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G e n e r a l 	 I n s t r u c t i o n s :
T h i s 	 q u e s t i o n 	 p a p e r 	 h a s 	 3 1 	 q u e s t i o n s 	 .
S e c t i o n 	 A 	 c o n s i s t s 	 o f 	 4 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h .
S e c t i o n 	 B 	 c o n s i s t s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h .
S e c t i o n 	 C 	 c o n s i s t s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h .
S e c t i o n 	 D 	 c o n s i s t s 	 o f 	 1 1 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y 	 t o 	 a t t e m p t .
A t t e m p t 	 t h e 	 p a p e r 	 n e a t l y 	 a n d 	 l e g i b l y .
S e c t i o n 	 – 	 A
1 . 	 W r i t e 	 t h e 	 m a t h e m a t i c a l 	 s t a t e m e n t 	 f o r 	 “ S u m 	 o f 	 t w e n t y - o n e 	 a n d 	 f i f t e e n 	 d i v i d e d 	 b y 	 t h e
d i f f e r e n c e 	 o f 	 e i g h t 	 a n d 	 t h r e e ” .
A n s . 	 	
2 . 	 I n 	 a 	 p i c t o g r a p h , 	 i f 	 t h e 	 s y m b o l 	 	 	 	 	 r e p r e s e n t s 	 5 0 	 s t u d e n t s , 	 t h e n 	 h o w 	 m a n y 	 s t u d e n t s
w i l l 	 b e 	 r e p r e s e n t e d 	 b y 	 t h e 	 s y m b o l 	 ?
A n s . 	 1 2 0
3 . 	 S o l v e 	 a n d 	 w r i t e 	 t h e 	 a n s w e r 	 i n 	 t h e 	 R o m a n 	 n u m e r a l : 	 C D X C I I 	 - 	 C D 	 = 	 _ _ _ _ _ _
A n s . 	 4 9 2 - 4 0 0 = 9 2 = X C I I
4 . 	 W h a t 	 f r a c t i o n 	 o f 	 a 	 r e v o l u t i o n 	 h a v e 	 y o u 	 t u r n e d 	 t h r o u g h 	 i f 	 y o u 	 s t a n d 	 f a c i n g 	 t h e 	 e a s t
a n d 	 t u r n 	 c l o c k w i s e 	 t o 	 f a c e 	 t h e 	 n o r t h ?
A n s . 	 o f 	 t h e 	 R e v o l u t i o n
Page 2


G e n e r a l 	 I n s t r u c t i o n s :
T h i s 	 q u e s t i o n 	 p a p e r 	 h a s 	 3 1 	 q u e s t i o n s 	 .
S e c t i o n 	 A 	 c o n s i s t s 	 o f 	 4 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h .
S e c t i o n 	 B 	 c o n s i s t s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h .
S e c t i o n 	 C 	 c o n s i s t s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h .
S e c t i o n 	 D 	 c o n s i s t s 	 o f 	 1 1 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y 	 t o 	 a t t e m p t .
A t t e m p t 	 t h e 	 p a p e r 	 n e a t l y 	 a n d 	 l e g i b l y .
S e c t i o n 	 – 	 A
1 . 	 W r i t e 	 t h e 	 m a t h e m a t i c a l 	 s t a t e m e n t 	 f o r 	 “ S u m 	 o f 	 t w e n t y - o n e 	 a n d 	 f i f t e e n 	 d i v i d e d 	 b y 	 t h e
d i f f e r e n c e 	 o f 	 e i g h t 	 a n d 	 t h r e e ” .
A n s . 	 	
2 . 	 I n 	 a 	 p i c t o g r a p h , 	 i f 	 t h e 	 s y m b o l 	 	 	 	 	 r e p r e s e n t s 	 5 0 	 s t u d e n t s , 	 t h e n 	 h o w 	 m a n y 	 s t u d e n t s
w i l l 	 b e 	 r e p r e s e n t e d 	 b y 	 t h e 	 s y m b o l 	 ?
A n s . 	 1 2 0
3 . 	 S o l v e 	 a n d 	 w r i t e 	 t h e 	 a n s w e r 	 i n 	 t h e 	 R o m a n 	 n u m e r a l : 	 C D X C I I 	 - 	 C D 	 = 	 _ _ _ _ _ _
A n s . 	 4 9 2 - 4 0 0 = 9 2 = X C I I
4 . 	 W h a t 	 f r a c t i o n 	 o f 	 a 	 r e v o l u t i o n 	 h a v e 	 y o u 	 t u r n e d 	 t h r o u g h 	 i f 	 y o u 	 s t a n d 	 f a c i n g 	 t h e 	 e a s t
a n d 	 t u r n 	 c l o c k w i s e 	 t o 	 f a c e 	 t h e 	 n o r t h ?
A n s . 	 o f 	 t h e 	 R e v o l u t i o n
S E C T I O N - B
5 . 	 W r i t e 	 t h e 	 n u m b e r 	 n a m e 	 o f 	 2 0 4 6 0 0 8 0 8 	 a c c o r d i n g 	 t o 	 t h e 	 I n t e r n a t i o n a l 	 s y s t e m 	 o f
n u m e r a t i o n .
A n s . 	 2 0 4 6 0 0 8 0 8 = 2 0 4 , 6 0 0 , 8 0 8
T w o 	 h u n d r e d 	 f o u r 	 m i l l i o n 	 s i x 	 h u n d r e d 	 t h o u s a n d 	 e i g h t 	 h u n d r e d 	 a n d 	 e i g h t .
6 . 	 M u l t i p l y 	 b y 	 s u i t a b l e 	 r e a r r a n g e m e n t : 	 5 	 x 	 8 7 	 x 	 2 0
A n s . 	 5 	 x 	 8 7 x 	 2 0
= 	 ( 5 	 x 	 2 0 ) 	 x 	 8 7
= 1 0 0 	 x 	 8 7 	 = 8 7 0 0
7 . 	 E x p r e s s 	 3 7 	 a s 	 p r o d u c t 	 o f 	 p r i m e 	 p l u s 	 1 .
A n s . 	 3 7 	 = 	 3 6 	 + 	 1
3 6 	 = 	 2 	 x 	 2 	 x 	 3 	 x 	 3
H e n c e , 	 3 7 	 = 	 2 	 x 	 2 	 x 	 3 	 x 	 3 	 + 	 1
8 . 	 S t a t e 	 t h e 	 r e l a t i o n s h i p 	 b e t w e e n 	 r a d i u s 	 & 	 d i a m e t e r 	 o f 	 a 	 c i r c l e . 	 E x p l a i n 	 t h r o u g h 	 a n
e x a m p l e .
A n s . 	 D 	 = 	 2 	 X 	 R 	 ( 1 )
E i t h e r 	 e x p l a i n e d 	 t h r o u g h 	 f i g u r e 	 o r 	 a n 	 e x a m p l e .
9 . 	 I n 	 a 	 M a t h e m a t i c s 	 t e s t , 	 t h e 	 f o l l o w i n g 	 m a r k s 	 w e r e 	 o b t a i n e d 	 b y 	 4 0 	 s t u d e n t s :
A r r a n g e 	 t h e s e 	 m a r k s 	 i n 	 a 	 t a b l e 	 u s i n g 	 t a l l y 	 m a r k s .
8 , 	 1 , 	 3 , 	 7 , 	 6 , 	 5 , 	 5 , 	 4 , 	 4 , 	 2 , 	 4 , 	 9 , 	 5 , 	 3 , 	 7 , 	 1 , 	 6 , 	 5 , 	 2 , 	 7 , 	 7 , 	 3 , 	 8 , 	 4 , 	 2 , 	 8 , 	 9 , 	 5 , 	 8 , 	 6 , 	 7 , 	 4 , 	 5 , 	 6 , 	 9 , 	 6 ,
4 , 	 4 , 	 6 , 	 6
A n s . 	 F r e q u e n c y 	 d i s t r i b u t i o n 	 t a b l e 	 t o 	 b e 	 n e a t l y 	 d r a w n
1 0 . 	 S t a t e 	 t h e 	 c l o s u r e 	 p r o p e r t y 	 o f 	 a d d i t i o n 	 o f 	 w h o l e 	 n u m b e r s . 	 G i v e 	 a n 	 e x a m p l e .
A n s . 	 a 	 + 	 b 	 = 	 c 	 w h e r e 	 a , 	 b 	 a n d 	 c 	 a r e 	 a l w a y s 	 w h o l e 	 n u m b e r s .
F o r 	 e x a m p l e : 	 5 	 + 	 3 	 = 	 8 	 w h e r e 	 5 , 	 3 	 a n d 	 8 	 a r e 	 a l l 	 w h o l e 	 n u m b e r s .
Page 3


G e n e r a l 	 I n s t r u c t i o n s :
T h i s 	 q u e s t i o n 	 p a p e r 	 h a s 	 3 1 	 q u e s t i o n s 	 .
S e c t i o n 	 A 	 c o n s i s t s 	 o f 	 4 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h .
S e c t i o n 	 B 	 c o n s i s t s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h .
S e c t i o n 	 C 	 c o n s i s t s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h .
S e c t i o n 	 D 	 c o n s i s t s 	 o f 	 1 1 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y 	 t o 	 a t t e m p t .
A t t e m p t 	 t h e 	 p a p e r 	 n e a t l y 	 a n d 	 l e g i b l y .
S e c t i o n 	 – 	 A
1 . 	 W r i t e 	 t h e 	 m a t h e m a t i c a l 	 s t a t e m e n t 	 f o r 	 “ S u m 	 o f 	 t w e n t y - o n e 	 a n d 	 f i f t e e n 	 d i v i d e d 	 b y 	 t h e
d i f f e r e n c e 	 o f 	 e i g h t 	 a n d 	 t h r e e ” .
A n s . 	 	
2 . 	 I n 	 a 	 p i c t o g r a p h , 	 i f 	 t h e 	 s y m b o l 	 	 	 	 	 r e p r e s e n t s 	 5 0 	 s t u d e n t s , 	 t h e n 	 h o w 	 m a n y 	 s t u d e n t s
w i l l 	 b e 	 r e p r e s e n t e d 	 b y 	 t h e 	 s y m b o l 	 ?
A n s . 	 1 2 0
3 . 	 S o l v e 	 a n d 	 w r i t e 	 t h e 	 a n s w e r 	 i n 	 t h e 	 R o m a n 	 n u m e r a l : 	 C D X C I I 	 - 	 C D 	 = 	 _ _ _ _ _ _
A n s . 	 4 9 2 - 4 0 0 = 9 2 = X C I I
4 . 	 W h a t 	 f r a c t i o n 	 o f 	 a 	 r e v o l u t i o n 	 h a v e 	 y o u 	 t u r n e d 	 t h r o u g h 	 i f 	 y o u 	 s t a n d 	 f a c i n g 	 t h e 	 e a s t
a n d 	 t u r n 	 c l o c k w i s e 	 t o 	 f a c e 	 t h e 	 n o r t h ?
A n s . 	 o f 	 t h e 	 R e v o l u t i o n
S E C T I O N - B
5 . 	 W r i t e 	 t h e 	 n u m b e r 	 n a m e 	 o f 	 2 0 4 6 0 0 8 0 8 	 a c c o r d i n g 	 t o 	 t h e 	 I n t e r n a t i o n a l 	 s y s t e m 	 o f
n u m e r a t i o n .
A n s . 	 2 0 4 6 0 0 8 0 8 = 2 0 4 , 6 0 0 , 8 0 8
T w o 	 h u n d r e d 	 f o u r 	 m i l l i o n 	 s i x 	 h u n d r e d 	 t h o u s a n d 	 e i g h t 	 h u n d r e d 	 a n d 	 e i g h t .
6 . 	 M u l t i p l y 	 b y 	 s u i t a b l e 	 r e a r r a n g e m e n t : 	 5 	 x 	 8 7 	 x 	 2 0
A n s . 	 5 	 x 	 8 7 x 	 2 0
= 	 ( 5 	 x 	 2 0 ) 	 x 	 8 7
= 1 0 0 	 x 	 8 7 	 = 8 7 0 0
7 . 	 E x p r e s s 	 3 7 	 a s 	 p r o d u c t 	 o f 	 p r i m e 	 p l u s 	 1 .
A n s . 	 3 7 	 = 	 3 6 	 + 	 1
3 6 	 = 	 2 	 x 	 2 	 x 	 3 	 x 	 3
H e n c e , 	 3 7 	 = 	 2 	 x 	 2 	 x 	 3 	 x 	 3 	 + 	 1
8 . 	 S t a t e 	 t h e 	 r e l a t i o n s h i p 	 b e t w e e n 	 r a d i u s 	 & 	 d i a m e t e r 	 o f 	 a 	 c i r c l e . 	 E x p l a i n 	 t h r o u g h 	 a n
e x a m p l e .
A n s . 	 D 	 = 	 2 	 X 	 R 	 ( 1 )
E i t h e r 	 e x p l a i n e d 	 t h r o u g h 	 f i g u r e 	 o r 	 a n 	 e x a m p l e .
9 . 	 I n 	 a 	 M a t h e m a t i c s 	 t e s t , 	 t h e 	 f o l l o w i n g 	 m a r k s 	 w e r e 	 o b t a i n e d 	 b y 	 4 0 	 s t u d e n t s :
A r r a n g e 	 t h e s e 	 m a r k s 	 i n 	 a 	 t a b l e 	 u s i n g 	 t a l l y 	 m a r k s .
8 , 	 1 , 	 3 , 	 7 , 	 6 , 	 5 , 	 5 , 	 4 , 	 4 , 	 2 , 	 4 , 	 9 , 	 5 , 	 3 , 	 7 , 	 1 , 	 6 , 	 5 , 	 2 , 	 7 , 	 7 , 	 3 , 	 8 , 	 4 , 	 2 , 	 8 , 	 9 , 	 5 , 	 8 , 	 6 , 	 7 , 	 4 , 	 5 , 	 6 , 	 9 , 	 6 ,
4 , 	 4 , 	 6 , 	 6
A n s . 	 F r e q u e n c y 	 d i s t r i b u t i o n 	 t a b l e 	 t o 	 b e 	 n e a t l y 	 d r a w n
1 0 . 	 S t a t e 	 t h e 	 c l o s u r e 	 p r o p e r t y 	 o f 	 a d d i t i o n 	 o f 	 w h o l e 	 n u m b e r s . 	 G i v e 	 a n 	 e x a m p l e .
A n s . 	 a 	 + 	 b 	 = 	 c 	 w h e r e 	 a , 	 b 	 a n d 	 c 	 a r e 	 a l w a y s 	 w h o l e 	 n u m b e r s .
F o r 	 e x a m p l e : 	 5 	 + 	 3 	 = 	 8 	 w h e r e 	 5 , 	 3 	 a n d 	 8 	 a r e 	 a l l 	 w h o l e 	 n u m b e r s .
S e c t i o n - C
1 1 . D i v i d e 	 3 0 3 0 3 0 0 	 b y 	 8 5 1 2 	 a n d 	 f i n d 	 t h e 	 q u o t i e n t 	 a n d 	 r e m a i n d e r .
A n s . 	 D i v i d e 	 3 0 3 0 3 0 0 	 b y 	 8 5 1 2
Q 	 = 	 3 5 6
R 	 = 	 2 8
1 2 . 	 S i m p l i f y 	 u s i n g 	 d i s t r i b u t i v e 	 p r o p e r t y 	 o f 	 w h o l e 	 n u m b e r s : 	 9 8 7 	 x 	 6 	 + 	 9 8 7 	 x 	 3 	 + 	 9 8 7
A n s . 	 9 8 7 	 x 	 6 	 + 	 9 8 7 	 x 	 3 	 + 	 9 8 7
U s i n g 	 d i s t r i b u t i v e 	 p r o p e r t y
= 	 9 8 7 	 x 	 ( 6 	 + 	 3 	 + 	 1 )
= 	 9 8 7 	 x 	 1 0
= 	 9 8 7 0
1 3 . 	 I f 	 L C M 	 o f 	 2 1 	 a n d 	 3 0 	 i s 	 2 1 0 , 	 w h a t 	 i s 	 t h e i r 	 H C F ?
A n s . 	 L . C . M . 	 = 	 2 1 0
O n e 	 n u m b e r 	 = 	 2 1
O t h e r 	 n u m b e r 	 = 3 0
H . C . F . 	 x 	 L . C . M . 	 = 	 P r o d u c t 	 o f 	 n u m b e r s
H . C . 	 F 	 x 	 2 1 0 	 = 	 2 1 	 x 	 3 0
H . C . 	 F 	 = 	 6 3 0 	 / 	 2 1 0 	 = 	 3
1 4 . 	 B y 	 u s i n g 	 l o n g 	 d i v i s i o n 	 m e t h o d , 	 f i n d 	 t h e 	 H C F 	 o f 	 1 7 6 0 , 	 4 0 4 8 , 	 3 6 3 2 	 a n d 	 7 6 0 8 .
A n s . 	 H C F 	 = 	 3 	 ( u s i n g 	 l o n g 	 d i v i s i o n 	 m e t h o d )
1 5 . 	 I n 	 t h e 	 f o l l o w i n g 	 f i g u r e , 	 n a m e :
a . 	 a n y 	 t w o 	 p a i r s 	 o f 	 p a r a l l e l 	 l i n e s .
b . 	 a n y 	 t w o 	 p a i r s 	 o f 	 i n t e r s e c t i n g 	 l i n e s .
c . 	 t h e 	 p o i n t 	 o f 	 i n t e r s e c t i o n 	 o f 	 l i n e 	 n 	 a n d 	 p .
Page 4


G e n e r a l 	 I n s t r u c t i o n s :
T h i s 	 q u e s t i o n 	 p a p e r 	 h a s 	 3 1 	 q u e s t i o n s 	 .
S e c t i o n 	 A 	 c o n s i s t s 	 o f 	 4 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h .
S e c t i o n 	 B 	 c o n s i s t s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h .
S e c t i o n 	 C 	 c o n s i s t s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h .
S e c t i o n 	 D 	 c o n s i s t s 	 o f 	 1 1 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y 	 t o 	 a t t e m p t .
A t t e m p t 	 t h e 	 p a p e r 	 n e a t l y 	 a n d 	 l e g i b l y .
S e c t i o n 	 – 	 A
1 . 	 W r i t e 	 t h e 	 m a t h e m a t i c a l 	 s t a t e m e n t 	 f o r 	 “ S u m 	 o f 	 t w e n t y - o n e 	 a n d 	 f i f t e e n 	 d i v i d e d 	 b y 	 t h e
d i f f e r e n c e 	 o f 	 e i g h t 	 a n d 	 t h r e e ” .
A n s . 	 	
2 . 	 I n 	 a 	 p i c t o g r a p h , 	 i f 	 t h e 	 s y m b o l 	 	 	 	 	 r e p r e s e n t s 	 5 0 	 s t u d e n t s , 	 t h e n 	 h o w 	 m a n y 	 s t u d e n t s
w i l l 	 b e 	 r e p r e s e n t e d 	 b y 	 t h e 	 s y m b o l 	 ?
A n s . 	 1 2 0
3 . 	 S o l v e 	 a n d 	 w r i t e 	 t h e 	 a n s w e r 	 i n 	 t h e 	 R o m a n 	 n u m e r a l : 	 C D X C I I 	 - 	 C D 	 = 	 _ _ _ _ _ _
A n s . 	 4 9 2 - 4 0 0 = 9 2 = X C I I
4 . 	 W h a t 	 f r a c t i o n 	 o f 	 a 	 r e v o l u t i o n 	 h a v e 	 y o u 	 t u r n e d 	 t h r o u g h 	 i f 	 y o u 	 s t a n d 	 f a c i n g 	 t h e 	 e a s t
a n d 	 t u r n 	 c l o c k w i s e 	 t o 	 f a c e 	 t h e 	 n o r t h ?
A n s . 	 o f 	 t h e 	 R e v o l u t i o n
S E C T I O N - B
5 . 	 W r i t e 	 t h e 	 n u m b e r 	 n a m e 	 o f 	 2 0 4 6 0 0 8 0 8 	 a c c o r d i n g 	 t o 	 t h e 	 I n t e r n a t i o n a l 	 s y s t e m 	 o f
n u m e r a t i o n .
A n s . 	 2 0 4 6 0 0 8 0 8 = 2 0 4 , 6 0 0 , 8 0 8
T w o 	 h u n d r e d 	 f o u r 	 m i l l i o n 	 s i x 	 h u n d r e d 	 t h o u s a n d 	 e i g h t 	 h u n d r e d 	 a n d 	 e i g h t .
6 . 	 M u l t i p l y 	 b y 	 s u i t a b l e 	 r e a r r a n g e m e n t : 	 5 	 x 	 8 7 	 x 	 2 0
A n s . 	 5 	 x 	 8 7 x 	 2 0
= 	 ( 5 	 x 	 2 0 ) 	 x 	 8 7
= 1 0 0 	 x 	 8 7 	 = 8 7 0 0
7 . 	 E x p r e s s 	 3 7 	 a s 	 p r o d u c t 	 o f 	 p r i m e 	 p l u s 	 1 .
A n s . 	 3 7 	 = 	 3 6 	 + 	 1
3 6 	 = 	 2 	 x 	 2 	 x 	 3 	 x 	 3
H e n c e , 	 3 7 	 = 	 2 	 x 	 2 	 x 	 3 	 x 	 3 	 + 	 1
8 . 	 S t a t e 	 t h e 	 r e l a t i o n s h i p 	 b e t w e e n 	 r a d i u s 	 & 	 d i a m e t e r 	 o f 	 a 	 c i r c l e . 	 E x p l a i n 	 t h r o u g h 	 a n
e x a m p l e .
A n s . 	 D 	 = 	 2 	 X 	 R 	 ( 1 )
E i t h e r 	 e x p l a i n e d 	 t h r o u g h 	 f i g u r e 	 o r 	 a n 	 e x a m p l e .
9 . 	 I n 	 a 	 M a t h e m a t i c s 	 t e s t , 	 t h e 	 f o l l o w i n g 	 m a r k s 	 w e r e 	 o b t a i n e d 	 b y 	 4 0 	 s t u d e n t s :
A r r a n g e 	 t h e s e 	 m a r k s 	 i n 	 a 	 t a b l e 	 u s i n g 	 t a l l y 	 m a r k s .
8 , 	 1 , 	 3 , 	 7 , 	 6 , 	 5 , 	 5 , 	 4 , 	 4 , 	 2 , 	 4 , 	 9 , 	 5 , 	 3 , 	 7 , 	 1 , 	 6 , 	 5 , 	 2 , 	 7 , 	 7 , 	 3 , 	 8 , 	 4 , 	 2 , 	 8 , 	 9 , 	 5 , 	 8 , 	 6 , 	 7 , 	 4 , 	 5 , 	 6 , 	 9 , 	 6 ,
4 , 	 4 , 	 6 , 	 6
A n s . 	 F r e q u e n c y 	 d i s t r i b u t i o n 	 t a b l e 	 t o 	 b e 	 n e a t l y 	 d r a w n
1 0 . 	 S t a t e 	 t h e 	 c l o s u r e 	 p r o p e r t y 	 o f 	 a d d i t i o n 	 o f 	 w h o l e 	 n u m b e r s . 	 G i v e 	 a n 	 e x a m p l e .
A n s . 	 a 	 + 	 b 	 = 	 c 	 w h e r e 	 a , 	 b 	 a n d 	 c 	 a r e 	 a l w a y s 	 w h o l e 	 n u m b e r s .
F o r 	 e x a m p l e : 	 5 	 + 	 3 	 = 	 8 	 w h e r e 	 5 , 	 3 	 a n d 	 8 	 a r e 	 a l l 	 w h o l e 	 n u m b e r s .
S e c t i o n - C
1 1 . D i v i d e 	 3 0 3 0 3 0 0 	 b y 	 8 5 1 2 	 a n d 	 f i n d 	 t h e 	 q u o t i e n t 	 a n d 	 r e m a i n d e r .
A n s . 	 D i v i d e 	 3 0 3 0 3 0 0 	 b y 	 8 5 1 2
Q 	 = 	 3 5 6
R 	 = 	 2 8
1 2 . 	 S i m p l i f y 	 u s i n g 	 d i s t r i b u t i v e 	 p r o p e r t y 	 o f 	 w h o l e 	 n u m b e r s : 	 9 8 7 	 x 	 6 	 + 	 9 8 7 	 x 	 3 	 + 	 9 8 7
A n s . 	 9 8 7 	 x 	 6 	 + 	 9 8 7 	 x 	 3 	 + 	 9 8 7
U s i n g 	 d i s t r i b u t i v e 	 p r o p e r t y
= 	 9 8 7 	 x 	 ( 6 	 + 	 3 	 + 	 1 )
= 	 9 8 7 	 x 	 1 0
= 	 9 8 7 0
1 3 . 	 I f 	 L C M 	 o f 	 2 1 	 a n d 	 3 0 	 i s 	 2 1 0 , 	 w h a t 	 i s 	 t h e i r 	 H C F ?
A n s . 	 L . C . M . 	 = 	 2 1 0
O n e 	 n u m b e r 	 = 	 2 1
O t h e r 	 n u m b e r 	 = 3 0
H . C . F . 	 x 	 L . C . M . 	 = 	 P r o d u c t 	 o f 	 n u m b e r s
H . C . 	 F 	 x 	 2 1 0 	 = 	 2 1 	 x 	 3 0
H . C . 	 F 	 = 	 6 3 0 	 / 	 2 1 0 	 = 	 3
1 4 . 	 B y 	 u s i n g 	 l o n g 	 d i v i s i o n 	 m e t h o d , 	 f i n d 	 t h e 	 H C F 	 o f 	 1 7 6 0 , 	 4 0 4 8 , 	 3 6 3 2 	 a n d 	 7 6 0 8 .
A n s . 	 H C F 	 = 	 3 	 ( u s i n g 	 l o n g 	 d i v i s i o n 	 m e t h o d )
1 5 . 	 I n 	 t h e 	 f o l l o w i n g 	 f i g u r e , 	 n a m e :
a . 	 a n y 	 t w o 	 p a i r s 	 o f 	 p a r a l l e l 	 l i n e s .
b . 	 a n y 	 t w o 	 p a i r s 	 o f 	 i n t e r s e c t i n g 	 l i n e s .
c . 	 t h e 	 p o i n t 	 o f 	 i n t e r s e c t i o n 	 o f 	 l i n e 	 n 	 a n d 	 p .
A n s . 	 a . 	 l , 	 m 	 a n d 	 m , 	 n
b . 	 n , 	 q 	 a n d 	 m , 	 q
c . 	 F
1 6 . 	 N a m e 	 s i x 	 a n g l e s 	 i n 	 t h e 	 f o l l o w i n g 	 f i g u r e 	 t h a t 	 h a v e 	 C 	 a s 	 a 	 v e r t e x :
A n s . 	 < A C B , 	 < A C P , 	 < A C Q , 	 < B C P , 	 < B C Q , 	 < P C Q
1 7 . 	 C l a s s i f y 	 t h e 	 t r i a n g l e s 	 o n 	 t h e 	 b a s i s 	 o f 	 s i d e s . 	 D r a w 	 t h e 	 f i g u r e s 	 a l s o .
A n s . 	 I s o s c e l e s , 	 E q u i l a t e r a l 	 a n d 	 S c a l e n e .
1 8 . 	 F r o m 	 t h e 	 g i v e n 	 f i g u r e 	 n a m e :
a 	 a 	 s e t 	 o f 	 c o l l i n e a r 	 p o i n t s
b 	 t w o 	 r a y s
c 	 a 	 l i n e
A n s . 	 a . 	 D , 	 O 	 a n d 	 B 	 ( 1 	 m k 	 e a c h )
b . 	 O D 	 a n d 	 O B
c . 	 D B
1 9 . 	 T h e 	 t a b l e 	 g i v e n 	 b e l o w 	 s h o w s 	 t h e 	 d a t a 	 r e g a r d i n g 	 t h e 	 i n d o o r 	 g a m e s 	 c h i l d r e n 	 o f 	 a
s o c i e t y 	 l i k e 	 t o 	 p l a y . 	 M a k e 	 a 	 p i c t o g r a p h 	 f o r 	 t h i s 	 d a t a .
G a m e s C a r o m C h e s s C h i n e s e 	 c h e c k e r S c r a b b l e
Page 5


G e n e r a l 	 I n s t r u c t i o n s :
T h i s 	 q u e s t i o n 	 p a p e r 	 h a s 	 3 1 	 q u e s t i o n s 	 .
S e c t i o n 	 A 	 c o n s i s t s 	 o f 	 4 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h .
S e c t i o n 	 B 	 c o n s i s t s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h .
S e c t i o n 	 C 	 c o n s i s t s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h .
S e c t i o n 	 D 	 c o n s i s t s 	 o f 	 1 1 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y 	 t o 	 a t t e m p t .
A t t e m p t 	 t h e 	 p a p e r 	 n e a t l y 	 a n d 	 l e g i b l y .
S e c t i o n 	 – 	 A
1 . 	 W r i t e 	 t h e 	 m a t h e m a t i c a l 	 s t a t e m e n t 	 f o r 	 “ S u m 	 o f 	 t w e n t y - o n e 	 a n d 	 f i f t e e n 	 d i v i d e d 	 b y 	 t h e
d i f f e r e n c e 	 o f 	 e i g h t 	 a n d 	 t h r e e ” .
A n s . 	 	
2 . 	 I n 	 a 	 p i c t o g r a p h , 	 i f 	 t h e 	 s y m b o l 	 	 	 	 	 r e p r e s e n t s 	 5 0 	 s t u d e n t s , 	 t h e n 	 h o w 	 m a n y 	 s t u d e n t s
w i l l 	 b e 	 r e p r e s e n t e d 	 b y 	 t h e 	 s y m b o l 	 ?
A n s . 	 1 2 0
3 . 	 S o l v e 	 a n d 	 w r i t e 	 t h e 	 a n s w e r 	 i n 	 t h e 	 R o m a n 	 n u m e r a l : 	 C D X C I I 	 - 	 C D 	 = 	 _ _ _ _ _ _
A n s . 	 4 9 2 - 4 0 0 = 9 2 = X C I I
4 . 	 W h a t 	 f r a c t i o n 	 o f 	 a 	 r e v o l u t i o n 	 h a v e 	 y o u 	 t u r n e d 	 t h r o u g h 	 i f 	 y o u 	 s t a n d 	 f a c i n g 	 t h e 	 e a s t
a n d 	 t u r n 	 c l o c k w i s e 	 t o 	 f a c e 	 t h e 	 n o r t h ?
A n s . 	 o f 	 t h e 	 R e v o l u t i o n
S E C T I O N - B
5 . 	 W r i t e 	 t h e 	 n u m b e r 	 n a m e 	 o f 	 2 0 4 6 0 0 8 0 8 	 a c c o r d i n g 	 t o 	 t h e 	 I n t e r n a t i o n a l 	 s y s t e m 	 o f
n u m e r a t i o n .
A n s . 	 2 0 4 6 0 0 8 0 8 = 2 0 4 , 6 0 0 , 8 0 8
T w o 	 h u n d r e d 	 f o u r 	 m i l l i o n 	 s i x 	 h u n d r e d 	 t h o u s a n d 	 e i g h t 	 h u n d r e d 	 a n d 	 e i g h t .
6 . 	 M u l t i p l y 	 b y 	 s u i t a b l e 	 r e a r r a n g e m e n t : 	 5 	 x 	 8 7 	 x 	 2 0
A n s . 	 5 	 x 	 8 7 x 	 2 0
= 	 ( 5 	 x 	 2 0 ) 	 x 	 8 7
= 1 0 0 	 x 	 8 7 	 = 8 7 0 0
7 . 	 E x p r e s s 	 3 7 	 a s 	 p r o d u c t 	 o f 	 p r i m e 	 p l u s 	 1 .
A n s . 	 3 7 	 = 	 3 6 	 + 	 1
3 6 	 = 	 2 	 x 	 2 	 x 	 3 	 x 	 3
H e n c e , 	 3 7 	 = 	 2 	 x 	 2 	 x 	 3 	 x 	 3 	 + 	 1
8 . 	 S t a t e 	 t h e 	 r e l a t i o n s h i p 	 b e t w e e n 	 r a d i u s 	 & 	 d i a m e t e r 	 o f 	 a 	 c i r c l e . 	 E x p l a i n 	 t h r o u g h 	 a n
e x a m p l e .
A n s . 	 D 	 = 	 2 	 X 	 R 	 ( 1 )
E i t h e r 	 e x p l a i n e d 	 t h r o u g h 	 f i g u r e 	 o r 	 a n 	 e x a m p l e .
9 . 	 I n 	 a 	 M a t h e m a t i c s 	 t e s t , 	 t h e 	 f o l l o w i n g 	 m a r k s 	 w e r e 	 o b t a i n e d 	 b y 	 4 0 	 s t u d e n t s :
A r r a n g e 	 t h e s e 	 m a r k s 	 i n 	 a 	 t a b l e 	 u s i n g 	 t a l l y 	 m a r k s .
8 , 	 1 , 	 3 , 	 7 , 	 6 , 	 5 , 	 5 , 	 4 , 	 4 , 	 2 , 	 4 , 	 9 , 	 5 , 	 3 , 	 7 , 	 1 , 	 6 , 	 5 , 	 2 , 	 7 , 	 7 , 	 3 , 	 8 , 	 4 , 	 2 , 	 8 , 	 9 , 	 5 , 	 8 , 	 6 , 	 7 , 	 4 , 	 5 , 	 6 , 	 9 , 	 6 ,
4 , 	 4 , 	 6 , 	 6
A n s . 	 F r e q u e n c y 	 d i s t r i b u t i o n 	 t a b l e 	 t o 	 b e 	 n e a t l y 	 d r a w n
1 0 . 	 S t a t e 	 t h e 	 c l o s u r e 	 p r o p e r t y 	 o f 	 a d d i t i o n 	 o f 	 w h o l e 	 n u m b e r s . 	 G i v e 	 a n 	 e x a m p l e .
A n s . 	 a 	 + 	 b 	 = 	 c 	 w h e r e 	 a , 	 b 	 a n d 	 c 	 a r e 	 a l w a y s 	 w h o l e 	 n u m b e r s .
F o r 	 e x a m p l e : 	 5 	 + 	 3 	 = 	 8 	 w h e r e 	 5 , 	 3 	 a n d 	 8 	 a r e 	 a l l 	 w h o l e 	 n u m b e r s .
S e c t i o n - C
1 1 . D i v i d e 	 3 0 3 0 3 0 0 	 b y 	 8 5 1 2 	 a n d 	 f i n d 	 t h e 	 q u o t i e n t 	 a n d 	 r e m a i n d e r .
A n s . 	 D i v i d e 	 3 0 3 0 3 0 0 	 b y 	 8 5 1 2
Q 	 = 	 3 5 6
R 	 = 	 2 8
1 2 . 	 S i m p l i f y 	 u s i n g 	 d i s t r i b u t i v e 	 p r o p e r t y 	 o f 	 w h o l e 	 n u m b e r s : 	 9 8 7 	 x 	 6 	 + 	 9 8 7 	 x 	 3 	 + 	 9 8 7
A n s . 	 9 8 7 	 x 	 6 	 + 	 9 8 7 	 x 	 3 	 + 	 9 8 7
U s i n g 	 d i s t r i b u t i v e 	 p r o p e r t y
= 	 9 8 7 	 x 	 ( 6 	 + 	 3 	 + 	 1 )
= 	 9 8 7 	 x 	 1 0
= 	 9 8 7 0
1 3 . 	 I f 	 L C M 	 o f 	 2 1 	 a n d 	 3 0 	 i s 	 2 1 0 , 	 w h a t 	 i s 	 t h e i r 	 H C F ?
A n s . 	 L . C . M . 	 = 	 2 1 0
O n e 	 n u m b e r 	 = 	 2 1
O t h e r 	 n u m b e r 	 = 3 0
H . C . F . 	 x 	 L . C . M . 	 = 	 P r o d u c t 	 o f 	 n u m b e r s
H . C . 	 F 	 x 	 2 1 0 	 = 	 2 1 	 x 	 3 0
H . C . 	 F 	 = 	 6 3 0 	 / 	 2 1 0 	 = 	 3
1 4 . 	 B y 	 u s i n g 	 l o n g 	 d i v i s i o n 	 m e t h o d , 	 f i n d 	 t h e 	 H C F 	 o f 	 1 7 6 0 , 	 4 0 4 8 , 	 3 6 3 2 	 a n d 	 7 6 0 8 .
A n s . 	 H C F 	 = 	 3 	 ( u s i n g 	 l o n g 	 d i v i s i o n 	 m e t h o d )
1 5 . 	 I n 	 t h e 	 f o l l o w i n g 	 f i g u r e , 	 n a m e :
a . 	 a n y 	 t w o 	 p a i r s 	 o f 	 p a r a l l e l 	 l i n e s .
b . 	 a n y 	 t w o 	 p a i r s 	 o f 	 i n t e r s e c t i n g 	 l i n e s .
c . 	 t h e 	 p o i n t 	 o f 	 i n t e r s e c t i o n 	 o f 	 l i n e 	 n 	 a n d 	 p .
A n s . 	 a . 	 l , 	 m 	 a n d 	 m , 	 n
b . 	 n , 	 q 	 a n d 	 m , 	 q
c . 	 F
1 6 . 	 N a m e 	 s i x 	 a n g l e s 	 i n 	 t h e 	 f o l l o w i n g 	 f i g u r e 	 t h a t 	 h a v e 	 C 	 a s 	 a 	 v e r t e x :
A n s . 	 < A C B , 	 < A C P , 	 < A C Q , 	 < B C P , 	 < B C Q , 	 < P C Q
1 7 . 	 C l a s s i f y 	 t h e 	 t r i a n g l e s 	 o n 	 t h e 	 b a s i s 	 o f 	 s i d e s . 	 D r a w 	 t h e 	 f i g u r e s 	 a l s o .
A n s . 	 I s o s c e l e s , 	 E q u i l a t e r a l 	 a n d 	 S c a l e n e .
1 8 . 	 F r o m 	 t h e 	 g i v e n 	 f i g u r e 	 n a m e :
a 	 a 	 s e t 	 o f 	 c o l l i n e a r 	 p o i n t s
b 	 t w o 	 r a y s
c 	 a 	 l i n e
A n s . 	 a . 	 D , 	 O 	 a n d 	 B 	 ( 1 	 m k 	 e a c h )
b . 	 O D 	 a n d 	 O B
c . 	 D B
1 9 . 	 T h e 	 t a b l e 	 g i v e n 	 b e l o w 	 s h o w s 	 t h e 	 d a t a 	 r e g a r d i n g 	 t h e 	 i n d o o r 	 g a m e s 	 c h i l d r e n 	 o f 	 a
s o c i e t y 	 l i k e 	 t o 	 p l a y . 	 M a k e 	 a 	 p i c t o g r a p h 	 f o r 	 t h i s 	 d a t a .
G a m e s C a r o m C h e s s C h i n e s e 	 c h e c k e r S c r a b b l e
N o . 	 o f 	 c h i l d r e n 1 5 4 0 2 0 2 5
A n s . 	 P i c t o g r a p h 	 f o r 	 t h e 	 d a t a 	 n e a t l y 	 d r a w n . 	 S c a l e 	 s h o w n .
2 0 . 	 R e a d 	 t h e 	 a d j o i n i n g 	 b a r 	 g r a p h 	 s h o w i n g 	 t h e 	 n u m b e r 	 o f 	 s t u d e n t s 	 i n 	 a 	 p a r t i c u l a r 	 c l a s s
o f 	 a 	 s c h o o l 	 e v e r y 	 y e a r .
A n s w e r 	 t h e 	 f o l l o w i n g 	 q u e s t i o n s :
a . 	 W h a t 	 i s 	 t h e 	 s c a l e 	 o f 	 t h i s 	 g r a p h ?
b . 	 H o w 	 m a n y 	 n e w 	 s t u d e n t s 	 h a v e 	 j o i n e d 	 t h e 	 s c h o o l 	 f o r 	 2 0 1 2 	 b a t c h ?
c . 	 I s 	 t h e 	 n u m b e r 	 o f 	 s t u d e n t s 	 i n 	 t h e 	 y e a r 	 2 0 1 3 	 t w i c e 	 t h a n 	 t h a t 	 i n 	 t h e 	 Y e a r 	 2 0 1 0 ?
A n s . 	 a . 	 1 	 u n i t 	 = 	 1 0 	 s t u d e n t s 	 ( 1 	 m k 	 e a c h )
b . 	 5 	 s t u d e n t s
c . 	 N o
S E C T I O N - D
2 1 . 	 M a k e 	 t h e 	 g r e a t e s t 	 a n d 	 t h e 	 s m a l l e s t 	 6 - d i g i t 	 n u m b e r s , 	 u s i n g 	 a n y 	 s i x - d i f f e r e n t 	 d i g i t
w i t h 	 3 	 a t 	 t h o u s a n d s 	 p l a c e 	 i n 	 e a c h 	 c a s e . 	 W r i t e 	 t h e m 	 i n 	 e x p a n d e d 	 f o r m s .
A n s . 	 G r e a t e s t 	 6 - d i g i t 	 n u m b e r 	 = 	 9 8 3 7 6 5
E x p a n d e d 	 f o r m 	 = 	 9 0 0 0 0 0 	 + 	 8 0 0 0 0 	 + 	 3 0 0 0 	 + 	 7 0 0 	 + 	 6 0 	 + 	 5
S m a l l e s t 	 6 - d i g i t 	 n u m b e r 	 = 	 1 0 3 2 4 5
E x p a n d e d 	 f o r m 	 = 	 1 0 0 0 0 0 	 + 	 3 0 0 0 	 + 	 2 0 0 	 + 	 4 0 	 + 	 5
2 2 . 	 T h e 	 h o b b i e s 	 o f 	 l a d i e s 	 o f 	 a 	 h o u s i n g 	 s o c i e t y 	 a r e 	 a s 	 f o l l o w s :
H o b b y L i s t e n i n g 	 t o 	 m u s i c D a n c i n g T r a v e l l i n g C o o k i n g R e a d i n g

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Ans. The CBSE Class 6 Math Past Year Paper-3 is a question paper that contains math problems and exercises specifically designed for students in Class 6. It is based on the CBSE curriculum and covers various topics taught in the class.

2. Why should I solve the CBSE Class 6 Math Past Year Paper-3?

Ans. Solving the CBSE Class 6 Math Past Year Paper-3 can be beneficial for students as it helps them understand the pattern of questions asked in previous exams. It allows them to practice and revise the concepts they have learned in class, helping them to improve their problem-solving skills and gain confidence in the subject.

3. How can I prepare for the CBSE Class 6 Math Past Year Paper-3?

Ans. To prepare for the CBSE Class 6 Math Past Year Paper-3, students can follow these steps: - Review and revise the math concepts taught in class. - Solve practice questions and exercises from their textbook. - Take help from reference books or online resources for additional practice. - Understand the question paper pattern and marking scheme. - Solve previous year papers and sample papers to get familiar with the exam format and types of questions asked.

4. Are there any tips to score well in the CBSE Class 6 Math Past Year Paper-3?

Ans. Yes, here are some tips to score well in the CBSE Class 6 Math Past Year Paper-3: - Understand the concepts thoroughly and practice regularly. - Focus on understanding the problem-solving techniques rather than just memorizing the steps. - Read the questions carefully and identify the key information before attempting to solve them. - Show all the steps and calculations clearly in the answer sheet. - Practice time management to ensure that you can complete the paper within the given time frame. - Review and double-check your answers before submitting the paper.

5. Where can I find the CBSE Class 6 Math Past Year Paper-3?

Ans. The CBSE Class 6 Math Past Year Paper-3 can be found on various educational websites, online platforms, or through offline study materials. Students can also check with their schools or teachers for access to previous year question papers.

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