advanced test 6 paper-1 key & sol.(08!05!2014)

Date : 08-05-2014RIIT JEE-ADVANCED

TEST [6][ Paper - 1 ]

JEE | MEDICAL-UG | BOARDS | KVPY | NTSE | OLYMPIADS

Target : JEE 2014

ANSWER KEY

MATHEMATICS

1. (C) 2. (B) 3. (C) 4. (B) 5. (C)6. (A) 7. (C) 8. (B) 9. (D) 10. (B)11. (A,B,D) 12. (C,D) 13. (A,C,D) 14. (A,C) 15. (A,D)16. (8) 17. (3) 18. (1) 19. (7) 20. (8)

PHYSICS

21. (D) 22. (C) 23. (D) 24. (A) 25. (B)

26. (A) 27. (C) 28. (D) 29. (B) 30. (B)

31. (ABC) 32. (ABCD) 33. (ACD) 34. (ACD) 35. (AC)

36. (2) 37. (1) 38. (6) 39. (3) 40. (4)

CHEMISTRY

41. (B) 42. (D) 43. (A) 44. (D) 45. (D)

46. (B) 47. (B) 48. (C) 49. (B) 50. (A)

51. (A,B,D) 52. (AD) 53. (AB) 54. (ABCD) 55. (ABCD)

56. (2) 57. (4) 58. (9) 59. (4) 60. (4)

RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014

2

PART-I: MATHEMATICS

= = = = = = = = = = = = = = = = = = = = == = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =1. (C)

1! 2! 3! 4! 33 Topic :- Number System / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir

2. (B)

22 2sin & 0 sin 1

4x y

xy

Topic :- Trigonometrical Ratios and Identities / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir3. (C)

Homogenise & checkTopic :- Pair of straight - lines / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir

4. (B)

tan tan 0A A Topic :-Properties and Solutions of triangle / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir

5. (C)

Equation of the tangent to the curve 2 5 6x x from origin at point 2, 5 6 is

2 5 6 2 5y x (putting 0x y ) 6

Slope of tangent at point 62 5 5 2 6x

Now take help of the graphTopic :- Application of Derivatives / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir

6. (A)

3 2

3 2

d x n n xx x n x

Topic :- Indefinite Integration / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir7. (C)

Use property IV of definite IntegrationTopic :- Definite Integration / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir

8. (B)

2 2 2

4

.2 2 2x xy e dx e ydy dx

y

2 2

2 22 2 0x xe ed d x x c

y y

Topic :- Differential equation / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir


3

9. (D)Length of diagonals of the parallelogram are equalTopic :- Complex Number / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir

10. (B)

1x y z

Topic :- Inverse Trigonometric function / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir11. (A,B,D)

Replace sin x with cosecx sin cosecx x 2sin 1x

Topic :- Functions / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir12. (C,D)

Period of f x can be 2 is a b

when ,a b f x has period . Let us consider the domain 0,

Case -I 0, ,2

f x 2 2sin cos sina b x a b x

where 2 2

sin ba b

and 2 2

cos aa b

is an a cute angle

Clearly maximum value will occur when 2

x

and minimum value at 0x or 2

x

Similarly Case - II ,2

x

Topic :- Functions / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir13. (A,C,D)

Analyse case by caseTopic :- Functions / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir

14. (A,C)

xx

etc.

2 2 2

2a b c

a b b c c a

x

q r b cr p c ap q a b

Topic :-Determinants and matrices / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir


4

15. (A,D)Given equation can be written as

22

tan 1sec dy yydx x x

Put 2tan sec dy dty t ydx dx

2

1 1dt tdx x x

which is a linear equations

1

.dx

xI F e x

2

1tx xdx cx

tanx y n x c Topic :- Differential Equations / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir

16. (8)

10 sin cosOA OB

10 2 sin4

max10 2OA OB

Also OA OB AB Topic :- Straight line / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir

17. (3)Clearly the given fixed point is focus of the parabola and the locus is directrix.Topic :- Parabola / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir

18. (1)20112011' ' 1P Q P P Q P

Topic :- Matrix and determinant / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir19. (7)

ˆˆ ˆ3 7A B i j k

Now max

ˆˆ ˆˆ ˆ3 7A B C i j k C

59 1 59 Topic :- Vector / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir

20. (8)Let first term is a and common difference is d.

12a d sum of first nine terms 12 9 27d Hence 200 12 9 27 220d

89 109 427 27

d d

Topic :- Sequence and series / Level :- II / (Adv. -1) Test - 6 / KGm Sir


5

PART-II: PHYSICS= = = = = = = = = = = = = = = = = = = = == = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =21. (D)

a

A1 2A

V

V

v sin n

nv cos

2 /n

Length of the side of the regular polygon is decreasing from a to zero at the rates 2cosV Vn

the

time after which the particles meet,

2cos

atv v

n

22 sin

a

vn

the distance covered by each particle = vt

22sin

a

n

Topic: Kinematic_L-2_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

22. (C)

1 12 22 2 2

m mTk k

112

mk

2 12mk

Topic: SHM_L-2__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir


6

23. (D)

6V

2V

1

1

The part of the circuit shown can be replaced by a single battery of emf

1 2 2 1

1 2

6 1 2 1 22

E r E rE vr r

Internal resistance 1 2

1 2

12

r rrr r

Hence original circuit diagram can be replaced by

2A BV V V Topic: Current Electricity_L-2__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

24. (A)For real object convex mirror always forms a virtual image

Using 1 1 1f v u we get , 1 1 1

v f u

For ,u f V is ve image is real

For ,u f V is ve image is virtual

option (A) is correctTopic: Optics_L-2_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

25. (B)Since temperature remains unchanged therefore , .Uf Ui So Q W In the first step which is isochoric,

0.W In second step, pressure pn

. Volume V is increased from V to nV

1p nW nV V PVn n

12 1RTn

Topic: Thermodynamic_L-I_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir


7

26. (A)Distance between plates on left hund side is d whereas on the right hand side is

sind t d l is small Mean distance between plates

12

d d l

12

d l

then using 0 ,ACd

we get

12 20 0 111 22

l l lCd dd lx

20 1

2l l

d d

Topic: Capacitors_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir27. (C)

Current in left network 6 29 3

A

Current in right network 12 49 3

A

2 4 43 5 2 5 103 3 3XYV

83

V

Topic: Current Electricity_L-I__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir28. (D)

By law of refraction sin constantn we get sin 90 sin 90n ( where is the angle of indinationof ray at B)

Then it implies that 1cosn

and 2tan 1n 3/ 2 3/ 41 1y y

or 3/ 4 3/ 4dy y or dx y dydx

or

3 14

1/ 443 14

yx y

or 4 256x yTopic: Optics_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir


8

29. (B)(B) Explanation

The equation of straight line AB passsing through two point, 0 0 0 0,3 & 3 ,V P V P is

0 00 0

0 0

3 33

P PP P V VV V

0 0 0

0

4PV PVPV

From ideal gas equation PV = nRT

0 0 0

0

4PV PVPV VTnR V nR

-----------------(1)

or2

0 0 0

0

4PV V PVTnRV

---------------------------(i)

For temperature to be maximum

0 0 00 4 2 0dT PV PVdV

Using the value of volume in equation (i)

we get 2

0 0 0 0 0max

0

4 2 2PV V P VT

nRV

2 20 0 0 0 0 0 0 0

max0 0

8 4 4 4PV PV PV PVTnRV nRV nR

choices (A), (C) & (D) are wrongTopic: Thermodynamics_L-II__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

30. (B)Using Fleming’s left hand rule, the Alpha particles, being positively charged and heavier, will be deflected tothe left but not large amount. Similarly electrons being negatively charged and lighter are deflected to theright.Topic: Magnetics_L-I_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

31. (ABC)

[sin sin ]XGIR

[cos cos ]YGIR

Now If then 2 sinxGlR

0YI so, choice (A) is correct and choice (D) is wrong.


9

If 2 ( If length of rod is infinite )

2sin sin2 2X

G GIr r

So, choice (B) is correct.

0YI

Relation between gravitational field intensity and gravitational potential,

dvIdr

0 2v

r

GdV drr

0 2 log loge eV G r

2 log loge eV G r

2 logerV G

loger

is undefined

i.e., choice (C) is correctTopic: Gravitation_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

32. (ABCD)ExplanationAngular momentum = Linear momentum x Perpendicular distance from the point of rotationL Jl

Also 2

3mlI

L I

2

3 3L Jl JI ml ml

Kinetic energy 2 2 2 2

23

22 23

L J l JKmlI m

3

2 2Cl JV

m

So. choices (A) , (B) , (C) and (D) are correct.Topic: Rotational_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir


10

33. (ACD)Explanation:

Epoch = Initial phase 2

( obvious )

velocity of wave 2 110 5

VK

units

velocity of particle 2(3.5)sin 2 102P

dyV t xdt

units are to be observed carefully.So choices (A), (C) and (D) are correct.Topic: Waves_L-I_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

34. (ACD)

pLi

7

O

O

O

Q value of reaction is

2 4 7.06 7 5.6Q MeV

Q = 17.28 MeVHence choice (A) is correct and choice (B) is wrong

Applying energy conservation

2pK Q K ----------------------(1)

where pK and K are the kinetic energies of proton and -particle respectively

From conservation of linear momentum,

2 2 2 cosp pm k m k ------------(2)

Squaring both sides

22 4 2 4 cosp p pm k m k

11616pk k

i.e, pK K --------------------------(3)

Solving (1) and (3) with Q = 17.28 MeVHence choice (c) and (d) are correct,Topic: Modern Physcis_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir


11

35. (AC)On contact , the net excess presure is given by

4 4 4 1 1 1r a b r a b

on merging 3 3 3

0 0 04 4 4 4 4 4

3 3 3P r P a P b

r a b

3 3 3 2 2 20 4P r a b a b r

r depends on 0P and

So, (a) and (c) are correct and (b) and (d) are incorrect.Topic: Properties of Matter_L-II__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

36. (2)

4 1 cos 2U x

duFdx

8sin 2x

8 2 .....x x is small

16x 16K

2 mTk

1216

sec2

2n Topic: SHM_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

37. (1)When shells are connected, charge on inner shell will be transferred to the outer shell

22 2i

K QKQVR R

i.e., 032KQVR

0V

1n Topic: Electrostatics_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir


12

38. (6)

V LVB= (1) (2) (3)= 6V

6R C LV V V V ( All are in parallel)

LdiV Ldt

6 2 didt

3 /di A Sdt

at 2 sec , 3 6I ATopic: EMI_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

39. (3)Blocks A & C both move due to friction. But less friction is available to A as compared to C. Becausenormal reaction between A and B is is less. Maximum friction between A and B can be

sf , max Am g

12

mg

maximum acceleration of A can be, maxmax

2sf gam

Also, max 3D

D

m gam m

3Dm m

3n Topic: NLM and Friction_L-II__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir

40. (4)Mechanical energy is conserved in both the cases

22 2

0 01 5 1 12 4 2 2

m V mV I

i.e., 2

2 2 00 0

2516

VIV Vm R

i.e., 2

2

25 116

mKmR

i.e., 34RK

4n Topic: Rotational dynamics_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir


13

PART-III: CHEMISTRY= = = = = = = = = = = = = = = = = = = = == = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =41. (B)

Structure with octet complete (I and III) are more stable than structure with incomplete octet (II and IV).(Most Important point to decide the stability of resonating structures )Negative charge on more electronegative atom is more stable.Topic:Concept of Resonance_L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

42. (D)1·5 0.0821 223

1mixdRTM

P

= 33.61

2

1mix CO COM M x M x

33.61 44 28 1x x

0.35x 1 0.65x (mole fraction of CO)Topic: Gaseous State _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

43. (A)

Topic: Chemical Bonding _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.44. (D)

In B-D glucose all OH & CH2OH at equatorial position (B-D glucose is more stable than D glucose)Topic: Carbohydrates _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

45. (D)Si does not disproportionate because it cannot take negative oxidation state.Topic: P-Block _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

46. (B)

Topic:Chemical Kinetices _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.47. (B)

2 388 802

gm gmFeS Fe O

Let FeS is x gm in 100 gm of ore. x gm FeS produces 80x/88 gm of Fe2O3.

80488

100 100

x x 44x

Topic: Mole Concept - 1 _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.


14

48. (C)H E nRT H E RT H E

Topic: Thermodynamics - 1 _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.49. (B)

both 3

||&

O

H C CH group are presentTopic: Carbonyl Compound - 1 _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

50. (A)

Topic: Alcohol, Alkene, Carbonyl (Mixed)_ L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

51. (A,B,D)

2 33 42B OH H O B OH H O

3 4B OH NaOH Na B OH

Topic: P-Block _ Sub Topic _ Boron Group _ L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

52. (AD)(A) 10–2M HCl will neutralise 10–2 M NaOH 7pH

(B) 1 410 10M HCl M HCl Resultant conc. = 5.05×10–3 M 2.3pH (C) NaCN will hydrolyse to give pH more than 7

(D) As 7a bpK pK pH

Topic: Inoic Equilibrium_ L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.53. (AB)

4 3 2 4312 4 3Al C H O Al OH CH

2 2 424 2Be C H O Be OH CH

Topic: Metal Carbides _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.


15

54. (ABCD)101

A

A

V litreP atm

isothermal

1

10

B

A AB

B

V litreP VP atmV

B C adiabatic process

PV K

B B C CP V P V

BC B

C

VP PV

For Monoatomic Gas 52

5 /3110

10CP

5 213 310 10

For Diatomic Gas 7 215 57 10 10

5 CP

As the curve for compression (AB) is higher than the cruve for expansion (BC) thre network in done on thesystem .Topic: Cycloalkanes _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

55. (ABCD)

(A)

O

O

H C3

H

(1) LiAlH4 (excess)

(2) H O2

OH

OH

H C3

H

opticallyin active

(B)

O

O

H C3

H

(1) CH MgBr3 (excess)(2) H O2

OH

OH

H C3

H

opticallyin active

(C)

(D)

Topic: Stereo Isomerism_L- 2_Target-14_Advanced Test [6]_P-1_KRch sir.


16

56. (2)

2

4

85

n factor of Cu S isn factor of KMnO is

8 1.25 5 ? ? 2Topic: Mole _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

57. (4)2 13.6IE Z eV

4 13.6 54.4IE of He eV 3 16 13.6 217.6IE of M eV

2 16Z 4Z Topic: Atomic Structure_L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

58. (9)Topic: Stereo Isomerism_L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

59. (4)

ElcB Mech occurs when

(1) Acidic H is present

(2) Poor leaving group is presentTopic: Elimination Reations_L- 2_Target-14_Advanced Test [6]_P-1_KRch sir.

60. (4)Topic: Carbon Family_ Sub Topic : Silicates _ L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.

advanced test 6 paper-1 key & sol.(08!05!2014)

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