inmo-2004 Previous year Question Papers of Indian National Mathematical Olympiad (INMO) with...
-
Upload
akshay-pandey -
Category
Documents
-
view
220 -
download
0
Transcript of inmo-2004 Previous year Question Papers of Indian National Mathematical Olympiad (INMO) with...
-
7/29/2019 inmo-2004 Previous year Question Papers of Indian National Mathematical Olympiad (INMO) with solutions
1/5
" $ ' )
1 2 4 6 8 9 @ B D F G I 6 8 Q D T U W G B F @ Y G a D F G Y d e g i q @ 8 r t @ I t x q q q G F D a t D @ B 6 @ 8 a 9 6 a t D 9 @ B D 9 d e q
e g q g i q i d F D 9 D I a @ Q D Y 2 W 6 9 D
G e i @ 9 D I a 9 x G a k m
k d o k e o k g o k i m G 8 B
I x o g i g e 2
F 6 Q D a t G a d e g i @ 9 G
) z { |2
" $ ' }
A K B
L
CMD
N
Q
Fig. 1.
~
9 D F Q D a t G a x @ 9 G G F G Y D Y Y 6 F G q k @ 9 a t D @ B 6 @ 8 a 6 x G 8 B t D 8 I D G Y 9 6 G 9 9 D 9
a t F 6 W t k 2 D a D a t D 6 @ 8 a 6 @ 8 a D F 9 D I a @ 6 8 6 d g G 8 B e i m G 8 B Y D a D a t D 6 @ 8 a 6 @ 8 a D F 9 D I a @ 6 8
6 e i G 8 B 2
4 6 8 9 @ B D F a t D a F @ G 8 Y D x 2 6 a D a t G a k @ 9 G F G Y Y D Y a 6 x G 8 B k @ 9 a t D @ B 6 @ 8 a 6 x 2
D 8 I D @ 9 a t D @ B 6 @ 8 a 6 2 @ 8 I D @ 9 G F G Y Y D Y a 6 d g q @ a 6 Y Y 6 r 9 a t G a @ 9 a t D @ B 6 @ 8 a
6 d g 2 6 r k @ 9 a t D I @ F I W I D 8 a F D 6 d e g G 8 B a t D D B @ G 8 e G 9 9 D 9 a t F 6 W t k 2
D F D a t D F D
G F D a r 6 6 9 9 @ @ Y @ a @ D 9
@ d e g @ 9 G F @ t a a F @ G 8 Y D r @ a t d e g o G 8 B o k m G 8 B
@ @ o k @ 8 r t @ I t I G 9 D e @ 9 D F D 8 B @ I W Y G F a 6 d g 2
W 6 9 D d e g o G 8 B o k 2
~
9 D F Q D a t G a k @ 9 a t D I @ F I W I D 8 a F D 6 a t D a F @ G 8 Y D i g e G 8 B
t D 8 I D i g e o 2 @ @ Y G F Y i d e o 2 a 6 Y Y 6 r 9 a t G a d i g o b 2 G 8 B d e g i @ 9 G
F D I a G 8 Y D 2 t @ 9 @ Y @ D 9 a t G a x @ 9 G F t 6 W 9 2
D 8 I D x o 1 G 8 B a t @ 9 @ Q D 9 g i o g e 2
t W 9 d e g i @ 9 G 9 U W G F D 2
8 a t D 9 D I 6 8 B I G 9 D q 6 9 D F Q D a t G a e i @ 9 D F D 8 B @ I W Y G F a 6 d g q x @ 9 G F G Y Y D Y a 6 d g G 8 B @ 9
G F G Y Y D Y a 6 e i 2
D 8 I D @ a 6 Y Y 6 r 9 a t G a @ 9 D F D 8 B @ I W Y G F a 6 x 2 @ @ Y G F F D G 9 6 8 @ 8 9 t 6 r 9 a t G a
x @ 9 G F D I a G 8 Y D 2
e JEE Mains/JEE Advanced Online Prep and Guidance on www.100Marks.in
-
7/29/2019 inmo-2004 Previous year Question Papers of Indian National Mathematical Olympiad (INMO) with solutions
2/5
9 @ 8 x o g i g e q r D D a a t G a g e i @ 9 9 @ @ Y G F a 6 x 2 8 G F a @ I W Y G F q x o
g e i o 9 G 2 @ 8 I D @ 9 G F G Y Y D Y a 6 i e q r D G Y 9 6 D a e k x o 2 @ 8 I D x @ 9 G I I Y @ I
U W G B F @ Y G a D F G Y r D G Y 9 6 D a x o x o 2
9 @ 8 a t D G I a a t G a e i @ 9 G F G Y Y D Y a 6 x q r D
D a k e o x o 2 @ 8 I D e i @ 9 D I a 9 g e d q r D G Y 9 6 t G Q D x e k o 2 t W 9
k x o x e o e o k
G 8 B e @ 9 G F G Y Y D Y a 6 k x 2 t @ 9 @ Q D 9 k @ 9 G F G Y Y D Y a 6 g G 8 B
k o k o e o g
a 6 Y Y 6 r 9 a t G a k g @ 9 G G F G Y Y D Y 6 F G 2 W a g o 2
D 8 I D k o 2 t @ 9 @ Y @ D 9
a t G a x @ 9 G 9 U W G F D 2 Y 9 6 6 9 D F Q D a t G a k x o G 8 B t D 8 I D g e d o k x o 2
t @ 9 @ Q D 9 g i d o G 8 B t D 8 I D d e g i @ 9 G F D I a G 8 Y D3 2 @ 8 I D e d o e g q @ a 6 Y Y 6 r 9 a t G a d e g i
@ 9 G 9 U W G F D 2
2 W 6 9 D @ 9 G F @ D F D G a D F a t G 8 2 @ 8 B G Y Y G @ F 9 6 @ 8 a D D F 9
9 G a @ 9 @ 8 a t D D U W G a @ 6 8
o
" $ ' }
D r F @ a D a t D D U W G a @ 6 8 @ 8 a t D 6 F
o
D 8 I D
o
@ 9 G 8 @ 8 a D D F 2 t @ 9 9 t 6 r 9 a t G a
B @ Q @ B D 9
G 8 B t D 8 I D G Y 9 6 B @ Q @ B D 9
2 W a q r D
t G Q D
o
o
a 6 Y Y 6 r 9 a t G a
B @ Q @ B D 9
2 @ 8 I D @ 9 G F @ D q a t D 6 8 Y B @ Q @ 9 6 F 9 6
G F D 1
G 8 B
2
@ 8 I D q r D G Y 9 6 t G Q D o
1 6 F
2
z ) | }
W 6 9 D o
1 2
~
Q @ 6 W 9 Y
o 1 @ 9 8 6 a 6 9 9 @ Y D 2 8 G I a q r D D a 1 o
o
1
o
1 r t @ I t @ 9 @ 6 9 9 @ Y D 2
~
8 a t D 6 a t D F t G 8 B
o
1 @ Q D 9
o
1 o
o
1 G 8 B
o
1
1 o 2
t W 9
o
o
2 t W 9
o
1
r t D 8 o
1 2 @ @ Y G F Y q
o
o
r t @ I t @ 9 8 6 a 6 9 9 @ Y D 2 4 6 8 9 @ B D F @ 8
o
q r D D a
o
6 F
o
o 2
D 8 I D
o
1
r t D F D o
1 2
D a W 9 I 6 8 9 @ B D F
o
2
D 8 I D
o
o
G 8 B 8 D @ a t D F 8 6 F
@ 9 B @ Q @ 9 @ Y D
2
o
q a t D 8
o
o
1
1 2
D 8 I D
o
1
1
1 o
1 2 s t @ 9 @ Q D 9
o
2 G @ 8
o
1
1
r t D 8 o
1 2
z ) | }
W 6 9 D o
1 2
o 1 q a t D 8
o
6 F
o
1 2
D G Y 9 6 D a
o
1
o
1
1
1
o
e JEE Mains/JEE Advanced Online Prep and Guidance on www.100Marks.in
-
7/29/2019 inmo-2004 Previous year Question Papers of Indian National Mathematical Olympiad (INMO) with solutions
3/5
G 8 B r D D a a t D 9 6 Y W a @ 6 8
o
1
2
~
8 a t D 6 a t D F t G 8 B
o
1 B 6 D 9 8 6 a t G Q D
G 8 9 6 Y W a @ 6 8 @ 8 a D F G Y 9 6 Y W a @ 6 8 6 F
2 @ @ Y G F Y q a t D F D @ 9 8 6 9 6 Y W a @ 6 8 @ 8 a t D I G 9 D
o 2 G @ 8
o
q r D D a
o
G 8 B t D 8 I D
o 2
D D a a t D 9 6 Y W a @ 6 8
o
1
2
o
q a t D 8
o
o
1
@ Q @ 8
o
1
1 G 8 B t D 8 I D
o
1
1
1 o
1 2 t @ 9 @ Q D 9
o
G 8 B t D 8 I D
o
1
2
@ 8 G Y Y
o
B 6 D 9 8 6 a t G Q D G 8 9 6 Y W a @ 6 8 2
2 @ 9 G F D G Y F 6 6 a 6 a t D D U W G a @ 6 8
o q F 6 Q D a t G a o 2 6 F G 8 F D G Y 8 W D F
q r D B D 8 6 a D
a t D F D G a D 9 a @ 8 a D D F 8 6 a D T I D D B @ 8
2
" $ ' } W 6 9 D @ 9 G F D G Y F 6 6 a 6 a t D @ Q D 8 D U W G a @ 6 8 2 t D 8
o
t @ 9 @ Q D 9
1 o 1 G 8 B t D 8 I D
1
1 o 1 2
~
9 D F Q D a t G a
1
o
2
1 q a t D 8
q @ Q @ 8
G 8 B t D 8 I D
1
1 2
1 q a t D 8
o
1 G 8 B t D 8 I D
1 2
t @ 9 G G @ 8 @ Q D 9
1
1 2
t D G 6 Q D F D 9 6 8 @ 8 9 t 6 r 9 a t G a 6 F q r D t G Q D
1 G 8 B t D 8 I D I G 8 8 6 a D D U W G Y
a 6 1 2
D I 6 8 I Y W B D a t G a G F D G Y F 6 6 a 6
o @ 9 6 9 @ a @ Q D
6 Q @ 6 W 9 Y o 2
6 r W 9 @ 8
o q r D D a
o
t D 9 a G a D D 8 a
o @ 9 D U W @ Q G Y D 8 a a 6 2
4 6 8 9 @ B D F
2 @ 8 I D q a t @ 9 @ 9 D U W @ Q G Y D 8 a a 6
2
9 @ 8 a t D
F D Y G a @ 6 8
1 q r D I G 8 r F @ a D
6 F
2 F D G a @ 8 a t @ 9 G 9 G U W G B F G a @ I q r D
D a a t @ 9 @ 9 D U W @ Q G Y D 8 a a 6
1
2 6 r 6 9 D F Q D a t G a @ a t D 8 1 o
1
1
r t @ I t @ 9 @ 6 9 9 @ Y D 2
1
q a t D 8 1 o
1
1 r t @ I t G G @ 8 @ 9 @ 6 9 9 @ Y D 2
D I 6 8 Y W B D a t G a
1
2 @ @ Y G F Y
@ 9 D U W @ Q G Y D 8 a a 6
r t @ I t @ 9 D U W @ Q G Y D 8 a a 6
2 W a a t @ 9 @ 9
1
r t @ I t @ 9 Q G Y @ B 2
D 8 I D
G 8 B r D D a
o 2
2 D a B D 8 6 a D a t D I @ F I W F G B @ W 9 6 G a F @ G 8 Y D d e g m
q
q @ a 9 9 @ B D 9 e g q g d q d e m G 8 B q q @ a 9
D T F G B @ @ 6 6 9 @ a D d q e q g 2 q F 6 Q D a t G a
@
G 8 B
m
@ @ G 8 B 2
" $ ' } D 8 6 r a t G a o
G 8 B o
q r t D F D
G F D a t D 9 @ B D 9 6 a t D a F @ G 8 Y D d e g q
o
G 8 B @ 9 a t D G F D G 6 d e gP 2 t W 9 a t D @ Q D 8 I 6 8 B @ a @ 6 8
a F G 8 9 Y G a D 9 a 6
e JEE Mains/JEE Advanced Online Prep and Guidance on www.100Marks.in
-
7/29/2019 inmo-2004 Previous year Question Papers of Indian National Mathematical Olympiad (INMO) with solutions
4/5
W a a @ 8
o
o
o q r D D a
o
o
o
G 8 B a t D I 6 8 B @ a @ 6 8 8 6 r
@ 9
W a
D F 6 8 9 6 F W Y G @ Q D 9 q
o
o
2
D 6 a G @ 8
2 T G 8 B @ 8 G 8 B D D I a @ 8 9 6 D I G 8 I D Y Y G a @ 6 8 9 q r D D a
W 6 9 D
2 t @ 9 @ Y @ D 9 a t G a
G 8 B t D 8 I D 2 t @ 9 @ Y @ D 9 a t G a
G 8 B
@ Q @ 8
o
r t @ I t
I 6 8 a F G B @ I a 9
2 @ @ Y G F Y q
@ 9 G Y 9 6 8 6 a 6 9 9 @ Y DS 2 t @ 9 F 6 Q D 9
@ 2
W 6 9 D
2 9 G 6 Q D a t @ 9 a G D 9 a t D 6 F
@ 8 I D
G 8 B
q r D t G Q D
2 t W 9
G 8 B
2
D 8 I D
o
r t @ I t I 6 8 a F G B @ I a 9
2
D 8 I D
2 @ @ Y G F Y q r D I G 8 F 6 Q D a t G a
2 t @ 9 F 6 Q D 9
@ @
2 D a B D 8 6 a D a t D 9 D a 6 G Y Y
a W Y D 9
6 6 9 @ a @ Q D @ 8 a D D F 9 9 W I t a t G a
o
2 4 6 8 9 @ B D F a t D 9 D a
o
@ 8 B a t D F D G a D 9 a I 6 6 8 B @ Q @ 9 6 F 6 G Y Y a t D D D F 9 6 2
" $ ' }
D 9 t 6 r a t G a a t D F D U W @ F D B I B @ 9 2 4 6 8 9 @ B D F G 8 D Y D D 8 a
2
D t G Q D
o
D
F 9 a 6 9 D F Q D a t G a 8 6 a G Y Y
I G 8 D 6 B B 2
~
a t D F r @ 9 D q r D t G Q D
1
6 B G 8 B t D 8 I D
6 B q r t @ I t @ 9 @ 6 9 9 @ Y D D I G W 9 D 8 6 9 U W G F D I G 8 D I 6 8 F W D 8 a a 6
6 B W Y 6 2 t W 9 G a Y D G 9 a 6 8 D 6
@ 9 D Q D 8 2
@ @ Y G F Y @ 8 6 8 D 6
@ 9 B @ Q @ 9 @ Y D q a t D 8
1
6 B G 8 B t D 8 I D
6 B r t @ I t G G @ 8 @ 9 @ 6 9 9 @ Y D D I G W 9 D 8 6 9 U W G F D @ 9 I 6 8 F W D 8 a a 6 6 B W Y 6 2 t W 9
B @ Q @ B D 9
2
t D F D G F D 9 D Q D F G Y 6 9 9 @ @ Y @ a @ D 9 6 F
2
z ) | }
W 6 9 D 6 8 D 6 a t D @ 9 D Q D 8 G 8 B a t D 6 a t D F 6 W F G F D 6 B B m 9 G
@ 9 D Q D 8 q
G F D 6 B B 2
t D 8
6 B 2
6 B q a t D 8
6 B G 8 B t D 8 I D
@ Q @ 8
2
6 B q a t D 8
6 B r t @ I t G G @ 8 @ Q D 9 a t G a
G 8 B
9 6 a t G a
2 a 6 Y Y 6 r 9 a t G a
G 8 B t D 8 I D
2
z ) | }
W 6 9 D
G F D D Q D 8 G 8 B
G F D 6 B B 2 t D 8
6 B 2 @ 8 I D
6 F 6 B W Y 6 q @ a 6 Y Y 6 r 9 a t G a
6 F !
6 B r t @ I t @ 9 @ 6 9 9 @ Y D 2
D 8 I D a t @ 9 I G 9 D B 6 D 9 8 6 a
G F @ 9 D 2
z ) | " }
a t F D D 6
G F D D Q D 8 G 8 B a r 6 6 B B q a t D 8
G 8 B t D 8 I D
2
z ) | }
6 W F 6
G F D D Q D 8 q a t D 8 G G @ 8
G 8 B
2
D F D G G @ 8 6 F G 8 9 @ T
a W Y D
@ 8 q r D 6 9 D F Q D a t G a
2 @ 8 I D
1
1
1
o
D 9 D D a t G a
1 q 1 q 1 q q q G 8 B t D 8 I D 2 t W 9 @ 9 a t D I B 6 2
e JEE Mains/JEE Advanced Online Prep and Guidance on www.100Marks.in
-
7/29/2019 inmo-2004 Previous year Question Papers of Indian National Mathematical Olympiad (INMO) with solutions
5/5
2
F 6 Q D a t G a a t D 8 W D F 6
a W Y D 9 6 6 9 @ a @ Q D @ 8 a D D F 9
9 G a @ 9 @ 8 a t D D U W G a @ 6 8
o
@ 9 G 8 $ $
@ 8 a D D F 2
" $ ' } D r F @ a D a t D D U W G a @ 6 8 @ 8 a t D 6 F
1
1
1
1
1
o
1
t D 8 W D F 6 Q D a W Y D
r t @ I t 9 G a @ 9 a t D @ Q D 8 F D Y G a @ 6 8 G 8 B 6 F r t @ I t
o
@ 9 D Q D 8 q
D I G W 9 D 6 F @
@ 9 G 9 6 Y W a @ 6 8 q a t D 8 9 6 @ 9
r t @ I t @ 9 B @ 9 a @ 8 I a F 6
2
@ @ Y G F Y a t D 8 W D F 6 Q D a W Y D 9 r t @ I t 9 G a @ 9 a t D D U W G a @ 6 8 G 8 B 6 F r t @ I t o
@ 9 G Y 9 6 D Q D 8 2
D 8 I D @ a 9 W ( I D 9 a 6 I 6 W 8 a 6 8 Y a t 6 9 D Q D a W Y D 9
6 F r t @ I t
o
o
2 t W 9 a t D
D U W G a @ 6 8 F D B W I D 9 a 6
1
o
1
D F D G G @ 8 a t D a W Y D
6 F r t @ I t
o @ 9 D Q D 8 D I G W 9 D r D I G 8 G 9 9 6 I @ G a D B @ D F D 8 a 9 6 Y W a @ 6 8
a 6 a t @ 9 Q D a W Y DS 2 t W 9 @ a 9 W ( I D 9 a 6 I 6 8 9 @ B D F a t D D U W G a @ 6 8
1
o
1
G 8 B 9 t 6 r a t G a a t D 8 W D F 6 G @ F 9
9 G a @ 9 @ 8 a t @ 9 D U W G a @ 6 8 @ 9 6 B B 2
t @ 9 F D B W I D 9 a 6
o
6 F
o 1
W a 6 9 D F Q D a t G a
1 o 1 2 1 o 2
o 2
o
2
o 1 2 1 o 2
o
2 o
2 o 1 2 1
6 a D a t G a 8 6 G I a 6 F @ 9 G a @ 6 8 6 1 G 9 F 6 B W I a 6 a r 6 8 D G a @ Q D 8 W D F 9 @ D Y B G 6 9 @ a @ Q D a W Y D
2
D 8 I D r D D a a t D 9 D 9 6 Y W a @ 6 8 9 2 t @ 9 F 6 Q D 9 a t G a a t D a 6 a G Y 8 W D F 6 Q D a W Y D 9
9 G a @ 9 @ 8 a t D @ Q D 8 D U W G a @ 6 8 @ 9 6 B B 2
e JEE Mains/JEE Advanced Online Prep and Guidance on www.100Marks.in