-1-

JEE-ADVANCEDMODEL GRAND TEST PAPER - I

Time : 3 hrs ] [Number of questions : 60

0ˆB B tk= !"

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2s time1s

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time

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1s 2s

1

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3

4m

5

4m /

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+ 012".$

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1 yµ =

+ )

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XThe path of the lightfollowed after successiverefraction is as shown

H

2

13

− -2

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( # 5

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B-

E

B LC

B LC

E

B

E LC

6 # 7'%$%

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-1

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9 '1: : ##

-

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-3-

; < 8

( )0 cosV t

IR

ω= -

( )0 cos / 2V tI

R

ω π+=

0 cosV tI

R

ω= 03 cosV tI

R

ω−=

= # ρ

>??%#

- @A

( )2 22 1

2 L

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2

1

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πρ

( )1

2 1

R

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1 *# %(1 #, - # - # # #

3 2 cm %1- #

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Section-II

(One or More options correct Type)

This section contains 5 multiple choice question. Each question has four choices (A), (B),(C) and (D) out of which ONE or MORE are correct.

8-##B#& '1#

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V

S

R

+q - q

time

charge

q1

qC2 = CC1 = C

8

qV

CR

−

-##2

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7 2

CV q+

3 -

% 0ˆB k− $# tany x θ= '1

# # 0ˆv i

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×Magnetic

θ(q, m)

y

x

# 0

mt

qB

θ=

-# 0

2 mt

qB

θ=

.## ( )0 0

0 0

sin 2 , 1 cos 2 ,0mv mv

qB qBθ θ

−

.## ( )0 0

0 0

sin , 1 cos ,0mv mv

qB qBθ θ

−

+ 8 77++11 #C#15

7%'+117 -7%'(117 10R = Ω 20R = Ω

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-5-

( # σ+ σ− # $DE# F ##G: # H I

#*3J 2k

m

-#*3J# 02

q

k

σ∈

#*3J- ##

6 --#68-#@ --@

6 -0%(C9%(C9

Section-III

(Integer value correct Type)

This section contains 5 questions. The answer to each question is a single digit integer, rangingfrom 0 to 9 (both inclusive)

0 > ω -$#B -

-$ 2 2mL

ke

ω3

< G

9 8

5m (C,

# -E 5 rad / s <

#D@4

P4 m/s

5 rad / s

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-6-

; : # G $#

G1

42

m andσρ

= =

σ

σ

= # 61 %#(0

α # 8 # #61

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, ##- G'G##

G'0/C8 # $ 7'(1F

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%'1C%

Section-I

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-*#-+11L

F0 0 F0 F+%

%% ##8 G- (61

#)

4

2344 10 J−× 2344 10 kJ−× 234.4 10 J−× 234.4 10 kJ−×

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-7-

%+ 8 JF*J61N*61N#- 8J #- NJ -%6N 61N 96N ++++N

%( < #1 2( ) ( ) ( ) ( ) ( ) ( )| | || | |s s aq C aq C s sAg AgBr KBr KCl AgCl Ag O

?P 4

@5 8$# -

A5 -#( ) ( )| || |

sp spAgBr AgClK K

Br Cl

Ag Ag Ag Ag

− −

+ +

?58$#

*5 -#( ) ( )sp spAgBr AgClK Cl K Br− − × < ×

A) P B) R C) QS D) PQRS

%6 $

3PCl 3NCl 5PCl 3AsCl

%0 ) # ##$ 4NH OH

4 4,CuSO CdSO ( )3 42,Cu NO ZnSO

3 3,FeCl AlCl -

%9 85 ( )3

2 6C o H O

+

− O 885 ( )

2

2 6C u H O

+

− O8885

2

6P t F−

− 875 ( )2 33

C o H O F−

-- -# $5

88888887 3 2sp d→ 88888887 2 3d sp→

8Q888 2 3d sp→ 8Q87

%; #!"#

5 32 5 ,

H OKCNDMSO heat prolonged heat

C H Cl X Y+

→ →

2 5C H CN 2 5 2 2C H CH NH 2 5C H CN 2 5 2C H CONH

2 5C H NC 2 5 3C H NHCH 2 5C H CN 2 5C H COOH

%= #5

3 3 2 :, Ph P CH CH Br A 2 5 :, A C H ONa B C O B C= + →

3CH

3CH

3 2 3Ph PCH CH Br− 3 3 Ph P CH CH

3CH

3CH

3C CH CH= − 3CH

3CH

2CH CH CH− =

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-8-

+1

O

OMe ’X’. ) -’ ’?X

OMe

O

OMe

O

OMe

:O:

#

Section-II

(One or More options correct Type)

This section contains 5 multiple choice question. Each question has four choices (A), (B),

(C) and (D) out of which ONE or MORE are correct.

+ ) CB?? 4

B $

#, ##- o oT A BP P P=

3- ,#- #

1J 2HgCl ,F1;0M8

8 - ###

+% ) C?P 4

8# 42

SnO Sn

8- 2SnO 22 3

SnO SnO

# -

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-9-

++ )3

3< 3 3 38

+( 8 .- -,4

,&.- 3AlCl

,&( ) 3 .3 22

BF HFCH C CH= →

,&.- 2 4H SO→

,&( ) 33 22

AlClCH C CH= →

+6 ) # # 4

3CH CHO O OH

3 2 2 2 3CH CH CH CH CH OCH−

OH

3CH CH−

3OCH

3OCH

Section-III

(Integer value correct Type)

This section contains 5 questions. The answer to each question is a single digit integer, ranging

from 0 to 9 (both inclusive)

+0 < 2 2 22NO H N O H O+ → + dp

dt −

61%6

#+0161# NO G#

#-8#NO G#-

dp

dt01;##

+11 61 B -

log 2 0.301;log 3 0.477; log 5 0.699;log 7 0.845

+9 ( )3Pt gly

+ RRRRR

+; 3 4 6 5 4 3, , , , ,NF CCl SF PCl SiF BCl E RRR

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-10-

+= 3 #

3 2 ?CH CH MgBr

O

O

Ph

O

Cl

O

O

O

H C H− −

O

O

3CH C N− ≡ 2CO $ O

O

(1 3#- 4

Section-I

( ? 1

( )3 9 1x x

f x =− +

. # #

[ ]1,2 -[ )1, 2 ( ]1, 2

(% ABC∆

S-S8 1r

10 1 r

r- 11 2

r

r< < 12 3

r

r 13 4

r

r

(+ 8 [ ] ( ): 0,1 0,f → ∞ -##1 1

0 0

( ) 1, ( )= =∫ ∫f x dx xf x dx α 1

2 2

0

( )x f x dx α=∫

% - 1 8

(( <-%+=

#-- 0

6C= -(C= ;C= C=

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-11-

(6 >-# B8$,

-$ xOA yOB xOB yOC xOC yOD xOD yOA+ = + = + = +

-

- -

(0 - G ( )( )( )2 22 2 2 4x k x k x kx k− − − + + − #

-% 1

(9 -

2

2sin 2 coslog sin 1 log sin 3

4 cos 4sin

x xdx a x b x c

x x

− = − + − +− −∫ #

3 11

,2 2

− -3 11

,2 2

3 11

,2 2

− 3 11

,2 2

− −

(; - - %1% #%1%

11( -110 116 (

(= >B-# ABC∆ 2 3 0OA OB OC+ + =

% -+C% + 6C+

61 > 5 2( ) 1p x x x= + + , 1 2 3 4 5, , , ,x x x xx 2( ) 2.g x x #

1 2 3 4 5( ) ( ) ( ) ( ) ( )g x g x g x g x g x C%+ -%+ .%+

Section-II

(One or More options correct Type)

This section contains 5 multiple choice question. Each question has four choices (A), (B),(C) and (D) out of which ONE or MORE are correct.

6 > ( ) ( )f x x 1 x x 1= + + − C4

f 1 3 -x 1- $'1 Rf 1 5

6% > 1 2 3 4 5 6a a a a a a

1 2 3 6........p a a a a= + + + +

1 3 3 5 5 1 2 4 4 6 6 2q a a a a a a a a a a a a= + + + + +

1 3 5 2 4 6r a a a a a a= + 3 22 0x px qx r− + − =

-( )1 2,a a --( )1 3,a a

-( )1 4,a a -( )3 5,a a

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-12-

6+ 8 : 2, 2 ( ) sin cos f N such that f x x x $

. - .

6( #- @0; 8 E +$&(&1'1+$&(.1'1

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1 !

2. 2n

n

n−

+

+

-$ +# -:( )( )( )

( )

23 21 2 !

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n n

n

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n

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2

1

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12 2n

n n n

n−

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+

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( )

22

1

. 1

2n

n n

n−

−

+

Section-III

(Integer value correct Type)

This section contains 5 questions. The answer to each question is a single digit integer, rangingfrom 0 to 9 (both inclusive)

60 # λ

( )( )( ) ( )( ) ( )0,x a x c x e x b x d a b c d eλ− − − + − − = > > > > RRRRRR

69 > 1 2, ,......., nz z z -. .,# $- 1 2 ....... 0+ + + =nz z z

1 1

Ren n

j

j k k

z

z= =

∑∑ RRRRRRRRRRRR

6; -$#2

1 1 1x y z

xy yz xz

+ + + + +

$#2

1 1 1x y z

x y z

+ + + + +

_________m n− =

6= >-3 3× $ 8 TAA I 23det( )A I− = RRRRR

01 /- -16- -$ +# - - (G&k N∈ -RRRR

!!!

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