Karnataka 2nd PUC Quarterly Exam Question Paper 2026 Mathematics

FOR KARNATAKA 2ND PUC QUARTERLY EXAM EXAM PREPARATION

Karnataka 2nd PUC
Quarterly Exam 2026
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

Karnataka 2nd PUC Quarterly Exam 2026 Question Paper Mathematics

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. c s e
em la
as a g
F I R S T Q U A R T E R L Y T E S T A U G U S T 2 02 6
C L A S S :I I PU C S U B J E C T :M A T H E M A T I C S ( 3 5 )
T im e :1 H r . 3 0 M in s . M a x . M a r k s : 40

I n s t r u c t io n s :
a ) T h e q ue s t io n p a p e r h a s 4 p a r t s n a m e l y A , B , C a n d D . A n s w e r a l l t hoef p1 a r mt sa. r k e a c h .
b ) Pa r t - A h a s 7 M ul t ip l e c h o ic e q ue s t io n s . 3 fil l in t h e b l a n k q ue s t io n s
c ) W r it e t h e q ue s t io n n u m b e r p r o p e r l y a s in d ic a t e d in t h e q ue s t io n p a p e r .
m
co
PA R T - A
A n s w e r a l l t h e m ulot ipml e c h o ic e q ue s t io n s : 7 x 1= 7 .
1) G ive n s e t A = ( 1,.c2, 3 } a n d a r e l a t io n R = { ( 3 , 1) , ( 1, 3 ) , ( 3 , 3 ) } , t h e r e l a t io n R wil l b e sem
A ) r e f l e x ive eifm
( 1, 1) is a d d e d B ) s ym m e t r ic if ( 2, 3 ) is a d d e d
l a
s
C ) t r a n s litaive if ( 1, 1) is a d d e d D ) s ym m e t r ic if ( 3 , 2) is a d d e d
a g
M a t c hgL is t I w it h L is t I I
2) a L is t I L is t I I

a ) D o m a in o f s i n x i) ( - , o o )
b ) D o m a in o f t a n x in ) [ 0, ]
c) Ran g e of c o s x i) [ - 1 , 1]
C h o o s e t h e c o r r e c t a n s w e r f r o m t h e o p t io n s g ive n b e l o w :
C ) a - ii, b - i, c - ii D ) a - ii, b - i, c - ii
A ) a - i, b - ii, c - ii B ) a - ii, b - ii, c - i m
c. o
3)
e m
is a s c a l a r m a t r ix , t h e n t h e v a l u e o f x is
B)0 l a s C) - 1
4)
A) 2
g D ) –2
I f A is a s q ua r e m a t r ix o f o r d e r tawo , a n d |A | = 3 , t h e n A | is e q ua l t o
2 1
A) 3 B)3 c) 3 D ) 12
5) I f A is a m a t r ix o f o r d e r 3 s u c h t h a t A ( a d j A ) = 10I t h e n ļ a d j A l is e q ua l t o
A ) 10 B ) 1 00 C) 30 D) 1
6) T h e d e r iva t ive o f s in ( x + 5 ) w it h r e s p e c t t o x is
A) c o s ( x + 5) B ) - c o s ( x ? + 5) C ) - 2x c o s ( x * + 5 ) D ) 2x c o s ( x ? + 5 )
d y is m
7)
m I f y = s in ( l o g x ) t h e n d x
.co
m .co s in ( l o g x )
B ) yi- y D )as e m
s e A) C)
g l
la
X

a
X X

ag II F il l in t h e b l a n k s b y c h o o s in g t h e a p p r o p r ia t e a n s w e r s g iv e n in t h e b r a c k e t : 3 x 1 - 3

3
- 2, 0,

8) T h e p r in c ip a l va l ue
of c os t h e n t h e v a l u e o f k is

9) I f A = [ a , ] is a s q ua r e m a t r ix o f o r d e r t h r e e , J A | = 3 a n d A , , is c o f a c t o r o f a , , t h e n
a , , A , t a , , A , , + a , , A , , is e q ua l t o
10) I f f ( x ) = |x + 2|, t h e n f is c o n t in uo us b ut n o t d if f e r e n t ia b l e a t x =
m ( PT . O . ) . c
c. o e m
m
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-2
PA R T - B
III A n s w e r a n y T H R E E q ue s t io n s : 3 x 2- 6
I ) I f f a n d g a r e r e a l va l ue d f un c t io n s d e f in e d b y f( x ) = c o s x a n d g ( x ) = 3 x ', t h e n f in d g o f a n d
fog .
12) Pr o v e t h a t

[1 2 3 [3 -1 3
an d B = t h e n fin d ( 2A - B ) .
-1 0 2
14) F in d t h e e q ua t io n of t h e lin e j o in in g t h e po in t s ( 1, 2) a n d (3, 6 ) us in g d e t e r m in a n t s .
15 ) D if f e r e n t ia t e x s in x wit h r e s p e c t t o x .
PA R T - C
IV A n s w e r a n y T H R E E q ue s t io n s o f t h e f o l l o win g : 3x 3=9
16 ) C h e c k wh e t h e r t h e r e l a t io n R in t h e s e t o f r e a l n um b e r s d e f in e d a s R = ( a , b ) : a < b ' } is
r e f l e x ive , s ym m e t r ic a n d t r a n s it ive .

17 ) E x p r e s s t a n
V 1+ x ' - I , x * 0, in t h e s im n pl e s t . f o r m .
X

3 5
18) E x p r e s s t h e m a t r ix a s t h e s u m o f a s ym m e t r ic a n d s k e w- s ym m e t r ic m a t r ix .
1 -1
k x + 1 if x < r if c o n t in u o u s a t
19 ) F in d t h e va l ue of 'k ' s o t h a t t h e f un c t io n f d e f in e d b y f ( x ) = c o s x if x >
X=T.

d y = - 4 s in t .
20) I f x = s in t a n d y = c o s 2t , t h e n p r o ve t h a t dx

PA R T - D
3 x 5 = 15
A n s w e r a n y T H R E E o f t h e f o l l o win g q ue s t io n s :
21) L e t f : N →Y b e f un c t io n d e f in e d a s f ( x ) = 4 x + 3 , wh e r e
Y = ye N :y= 4 x + 3 f o r s o m e x e N . S h o w t h a t f is in ve r t ib l e a n d a l s o f in d it s in ve r s e .
6 7 f o 1 1| [2
22) If A =- 6 0 8. B = 1 0 2 C = - 2
7 -8 0 1 2 0 3

C a l c ul a t e A C , B C a n d ( A + B ) C . A l s o ve r if y t h a t ( A + B ) C = A C + B C .
23 ) S o l ve t h e f o l l o win g s ys t e m o f l in3 e a r e q ua t io n s b y m a t r ix m e t h o d :
2x + y+ z = 1; x - 2y- z = 2 3 y- 5 z = 9 .
24) I f y= ( t a n - ' x ) ', t h e n s h o w t h at ( x ² +1) y, + 2x ( x ² +1) y, = 2.
d 'y d y
25 ) I f y = 3 c o s ( l o g x ) + 4 s in ( l o g x ) , t h e n p r o ve t h a t x . d y? - + X d x + y = 0.
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