Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > Class 7 Math: CBSE Past Year Paper - 6
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S E C T I O N – A [ 1 m a r k e a c h ]
1 . W h a t i s t h e d e g r e e o f t h e p o l y n o m i a l x 3 y – 2 x y 4 + 1 ?
A n s . D e g r e e = 5
2 . A d i c e i s t h r o w n a t r a n d o m , f i n d t h e p r o b a b i l i t y o f g e t t i n g a n u m b e r d i v i s i b l e b y 3 .
A n s .
3 . W r i t e t h e n u m b e r o f s i d e s o f t h e b a s e i n a p e n t a g o n a l p r i s m .
A n s . 5
4 . C o m p u t e t h e r a n g e o f 4 . 9 , 5 . 5 , 2 5 . 6 , 2 1 . 3 , 0 . 6 , 2 . 2 , 0 . 5 .
A n s . R a n g e = 2 5 . 6 - 0 . 5 = 2 5 . 1
S E C T I O N – B [ 2 m a r k s e a c h ]
5 . A m a n t r a v e l l e d 9 0 k m t o t h e n o r t h o f J a i p u r a n d t h e n 1 5 0 k m t o t h e s o u t h o f i t . H o w
f a r f r o m J a i p u r w a s h e f i n a l l y ?
A n s . N o r t h = + 9 0 k m
S o u t h = - 1 5 0 k m - - - - - - - ( 0 . 5 )
F i n a l = + 9 0 - 1 5 0 = - 6 0 k m - - - - - - - ( 1 )
H e n c e h e i s 6 0 k m s o u t h f r o m J a i p u r - - - - - - - ( 0 . 5 )
6 . C o m p l e t e t h e f o l l o w i n g t a b l e :
A n s .
( 0 . 5 m a r k s e a c h b o x )
Page 2
S E C T I O N – A [ 1 m a r k e a c h ]
1 . W h a t i s t h e d e g r e e o f t h e p o l y n o m i a l x 3 y – 2 x y 4 + 1 ?
A n s . D e g r e e = 5
2 . A d i c e i s t h r o w n a t r a n d o m , f i n d t h e p r o b a b i l i t y o f g e t t i n g a n u m b e r d i v i s i b l e b y 3 .
A n s .
3 . W r i t e t h e n u m b e r o f s i d e s o f t h e b a s e i n a p e n t a g o n a l p r i s m .
A n s . 5
4 . C o m p u t e t h e r a n g e o f 4 . 9 , 5 . 5 , 2 5 . 6 , 2 1 . 3 , 0 . 6 , 2 . 2 , 0 . 5 .
A n s . R a n g e = 2 5 . 6 - 0 . 5 = 2 5 . 1
S E C T I O N – B [ 2 m a r k s e a c h ]
5 . A m a n t r a v e l l e d 9 0 k m t o t h e n o r t h o f J a i p u r a n d t h e n 1 5 0 k m t o t h e s o u t h o f i t . H o w
f a r f r o m J a i p u r w a s h e f i n a l l y ?
A n s . N o r t h = + 9 0 k m
S o u t h = - 1 5 0 k m - - - - - - - ( 0 . 5 )
F i n a l = + 9 0 - 1 5 0 = - 6 0 k m - - - - - - - ( 1 )
H e n c e h e i s 6 0 k m s o u t h f r o m J a i p u r - - - - - - - ( 0 . 5 )
6 . C o m p l e t e t h e f o l l o w i n g t a b l e :
A n s .
( 0 . 5 m a r k s e a c h b o x )
7 . I s e v e r y r a t i o n a l n u m b e r a f r a c t i o n ? G i v e a r e a s o n i n s u p p o r t o f y o u r a n s w e r .
A n s . E v e r y r a t i o n a l n u m b e r n e e d n o t b e a f r a c t i o n a s r a t i o n a l n u m b e r s c a n b e m a d e u p o f
i n t e g e r s w h e r e a s f r a c t i o n s a r e m a d e u p o f w h o l e n u m b e r s .
8 . E x p r e s s i n d e c i m a l f o r m . I s i t t e r m i n a t i n g o r n o n - t e r m i n a t i n g ?
A n s .
I t i s n o n - t e r m i n a t i n g r e p e a t i n g d e c i m a l r e p r e s e n t a t i o n . - - - ( 0 . 5 )
9 . T h i s i s a m a g i c s q u a r e a s t h e s u m i n e a c h r o w , c o l u m n a n d d i a g o n a l i s t h e s a m e . F i n d
t h e s u m o f e a c h r o w , c o l u m n , d i a g o n a l w h e n a = 5 .
A n s . S u m = 3 a 2 - - - - - - - - - - - - - ( 1 )
V a l u e f o r a = 5 i s 7 5 - - - - - - - - ( 1 )
1 0 . T h e e x t e r i o r a n g l e
A n s .
S E C T I O N – C [ 3 m a r k s e a c h ]
1 1 . S i m p l i f y :
1 2 ÷ [ 1 5 – { 9 ÷ ( 1 7 + 3 x 2 – 2 0 ) } ]
A n s . 1 2 ÷ [ 1 5 – { 9 ÷ ( 1 7 + 3 x 2 – 2 0 ) } ]
S o l v i n g u s i n g B O D M A S a n d g e t t i n g t h e a n s w e r 1
1 2 . I f t h e c o s t o f 2 0 M a t h e m a t i c s b o o k s o f c l a s s V I I i s R s . 3 9 0 . 5 0 , w h a t i s t h e c o s t o f 2 s u c h
M a t h e m a t i c s b o o k s ?
Page 3
S E C T I O N – A [ 1 m a r k e a c h ]
1 . W h a t i s t h e d e g r e e o f t h e p o l y n o m i a l x 3 y – 2 x y 4 + 1 ?
A n s . D e g r e e = 5
2 . A d i c e i s t h r o w n a t r a n d o m , f i n d t h e p r o b a b i l i t y o f g e t t i n g a n u m b e r d i v i s i b l e b y 3 .
A n s .
3 . W r i t e t h e n u m b e r o f s i d e s o f t h e b a s e i n a p e n t a g o n a l p r i s m .
A n s . 5
4 . C o m p u t e t h e r a n g e o f 4 . 9 , 5 . 5 , 2 5 . 6 , 2 1 . 3 , 0 . 6 , 2 . 2 , 0 . 5 .
A n s . R a n g e = 2 5 . 6 - 0 . 5 = 2 5 . 1
S E C T I O N – B [ 2 m a r k s e a c h ]
5 . A m a n t r a v e l l e d 9 0 k m t o t h e n o r t h o f J a i p u r a n d t h e n 1 5 0 k m t o t h e s o u t h o f i t . H o w
f a r f r o m J a i p u r w a s h e f i n a l l y ?
A n s . N o r t h = + 9 0 k m
S o u t h = - 1 5 0 k m - - - - - - - ( 0 . 5 )
F i n a l = + 9 0 - 1 5 0 = - 6 0 k m - - - - - - - ( 1 )
H e n c e h e i s 6 0 k m s o u t h f r o m J a i p u r - - - - - - - ( 0 . 5 )
6 . C o m p l e t e t h e f o l l o w i n g t a b l e :
A n s .
( 0 . 5 m a r k s e a c h b o x )
7 . I s e v e r y r a t i o n a l n u m b e r a f r a c t i o n ? G i v e a r e a s o n i n s u p p o r t o f y o u r a n s w e r .
A n s . E v e r y r a t i o n a l n u m b e r n e e d n o t b e a f r a c t i o n a s r a t i o n a l n u m b e r s c a n b e m a d e u p o f
i n t e g e r s w h e r e a s f r a c t i o n s a r e m a d e u p o f w h o l e n u m b e r s .
8 . E x p r e s s i n d e c i m a l f o r m . I s i t t e r m i n a t i n g o r n o n - t e r m i n a t i n g ?
A n s .
I t i s n o n - t e r m i n a t i n g r e p e a t i n g d e c i m a l r e p r e s e n t a t i o n . - - - ( 0 . 5 )
9 . T h i s i s a m a g i c s q u a r e a s t h e s u m i n e a c h r o w , c o l u m n a n d d i a g o n a l i s t h e s a m e . F i n d
t h e s u m o f e a c h r o w , c o l u m n , d i a g o n a l w h e n a = 5 .
A n s . S u m = 3 a 2 - - - - - - - - - - - - - ( 1 )
V a l u e f o r a = 5 i s 7 5 - - - - - - - - ( 1 )
1 0 . T h e e x t e r i o r a n g l e
A n s .
S E C T I O N – C [ 3 m a r k s e a c h ]
1 1 . S i m p l i f y :
1 2 ÷ [ 1 5 – { 9 ÷ ( 1 7 + 3 x 2 – 2 0 ) } ]
A n s . 1 2 ÷ [ 1 5 – { 9 ÷ ( 1 7 + 3 x 2 – 2 0 ) } ]
S o l v i n g u s i n g B O D M A S a n d g e t t i n g t h e a n s w e r 1
1 2 . I f t h e c o s t o f 2 0 M a t h e m a t i c s b o o k s o f c l a s s V I I i s R s . 3 9 0 . 5 0 , w h a t i s t h e c o s t o f 2 s u c h
M a t h e m a t i c s b o o k s ?
A n s . C o s t o f 2 0 M a t h e m a t i c s b o o k s = R s . 3 9 0 . 5 0
C o s t o f 1 M a t h e m a t i c s b o o k s = R s . 3 9 0 . 5 0 ÷ 2 0 = R s . 1 9 . 5 2 5 - - - - - - - - - - - - - - ( 1 . 5 )
C o s t o f 2 M a t h e m a t i c s b o o k s = R s . 1 9 . 5 2 5 x 2 = R s . 3 9 . 0 5 - - - - - - - - - - - - - ( 1 . 5 )
1 3 . W h a t s h o u l d b e s u b t r a c t e d f r o m x
2
+ x y + y
2
+ x + 2 y – 3 t o o b t a i n x 2 – 3 y 2 + 4 x y – 7 ?
A n s . R e q u i r e d e x p r e s s i o n = x 2 + x y + y 2 + x + 2 y – 3 – ( x 2 – 3 y 2 + 4 x y – 7 ) - - - - - - - - - - - - ( 1 )
= x 2 + x y + y 2 + x + 2 y – 3 – x 2 + 3 y 2 - 4 x y + 7 - - - - - - - - - - - - ( 1 )
= - 3 x y + 4 y 2 + x + 2 y + 4 - - - - - - - - - - - - ( 1 )
1 4 . I n a c l a s s t e s t 3 m a r k s a r e a w a r d e d f o r e v e r y c o r r e c t a n s w e r a n d ( - 2 ) m a r k s a r e
g i v e n f o r e v e r y i n c o r r e c t a n s w e r a n d 0 f o r q u e s t i o n s n o t a t t e m p t e d .
a . M o h a n g e t s f o u r c o r r e c t a n d s i x i n c o r r e c t a n s w e r s . W h a t i s h i s s c o r e ?
b . R a m s c o r e s 2 0 m a r k s , i f h e g e t s 1 2 c o r r e c t a n s w e r s t h e n , f i n d t h e n u m b e r o f i n c o r r e c t
a n s w e r s ?
c . H e e n a s c o r e s - 5 m a r k s , i f s h e g e t s 7 c o r r e c t a n s w e r s t h e n , f i n d t h e n u m b e r o f
i n c o r r e c t a n s w e r s ?
A n s . a . M o h a n ’ s s c o r e = 4 x 3 + 6 x ( - 2 ) = 1 2 - 1 2 = 0 - - - - - - - - - - - - ( 1 )
b . 2 0 = 1 2 x 3 + i n c o r r e c t x ( - 2 ) = > 2 0 – 3 6 = i n c o r r e c t x ( - 2 ) = > i n c o r r e c t = 8 - - - - - - - - - - - - ( 1 )
c . - 5 = 7 x 3 + i n c o r r e c t x ( - 2 ) = > - 5 - 2 1 = i n c o r r e c t x ( - 2 ) = > i n c o r r e c t = 1 3 - - - - - - - - - - - - ( 1 )
1 5 . T h e p r o d u c t o f t w o r a t i o n a l n u m b e r s i s . I f o n e o f t h e m i s , f i n d t h e o t h e r .
A n s .
O t h e r n o . - - ( 1 )
1 6 . I d e n t i f y t h e s o l i d s h a p e :
a . I h a v e o n l y o n e c u r v e d f a c e w i t h o u t a n y e d g e s o r v e r t i c e s .
b . I h a v e f i v e f a c e s o f t h e s a m e s h a p e a n d o n e f a c e i s d i f f e r e n t .
c . M y t w o f a c e s a r e c o n g r u e n t t r i a n g l e s a n d o t h e r s a r e a l l r e c t a n g l e s .
A n s . a . S p h e r e - - - - - ( 1 )
b . P e n t a g o n a l p y r a m i d - - - - - ( 1 )
c . T r i a n g u l a r p r i s m - - - - - ( 1 )
Page 4
S E C T I O N – A [ 1 m a r k e a c h ]
1 . W h a t i s t h e d e g r e e o f t h e p o l y n o m i a l x 3 y – 2 x y 4 + 1 ?
A n s . D e g r e e = 5
2 . A d i c e i s t h r o w n a t r a n d o m , f i n d t h e p r o b a b i l i t y o f g e t t i n g a n u m b e r d i v i s i b l e b y 3 .
A n s .
3 . W r i t e t h e n u m b e r o f s i d e s o f t h e b a s e i n a p e n t a g o n a l p r i s m .
A n s . 5
4 . C o m p u t e t h e r a n g e o f 4 . 9 , 5 . 5 , 2 5 . 6 , 2 1 . 3 , 0 . 6 , 2 . 2 , 0 . 5 .
A n s . R a n g e = 2 5 . 6 - 0 . 5 = 2 5 . 1
S E C T I O N – B [ 2 m a r k s e a c h ]
5 . A m a n t r a v e l l e d 9 0 k m t o t h e n o r t h o f J a i p u r a n d t h e n 1 5 0 k m t o t h e s o u t h o f i t . H o w
f a r f r o m J a i p u r w a s h e f i n a l l y ?
A n s . N o r t h = + 9 0 k m
S o u t h = - 1 5 0 k m - - - - - - - ( 0 . 5 )
F i n a l = + 9 0 - 1 5 0 = - 6 0 k m - - - - - - - ( 1 )
H e n c e h e i s 6 0 k m s o u t h f r o m J a i p u r - - - - - - - ( 0 . 5 )
6 . C o m p l e t e t h e f o l l o w i n g t a b l e :
A n s .
( 0 . 5 m a r k s e a c h b o x )
7 . I s e v e r y r a t i o n a l n u m b e r a f r a c t i o n ? G i v e a r e a s o n i n s u p p o r t o f y o u r a n s w e r .
A n s . E v e r y r a t i o n a l n u m b e r n e e d n o t b e a f r a c t i o n a s r a t i o n a l n u m b e r s c a n b e m a d e u p o f
i n t e g e r s w h e r e a s f r a c t i o n s a r e m a d e u p o f w h o l e n u m b e r s .
8 . E x p r e s s i n d e c i m a l f o r m . I s i t t e r m i n a t i n g o r n o n - t e r m i n a t i n g ?
A n s .
I t i s n o n - t e r m i n a t i n g r e p e a t i n g d e c i m a l r e p r e s e n t a t i o n . - - - ( 0 . 5 )
9 . T h i s i s a m a g i c s q u a r e a s t h e s u m i n e a c h r o w , c o l u m n a n d d i a g o n a l i s t h e s a m e . F i n d
t h e s u m o f e a c h r o w , c o l u m n , d i a g o n a l w h e n a = 5 .
A n s . S u m = 3 a 2 - - - - - - - - - - - - - ( 1 )
V a l u e f o r a = 5 i s 7 5 - - - - - - - - ( 1 )
1 0 . T h e e x t e r i o r a n g l e
A n s .
S E C T I O N – C [ 3 m a r k s e a c h ]
1 1 . S i m p l i f y :
1 2 ÷ [ 1 5 – { 9 ÷ ( 1 7 + 3 x 2 – 2 0 ) } ]
A n s . 1 2 ÷ [ 1 5 – { 9 ÷ ( 1 7 + 3 x 2 – 2 0 ) } ]
S o l v i n g u s i n g B O D M A S a n d g e t t i n g t h e a n s w e r 1
1 2 . I f t h e c o s t o f 2 0 M a t h e m a t i c s b o o k s o f c l a s s V I I i s R s . 3 9 0 . 5 0 , w h a t i s t h e c o s t o f 2 s u c h
M a t h e m a t i c s b o o k s ?
A n s . C o s t o f 2 0 M a t h e m a t i c s b o o k s = R s . 3 9 0 . 5 0
C o s t o f 1 M a t h e m a t i c s b o o k s = R s . 3 9 0 . 5 0 ÷ 2 0 = R s . 1 9 . 5 2 5 - - - - - - - - - - - - - - ( 1 . 5 )
C o s t o f 2 M a t h e m a t i c s b o o k s = R s . 1 9 . 5 2 5 x 2 = R s . 3 9 . 0 5 - - - - - - - - - - - - - ( 1 . 5 )
1 3 . W h a t s h o u l d b e s u b t r a c t e d f r o m x
2
+ x y + y
2
+ x + 2 y – 3 t o o b t a i n x 2 – 3 y 2 + 4 x y – 7 ?
A n s . R e q u i r e d e x p r e s s i o n = x 2 + x y + y 2 + x + 2 y – 3 – ( x 2 – 3 y 2 + 4 x y – 7 ) - - - - - - - - - - - - ( 1 )
= x 2 + x y + y 2 + x + 2 y – 3 – x 2 + 3 y 2 - 4 x y + 7 - - - - - - - - - - - - ( 1 )
= - 3 x y + 4 y 2 + x + 2 y + 4 - - - - - - - - - - - - ( 1 )
1 4 . I n a c l a s s t e s t 3 m a r k s a r e a w a r d e d f o r e v e r y c o r r e c t a n s w e r a n d ( - 2 ) m a r k s a r e
g i v e n f o r e v e r y i n c o r r e c t a n s w e r a n d 0 f o r q u e s t i o n s n o t a t t e m p t e d .
a . M o h a n g e t s f o u r c o r r e c t a n d s i x i n c o r r e c t a n s w e r s . W h a t i s h i s s c o r e ?
b . R a m s c o r e s 2 0 m a r k s , i f h e g e t s 1 2 c o r r e c t a n s w e r s t h e n , f i n d t h e n u m b e r o f i n c o r r e c t
a n s w e r s ?
c . H e e n a s c o r e s - 5 m a r k s , i f s h e g e t s 7 c o r r e c t a n s w e r s t h e n , f i n d t h e n u m b e r o f
i n c o r r e c t a n s w e r s ?
A n s . a . M o h a n ’ s s c o r e = 4 x 3 + 6 x ( - 2 ) = 1 2 - 1 2 = 0 - - - - - - - - - - - - ( 1 )
b . 2 0 = 1 2 x 3 + i n c o r r e c t x ( - 2 ) = > 2 0 – 3 6 = i n c o r r e c t x ( - 2 ) = > i n c o r r e c t = 8 - - - - - - - - - - - - ( 1 )
c . - 5 = 7 x 3 + i n c o r r e c t x ( - 2 ) = > - 5 - 2 1 = i n c o r r e c t x ( - 2 ) = > i n c o r r e c t = 1 3 - - - - - - - - - - - - ( 1 )
1 5 . T h e p r o d u c t o f t w o r a t i o n a l n u m b e r s i s . I f o n e o f t h e m i s , f i n d t h e o t h e r .
A n s .
O t h e r n o . - - ( 1 )
1 6 . I d e n t i f y t h e s o l i d s h a p e :
a . I h a v e o n l y o n e c u r v e d f a c e w i t h o u t a n y e d g e s o r v e r t i c e s .
b . I h a v e f i v e f a c e s o f t h e s a m e s h a p e a n d o n e f a c e i s d i f f e r e n t .
c . M y t w o f a c e s a r e c o n g r u e n t t r i a n g l e s a n d o t h e r s a r e a l l r e c t a n g l e s .
A n s . a . S p h e r e - - - - - ( 1 )
b . P e n t a g o n a l p y r a m i d - - - - - ( 1 )
c . T r i a n g u l a r p r i s m - - - - - ( 1 )
1 7 . C a l c u l a t e t h e m e a n o f t h e f o l l o w i n g d a t a :
A n s . C a l c u l a t i n g
1 8 . F i n d t h e m e d i a n o f a l l t h e p r i m e n u m b e r s l y i n g b e t w e e n 1 a n d 5 0 .
A n s . P r i m e n u m b e r s l y i n g b e t w e e n 1 a n d 5 0 = 2 , 3 , 5 , 7 , 1 1 , 1 3 , 1 7 , 1 9 , 2 3 , 2 9 , 3 1 , 3 7 , 4 1 , 4 3 , 4 7
N = 1 5 ( o d d )
M e d i a n = o b s e r v a t i o n = 8 t h o b s e r v a t i o n = 1 9
1 9 . I s l ? J u s t i f y y o u r a n s w e r .
A n s . V e r t i c a l l y o p p o s i t e a n g l e o f i s t h e c o - i n t e r i o r a n g l e o f a n d t h e i r s u m i s 1 8 0 0 - -
- - ( 2 ) S i n c e t h e s u m o f c o - i n t e r i o r a n g l e s o n t h e s a m e s i d e o f t h e t r a n s v e r s a l i s 1 8 0 0 h e n c e
l i n e s a r e p a r a l l e l . - - - - ( 1 )
2 0 . A M a t h e m a t i c s t e a c h e r w a n t s t o s e e w h e t h e r t h e n e w t e c h n i q u e o f t e a c h i n g , w h i c h
s h e a p p l i e d a f t e r h a l f y e a r l y w a s e f f e c t i v e o r n o t . S h e t a k e s t h e m a r k s o f 5 c h i l d r e n i n
t h e h a l f y e a r l y t e s t ( o u t o f 5 0 ) a n d t h e n t h e a n n u a l t e s t ( o u t o f 5 0 ) a n d r e c o r d s t h e
f o l l o w i n g s c o r e s .
D r a w a d o u b l e b a r g r a p h . D o y o u t h i n k h e r n e w t e c h n i q u e h a s i m p r o v e d t h e r e s u l t o f
t h e s t u d e n t s ?
Page 5
S E C T I O N – A [ 1 m a r k e a c h ]
1 . W h a t i s t h e d e g r e e o f t h e p o l y n o m i a l x 3 y – 2 x y 4 + 1 ?
A n s . D e g r e e = 5
2 . A d i c e i s t h r o w n a t r a n d o m , f i n d t h e p r o b a b i l i t y o f g e t t i n g a n u m b e r d i v i s i b l e b y 3 .
A n s .
3 . W r i t e t h e n u m b e r o f s i d e s o f t h e b a s e i n a p e n t a g o n a l p r i s m .
A n s . 5
4 . C o m p u t e t h e r a n g e o f 4 . 9 , 5 . 5 , 2 5 . 6 , 2 1 . 3 , 0 . 6 , 2 . 2 , 0 . 5 .
A n s . R a n g e = 2 5 . 6 - 0 . 5 = 2 5 . 1
S E C T I O N – B [ 2 m a r k s e a c h ]
5 . A m a n t r a v e l l e d 9 0 k m t o t h e n o r t h o f J a i p u r a n d t h e n 1 5 0 k m t o t h e s o u t h o f i t . H o w
f a r f r o m J a i p u r w a s h e f i n a l l y ?
A n s . N o r t h = + 9 0 k m
S o u t h = - 1 5 0 k m - - - - - - - ( 0 . 5 )
F i n a l = + 9 0 - 1 5 0 = - 6 0 k m - - - - - - - ( 1 )
H e n c e h e i s 6 0 k m s o u t h f r o m J a i p u r - - - - - - - ( 0 . 5 )
6 . C o m p l e t e t h e f o l l o w i n g t a b l e :
A n s .
( 0 . 5 m a r k s e a c h b o x )
7 . I s e v e r y r a t i o n a l n u m b e r a f r a c t i o n ? G i v e a r e a s o n i n s u p p o r t o f y o u r a n s w e r .
A n s . E v e r y r a t i o n a l n u m b e r n e e d n o t b e a f r a c t i o n a s r a t i o n a l n u m b e r s c a n b e m a d e u p o f
i n t e g e r s w h e r e a s f r a c t i o n s a r e m a d e u p o f w h o l e n u m b e r s .
8 . E x p r e s s i n d e c i m a l f o r m . I s i t t e r m i n a t i n g o r n o n - t e r m i n a t i n g ?
A n s .
I t i s n o n - t e r m i n a t i n g r e p e a t i n g d e c i m a l r e p r e s e n t a t i o n . - - - ( 0 . 5 )
9 . T h i s i s a m a g i c s q u a r e a s t h e s u m i n e a c h r o w , c o l u m n a n d d i a g o n a l i s t h e s a m e . F i n d
t h e s u m o f e a c h r o w , c o l u m n , d i a g o n a l w h e n a = 5 .
A n s . S u m = 3 a 2 - - - - - - - - - - - - - ( 1 )
V a l u e f o r a = 5 i s 7 5 - - - - - - - - ( 1 )
1 0 . T h e e x t e r i o r a n g l e
A n s .
S E C T I O N – C [ 3 m a r k s e a c h ]
1 1 . S i m p l i f y :
1 2 ÷ [ 1 5 – { 9 ÷ ( 1 7 + 3 x 2 – 2 0 ) } ]
A n s . 1 2 ÷ [ 1 5 – { 9 ÷ ( 1 7 + 3 x 2 – 2 0 ) } ]
S o l v i n g u s i n g B O D M A S a n d g e t t i n g t h e a n s w e r 1
1 2 . I f t h e c o s t o f 2 0 M a t h e m a t i c s b o o k s o f c l a s s V I I i s R s . 3 9 0 . 5 0 , w h a t i s t h e c o s t o f 2 s u c h
M a t h e m a t i c s b o o k s ?
A n s . C o s t o f 2 0 M a t h e m a t i c s b o o k s = R s . 3 9 0 . 5 0
C o s t o f 1 M a t h e m a t i c s b o o k s = R s . 3 9 0 . 5 0 ÷ 2 0 = R s . 1 9 . 5 2 5 - - - - - - - - - - - - - - ( 1 . 5 )
C o s t o f 2 M a t h e m a t i c s b o o k s = R s . 1 9 . 5 2 5 x 2 = R s . 3 9 . 0 5 - - - - - - - - - - - - - ( 1 . 5 )
1 3 . W h a t s h o u l d b e s u b t r a c t e d f r o m x
2
+ x y + y
2
+ x + 2 y – 3 t o o b t a i n x 2 – 3 y 2 + 4 x y – 7 ?
A n s . R e q u i r e d e x p r e s s i o n = x 2 + x y + y 2 + x + 2 y – 3 – ( x 2 – 3 y 2 + 4 x y – 7 ) - - - - - - - - - - - - ( 1 )
= x 2 + x y + y 2 + x + 2 y – 3 – x 2 + 3 y 2 - 4 x y + 7 - - - - - - - - - - - - ( 1 )
= - 3 x y + 4 y 2 + x + 2 y + 4 - - - - - - - - - - - - ( 1 )
1 4 . I n a c l a s s t e s t 3 m a r k s a r e a w a r d e d f o r e v e r y c o r r e c t a n s w e r a n d ( - 2 ) m a r k s a r e
g i v e n f o r e v e r y i n c o r r e c t a n s w e r a n d 0 f o r q u e s t i o n s n o t a t t e m p t e d .
a . M o h a n g e t s f o u r c o r r e c t a n d s i x i n c o r r e c t a n s w e r s . W h a t i s h i s s c o r e ?
b . R a m s c o r e s 2 0 m a r k s , i f h e g e t s 1 2 c o r r e c t a n s w e r s t h e n , f i n d t h e n u m b e r o f i n c o r r e c t
a n s w e r s ?
c . H e e n a s c o r e s - 5 m a r k s , i f s h e g e t s 7 c o r r e c t a n s w e r s t h e n , f i n d t h e n u m b e r o f
i n c o r r e c t a n s w e r s ?
A n s . a . M o h a n ’ s s c o r e = 4 x 3 + 6 x ( - 2 ) = 1 2 - 1 2 = 0 - - - - - - - - - - - - ( 1 )
b . 2 0 = 1 2 x 3 + i n c o r r e c t x ( - 2 ) = > 2 0 – 3 6 = i n c o r r e c t x ( - 2 ) = > i n c o r r e c t = 8 - - - - - - - - - - - - ( 1 )
c . - 5 = 7 x 3 + i n c o r r e c t x ( - 2 ) = > - 5 - 2 1 = i n c o r r e c t x ( - 2 ) = > i n c o r r e c t = 1 3 - - - - - - - - - - - - ( 1 )
1 5 . T h e p r o d u c t o f t w o r a t i o n a l n u m b e r s i s . I f o n e o f t h e m i s , f i n d t h e o t h e r .
A n s .
O t h e r n o . - - ( 1 )
1 6 . I d e n t i f y t h e s o l i d s h a p e :
a . I h a v e o n l y o n e c u r v e d f a c e w i t h o u t a n y e d g e s o r v e r t i c e s .
b . I h a v e f i v e f a c e s o f t h e s a m e s h a p e a n d o n e f a c e i s d i f f e r e n t .
c . M y t w o f a c e s a r e c o n g r u e n t t r i a n g l e s a n d o t h e r s a r e a l l r e c t a n g l e s .
A n s . a . S p h e r e - - - - - ( 1 )
b . P e n t a g o n a l p y r a m i d - - - - - ( 1 )
c . T r i a n g u l a r p r i s m - - - - - ( 1 )
1 7 . C a l c u l a t e t h e m e a n o f t h e f o l l o w i n g d a t a :
A n s . C a l c u l a t i n g
1 8 . F i n d t h e m e d i a n o f a l l t h e p r i m e n u m b e r s l y i n g b e t w e e n 1 a n d 5 0 .
A n s . P r i m e n u m b e r s l y i n g b e t w e e n 1 a n d 5 0 = 2 , 3 , 5 , 7 , 1 1 , 1 3 , 1 7 , 1 9 , 2 3 , 2 9 , 3 1 , 3 7 , 4 1 , 4 3 , 4 7
N = 1 5 ( o d d )
M e d i a n = o b s e r v a t i o n = 8 t h o b s e r v a t i o n = 1 9
1 9 . I s l ? J u s t i f y y o u r a n s w e r .
A n s . V e r t i c a l l y o p p o s i t e a n g l e o f i s t h e c o - i n t e r i o r a n g l e o f a n d t h e i r s u m i s 1 8 0 0 - -
- - ( 2 ) S i n c e t h e s u m o f c o - i n t e r i o r a n g l e s o n t h e s a m e s i d e o f t h e t r a n s v e r s a l i s 1 8 0 0 h e n c e
l i n e s a r e p a r a l l e l . - - - - ( 1 )
2 0 . A M a t h e m a t i c s t e a c h e r w a n t s t o s e e w h e t h e r t h e n e w t e c h n i q u e o f t e a c h i n g , w h i c h
s h e a p p l i e d a f t e r h a l f y e a r l y w a s e f f e c t i v e o r n o t . S h e t a k e s t h e m a r k s o f 5 c h i l d r e n i n
t h e h a l f y e a r l y t e s t ( o u t o f 5 0 ) a n d t h e n t h e a n n u a l t e s t ( o u t o f 5 0 ) a n d r e c o r d s t h e
f o l l o w i n g s c o r e s .
D r a w a d o u b l e b a r g r a p h . D o y o u t h i n k h e r n e w t e c h n i q u e h a s i m p r o v e d t h e r e s u l t o f
t h e s t u d e n t s ?
A n s . 2 0 . D r a w i n g t h e d o u b l e b a r g r a p h - - - - - - - - - - - ( 2 . 5 )
Y e s , t h e n e w t e c h n i q u e h a s i m p r o v e d t h e r e s u l t o f t h e s t u d e n t s . - - - ( 0 . 5 )
S E C T I O N – D [ 4 m a r k s e a c h ]
2 1 . S i m p l i f y :
( 4 3 . 7 – 1 8 . 2 3 + 9 6 . 3 8 – 2 7 . 6 2 ) ÷ 9
A n s . 2 1 . ( 4 3 . 7 – 1 8 . 2 3 + 9 6 . 3 8 – 2 7 . 6 2 ) ÷ 9
= ( 1 4 0 . 0 8 – 4 5 . 8 5 ) ÷ 9 - - - - - - - - ( 2 )
= 9 4 . 2 3 ÷ 9 - - - - - - - - ( 1 )
= 1 0 . 4 7 - - - - - - - - ( 1 )
2 2 . H o w m a n y i c e c r e a m c o n e s c a n b e m a d e f r o m a 4 . 5 1 K g b o x o f i c e c r e a m i f e a c h i c e
c r e a m c o n e c o n t a i n s 2 2 g o f i c e c r e a m ?
A n s . W e i g h t o f b o x o f i c e - c r e a m s = 4 . 5 1 k g = 4 5 1 0 g - - - - - - - - - - ( 1 )
W e i g h t o f e a c h i c e c r e a m c o n e = 2 2 g
N o . o f i c e - c r e a m c o n e s r e q u i r e d = W e i g h t o f b o x o f i c e - c r e a m s ÷ W e i g h t o f e a c h i c e c r e a m
c o n e - ( 1 ) = 4 5 1 0 ÷ 2 2 = 2 0 5
2 3 . A y u s h i b o u g h t 1 5 0 . 2 5 k g p u l s e s , 5 0 0 . 7 5 k g w h e a t a n d 2 7 5 . 5 0 k g r i c e . S h e s e n t a l l t h e s e
t h i n g s t o t h e f l o o d a f f e c t e d a r e a s i n t h e r a i n y s e a s o n .
a . H o w m u c h t o t a l q u a n t i t y d i d s h e b u y ?
b . H o w m u c h m o r e w h e a t d i d s h e b u y t h a n p u l s e s ?
c . W h a t m o r a l d o y o u l e a r n f r o m i t ?
A n s . a . T o t a l q u a n t i t y s h e b o u g h t = 1 5 0 . 2 5 + 5 0 0 . 7 5 + 2 7 5 . 5 0 k g = 9 2 6 . 5 0 k g … … … . . ( 2 )
b . M o r e w h e a t s h e b u y t h a n p u l s e s = 5 0 0 . 7 5 – 1 5 0 . 2 5 = 3 5 0 . 5 k g - - - - - - ( 1 )
c . H e l p i n g i n d i s a s t e r … … … . . ( 1 )
2 4 . D i v i d e t h e s u m o f a n d b y t h e i r d i f f e r e n c e .
A n s . 4 . S u m = - - - - ( 1 )
D i f f e r e n c e = - - - - ( 1 )
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FAQs on Class 7 Math: CBSE Past Year Paper - 6 - Mathematics (Maths) Class 7
| 1. What are the important topics to study for Class 7 Math CBSE exam? |  |
Ans. The important topics to study for Class 7 Math CBSE exam include integers, fractions and decimals, algebraic expressions, equations and inequalities, geometry, data handling, and practical geometry.
| 2. How can I score well in the Class 7 Math CBSE exam? | |
Ans. To score well in the Class 7 Math CBSE exam, you should practice solving a variety of problems from each chapter, understand the concepts thoroughly, revise regularly, and solve previous year papers and sample papers. Additionally, seeking help from your teacher or tutor can also be beneficial.
| 3. What is the best way to prepare for the Class 7 Math CBSE exam? | |
Ans. The best way to prepare for the Class 7 Math CBSE exam is to follow a structured study plan. Start by understanding the concepts of each chapter, practice solving problems, revise regularly, and make use of resources such as textbooks, reference books, and online materials. It is also advisable to solve previous year papers and sample papers to get familiar with the exam pattern.
| 4. Are there any online resources available for Class 7 Math CBSE exam preparation? | |
Ans. Yes, there are several online resources available for Class 7 Math CBSE exam preparation. You can find video tutorials, practice questions, interactive quizzes, and study materials on various educational websites. Some popular online platforms for CBSE exam preparation include Khan Academy, BYJU'S, and TopperLearning.
| 5. How can I manage my time effectively during the Class 7 Math CBSE exam? | |
Ans. To manage your time effectively during the Class 7 Math CBSE exam, it is important to practice solving problems within a stipulated time frame. Divide your time equally among the different sections of the exam. Start with the questions you are confident about and then move on to the more challenging ones. Avoid spending too much time on a single question and leave some time for revising your answers.
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