Class: SZ1 JEE-MAIN MODEL Date: 25-04-2020 Time: 3hrs WTM ... ·...

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Class: SZ1 JEE-MAIN MODEL Date: 25-04-2020

Time: 3hrs WTM-17 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-17_QP_Exam.Dt.25-04-2020

Narayana CO Schools

2

–:SZ1 Jee-Main Exam Syllabus (25-04-20):–

TOPICS

PHYSICS

PRESENT WEEK 50%:

Potential inside a metal body, Charge distribution of a metal body,

Potential due to a charged sphere, Non-conducting uniformly

charged sphere, P.D. between two points in E.F, P.D. due to very

large sized bodies, Relation between electric field and potential in

a region, Applications

PREVIOUS WEEK 50%:

Electrostatic P.E., Interaction Energy, Interaction Energy of a system

of two charged particles and for a system of charged particles,

Electrical potential, Potential due to a point charge, Charged rod,

Charged ring, Uniformly charged disc, Electric potential of an

annulus, On the edge of a uniformly charged disc, at the centre of

a Hemisphere having uniform charge density, Applications.

TOPICS

CHEMISTRY

PRESENT WEEK 50%:

Conductometric Titrations

PREVIOUS WEEK 50%:

Standard Potential of Half cells, Electrolytic Concentration Cells,

Problems.

TOPICS

MATHS

PRESENT WEEK 50%:

Section Formula, Area of a Triangle. Locus Problems, Rotation and

Coni's Formula, Equation of a Line and a Circle in Complex form,

Geometrical Applications, Related Problems.

PREVIOUS WEEK 50%:

De Moivre's Theorem, both for integral and rational index, Cube

roots and nth roots of Unity, and their Geometrical Interpretation,

Applications of De Moivre's Theorem, Related Problems, Logarithm

of a Complex Number, Related Problems.


Narayana CO Schools

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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 electric field at the origin is along the positive x-axis. A small

circle is drawn with the centre at the origin cutting the axes at

points A, B, C and D having coordinates (a, 0), (0, a), (–a, 0), (0, –a)

respectively. Out of the points on the periphery of the circle, the

potential is minimum at

1) A 2) B 3) C 4) D

02. Uniform electric field of magnitude 1100Vm− in space is directed

along the line 3 .y x= + Find the potential difference between points

( )3,1A and ( )1,3 .B

1) 0 V 2) –200 V 3) 200 V 4) 1 V

03. Two circular loops of radii 0.05 and 0.09 m, respectively, are put

such that their axes coincide and their centers are 0.12 m apart. A

charge of 610 C− is spread uniformly on each loop. Find the potential

difference between the centers of the loops.

1) 81 KV 2) 71 KV 3) 91 KV 4) 110 KV

04. An infinite number of concentric rings carry a charge Q each

alternately positive and negative. Their radii are 1, 2, 4, 8….meters

in geometrical progression as shown in the figure. The potential at

the centre of the rings will be

1) zero 2) 012

Q

3)

08

Q

4)

06

Q


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05. A metal sphere of radius 3.2m is emitting 92×10 electrons per

second from its surface. It stops emitting electrons when the

potential reaches 90 volt. Then choose correct options.

A) It happens in 100 seconds

B) It happens in 50 seconds

C) Intensity by then is 28.12 v/m

D) Intensity by then is 14.06 v/m

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

06. The field potential in a certain region of space depends only on the

x coordinate as 3ax b = − + , a and b are constants, the distribution

of the space charge ( )x is

1) 0

6 ax 2) 0

2 ax 3) 0

4 ax 4) 0

8 ax

07. The electric field strength vector at the centre of a ball of radius R

with volume charge density ar = , where a is a constant vector,

and r is a radius vector drawn from the ball’s centre is

1)

−= 2

0

1

4E aR 2)

−= 2

0

1

6E aR

3)

−= 2

0

1

2E aR 4)

−= 2

0

1

8E aR

08. Two small equally charged spheres, each of mass m, are suspended

from the same point by silk threads of length l. The distance

between the spheres x<<l . The rate dq/dt with which the charge

leaks off each sphere if their approach velocity varies as / xV a=

is (where a is a constant).

1)

06 2 /

2

mg l

a 2)

0

3 2 /

6

mg l

a

3)

02 2 /

3

mg l

a 4)

03 2 /

2

a mg l


Narayana CO Schools

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09. When the separation between two charges is increased, the electric

potential energy of the charges

1) may increase or decrease 2) increases

3) decreases 4) remains the same

10. A thin wire ring of radius R has an electric charge q. The increment

of the force stretching the wire if a point charge 0q is placed at the

ring’s centre is

1)

= 0

2 2

02

qqT

R 2)

= 0

2 2

012

qqT

R

3)

= 0

2 2

08

qqT

R 4)

= 0

2 2

024

qqT

R

11. The electric field strength vector if the potential of this field depends

on x, y coordinates as ( )2 2a x y = − is (Where a is a constant).

1) ( )= − −2E a xi yj 2) ( )= − −4E a xi yj

3) ( )= − −6E a xi yj 4) ( )= − −E a xi yj

12. Consider a metal sphere, of radius R that is cut in two along a plane

whose minimum distance from the sphere’s centre is h. Sphere is

uniformly charged by a total electric charge Q. The force necessary

to hold the two parts of the sphere together is

1) ( )2

2 2

4

04

QF R h

R= − 2)

2

2

04

QF

R=

3) ( )2

3

032

QF R h

R= − 4) ( )

2

2 2

4

032

QF R h

R= −


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13. A uniformly charged thin spherical shell of radius R carries uniform

surface charge density of per unit area. It is made of two

hemispherical shells, held together by pressing them with force F.

F is proportional to

1) 2 2

0

1R

2) 2

0

1R

3)

2

0

1

R

4)

2

2

0

1

R

14. Two charges C and C− − − 8 84 10 6 10 are at points A and B

respectively, 50 cm apart. The electrical potential due to them zero

on the line AB at a distance from A equal to

1) cm10 2) cm20 3) cm30 4) cm40

15. A and B are two points in an electric field. If the work done in

carrying 4.0 C of electric charge from A to B is 16.0J, the potential

difference between A and B is

1) Zero 2) 2.0 V 3) 4.0 V 4) 16.0 V

16. The electric potential at centre O is

1) Q

d0

1 10

4 2)

Q

d0

1 10

4 2 3)

Q

d0

1 100

4 4)

Q

d 20

1 100

4

17. Four identical charges each of charge q are placed at the corners of

a square. Then at the centre of the square the resultant electric

intensity E and the net electric potential V are

1) E V =0, 0 2) E V= =0, 0

3)E V= 0, 0 4) E V 0, 0


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18. Three equal charges of +6 nC each, are located at the corners of an

equilateral triangle of side 12 cm. Potential at the centre of the base

of the triangle is (approximately)

1) 2230 V 2) 2320 V 3) 2032 V 4) 2302 V

19. Two points P and Q are maintained at the potentials of 10 V and -

4V. respectively. the work done in the moving 100 electrons from P

to Q is

1) J−− 162.24 10 2) J− 162.24 10

3) J−− 179.60 10 4) J− 179.60 10

20. The potential at a point due to charge of C− 75 10 located 10 cm

away is

1) V 53.5 10 2) V 43.5 10

3) V 44.5 10 4) V 54.5 10

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. The electric potential decreases from 120V to 80V as one moves on

the x-axis from 1x cm= − to 1 .x cm= + The electric field at the origin

may be equal to _____________V/cm.


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22. The electric field in a region is directed outward and is proportional

to the distance ( )r from the origin. Taking the electric potential at

the origin to be zero, it is proportional to .Pr Then the value of P is

23. Two charges 10 C and 20 C are placed a separation of 2 .cm The

electrical potential due to the pair at the middle point of the line

joining the two charges is ________ .MV

24. The electric field in a region given by 3

.A

E ix

=

The expression for

the potential in the region assuming the potential at infinity to be

zero is 2

.A

Nx Then the value of N is

25. Charges 62 10 C− and 61 10 C− are placed at corners A and B of a

square of side 5cm as shown in figure. The work will be done

against the electric field in moving a charge of 61 10− from C to D is

3________ 10 Joules−


Narayana CO Schools

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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. Given below is a conductometric titration plot. In that conductance

of a solution in flask is plotted on x-axis (shown as a) and the

volume of the titrant added from burette is plotted on y-axis (shown

as b). Which of the following option(s) is/are correct?

1) it corresponds to a titration of NaOH (in flask) versus HCl

(in burette)

2) it corresponds to a titration of AgNO3 (in flask) versus KCl (in

burette)

3) it corresponds to titration of mixed acid HCl + CH3COOH versus

NaOH (in flask)

4) it corresponds to titration of NaOH (in flask) versus mixed acid

HCl + CH3COOH (in burette)

27. Cell reaction of which of the following cells represents

neutralization reaction of a strong acid by a strong base?

1) 2 2Pt|H |HCl||NaOH|O |Pt

2) 2 2Pt|H |NaOH||HCl|O |Pt

3) 2 2Pt|H |NaOH||NH OH|H |Pt4

4) 2 2Pt|O |NaOH||HCl|O |Pt


Narayana CO Schools

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28. Which of the following is concentration cell?

1) ( ) ( )1 2

2 2P P

Pt|H g |HCl|H g |Pt 2) ( ) ( )1 2

2 2

C CZn s |Zn ||Cu |Cu s+ +

3) ( ) ( )21

2

CC

Ag|Ag aq ||Cu aq |Cu+ + 4) ( ) ( )

1 2

2 2P P

Pt|Cl g |HCl|H g |Pt

29. Determine the standard reduction potential for the half reaction:

2Cl 2e 2Cl− −+ → ?

Given: 2 o2 cellPt 2Cl Pt Cl E 0.15V+ −+ → + = − ; 2 oPt 2e Pt E 1.20V+ −+ → =

1) 13.5 V 2) 1.35 V 3) 2.7 V 4) 0.67 V

30. Which of the following is correct about the below conductometric

graph

1) it is a strong acid vs strong base graph

2) it is a mixture of weak acid and strong acid vs strong base graph

3) it is a strong acid vs weak base graph

4) it is a weak acid vs weak base graph

31. Calculate the EMF of a Daniel cell when the concentration of

4ZnSO and 4CuSO are 0.001 M and 0.1 M respectively . The

standard potential of the cell is 1.1 V.

1) 0.0591 V 2) 11.59 V 3) 1.1591 V 4) 0.0295 V

32. When a weak base is added to strong acid gradually

1) The conductance increases first

2) The conductance decreases first

3) The conductance increases first and then decreases

4) No change in conductance


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33. Calculate the EMF of the cell: ( ) ( )2 2Zn|Zn 0.01M ||Zn 0.1M |Zn+ + at

298 K.

1) 0.0295 V 2) 0.295 V 3) 2.95 V 4) 3.0 V

34. Calculate the EMF of the cell,

( ) ( ) ( )21 2Zn Hg C M |Zn aq |Hg Zn C M+− − at

025 ,C if the concentrations

of the zinc amalgam are; C1=10g per 100g of mercury and C2=1g

per 100g of mercury.

1) 2.95 V 2) 0.295 V 3) 0.0295 V 4) 3.0 V

35. At what concentration of 2Cu + in a solution of 4CuSO will the

elelctrode potential be zero at 25ºC?

-12(anti log ( 11.53 2.95 10 ))− =

Given: ( ) 0 2E Cu Cu 0 .| .34 V+ = −

(anti log (-11.53=2.95 x 10-12))

1) 1229.5 10− 2) 136.0 10− 3)

133.0 10− 4) 122.95 10−

36. The correct statement about electrolyte concentration cell is?

1) the electrode material and the solution in both half-cells are

composed of the same substances

2) only the concentrations of solutions of the same substances is

different

3) ocellE 0=

4) All of these

37. What happens when strong base (NaOH) is added gradually to a

weak acid (CH3COOH)

1) Conductivity decreases gradually

2) Conductivity increases gradually

3) Conductivity first increases and then decreases

4) Conductivity neither decreases nor increases


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38. In case of concentration cells for spontaneous cell reaction

1) Concentration of anodic compartment < cathodic compartment

2) Concentration of cathodic compartment < anodic compartment

3) Concentration of cathodic compartment = anodic compartment

4) All of these

39. In a conductometric titration when weak base (NH4OH) is added

gradually to a weak acid (CH3COOH)

1) After the equivalence point conductance virtually remains

same

2) After the equivalence point conductance decreases

3) After the equivalence point conductance increases

4) Conductance first decreases after the equivalence point

conductance increases

40. ( )3HNO aq is titrated with ( )NaOH aq conductometrically, graphical

representation of the titration as:

1)

2)

3)

4)


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41. Which of the following plots will obtained for a conductometric

titration of strong acid against a weak base?

1)

2)

3)

4)

42. Identify the correct conductometric plot corresponds to the titration

of strong acid verses strong base?

1)

2)

3)

4)


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43. Which of the following plots will obtained for a conductometric

titration of weak acid against a strong base?

1)

2)

3)

4)

44. The below conductometric plot corresponds to the titration of

1) Strong acid vs strong base

2) Weak acid vs strong base

3) Strong acid vs weak base

4) Weak acid vs weak base

45. In a titration when ( )3AgNO aq was added gradually to ( )KCl aq

solution conductivity of the solution is

1) Decreases first and then increases

2) increases first and then Decreases

3) Always decreases

4) Initially slightly increase but after end point increases rapidly


Narayana CO Schools

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

values comprising of positive or negative decimal numbers (place value


46. For a concentration cell oE = ?

47. In a concentration cell the same reactants are present in both the

anode and the cathode compartments, but at different

concentrations. Calculate the EMF of a cell containing 0.040 M

3Cr + in one compartment and 1.0 M 3Cr + in the other if Cr

electrodes are used in both.

48. What will be the emf of the following cell at 025 C (Log(5)=0.698)

( ) ( )2 210atm 2atm

Pt| H g |HCl|H g |Pt

49. Calculate PH of anodic compartment of the following cell

( ) ( ) ( ) ( )2 2 cellPt H |H xM ||H 1M |Pt H if E 0.2364V

1atm 1atm

+ + =

50. If for the concentration cell. ( ) ( ) ( ) ( )n n

s aq aq s

1 1X |X M ||X M |X

20 2+ +

,

cellE 0.029Vat 298K= calculate n.


Narayana CO Schools

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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. tan lna b a ib

ib a a ib

− − =

+ (where ,a b R+ and 1i = −

1) 1 2) 2 3) 1

2 4) 1−

52. Least positive argument of the 4th root of the complex number

2 12i− is equal to

1) 6

2)

5

12

3)

7

12

4)

11

12

53. Sum of the common roots of the equations 3 22 2 1 0z z z+ + + = and

97 29 1 0z z+ + = is equal to

1) 1 2) 1− 3) 0 4) 2−

54. In the argand plane, if three complex numbers are in A.P, then they

lie on

1) a circle 2) straight line

3) an ellipse 4) parabola

55. The value of 10

1

2 2sin cos

11 11k

k ki

=

−

is equal to

1) 1− 2) 0 3) i− 4) i

56. If 2 5

3

z iu

z

+=

− and 2,u = then the locus of z is

1) a straight line 2) a parabola

3) a circle 4) an ellipse


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57. If z is a complex number then the locus of z satisfying the

condition 2 1 2z z− = − is

1) a parabola

2) a pair of lines

3) a circle

4) perpendicular bisector of the segment joining 1

2z = and 2z =

58. If 8 8

cos sin ,11 11

i

= + then real part of 5

1

k

k=

is equal to

1) 1

2 2) 0 3)

1

2− 4) 1

59. If , ,a b c are distinct integers and 1 is a cube root of unity, then

minimum value of 2 2a b c a b c+ + + + + is equal to

1) 6 2 2) 2 3 3) 4 6 4) 2 6

60. If ( ) ( )1 2,A z B z and ( )3C z are the vertices of ,ABC such that

1 2 3z z z= = and 1 2 1 2 ,z z z z+ = − then C is equal to

1) 2

2)

4

3)

3

4)

6

61. In the argand plane, the points A,B and C represent the complex

numbers ,z z and ,z z+ where 0z and 2

.3

cis

= If area of ABC

is 3 sq.unit, then z is equal to

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

2


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62. If the roots of the equation ( ) ( )3 22cos 1 2cos 1 1 0z z z− + + + − = are

the affixes of the vertices of a triangle in the vertices of a triangle in

the argand plane ( )0 of maximum area, then the perimeter

of the triangle is

1) 4 3 2) 3 3 3) 2 3 4) 6

63. If 1 2 11, , ,....., n− are the roots of unity, then

1 2 1

1 1 1.....

3 3 3 n−

+ + + =− − −

1) 1.3 1

3 1 2

n

n

n −

+−

2) 1.3

13 1

n

n

n −

−−

3) 1.3

13 1

n

n

n −

+−

4) 1.3 1

3 1 2

n

n

n −

−−

64. Let z be a complex number such that 012cos3 ,z

z+ = then the value

of 2000

2000

11z

z+ + is equal to

1) 0 2) 1− 3) 3 1+ 4) ( )3 1− −

65. Let z be a root of 5 1 0z − = and 1z , then the value of 15 16 50....z z z+ + +

is equal to

1) 1 2) -1 3) 0 4) 5

66. If is 5th root of 2 and 2 ,x = + then the value of 5 210 10x x x− − =

1) 4 2) 6 3) 20 4) 12

67. The number of 15th roots of unity which are also 25th roots of unity

is

1) 3 2) 1 3) 5 4) 10


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68. 1 2 3 4, , ,z z z z are distinct complex numbers representing the vertices

of quadrilateral ABCD taken in order. If 1 4 2 3z z z z− = − and

4 1

2 1

arg ,2

z z

z z

− =

− then the quadrilateral is a

1) rectangle 2) rhombus

3) square 4) trapezium

69. If z x iy= + and 1

,iz

z i

− =

− then 1 = implies that in the complex

plane

1) z lies on the imaginary axis

2) z lies on the real axis

3) z lies on the unit circle

4) z lies on a circle with radius 2

70. If ,iz i= then loge z is equal to

1) 2

− 2)

2

i− 3)

2

i 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


71. If 2, are cube roots of unity and 21 1 1

2 ,a b c

+ + = + + +

2 2 2

1 1 12 ,

a b c+ + =

+ + + then

1 1 1

1 1 1a b c+ +

+ + + is equal to


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72. The adjacent vertices of a regular polygon of n sides are the points

z and its conjugate .z If ( )

( )2 1,

m

e

I z

R z= − then the value of n is equal

to

73. The solutions of the equation 4 3 24 6 4 0z z i z zi i+ − − − = are the vertices

of a convex polygon in the complex plane. If the area of the polygon

is k then the value of 4k is equal to

74. Given 1z is satisfying the equation 3z = and 1

1

1,x iy z

z+ = + if

2 2 1,

100 64

x y

k+ = then 5k is equal to

75. If 1

1zz

+ = and 2005

2005

1a z

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

n

−

when 1n and 2 2 13a b+ = , then is equal to

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