class: sz3 jee-main model date: 12-07-2020 time: 3hrs wtm-06 … · 2020-07-12 ·...

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Class: SZ3 JEE-MAIN MODEL Date: 12-07-2020

Time: 3hrs WTM-06 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/

SZ3_JEE-MAIN_WTM-06_QP_Dt.12-07-2020

Narayana CO Schools

2

–:SZ3 Jee-Main Exam Syllabus (12-07-20):–

TOPICS

PHYSICS

PRESENT WEEK 50%:

Multiplication of Vectors by a Scalar, Scalar Product, Vector

Product, Worksheet Practice

PREVIOUS WEEK 50%:

Resolution of Vectors, Direction Cosines, Lami's Theorem,

Applications, Worksheet Practice.

TOPICS

CHEMISTRY

PRESENT WEEK 50%:

Crystal lattice of NaCl, CsCl, unit cell, coordination number, limiting

radius ratio, Properties of ionic compounds, Covalent bond,

formation Lewis dot structures, types, Co - valency, formal charge,

Resonance, characteristics of resonance, Properties of covalent

compounds.

PREVIOUS WEEK 50%:

Filling of orbitals in atoms, Aufbau Principle, Pauli’s exclusion

Principle and Hund’s rule of maximum multiplicity. Electronic

Configuration up to 30, Magnetic moments, Chemical bonding:

Introduction, electronic theory of valency, octet rule Ionic bond,

formation, factors favourable for the formation of ionic bond,

electro valency, Crystal lattice energy, born Haber cycle, Fajans

rules

TOPICS

MATHS

PRESENT WEEK 50%:

Transformations: Standard Formulae of Trigonometric

Transformations, Conditional Identities, Related Problems.

PREVIOUS WEEK 50%:

Important Standard Results On Multiple And Sub Multiple Angles,

Problems On Standard Results, Problems Related C±S<0 AND

C±S>0. Miscellaneous Problems.

SZ3 _JEE-MAIN_WTM-06_QP_Dt.12-07-2020

Narayana CO Schools

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SECTION-I(1-20)

(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. If a and b are two vectors such that 4a = , 1/2b = and

. 1a b = − , find the angle between a and b

1) 120º 2) 60º 3) 90º 4) 30º

02. Cross product of vectors obeys

1) commutative law 2) associative law

3) distributive law 4) all the above

03. Find a unit vector perpendicular to each one of the vectors

ˆ ˆ ˆ4 3a i j k= − + and ˆ ˆ ˆ3 2b i j k= + −

1) ˆ ˆ ˆ5 13 11

215

i j k− + + 2)

ˆ ˆ ˆ5 13 11

310

i j k− + +

3) ˆ ˆ ˆ5 13 11

315

i j k− + + 4) 0

04. Distributive law is obeyed by

1) scalar product 2) vector product

3) both 1 and 2 are correct 4) both 1 and 2 are incorrect

05. Let ,a b and c be three vectors such that 0.a b c+ + = If

3, 4 5,a b and c= = = the value of . . .a b b c c a+ + is

1) 20 2) – 25 3) 30 4) 15


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06. For a vector a is three dimensional space, the value of the

expression 2 2 2

i a j a k a + + is

1) a2 2) 3a2 3) 2a2 4) 0

07. The angle between ( ) ( )A B and B A is ( in radian )

1) 2

2) 3)

4

4) zero

08. If 2 3 6A i j k= + + and 3 6 2B i j k= − + then vector perpendicular to

both A and B has magnitude K times that of 6 2 3i j k+ − . Then K is

1) 1 2) 3 3) 7 4) 9

09. If 2 3 2 3A i j and B j k= + = + the component of B along A is

1) 6 2) 1

6 3)

6

13 4)

6

13

10. If ,A Band C are coplanar vectors, then

1) ( ). 0A B C = 2) ( ). 0A B C =

3) ( ). . 0A B C = 4) all the above are true

11. The angle between the vectors ( )i j k+ + and ( )i j k− − is

1) 1 8sin

3

− 2) 1 2cos

3

−

3) 1 8cos

3

− 4) 1 8sin

9

−

12. A Vector P points vertically downwards and another vector Q

points towards north then. The vector P Q points towards.

1) East 2) West

3) South 4) Vertically up

13. A 10 kg body is suspended by a rope is pulled by means of a

horizontal force to make 060 by rope to vertical. The horizontal

force is

1) 10kgwt 2) 30kgwt

3) 10 3kgwt 4) 30 3kgwt


Narayana CO Schools

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14. If ' 'P is in equilibrium then 1

2

T

T is

1) 3 2) 2 3) 1

3 4)

1

2

15. If ' 'O is at equilibrium then the value of the tension 1T and 2T are,

(20N is acting vertically downwards at O).

1) 20N, 30N 2) 20 3 ,20N N

3) 20 3 ,20 3N N 4) 10 ,30N N

16. A force 10N is resolved into the perpendicular components. If the

first component makes. 030 with the force, the magnitudes of the

components are

1) 5N, 5N 2) 5 2 ,5N N

3) 5 3 ,5N N 4) 10 ,10 3N N


Narayana CO Schools

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17. If ˆ ˆ ˆ2 3 4A i j k= − + , its components in YZ- plane and ZX- plane are

respectively

1) 13 and 5 2) 5 and 2 5

3) 2 5 and 13 4) 13 and 29

18. A car weighting 100 kg is on a slope that makes an angle 030 with

the horizontal. The component of car’s weight parallel to the slope

is ( )210g ms−=

1) 500N 2) 1000N 3) 15000N 4) 20000N

19. A man walks towards east with certain velocity. A car is travelling

along a road which is 30º west of north. While a bus is travelling in

another road which is 60º south of west. Find the angle between

velocity vector of man and car

1) 60º 2) 120º 3) 90º 4) 30º

20. A bird moves in such a way that it has a displacement of 12 m

towards east, 5 m towards north and 9 m vertically upwards. Find

the magnitude of its displacement

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


Narayana CO Schools

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SECTION-II(21-25)

(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. If vectors P, Q and R have magnitudes 5, 12 and 13 units and

P Q R+ = , then the angle between Q and R is 1 4

cos13

N−

. Then

the value of N is

22. If 2A i j k= + − , 2 3B i j k= + + and 6 2 6C i j k= − − , then the

angle between ( )A B+ and C will be 018N , then the value N is

23. If 1a and 2a are two non collinear unit vectors and if 1 2 3a a+ =

, then the value of ( ) ( )1 2 1 2. 2a a a a− − is p/2. Then the value of p

is

24. The components of a vector along the x and y directions are (n+1)

and 1 respectively. If the coordinate system is rotated by an angle

60º then the components changes to n and 3. Then the value of

n is

25. A bird moves with velocity 120ms− in a direction making an angle

of 60º with the eastern line and 60º with vertical upward. The

velocity vector in rectangular form is + +ˆ ˆ ˆ10 10 2i j Nk . Then the

value of N is


Narayana CO Schools

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SECTION-I(26-45)


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. In which of the following compounds resonance does not occurs

1) 2H O 2)

2SiO 3) 3SO 4) Both (1) and (2)

27. Resonance in molecules influences

1) Bond length 2) Bond strength

3) Bond polarity 4) All of these

28. The more stable lewis dot structure for CO molecule is

1) 2) 3) 4)

29. Covalent compounds are generally soluble in

1) Polar solvents 2) Non-polar solvents

3) Concentrated acids 4) All solvents

30. Which of the following lewis dot structure is not correct for nitrite

ion?

1) 2) 3) 4)

31. Covalency of Aluminium in ( )2

2 5AlCl H O

+

are respectively

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

32. In 2N O molecule, shown by lewis dot structure

31 2 ..

: :..

N N O − the

formal charges of first, second and third atoms in sequence are

1) 1,0, 1+ − 2) 0, 1, 1+ − 3) 1,0, 1− + 4) 0, 1, 1− +

33. Maximum number of covalent bonds by which two atoms can be

bonded to each other

1) four 2) two

3) three 4) no fixed number


Narayana CO Schools

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34. Which one of the following molecules contains both ionic and

covalent bonds?

1) 2 2CH Cl 2)

2 4K SO 3) 2BeCl 4)

2SO

35. Coordination number of NaCl is

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

36. If Pauli’s exclusion principle is not known, the electronic

arrangement of Lithium atom is

1) 2 11 2s s 2) 1 21 2s s 3) 31s 4) 2 1 11 2 2s s p

37. 2 3,Mg Al+ + have identical_____________

1) Configuration 2) Atoms

3) Ions 4) Molecules

38. The pair of ions having same electronic configuration is __________

1) 3 3,Cr Fe+ + 2) 3 2,Fe Mn+ +

3) 3 3,Fe Co+ + 4) 3 3,Sc Cr+ +

39. Ionic compounds do not exhibit space isomerism because

1) They are solids

2) The ionic bond is non directional

3) They are electrolytes

4) They contain ions

40. Stability of ionic compounds is influenced by

1) Electronegativity 2) Lattice energy

3) Sublimation energy 4) Electron affinity

41. Among ,NaF RbF and CsF more ionic and strongly ionic are

1) ,RbF CsF 2) ,NaF NaF

3) ,CsF NaF 4) ,CsF CsF

42. How many unit cells are present in a cube shaped ideal crystal of

NaCl of mass 1 g? (Atomic masses : Na = 23, Cl = 35.5)

1) 211.7 10 unit cell 2) 212.57 10 unit cell

3) 215.14 10 unit cell 4) 211.28 10 unit cell


Narayana CO Schools

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43. AB is an ionic solid. The ionic radii of A+ and B− are respectively cr

and ar . Lattice energy of AB is proportional to

1) c

a

r

r 2) ( )c ar r+ 3) a

c

r

r 4)

1

c ar r+

44. Which of the following reaction involves the Liberation of energy?

1) ( ) ( )s gNa Na+⎯⎯→ 2) ( ) ( )2 2

g gCl Cl⎯⎯→

3) ( ) ( ) ( )g g sNa Cl NaCl+ −+ ⎯⎯→ 4) ( ) ( ) ( )s g g

NaCl Na Cl+ −⎯⎯→ +

45. The cation with high polarising power is

1) 2Mg + 2) 1K + 3) 1Cu+ 4) 3Al +

SECTION-II(46-50)



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. How many electrons are delocalised in Pyridine?

47. A compound of vanadium possesses of magnetic moment of

1.73BM. The oxidation state of Vanadium in this compound is

48. Magnetic moment of xM + is 24 .BM The number of unpaired

electrons in xM + is

49. How many of the following compounds violate octet rule?

I) 5BrF II) 6SF III) 7IF

IV) 4XeOF V)

2ClF VI) 4PCl+

50. Total number (sum) of valence electrons present in 2

3CO −


Narayana CO Schools

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SECTION-I (51-70)


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. sin47 sin25 sin61 sin11− + − =

1) cos7 2) sin7 3) 2cos7 4) 2sin7

52. sin 70 cos 40

cos70 sin 40

+

+ =

1) 3 2) 3 3) 1

3 4)

1

2

53. If sin sin ,cos cosa b+ = + = , then ( )sin + =

1) ab 2) a b+ 3) 2 2

2ab

a b− 4)

2 2

2ab

a b+

54. If cos cos ,sin sina b+ = + = and 2 − = , then cos3

cos

=

1) 2 2 2a b+ − 2)

2 2 3a b+ − 3) 2 23 a b− − 4)

2 2

4

a b+

55. In ABC , sin 2 sin 2 sin 2

cos cos cos 1

A B C

A B C

+ +

+ + − =

1) 4cos cos cos2 2 2

A B C 2) 4sin sin sin

2 2 2

A B C

3) 8cos cos cos2 2 2

A B C 4) 1 4sin sin sin

2 2 2

A B C+

56. If ( )1

sin sin 25

B A B= + , then ( )tan

tan

A B

A

+ is equal to

1) 5

3 2)

2

3 3)

3

2 4)

3

5

57. If A B C+ = , then 2 2 2cos cos cos 2cos cos cosA B C A B C+ + − =

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

58. 2 2sin 14 cos 16 sin14 cos16 + − =

1) 1

4 2)

3

4 3)

1

2 4)

3

2


Narayana CO Schools

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59. If ( ) ( )cos 60 ,cos ,cos 60− + are in H.P., then cos =

1) 2

3 2)

2

3 3)

3

2 4)

3

2

60. 2 2sin 8 sin 7

sin8 cos8 sin 7 cos7

−

− =

1) 1

2 3+ 2)

1

2 3− 3)

1

3 2− 4) 2 3+

61. If 90 180 , then 1 cos 2 1 cos 2

1 cos 2 1 cos 2

+ + −

+ − − =

1) tan4

+

2) tan

4

−

3) cot 4) tan

62. If

2

2

tan 194

cosec cos cot 4 sec2 2

tan 14

− − = +

− +

, then =

1) 2) 2 3) 22

− 4) 4

63. The value of 2

2

1 tan 15

1 tan 15

−

+ is equal to

1) 1 2) 3 3) 3

2 4) 2

64. If tan , tan2 2

are the roots of

28 26 15 0x x− + = then ( )cos + =

1) 627

725 2)

547

715 3)

547

715

− 4)

627

725

−

65. If 1

2cos 20xx

+ = then the value of 3

3

1x

x+ =

1) 1

4 2)

1

2 3) 1 4)

1

8

66. If 1 cos

tansin

BA

B

−= , then tan2 tanA B− =

1) 0 2) 1 3) 1

2 4)

1

4


Narayana CO Schools

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67. If 2 tan tan2 2

= , then

3 5cos

5 3cos

+

+ =

1) cos 2) sin 3) tan 4) cot

68. If 1

tan7

= , is acute, then cos2 is equal to

1) 12

25 2)

24

25 3)

48

25 4)

24

25−

69. If sec cos 1− = , then 2tan

2

=

1) 5 2+ 2) 5 2− 3) 2 5− 4) 0

70. If ( )sin a+ = and ( )sin b+ = , then ( ) ( )cos2 4 cosab− − − =

1) 2 21 a b− − 2)

2 21 2 2a b− −

3) 2 22 a b+ − 4)

2 22 a b− −

SECTION-II(71-75)



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. 2 2 2 2 2 2sin 12 sin 21 sin 39 sin 48 sin 9 sin 18+ + + − − is equal to ______

72. If ( ) ( )2 2 2cos cos sin sin .sin

2k

− − + − =

, then

2 24k + is equal to

73. If 2 4 8 14 1

cos cos cos cos15 15 15 15 k

= , then k is equal to ______


Narayana CO Schools

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74. If 2 2 cos 1 674a a x− + = and tan 7

2

x =

, then the integral value of a is

_____

75. If 1 2 3 4 5 6

14cos36 cot 7

2n n n n n n

+ = + + + + + then the value of

6

1

i

i

n=

is equal to

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class: sz3 jee-main model date: 12-07-2020 time: 3hrs wtm-06 … · 2020-07-12 ·...

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