 1B =

3) The maximum value of A is 4 for all 0, 0x y

4) 2 1B = −

56. The value of 4 3 212 23 16Z Z Z Z− − + + when ( )

15 3

2Z i= − is

1) 4 2) 5 3) 9 4) 12


Narayana CO Schools

15

57. If , ,x y z are distinct complex numbers such that

0,x y z

y z z x x y+ + =

− − − then the value of

( ) ( ) ( )

2 2 2

2 2 2

x y z

y z z x x y+ + =

− − −

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

58. Let , 1,2,3,4.kz k k= = If 1 2 3 1 2 4 1 3 4 2 3 416 9 4 72z z z z z z z z z z z z+ + + = then the

value of 1 2 3 4

1 4 9 16

z z z z+ + + =

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

59. If 1z and

2z are two non-zero complex numbers such that

1 2 1 2 ,z z z z+ = − then the difference between the arguments of 1z and

2z is

1) 2

2)

3

3)

4

4) 0

60. If ( ) ( )2 4

2 2 3 3 ,z i i i− = + then the principal value of the ( )arg z is

1) 6

2)

3

3)

6

− 4)

3

−

61. The modulus-amplitude form of ( )1 cos 2 sin 2i+ + for 3

2 2

is

1) ( )2cos cos sin + 2) ( )2cos cos sin− +

3) ( ) ( )( )2cos cos sin − + − 4) ( ) ( )( )2cos cos sin− − + −

62. If ( ) ( )10 10

1 3 1 3 ,z i i= + + − then arg z is

1) 2

2) 3)

4

4)

6

63. If 1 2 32, 3, 4z z z= = = and

1 2 3 5z z z+ + = then 2 3 3 1 1 24 9 16z z z z z z+ + =

1) 20 2) 24 3) 48 4) 120

64. z is a complex number such that 2 5,z i+ − = then maximum value

of 3 9 7z i+ − is

1) 20 2) 15 3) 5 4) 16


Narayana CO Schools

16

65. If 1 2,z z are two complex numbers such that

1 21, 1,z z= = then the

maximum value of 1 2 1 2z z z z+ + − is

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

66. z is a complex number such that 3 2 4,z i− + = then the absolute

difference between the maximum and minimum values of z is

1) 8 2) 4 3) 2 13 4) 4 13

67. If z is a complex number such that 1 1,z − = then 1 1

arg2z

−

may

be

1) 6

2)

2

− 3)

4

4)

4

−

68. If ( ) 3 22 2 7 72,f x x x x= + − + then the value of 3 5

2

if

− =

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

69. If ( ) 2 2 21 , 1,z a b ic a b c+ = + + + = then 1

1

iz

iz

+=

−

1) 1

a ib

c

−

+ 2)

1

a ib

c

+

+ 3)

1

a ib

c

+

− 4)

1

a ib

c

−

−

70. If z x iy= − (where , , ,x y p q R ) and 1

3 ,z p iq= + then ( )2 2

x y

p q

p q

+

+ is

equal to

1) 1 2) 1− 3) 2 4) 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, -

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

71. If 2

1

3

5

iz

z is purely real, then 1 2

1 2

3 75

3 7

z z

z z

+=

−


Narayana CO Schools

17

72. If 2 1 0,z z i+ + + = then 2

z is

73. If 23 ix y− + and 2 4x y i+ + are conjugate to each other then x y+ is

equal to ( where ,x y R )

74. 1z and

2z are two complex numbers such that 1 2

1 2

2

2

z z

z z

−

− is

unimodular , while 2z is not unimodular, then

1z must be

75. For all complex numbers 1 2,z z satisfying

1 12z = and 2 3 4 5,z i− − =

then the maximum value of 1 2z z− is equal to

"Focus on the possibilities for Success, not on the potential for failure"

Class: SZ1 JEE-MAIN MODEL Date: 11-04-2020 Time: 3hrs WTM ... · charged ring, Charged circular arc...

Documents

Transcript of Class: SZ1 JEE-MAIN MODEL Date: 11-04-2020 Time: 3hrs WTM ... · charged ring, Charged circular arc...