jee advanced model grand test paper- i -...
TRANSCRIPT
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JEE-ADVANCEDMODEL GRAND TEST PAPER - I
Time : 3 hrs ] [Number of questions : 60
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AV
time
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BV
1s 2s
1
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3
4m
5
4m /
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+ 012".$
$ 2
2
1 yµ =
+ )
34
60º
Y
XThe path of the lightfollowed after successiverefraction is as shown
H
2
13
− -2
3 ( )3 1− /
( # 5
E LC
B-
E
B LC
B LC
E
B
E LC
6 # 7'%$%
0
4x
ε− -
0
4
ε− 04ε− 02ε−
0 8 ## ## - - 5
-1
2+
1
3
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-
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; < 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
R R
πρ−
-2
1
2
RL ln
R
ρπ
2
1
2R
L lnR
πρ
( )1
2 1
R
L R R
ρπ−
1 *# %(1 #, - # - # # #
3 2 cm %1- #
+- -
% -+ ( 6
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
CV q−
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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( # 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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; : # G $#
G1
42
m andσρ
= =
σ
σ
= # 61 %#(0
α # 8 # #61
# &$ $
%1 11 - F
'1F(%8- GJ'1;G#
, ##- G'G##
G'0/C8 # $ 7'(1F
(+) F#4@1'16/C
%'1C%
Section-I
% * ###,&(1GK
&%1K L# 7##%9M$#2H Oln P
-*#-+11L
F0 0 F0 F+%
%% ##8 G- (61
#)
4
2344 10 J−× 2344 10 kJ−× 234.4 10 J−× 234.4 10 kJ−×
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%+ 8 JF*J61N*61N#- 8J #- NJ -%6N 61N 96N ++++N
%( < #1 2( ) ( ) ( ) ( ) ( ) ( )| | || | |s s aq C aq C s sAg AgBr KBr KCl AgCl Ag O
?P 4
@5 8$# -
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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+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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++ )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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+= 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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(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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6+ 8 : 2, 2 ( ) sin cos f N such that f x x x $
. - .
6( #- @0; 8 E +$&(&1'1+$&(.1'1
@'1 -' 5@'; 'C%
66 8-:-&%##
-1%#--
$ %# -:( )( ) 1
1 !
2. 2n
n
n−
+
+
-$ +# -:( )( )( )
( )
23 21 2 !
2
n n
n
C n C n
n
+ − −
+
$ +# -:( ) ( )
( )
2
1
. 1 . 1
12 2n
n n n
n−
− +
+
$ %# -:( )
( )
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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