HBSE Class 12 Question Paper 2026 Maths

FOR HBSE CLASS 12 EXAM PREPARATION

HBSE Class 12 2026
Question Paper · Maths
EXAM YEAR TYPE SUBJECT

HBSE Class 12 2026 Question Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

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CLASS : 12th (Sr. Secondary) Code No. 3632

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3632/(Set : A) P. T. O.

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(2) 3632/(Set : A)
• #8 #6 $ 9 $1 -" 9 $ 5 $2 ) :#
- $ ! 1! ; *+ # <"
, *
! - ! . (
!

• *+ =16 = 6 1 # !/ #8 * 2
&'2> 6 : # 1 ,1# # "
# $ ! (
$ ! "# $ % $ & ' ( $ ) $
* !
2 6 7
/0 :# $ 1 6 !"

/ 0 ? ? !/ - % 7 @$A
@$A/ @'A/ @ A/ @ A <1 @ A '( < ! 7
- % @$A 7 - % ? - '# ? !" ?B ? # $ !"
- % @@''A 7 - % ? - ? !" ?B ? $ $
!"
- %@ A7 - % ? - )7 ? !" ?B ? % $
!"
- %@A7 - % ? - ? !" ?B ? & $
!"
- %@ A7 - % ? - # ? !" ?B ? ' $
!"

3632/(Set : A)

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(3) 3632/(Set : A)
/ 0 ? ) ? $ 1 ; !" $ ?B < 1 ;
!"
C $ # *+ , $1 B # # <"
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/(0 C $ m
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# *+ , 0 $1 - <"
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$
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# $+ #
ag
/0 ag ,+ # # $ !-+ # $.
/ 0 $ ( )/
% 0 0$ 010$ 0 0& 0 0 0 0
0 0 1 ' . ( *
#

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$
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0 0 1 #* ( *
%

0 0 1 ) +$ (*
&

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0 0 1 "$ ( *

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em
( # ! 2 (

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/(0 2 ! " % "

/( 0 3 ,

3632/(Set : A) P. T. O.

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(4) 3632/(Set : A)
- %–$
SECTION – A

")%−' D : !/ * → !/ ' " !7 1
" < ! # $ ! $ E)
+" 1 $ E)
!" < ! # $! $ E)
," 6 #
- * → " %−' . " *
"
+"
!"
,"

−#
/ - !7 1

π π
" 0. π +" − .
$ $

π π
!" − . ," 6 #
$ $

−#
1 / / *

π π
" 0. π +" − .
$ $

π π
!" − . ," 2
$ $

3632/(Set : A)

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(5) 3632/(Set : A)
$
+ ."
4$×$ # $F = ! 4 = [ .] . . = . $F = 4 !7 1
$

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+ . "$
! / $×$
m 3 4. 4 = [ .] . 4 . = *

.co m
$

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4 = la
g
0
$! 1 =
# 0
!/ ! 4 $ = 51 7 ag 1
a $ %
.
0 #

" )' +" ) ±%

!" ) −% ," ) −'

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0 # 0
4= 1 = 4 $ = 51 . 7
$ % 0 #

" )' +" ) ±%

m
m!" ) −% ," ) −'
.co
m .co s em
s e $
−#
g la! GGGGGGGGGG"
la a
< )# C "= ≠# 1
g
−#
a =#
$
−#
1 4 / "= ≠# / )# (((((((((((((
−#
=#

3632/(Set : A) P. T. O.

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(6) 3632/(Set : A)
!
5 θ6 θ". ! 5 #−/ θ". ?H " 1

!
. 5 θ6 θ". ! 5 #−/ θ"(

#
! ' ' !7 1
#+ "

" " 6

+" 7 " 76

!" 7# " 76

," #6 "6

#
8 *
#+ "

" " 6

+" 7 " 76

!" 7# " 76

," #6 "6

:
9
' ' !7 1
/
:
9
8 *
/

3632/(Set : A)

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(7) 3632/(Set : A)
# ; + % ;. + % ; $! %; − $ ;. + ; '# !7 1

" 0° +" '&°
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!" :0° ," 50°
e m
e m ; + % ;. + % ; %; − $ ;. + ;
l as
s
1 < 4 / *

0°g
" a
l a
+" '&°
ag
!" :0° ," 50°

! $8 I ! GGGGGGGGGGG " 1

, / / ! 3 ((((((((((( (

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$ % $
! ! !
$1 # $
+ + +# = 0 #J !7 1

" % +" $

$ : m
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!" # ,"
m
c. o 1 $ % $
s e!m+ # = 0
em
! !
la
8 + + *
s g
$

g la a
a " % +" $

!" # ," 2

3632/(Set : A) P. T. O.

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(8) 3632/(Set : A)
% $ %
4" = . #" = $! 4 ∪ #" = . # 4" !7 1
#0 & &

# #
" +"
' %

& =
!" ,"
#$ #$

% $ %
4" = . #" = 4 ∪ #" = . # 4" *
#0 & &

# #
" +"
' %

& =
!" ,"
#$ #$

< *) $: K - $ #? !7 1
#
" 0 +"
%
# #
!" ,"
#$ %:

1 < < < < / / (>
/ *
#
" 0 +"
%
# #
!" ,"
#$ %:

3632/(Set : A)

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(9) 3632/(Set : A)
$ ' $ '
= . &: 1 ! 7 1
& # :

m
" % +" %

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!" − % ," %. − %
e m
$ '
=
e
$
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< *
l as
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ag
" %g
a +" %
!" − % ," %. − %

# < E )? . " * ) − $. @ :A D ? + '> /! & -
# *+ <7 1

" $. '" ∈ +" %. 9" ∈
m
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9. :" ∈

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- < < )? . "* ) − $. @ :A. /
$$ 4 *

" $. '" ∈ +" %. 9" ∈

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!" :. 9" ∈ ," 9. :" ∈
m
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! GGGGGGGGG" las
las # 6 -
=
=
=
=
$
#
ag
1

ag −& ! +' :−6
1 / 8 = = (((((((((( (
= = $

3632/(Set : A) P. T. O.

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( 10 ) 3632/(Set : A)
! 10 ! $ = ' . ! $8 <1 - !)% J 8 8 C !7 1

5
" $ +"
'

5 5
!" ,"
% $

< < / !$ = ' . ! 3 !)% *

5
" $ +"
'

5 5
!" ,"
% $

! +!
$1 # = F !7 1

" + −! = +" + ! =

− −
!" + ! = ," + −! =

! +!
1 8 = *

" + −! = +" + ! =

− −
!" + ! = ," + −! =

3632/(Set : A)

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( 11 ) 3632/(Set : A)
$: <1 $> ? 7
& - ? # 1 " ! 7 $: 2 3 $! 2 3$ ? # < <
* 5 1 ; < *+ 7
m
## $ 4 #
m
1 # 5+ # #
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1
m .co / #7 0 ' ## $ 2 3
s e m
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a# g #
# 2 3$ ! (

g l a
# $: a 2 3
#
6 $8 ' ' L / * I ± . .
% % %
!" 1
2 3 D . ! $ ! 6 $8 0 7 α. β. γ ' !/ *
I / α. / β. / γ !"
" $: " <1 " # ! ". $ : " # #F - !"
$: " <1 # /! 2 m ". $ : " # #F - # "!
co
+" "

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!" $: " # !/ 2 " !"
," $: " !/ 2 " # !"
## $ 2 3 / B 8 4 / 3
# # #
/ / / ± . . (
% % %

o m. ! 6
c
# 2 3 / B α. β. γ 4 /
m / .α. / β. / γ(
c. o " + 3 / . / /
s em "
s em " "
g l a / /

la a
3 "(

ag +" + " " . < "
/ / 3 "(
!" " .< " (
," " .< " (
3632/(Set : A) P. T. O.

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( 12 ) 3632/(Set : A)
$: 2 3 4 $! # , $ 1 #6 J ( !/ 4" ) 0('. 4 ∪ #" ) 0(: $ !

#" ) . ) 0($ 1

2 3 J( 4 $! # , $ 1 #6 J ( / 4 ∩ #" ) 4" ( #"

!"
" $: " <1 " # ! ". $ : " # #F - !"
+" $: " <1 " # /! 2 ". $ : " # #F - # "!

!" $: " # !/ 2 " !"
," $: " !/ 2 " # !"
## $ 2 3 4 # 3/ /
4" ) 0('. 4 ∪ #" ) 0(: #" ) . ) 0($

# 2 3 14 4 # 3/

4 ∩ #" ) 4"( #"(

" + " " " / /

3 "(

+" + " " . < "

/ / 3 "(

!" " .< " (

," " .< " (

3632/(Set : A)

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( 13 ) 3632/(Set : A)
- %–'
SECTION – B

m
# < #
m 1M , , : < E !" E
.co
) ? #. $ " * #. $
.co A! < '> !" N # < < ; '> !"
s e m 2

s em < la )
( ag
- < 4 .
? # . $ "l*a # . $
ag
/ A. 4 8 /

0 $! 6
4C4 5 1 / . !. 6 O # </ 4= ! −6 " 2
−! 6
0 $! 6
. !. 6 4C4 5 1. 4 4= ! −6 (

om
−! 6

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< J $ 9 / % # 'P4 !" 8 C 'P4 ! '
# ' 6 #$ / !" 2

1 / < / 9 / % ( 4
/ / 4 #$ / D

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s em
s e g la
g la $ O # < "= $ $ −% ?+ C . "a
1> 6 / <" Ð "
a 4 / / . "= $ $ −% . " /
<" / (

3632/(Set : A) P. T. O.

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( 14 ) 3632/(Set : A)
!
$1 # + $! = $ F O # <" 2

!
8 + $! = $ (

$ 1

OR

$1 # ! ! − !)0 F O # <"
8 ! ! − ! ) 0(

&$ + # $E)# C(# 6 %I%# < ' < # + ' ? , <
<" + ' $! # 5 #5 ? !Q 2

1 / 4 // 4 / /B &$ 4
/ (> < < 4 / B
/ 4 / D

- %–

SECTION – C

−# / %π π
.− < < . -" 3
#− $ $

−# / %π π
3 .− < < (
#− $ $

3632/(Set : A)

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( 15 ) 3632/(Set : A)
$ 1
OR
m
m .co
.co m
O 7
s e
s em−# # l a
la $ ag
$
$ −# # − !
g
−#
+/ 7 7 < #. ! > 0. ! < #
a #+ $
# + !$

*

$
−# # −# $ −# # − !
$
+/ 7 7 < #. ! > 0. ! < #
$ #+ # + !$

m
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% % −#
! # 6 $F = 4 = −$ −$ # < $F = < 1 $F =
−' −& $
C . F 5 " 3
% % −#
m
c om
3 3 4 = −$ −$ #
m .c/o B 4

m . −' −& $
s e
s e / 3(
g l a
g la a
a !
=! !/
!
O # <" 3

! !
. =! (

3632/(Set : A) P. T. O.

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( 16 ) 3632/(Set : A)
/ −#
# != −# < <# !/ 6< 7 3
$
! !
# − $" − − $! = 0
$

/ −#
!= −# < < #. 4 *
$
! !
# − $" − − $! = 0
$

O 7 3
−#
/
#− $

*
−#
/
#− $

$ 1

OR

O 7

$

*

$

3632/(Set : A)

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m
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( 17 ) 3632/(Set : A)
→ → → → → →
= $; + $ ;. + % ; . = − ; + $ ;. + ; $! = %; + ;. ? ! 6 λ .

' !/ λ O # <" 3
m
m
c. o → = −; + $ ;. + ; m .co
e
→ → → →
= $; + $ ;. + % ; .
e m = %; + ;. / 6 λ
l as
a
l/ s →
ag
ag . λ(

- %–

SECTION – D

m
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& - # $F = 1> # <7 5

% 6 $! − $6 %

6 $! 6 %6 :
m
m
c. o E
$ 8!96)$
m.co
m s e
a
4 8 < 3 *
s e g l
g la % 6 $! − $6 % a
a
6 $! 6 %6 :

$ 8!96)$

3632/(Set : A) P. T. O.

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( 18 ) 3632/(Set : A)
$ 1

OR

$ −% &
4= % $ −' $F = 4 −# O # < $! #
# # −$

# <7
$ − %! 6 &6 ##

% 6 $! F '6 −&

6 ! F $6 F%

$ −% &
4= % $ −' . 4 −# . 4 −# 8 *
# # −$

$ − %! 6 &6 ##

% 6 $! F '6 −&

6 ! F $6 F%

- ! ) % 6 $. $8 <1 ( )− <1 ) J 8 8 C O # <" 5

< < ! ) % 6 $. 3
)− ) (

3632/(Set : A)

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( 19 ) 3632/(Set : A)
$ 1
OR

m
.co
$
!$
#J 61+ + $ =#
mJ 8 8 C O # <"
.co m
$

m/ s e
s e $
!$ l a
l a ag
< + = #(
g
$ $

a
→ →
-$ = : ; + $ ;. + $ ; + λ ; − $ ;. + $ ; " $! = −' ; − ; + µ % ; − $ ;. − $ ; " '# #
2 = =#O # <" 5

→
/ < 4 = : ; + $ ;. + $ ; + λ ; − $ ;. + $ ; "

m
.co
→
= −' ; − ; + µ % ; − $ ;. − $ ; " (

e m
las
ag
$ 1

OR

− 9 ! + #5 6 − #0
'2 #. $. −'" 1 # $! -$ = = $!
m
% − #: =

m
c. o −%#& = ! −9$5 = 6−−&& m .co
m
' - # O # <"
s e
s e g l a
g la a
a / 8 #. $. −'"

− 9 ! + #5 6 − #0 − #& ! − $5 6 − &
/ 4 = = = = (
% − #: = % 9 −&

3632/(Set : A) P. T. O.

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( 20 ) 3632/(Set : A)
$ -# 1> & , # <7 5

& F 1 > $ 6 :5 6 $! 2 = $! $> O # <

6 $! ≥ #00. $ − ! ≤ 0. $ 6 ! ≤ $00. . ! ≥ 0

E 4 < / *

G 3 G :5 6 $!

E <H / /

6 $! ≥ #00. $ − ! ≤ 0. $ 6 ! ≤ $00. . ! ≥ 0

$ 1
OR

$ -# 1> & , # <7
& F 1 > $ 6 :5 6! $> O # <

6 '! ≤ 9. $ 6 %! ≤ #$. % 6 ! ≤ 5. . ! ≥ 0

E 4 < / *

3 G :5 6!

E <H / /

6 '! ≤ 9. $ 6 %! ≤ #$. % 6 ! ≤ 5. . ! ≥ 0

3632/(Set : A)

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( 21 ) 3632/(Set : A)
- %–

m
.co
SECTION – E
m
<m
.co O ! * (S / ' / , a=(s
e m
< % R5(
s e # - $ !" $ :1
g l
g a
l 1 < 0 7 % . # . # $ ! $ !"
a
a# $2 $ # ?
#0 &
1 (S / ' $ !
#0 &

, =( $ !/ * $ # ? < 0 7 # . # $! #
!/ # $2
' % #$
1 $ * # # !"

T # 6 = $> & ? *+
m
# <7

m .co
s e
g la
a
" * #$ #? / 1 # $2 1 $ <" 1

" 1 $ / * (S $ #? O # <" 2

" : " ? # 6? ' <" 1

o m
m / c
B. 4
.co m
3 /
s e<
s em < < 4 / < . < . /
l a
g la /
% # #
. .
$
( 1 ag< < 4 <
a #0 & #0 &
# # #
. . / < .< / / .<
' % #$
/ < . 4 < (

3632/(Set : A) P. T. O.

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( 22 ) 3632/(Set : A)
< 4 4 8 *

" I < < 4 < . 4 / <

(

" > . .4 < < / < D

" 2 < < "(

! ". 0. $ < C !7

" = − "
0 0

> 6 $> & ? *+ 7

−/
" "= 2
#+ /
O # <7
π $
"
0

" ") #6 " 2

O # <7
π '
"
0

3632/(Set : A)

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( 23 ) 3632/(Set : A)
" / / 0. . *

" = − "
m
m
c. o <
0 0

m .co
m s e
a
< 4 4
s e l
a ag
8 *
g l
"
a "= −/
#+ /

*

π $
"
0
m
m .co
s e
g la
a
" ") #6 "

*

π '
"
0
o m
m c
1 6 (. ' <
c. o < C #% × 9 #$ ?B
s em
s em %4 P5 < = ' !"
g la
g la a
a T # 6 = $> & ? *+ 7

" ? ' = $> $ O # <" 2

3632/(Set : A) P. T. O.

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( 24 ) 3632/(Set : A)
" $> $ 1 = # 1 <5 #Q 1

" $> $ 1 = ' < ( <16 #: O " 1

< 3 < / / < 8 8 /
/ % < 9 /
(

< < 4 4
8 *

" / < 3(

" > 4 < < 3D

" > 4 < 8 8 < 3D

S

3632/(Set : A)

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