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Page 1
C l a s s – X I
M A T H E M A T I C S
T i m e a l l o w e d : 3 h o u r s , M a x i m u m M a r k s : 1 0 0
G e n e r a l I n s t r u c t i o n s :
a ) 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 .
b ) T h e q u e s t i o n p a p e r c o n s i s t s o f 2 6 q u e s t i o n s d i v i d e d i n t o t h r e e s e c t i o n s A , B a n d C . S e c t i o n
A c o m p r i s e s o f 6 q u e s t i o n s o f o n e m a r k e a c h , S e c t i o n B c o m p r i s e s o f 1 3 q u e s t i o n s o f f o u r
m a r k s e a c h a n d S e c t i o n C c o m p r i s e s o f 7 q u e s t i o n s o f s i x m a r k s e a c h .
c ) A l l q u e s t i o n s i n S e c t i o n A a r e t o b e a n s w e r e d i n o n e w o r d , o n e s e n t e n c e o r a s p e r t h e e x a c t
r e q u i r e m e n t o f t h e q u e s t i o n .
d ) U s e o f c a l c u l a t o r s i s n o t p e r m i t t e d .
S e c t i o n A
1 . I d e n t i f y a f u n c t i o n s o t h a t
S o l :
2 . I f A = { ( x , y ) : y = a x , x R } a n d B = { ( x , y ) : y = a - x , x R } t h e n w h a t i s
S o l : W h e n i n b o t h c a s e s . H e n c e
3 . I f R i s a r e l a t i o n f r o m a s e t A c o n t a i n i n g e l e m e n t s t o a s e t B c o n t a i n i n g e l e m e n t s
t h e f i n d t h e n u m b e r o f s u b s e t s o f
S o l :
4 . C h e c k w h e t h e r t h e g i v e n l i n e s a r e p a r a l l e l o r p e r p e n d i c u l a r .
S o l : T h e y a r e p a r a l l e l s i n c e
Page 2
C l a s s – X I
M A T H E M A T I C S
T i m e a l l o w e d : 3 h o u r s , M a x i m u m M a r k s : 1 0 0
G e n e r a l I n s t r u c t i o n s :
a ) 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 .
b ) T h e q u e s t i o n p a p e r c o n s i s t s o f 2 6 q u e s t i o n s d i v i d e d i n t o t h r e e s e c t i o n s A , B a n d C . S e c t i o n
A c o m p r i s e s o f 6 q u e s t i o n s o f o n e m a r k e a c h , S e c t i o n B c o m p r i s e s o f 1 3 q u e s t i o n s o f f o u r
m a r k s e a c h a n d S e c t i o n C c o m p r i s e s o f 7 q u e s t i o n s o f s i x m a r k s e a c h .
c ) A l l q u e s t i o n s i n S e c t i o n A a r e t o b e a n s w e r e d i n o n e w o r d , o n e s e n t e n c e o r a s p e r t h e e x a c t
r e q u i r e m e n t o f t h e q u e s t i o n .
d ) U s e o f c a l c u l a t o r s i s n o t p e r m i t t e d .
S e c t i o n A
1 . I d e n t i f y a f u n c t i o n s o t h a t
S o l :
2 . I f A = { ( x , y ) : y = a x , x R } a n d B = { ( x , y ) : y = a - x , x R } t h e n w h a t i s
S o l : W h e n i n b o t h c a s e s . H e n c e
3 . I f R i s a r e l a t i o n f r o m a s e t A c o n t a i n i n g e l e m e n t s t o a s e t B c o n t a i n i n g e l e m e n t s
t h e f i n d t h e n u m b e r o f s u b s e t s o f
S o l :
4 . C h e c k w h e t h e r t h e g i v e n l i n e s a r e p a r a l l e l o r p e r p e n d i c u l a r .
S o l : T h e y a r e p a r a l l e l s i n c e
5 . F i n d t h e a r e a o f t h e t r i a n g l e w h o s e v e r t i c e s a r e ( 2 , 0 ) , ( 5 , 3 ) , ( 2 , 6 )
S o l : A r e a o f a t r i a n g l e
=
6 . W r i t e t h e e q u a t i o n o f a c i r c l e w i t h c e n t e r ( 0 , 0 ) a n d r a d i u s 5 .
S o l :
S e c t i o n B
7 . S o l v e
S o l :
8 . P r o v e b y m a t h e m a t i c a l i n d u c t i o n t h a t .
S o l : L e t b e t h e s t a t e m e n t g i v e n b y
= 1 , T r u e
L e t i t b e t r u e f o r n = m
1 + 2 + 3 + . . . . + m =
1 + 2 + 3 + . . . . + m + ( m + 1 ) = + ( m + 1 )
Page 3
C l a s s – X I
M A T H E M A T I C S
T i m e a l l o w e d : 3 h o u r s , M a x i m u m M a r k s : 1 0 0
G e n e r a l I n s t r u c t i o n s :
a ) 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 .
b ) T h e q u e s t i o n p a p e r c o n s i s t s o f 2 6 q u e s t i o n s d i v i d e d i n t o t h r e e s e c t i o n s A , B a n d C . S e c t i o n
A c o m p r i s e s o f 6 q u e s t i o n s o f o n e m a r k e a c h , S e c t i o n B c o m p r i s e s o f 1 3 q u e s t i o n s o f f o u r
m a r k s e a c h a n d S e c t i o n C c o m p r i s e s o f 7 q u e s t i o n s o f s i x m a r k s e a c h .
c ) A l l q u e s t i o n s i n S e c t i o n A a r e t o b e a n s w e r e d i n o n e w o r d , o n e s e n t e n c e o r a s p e r t h e e x a c t
r e q u i r e m e n t o f t h e q u e s t i o n .
d ) U s e o f c a l c u l a t o r s i s n o t p e r m i t t e d .
S e c t i o n A
1 . I d e n t i f y a f u n c t i o n s o t h a t
S o l :
2 . I f A = { ( x , y ) : y = a x , x R } a n d B = { ( x , y ) : y = a - x , x R } t h e n w h a t i s
S o l : W h e n i n b o t h c a s e s . H e n c e
3 . I f R i s a r e l a t i o n f r o m a s e t A c o n t a i n i n g e l e m e n t s t o a s e t B c o n t a i n i n g e l e m e n t s
t h e f i n d t h e n u m b e r o f s u b s e t s o f
S o l :
4 . C h e c k w h e t h e r t h e g i v e n l i n e s a r e p a r a l l e l o r p e r p e n d i c u l a r .
S o l : T h e y a r e p a r a l l e l s i n c e
5 . F i n d t h e a r e a o f t h e t r i a n g l e w h o s e v e r t i c e s a r e ( 2 , 0 ) , ( 5 , 3 ) , ( 2 , 6 )
S o l : A r e a o f a t r i a n g l e
=
6 . W r i t e t h e e q u a t i o n o f a c i r c l e w i t h c e n t e r ( 0 , 0 ) a n d r a d i u s 5 .
S o l :
S e c t i o n B
7 . S o l v e
S o l :
8 . P r o v e b y m a t h e m a t i c a l i n d u c t i o n t h a t .
S o l : L e t b e t h e s t a t e m e n t g i v e n b y
= 1 , T r u e
L e t i t b e t r u e f o r n = m
1 + 2 + 3 + . . . . + m =
1 + 2 + 3 + . . . . + m + ( m + 1 ) = + ( m + 1 )
P ( m + 1 ) = + ( m + 1 )
P ( m + 1 ) =
P ( m + 1 ) =
T h u s P ( m ) i s t r u e P ( m + 1 ) i s T r u e
9 . F i n d t h e s q u a r e r o o t o f .
S o l : L e t =
1 0 . S o l v e t h e i n e q u a l i t y .
S o l :
1 1 . F i n d t h e v a l u e o f i f 1 2 C x = 1 2 C x + 4 .
S o l : x + x + 4 = 1 2
2 x = 8
x = 4
1 2 . T h r e e c a r s a r e t h e r e i n a r a c e . C a r A i s 3 t i m e s a s l i k e l y t o w i n a s c a r B . C a r B i s t w i c e
a s l i k e l y t o w i n a s c a r C . W h a t i s t h e p r o b a b i l i t y o f w i n n i n g e a c h c a r .
S o l : L e t b e t h e p r o b a b i l i t y o f w i n n i n g C a r C ,
P ( C ) = p
P ( B ) = 2 p
P ( A ) = 6 p
P ( A ) + P ( B ) + P ( C ) = 1
Page 4
C l a s s – X I
M A T H E M A T I C S
T i m e a l l o w e d : 3 h o u r s , M a x i m u m M a r k s : 1 0 0
G e n e r a l I n s t r u c t i o n s :
a ) 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 .
b ) T h e q u e s t i o n p a p e r c o n s i s t s o f 2 6 q u e s t i o n s d i v i d e d i n t o t h r e e s e c t i o n s A , B a n d C . S e c t i o n
A c o m p r i s e s o f 6 q u e s t i o n s o f o n e m a r k e a c h , S e c t i o n B c o m p r i s e s o f 1 3 q u e s t i o n s o f f o u r
m a r k s e a c h a n d S e c t i o n C c o m p r i s e s o f 7 q u e s t i o n s o f s i x m a r k s e a c h .
c ) A l l q u e s t i o n s i n S e c t i o n A a r e t o b e a n s w e r e d i n o n e w o r d , o n e s e n t e n c e o r a s p e r t h e e x a c t
r e q u i r e m e n t o f t h e q u e s t i o n .
d ) U s e o f c a l c u l a t o r s i s n o t p e r m i t t e d .
S e c t i o n A
1 . I d e n t i f y a f u n c t i o n s o t h a t
S o l :
2 . I f A = { ( x , y ) : y = a x , x R } a n d B = { ( x , y ) : y = a - x , x R } t h e n w h a t i s
S o l : W h e n i n b o t h c a s e s . H e n c e
3 . I f R i s a r e l a t i o n f r o m a s e t A c o n t a i n i n g e l e m e n t s t o a s e t B c o n t a i n i n g e l e m e n t s
t h e f i n d t h e n u m b e r o f s u b s e t s o f
S o l :
4 . C h e c k w h e t h e r t h e g i v e n l i n e s a r e p a r a l l e l o r p e r p e n d i c u l a r .
S o l : T h e y a r e p a r a l l e l s i n c e
5 . F i n d t h e a r e a o f t h e t r i a n g l e w h o s e v e r t i c e s a r e ( 2 , 0 ) , ( 5 , 3 ) , ( 2 , 6 )
S o l : A r e a o f a t r i a n g l e
=
6 . W r i t e t h e e q u a t i o n o f a c i r c l e w i t h c e n t e r ( 0 , 0 ) a n d r a d i u s 5 .
S o l :
S e c t i o n B
7 . S o l v e
S o l :
8 . P r o v e b y m a t h e m a t i c a l i n d u c t i o n t h a t .
S o l : L e t b e t h e s t a t e m e n t g i v e n b y
= 1 , T r u e
L e t i t b e t r u e f o r n = m
1 + 2 + 3 + . . . . + m =
1 + 2 + 3 + . . . . + m + ( m + 1 ) = + ( m + 1 )
P ( m + 1 ) = + ( m + 1 )
P ( m + 1 ) =
P ( m + 1 ) =
T h u s P ( m ) i s t r u e P ( m + 1 ) i s T r u e
9 . F i n d t h e s q u a r e r o o t o f .
S o l : L e t =
1 0 . S o l v e t h e i n e q u a l i t y .
S o l :
1 1 . F i n d t h e v a l u e o f i f 1 2 C x = 1 2 C x + 4 .
S o l : x + x + 4 = 1 2
2 x = 8
x = 4
1 2 . T h r e e c a r s a r e t h e r e i n a r a c e . C a r A i s 3 t i m e s a s l i k e l y t o w i n a s c a r B . C a r B i s t w i c e
a s l i k e l y t o w i n a s c a r C . W h a t i s t h e p r o b a b i l i t y o f w i n n i n g e a c h c a r .
S o l : L e t b e t h e p r o b a b i l i t y o f w i n n i n g C a r C ,
P ( C ) = p
P ( B ) = 2 p
P ( A ) = 6 p
P ( A ) + P ( B ) + P ( C ) = 1
p + 2 p + 6 p = 1
9 p = 1
p =
P ( C ) =
P ( B ) =
P ( A ) =
1 3 . I f i s a f u n c t i o n t h a t c o n t a i n s 3 i n i t s d o m a i n a n d r a n g e a n d s a t i s f y t h e r e l a t i o n
f i n d f ( 3 )
S o l : L e t s a t i s f y t h e r e l a t i o n
f ( f ( a ) ) . ( 1 + f ( a ) ) = - f ( a )
f ( 3 ) . ( 4 ) = - 3
f ( 3 ) = -
1 4 . I f p r o v e t h a t .
S o l :
1 5 . F i n d t w o n u m b e r s s u c h t h a t t h e i r a r i t h m e t i c m e a n i s 1 5 a n d G e o m e t r i c m e a n i s 9
w i t h o u t u s i n g t h e i d e n t i t y
S o l : F o r m a q u a d r a t i c e q u a t i o n s u m o f w h o s e r o o t s a r e 3 0 a n d p r o d u c t o f t h e r o o t s i s 8 1
- x ( 3 0 ) + 8 1 = 0
- 3 x - 2 7 x + 8 1 = 0
x ( x - 3 ) - 2 7 ( x - 3 )
Page 5
C l a s s – X I
M A T H E M A T I C S
T i m e a l l o w e d : 3 h o u r s , M a x i m u m M a r k s : 1 0 0
G e n e r a l I n s t r u c t i o n s :
a ) 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 .
b ) T h e q u e s t i o n p a p e r c o n s i s t s o f 2 6 q u e s t i o n s d i v i d e d i n t o t h r e e s e c t i o n s A , B a n d C . S e c t i o n
A c o m p r i s e s o f 6 q u e s t i o n s o f o n e m a r k e a c h , S e c t i o n B c o m p r i s e s o f 1 3 q u e s t i o n s o f f o u r
m a r k s e a c h a n d S e c t i o n C c o m p r i s e s o f 7 q u e s t i o n s o f s i x m a r k s e a c h .
c ) A l l q u e s t i o n s i n S e c t i o n A a r e t o b e a n s w e r e d i n o n e w o r d , o n e s e n t e n c e o r a s p e r t h e e x a c t
r e q u i r e m e n t o f t h e q u e s t i o n .
d ) U s e o f c a l c u l a t o r s i s n o t p e r m i t t e d .
S e c t i o n A
1 . I d e n t i f y a f u n c t i o n s o t h a t
S o l :
2 . I f A = { ( x , y ) : y = a x , x R } a n d B = { ( x , y ) : y = a - x , x R } t h e n w h a t i s
S o l : W h e n i n b o t h c a s e s . H e n c e
3 . I f R i s a r e l a t i o n f r o m a s e t A c o n t a i n i n g e l e m e n t s t o a s e t B c o n t a i n i n g e l e m e n t s
t h e f i n d t h e n u m b e r o f s u b s e t s o f
S o l :
4 . C h e c k w h e t h e r t h e g i v e n l i n e s a r e p a r a l l e l o r p e r p e n d i c u l a r .
S o l : T h e y a r e p a r a l l e l s i n c e
5 . F i n d t h e a r e a o f t h e t r i a n g l e w h o s e v e r t i c e s a r e ( 2 , 0 ) , ( 5 , 3 ) , ( 2 , 6 )
S o l : A r e a o f a t r i a n g l e
=
6 . W r i t e t h e e q u a t i o n o f a c i r c l e w i t h c e n t e r ( 0 , 0 ) a n d r a d i u s 5 .
S o l :
S e c t i o n B
7 . S o l v e
S o l :
8 . P r o v e b y m a t h e m a t i c a l i n d u c t i o n t h a t .
S o l : L e t b e t h e s t a t e m e n t g i v e n b y
= 1 , T r u e
L e t i t b e t r u e f o r n = m
1 + 2 + 3 + . . . . + m =
1 + 2 + 3 + . . . . + m + ( m + 1 ) = + ( m + 1 )
P ( m + 1 ) = + ( m + 1 )
P ( m + 1 ) =
P ( m + 1 ) =
T h u s P ( m ) i s t r u e P ( m + 1 ) i s T r u e
9 . F i n d t h e s q u a r e r o o t o f .
S o l : L e t =
1 0 . S o l v e t h e i n e q u a l i t y .
S o l :
1 1 . F i n d t h e v a l u e o f i f 1 2 C x = 1 2 C x + 4 .
S o l : x + x + 4 = 1 2
2 x = 8
x = 4
1 2 . T h r e e c a r s a r e t h e r e i n a r a c e . C a r A i s 3 t i m e s a s l i k e l y t o w i n a s c a r B . C a r B i s t w i c e
a s l i k e l y t o w i n a s c a r C . W h a t i s t h e p r o b a b i l i t y o f w i n n i n g e a c h c a r .
S o l : L e t b e t h e p r o b a b i l i t y o f w i n n i n g C a r C ,
P ( C ) = p
P ( B ) = 2 p
P ( A ) = 6 p
P ( A ) + P ( B ) + P ( C ) = 1
p + 2 p + 6 p = 1
9 p = 1
p =
P ( C ) =
P ( B ) =
P ( A ) =
1 3 . I f i s a f u n c t i o n t h a t c o n t a i n s 3 i n i t s d o m a i n a n d r a n g e a n d s a t i s f y t h e r e l a t i o n
f i n d f ( 3 )
S o l : L e t s a t i s f y t h e r e l a t i o n
f ( f ( a ) ) . ( 1 + f ( a ) ) = - f ( a )
f ( 3 ) . ( 4 ) = - 3
f ( 3 ) = -
1 4 . I f p r o v e t h a t .
S o l :
1 5 . F i n d t w o n u m b e r s s u c h t h a t t h e i r a r i t h m e t i c m e a n i s 1 5 a n d G e o m e t r i c m e a n i s 9
w i t h o u t u s i n g t h e i d e n t i t y
S o l : F o r m a q u a d r a t i c e q u a t i o n s u m o f w h o s e r o o t s a r e 3 0 a n d p r o d u c t o f t h e r o o t s i s 8 1
- x ( 3 0 ) + 8 1 = 0
- 3 x - 2 7 x + 8 1 = 0
x ( x - 3 ) - 2 7 ( x - 3 )
( x - 3 ) ( x - 2 7 ) = 0
H e n c e t h e n u m b e r s a r e 3 a n d 2 7
1 6 . L e t b e a f u n c t i o n g i v e n b y f ( x ) = + 2 f i n d f - 1 ( 2 7 )
S o l : L e t b e a f u n c t i o n g i v e n b y f ( x ) = + 2 f i n d f - 1 ( 2 7 )
f ( x ) = + 2
+ 2 = 2 7
= 2 5
x = 5
f - 1 ( 2 7 ) = { - 5 , 5 }
1 7 . F i n d t h e d o m a i n a n d r a n g e o f t h e f u n c t i o n w h e r e a i s a p o s i t i v e
i n t e g e r .
S o l : T h e f u n c t i o n i s d e f i n e d f o r a l l v a l u e s o f x w h e r e t h e d e n o m i n a t o r i s n o t e q u a l t o z e r o
H e n c e d o m a i n =
R a n g e o f
L e t
R a n g e o f
1 8 . F i n d t h e l i m i t o f
S o l : R a t i o n a l i z e t h e n u m e r a t o r
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FAQs on Past Year Paper, Maths(Set - 1), 2019, Class 11 - Mathematics (Maths) Class 11 - Commerce
| 1. How can I download the past year paper for Maths(Set - 1) of Class 11 for 2019? |  |
Ans. You can download the past year paper for Maths(Set - 1) of Class 11 for 2019 by searching for it on educational websites, online forums, or by visiting the official website of your respective educational board. Many websites provide free access to past year papers in PDF format that can be easily downloaded and used for exam preparation.
| 2. What is the difficulty level of the Maths(Set - 1) exam for Class 11 in 2019? | |
Ans. The difficulty level of the Maths(Set - 1) exam for Class 11 in 2019 can vary from board to board. However, generally, the exam is designed to test the fundamental concepts and problem-solving skills of students. It may include questions of varying complexity, ranging from basic concepts to more challenging problems. It is advisable to thoroughly understand the syllabus and practice solving different types of questions to prepare effectively for the exam.
| 3. Are the questions in the Maths(Set - 1) exam for Class 11 in 2019 from the textbook? | |
Ans. The questions in the Maths(Set - 1) exam for Class 11 in 2019 can be based on the textbook as well as other reference materials. While the textbook forms the primary source of study, the exam may also include additional questions to assess the depth of a student's understanding and application of concepts. It is important to study the textbook thoroughly and practice solving additional questions from various sources to be well-prepared for the exam.
| 4. How should I prepare for the Maths(Set - 1) exam for Class 11 in 2019? | |
Ans. To prepare for the Maths(Set - 1) exam for Class 11 in 2019, it is crucial to have a clear understanding of the syllabus and the topics covered. Start by organizing your study material, including textbooks, reference books, and past year papers. Create a study schedule and allocate dedicated time for each topic. Practice solving different types of questions, including numerical problems and conceptual questions. Additionally, work on improving your problem-solving skills by attempting previous year papers and sample papers.
| 5. Are there any online resources available for the Maths(Set - 1) exam preparation of Class 11 in 2019? | |
Ans. Yes, there are several online resources available for the Maths(Set - 1) exam preparation of Class 11 in 2019. You can find educational websites, online forums, and video tutorials that provide study materials, practice questions, and explanations for various topics. Additionally, there are online platforms that offer interactive quizzes and mock tests to help you assess your preparation level. Make use of these resources to supplement your study and enhance your understanding of the subject.
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Document Description: Past Year Paper, Maths(Set - 1), 2019, Class 11 for Commerce 2025 is part of Mathematics (Maths) Class 11 preparation.
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