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Page 1
Q u e s t i o n 1
l i m
x ? 8
{ x -
n
v ( x - a
1
) ( x - a
2
) . . . ( x - a
n
) } w h e r e a
1
, a
2
, . . . , a
n
a r e p o s i t i v e
r a t i o n a l n u m b e r s . T h e l i m i t
O p t i o n s :
A . d o e s n o t e x i s t
B . i s
a
1
+ a
2
+ . . . a
n
n
C . i s
n
v a
1
a
2
. . . a
n
D . i s
n
a
1
+ a
2
+ . . . a
n
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 2
S u p p o s e f : R ? R b e g i v e n b y
f ( x ) =
1 i f x = 1
e
( x
1 0
- 1 )
+ ( x - 1 )
2
s i n
1
x - 1
i f x ? 1
.
t h e n
O p t i o n s :
A . f
'
( 1 ) d o e s n o t e x i s t
B . f
'
( 1 ) e x i s t s a n d i s z e r o
C . f
'
( 1 ) e x i s t a n d i s 9
D . f
'
( 1 ) e x i s t s a n d i s 1 0
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
{
WBJEE 2023 Solved Paper
Mathematics
Page 2
Q u e s t i o n 1
l i m
x ? 8
{ x -
n
v ( x - a
1
) ( x - a
2
) . . . ( x - a
n
) } w h e r e a
1
, a
2
, . . . , a
n
a r e p o s i t i v e
r a t i o n a l n u m b e r s . T h e l i m i t
O p t i o n s :
A . d o e s n o t e x i s t
B . i s
a
1
+ a
2
+ . . . a
n
n
C . i s
n
v a
1
a
2
. . . a
n
D . i s
n
a
1
+ a
2
+ . . . a
n
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 2
S u p p o s e f : R ? R b e g i v e n b y
f ( x ) =
1 i f x = 1
e
( x
1 0
- 1 )
+ ( x - 1 )
2
s i n
1
x - 1
i f x ? 1
.
t h e n
O p t i o n s :
A . f
'
( 1 ) d o e s n o t e x i s t
B . f
'
( 1 ) e x i s t s a n d i s z e r o
C . f
'
( 1 ) e x i s t a n d i s 9
D . f
'
( 1 ) e x i s t s a n d i s 1 0
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
{
WBJEE 2023 Solved Paper
Mathematics
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 3
L e t f : [ 1 , 3 ] ? R b e c o n t i n u o u s a n d b e d e r i v a b l e i n ( 1 , 3 ) a n d
f
'
( x ) = [ f ( x ) ]
2
+ 4 ? x ? ( 1 , 3 ) . T h e n
O p t i o n s :
A . f ( 3 ) - f ( 1 ) = 5 h o l d s
B . f ( 3 ) - f ( 1 ) = 5 d o e s n o t h o l d
C . f ( 3 ) - f ( 1 ) = 3 h o l d s
D . f ( 3 ) - f ( 1 ) = 4 h o l d s
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 4
f ( x ) i s a d i f f e r e n t i a b l e f u n c t i o n a n d g i v e n f
'
( 2 ) = 6 a n d f
'
( 1 ) = 4 , t h e n
L =
l i m
h ? 0
f ( 2 + 2 h + h
2
) - f ( 2 )
f ( 1 + h - h
2
) - f ( 1 )
O p t i o n s :
A . d o e s n o t e x i s t
B . e q u a l t o - 3
C . e q u a l t o 3
D . e q u a l t o 3 / 2
A n s w e r : C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 5
L e t c o s
- 1 y
b
= l o g
e
x
n
n
, t h e n A y
2
+ B y
1
+ C y = 0 i s p o s s i b l e f o r , w h e r e
y
2
=
d
2
y
d x
2
, y
1
=
d y
d x
( ) ( )
Page 3
Q u e s t i o n 1
l i m
x ? 8
{ x -
n
v ( x - a
1
) ( x - a
2
) . . . ( x - a
n
) } w h e r e a
1
, a
2
, . . . , a
n
a r e p o s i t i v e
r a t i o n a l n u m b e r s . T h e l i m i t
O p t i o n s :
A . d o e s n o t e x i s t
B . i s
a
1
+ a
2
+ . . . a
n
n
C . i s
n
v a
1
a
2
. . . a
n
D . i s
n
a
1
+ a
2
+ . . . a
n
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 2
S u p p o s e f : R ? R b e g i v e n b y
f ( x ) =
1 i f x = 1
e
( x
1 0
- 1 )
+ ( x - 1 )
2
s i n
1
x - 1
i f x ? 1
.
t h e n
O p t i o n s :
A . f
'
( 1 ) d o e s n o t e x i s t
B . f
'
( 1 ) e x i s t s a n d i s z e r o
C . f
'
( 1 ) e x i s t a n d i s 9
D . f
'
( 1 ) e x i s t s a n d i s 1 0
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
{
WBJEE 2023 Solved Paper
Mathematics
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 3
L e t f : [ 1 , 3 ] ? R b e c o n t i n u o u s a n d b e d e r i v a b l e i n ( 1 , 3 ) a n d
f
'
( x ) = [ f ( x ) ]
2
+ 4 ? x ? ( 1 , 3 ) . T h e n
O p t i o n s :
A . f ( 3 ) - f ( 1 ) = 5 h o l d s
B . f ( 3 ) - f ( 1 ) = 5 d o e s n o t h o l d
C . f ( 3 ) - f ( 1 ) = 3 h o l d s
D . f ( 3 ) - f ( 1 ) = 4 h o l d s
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 4
f ( x ) i s a d i f f e r e n t i a b l e f u n c t i o n a n d g i v e n f
'
( 2 ) = 6 a n d f
'
( 1 ) = 4 , t h e n
L =
l i m
h ? 0
f ( 2 + 2 h + h
2
) - f ( 2 )
f ( 1 + h - h
2
) - f ( 1 )
O p t i o n s :
A . d o e s n o t e x i s t
B . e q u a l t o - 3
C . e q u a l t o 3
D . e q u a l t o 3 / 2
A n s w e r : C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 5
L e t c o s
- 1 y
b
= l o g
e
x
n
n
, t h e n A y
2
+ B y
1
+ C y = 0 i s p o s s i b l e f o r , w h e r e
y
2
=
d
2
y
d x
2
, y
1
=
d y
d x
( ) ( )
O p t i o n s :
A . A = 2 , B = x
2
, C = n
B . A = x
2
, B = x , C = n
2
C . A = x , B = 2 x , C = 3 n + 1
D . A = x
2
, B = 3 x , C = 2 n
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 6
I f I = ?
x
2
d x
( x s i n x + c o s x )
2
= f ( x ) + t a n x + c , t h e n f ( x ) i s
O p t i o n s :
A .
s i n x
x s i n x + c o s x
B .
1
( x s i n x + c o s x )
2
C .
- x
c o s x ( x s i n x + c o s x )
D .
1
s i n x ( x c o s x + s i n x )
A n s w e r : C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 7
I f ?
d x
( x + 1 ) ( x - 2 ) ( x - 3 )
=
1
k
l o g
e
| x - 3 |
3
| x + 1 |
( x - 2 )
4
+ c , t h e n t h e v a l u e o f k i s
O p t i o n s :
A . 4
B . 6
C . 8
D . 1 2
{ }
Page 4
Q u e s t i o n 1
l i m
x ? 8
{ x -
n
v ( x - a
1
) ( x - a
2
) . . . ( x - a
n
) } w h e r e a
1
, a
2
, . . . , a
n
a r e p o s i t i v e
r a t i o n a l n u m b e r s . T h e l i m i t
O p t i o n s :
A . d o e s n o t e x i s t
B . i s
a
1
+ a
2
+ . . . a
n
n
C . i s
n
v a
1
a
2
. . . a
n
D . i s
n
a
1
+ a
2
+ . . . a
n
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 2
S u p p o s e f : R ? R b e g i v e n b y
f ( x ) =
1 i f x = 1
e
( x
1 0
- 1 )
+ ( x - 1 )
2
s i n
1
x - 1
i f x ? 1
.
t h e n
O p t i o n s :
A . f
'
( 1 ) d o e s n o t e x i s t
B . f
'
( 1 ) e x i s t s a n d i s z e r o
C . f
'
( 1 ) e x i s t a n d i s 9
D . f
'
( 1 ) e x i s t s a n d i s 1 0
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
{
WBJEE 2023 Solved Paper
Mathematics
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 3
L e t f : [ 1 , 3 ] ? R b e c o n t i n u o u s a n d b e d e r i v a b l e i n ( 1 , 3 ) a n d
f
'
( x ) = [ f ( x ) ]
2
+ 4 ? x ? ( 1 , 3 ) . T h e n
O p t i o n s :
A . f ( 3 ) - f ( 1 ) = 5 h o l d s
B . f ( 3 ) - f ( 1 ) = 5 d o e s n o t h o l d
C . f ( 3 ) - f ( 1 ) = 3 h o l d s
D . f ( 3 ) - f ( 1 ) = 4 h o l d s
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 4
f ( x ) i s a d i f f e r e n t i a b l e f u n c t i o n a n d g i v e n f
'
( 2 ) = 6 a n d f
'
( 1 ) = 4 , t h e n
L =
l i m
h ? 0
f ( 2 + 2 h + h
2
) - f ( 2 )
f ( 1 + h - h
2
) - f ( 1 )
O p t i o n s :
A . d o e s n o t e x i s t
B . e q u a l t o - 3
C . e q u a l t o 3
D . e q u a l t o 3 / 2
A n s w e r : C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 5
L e t c o s
- 1 y
b
= l o g
e
x
n
n
, t h e n A y
2
+ B y
1
+ C y = 0 i s p o s s i b l e f o r , w h e r e
y
2
=
d
2
y
d x
2
, y
1
=
d y
d x
( ) ( )
O p t i o n s :
A . A = 2 , B = x
2
, C = n
B . A = x
2
, B = x , C = n
2
C . A = x , B = 2 x , C = 3 n + 1
D . A = x
2
, B = 3 x , C = 2 n
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 6
I f I = ?
x
2
d x
( x s i n x + c o s x )
2
= f ( x ) + t a n x + c , t h e n f ( x ) i s
O p t i o n s :
A .
s i n x
x s i n x + c o s x
B .
1
( x s i n x + c o s x )
2
C .
- x
c o s x ( x s i n x + c o s x )
D .
1
s i n x ( x c o s x + s i n x )
A n s w e r : C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 7
I f ?
d x
( x + 1 ) ( x - 2 ) ( x - 3 )
=
1
k
l o g
e
| x - 3 |
3
| x + 1 |
( x - 2 )
4
+ c , t h e n t h e v a l u e o f k i s
O p t i o n s :
A . 4
B . 6
C . 8
D . 1 2
{ }
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 8
t h e e x p r e s s i o n
n
?
0
[ x ] d x
n } x } d x
?
0
, w h e r e [ x ] a n d { x } a r e r e s p e c t i v e l y i n t e g r a l a n d
f r a c t i o n a l p a r t o f x a n d n ? N , i s e q u a l t o
O p t i o n s :
A .
1
n - 1
B .
1
n
C . n
D . n - 1
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 9
T h e v a l u e
1 / 2
?
0
d x
1 - x
2 n
i s ( n ? N )
O p t i o n s :
A . l e s s t h a n o r e q u a l t o
p
6
B . g r e a t e r t h a n o r e q u a l t o 1
C . l e s s t h a n
1
2
D . g r e a t e r t h a n
p
6
A n s w e r : A
S o l u t i o n :
v
Page 5
Q u e s t i o n 1
l i m
x ? 8
{ x -
n
v ( x - a
1
) ( x - a
2
) . . . ( x - a
n
) } w h e r e a
1
, a
2
, . . . , a
n
a r e p o s i t i v e
r a t i o n a l n u m b e r s . T h e l i m i t
O p t i o n s :
A . d o e s n o t e x i s t
B . i s
a
1
+ a
2
+ . . . a
n
n
C . i s
n
v a
1
a
2
. . . a
n
D . i s
n
a
1
+ a
2
+ . . . a
n
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 2
S u p p o s e f : R ? R b e g i v e n b y
f ( x ) =
1 i f x = 1
e
( x
1 0
- 1 )
+ ( x - 1 )
2
s i n
1
x - 1
i f x ? 1
.
t h e n
O p t i o n s :
A . f
'
( 1 ) d o e s n o t e x i s t
B . f
'
( 1 ) e x i s t s a n d i s z e r o
C . f
'
( 1 ) e x i s t a n d i s 9
D . f
'
( 1 ) e x i s t s a n d i s 1 0
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
{
WBJEE 2023 Solved Paper
Mathematics
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 3
L e t f : [ 1 , 3 ] ? R b e c o n t i n u o u s a n d b e d e r i v a b l e i n ( 1 , 3 ) a n d
f
'
( x ) = [ f ( x ) ]
2
+ 4 ? x ? ( 1 , 3 ) . T h e n
O p t i o n s :
A . f ( 3 ) - f ( 1 ) = 5 h o l d s
B . f ( 3 ) - f ( 1 ) = 5 d o e s n o t h o l d
C . f ( 3 ) - f ( 1 ) = 3 h o l d s
D . f ( 3 ) - f ( 1 ) = 4 h o l d s
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 4
f ( x ) i s a d i f f e r e n t i a b l e f u n c t i o n a n d g i v e n f
'
( 2 ) = 6 a n d f
'
( 1 ) = 4 , t h e n
L =
l i m
h ? 0
f ( 2 + 2 h + h
2
) - f ( 2 )
f ( 1 + h - h
2
) - f ( 1 )
O p t i o n s :
A . d o e s n o t e x i s t
B . e q u a l t o - 3
C . e q u a l t o 3
D . e q u a l t o 3 / 2
A n s w e r : C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 5
L e t c o s
- 1 y
b
= l o g
e
x
n
n
, t h e n A y
2
+ B y
1
+ C y = 0 i s p o s s i b l e f o r , w h e r e
y
2
=
d
2
y
d x
2
, y
1
=
d y
d x
( ) ( )
O p t i o n s :
A . A = 2 , B = x
2
, C = n
B . A = x
2
, B = x , C = n
2
C . A = x , B = 2 x , C = 3 n + 1
D . A = x
2
, B = 3 x , C = 2 n
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 6
I f I = ?
x
2
d x
( x s i n x + c o s x )
2
= f ( x ) + t a n x + c , t h e n f ( x ) i s
O p t i o n s :
A .
s i n x
x s i n x + c o s x
B .
1
( x s i n x + c o s x )
2
C .
- x
c o s x ( x s i n x + c o s x )
D .
1
s i n x ( x c o s x + s i n x )
A n s w e r : C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 7
I f ?
d x
( x + 1 ) ( x - 2 ) ( x - 3 )
=
1
k
l o g
e
| x - 3 |
3
| x + 1 |
( x - 2 )
4
+ c , t h e n t h e v a l u e o f k i s
O p t i o n s :
A . 4
B . 6
C . 8
D . 1 2
{ }
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 8
t h e e x p r e s s i o n
n
?
0
[ x ] d x
n } x } d x
?
0
, w h e r e [ x ] a n d { x } a r e r e s p e c t i v e l y i n t e g r a l a n d
f r a c t i o n a l p a r t o f x a n d n ? N , i s e q u a l t o
O p t i o n s :
A .
1
n - 1
B .
1
n
C . n
D . n - 1
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 9
T h e v a l u e
1 / 2
?
0
d x
1 - x
2 n
i s ( n ? N )
O p t i o n s :
A . l e s s t h a n o r e q u a l t o
p
6
B . g r e a t e r t h a n o r e q u a l t o 1
C . l e s s t h a n
1
2
D . g r e a t e r t h a n
p
6
A n s w e r : A
S o l u t i o n :
v
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 1 0
I f I
n
=
p
2
?
0
c o s
n
x c o s n x d x , t h e n I
1
, I
2
, I
3
. . . a r e i n
O p t i o n s :
A . A . P .
B . G . P .
C . H . P .
D . n o s u c h r e l a t i o n
A n s w e r : D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 1 1
I f y =
x
l o g
e
| c x |
i s t h e s o l u t i o n o f t h e d i f f e r e n t i a l e q u a t i o n
d y
d x
=
y
x
+ f
x
y
,
t h e n f
x
y
i s g i v e n b y
O p t i o n s :
A .
y
2
x
2
B . -
y
2
x
2
C .
x
2
y
2
D . -
x
2
y
2
A n s w e r : B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
( )
( )
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