Karnataka 1st PUC Preparatory Exam Question Paper 2026 Mathematics

FOR KARNATAKA 1ST PUC PREPARATORY EXAM EXAM PREPARATION

Karnataka 1st PUC
Preparatory Exam
2026
Question Paper ·
Mathematics
EXAM YEAR TYPE

Karnataka 1st PUC Preparatory Exam 2026 Question Paper
SUBJECT

Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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D E P A R T M E N T O F S C H O O L E D U C A T I O N ( PaRgE U N I V E R S I T Y )
GOVERNMENT OF KARNATAKA

PREPARATORY EXAMINATION
I P.U.C: MATHEMATICS (35): 2025-26
Time : 3 hours Max. Marks : 80

Instructions :
m . c o
T h e q u e s t i o n p a p e r o h a s f v e p a r t s n a m e l y A, B, C , D a n d E . A n s w e r al l t he part s.
c
1 5 .M C Q ’ s , 5 F l l i n t he b l a n k s o f 1 m a r k each. em
1)
2) PART A has m
e l as
3) F o r q u e s t ilo a s
ns having figure/graph, alternate questions are given at the end of a g
g
q u e s t iao n p a p e r i n s e p a r a t e sect i on f o r vi sual l y c h a l l e n g e d st udent s.

PART A

I. A n s w e r A L L t h e M u l t i p l e C h o i c e Q u e s t i o n s 15 x1 = 15

1. I f U i s u n i v e r s a l s e t a n d A c U, t h e n U ’ N A =
m
.co
A) A B) U C) A’ D) 0 .

e m
as
2. I f (x - 1, y + 2) = (1, 5) , t h e n ( x, y) i s
3 , 2l)
C) ( g
A ) (1, 2) B) (2, 3)
3. M a t c h Li st I w i t h Li st I I
a D) (2,1)

List I List II

a) D o m n a i n o f s i n x i) ( - o , ) - { n n : n E Z}
b) Domnain of cotx ii) - 1 , 1 ]
c)Range of cosx ii) ( - o , c o )
m
m
C h o o s e t h e correct
c. oA) a-i , b- i i ,
answer from the options given below:
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c-i i B) a- i i i , b- i i , c- i
s e
s em C ) a-i i , b-i , c- i i i g la
gla 4. T h e c o n j u g a t e o f a c o m p l e x n u m b e r - 5 + 3i
D ) a - i i , b-i , c-i i
a
(A) -5-3i (B) 5-3i ( C ) ) - 5 + 3i (D) 5+3i.

5. T h e s o l u t i o n o f - 8 < 5 x - 3 < 7 is
( A ) - 1 s x < 2. B) - 1 < x < 2 C) - 1 s x s 2 D) 2 < x s - 1.

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6. I f 6!
+ 7=
!
,8 ! then x =
(A) 5 6 (B)49 (C)64 (D) 81.
7. T h e v a l u e of 10c, + 10c, + 10cC, t + 1 0 c , , is

(A) 1024 (B) 1 0 2 3 (C) 1022 (D) 5 1 2

8. T h e 4t h t e r m of t h e s e q u e n c e def i ned by a, = 1 = 4, a , = a , - 1 t a n - 2 , 1 > 2 1s
(A) 9 (B) 5 (C) 2 ( D ) 3.

9. Equat i on of t he l i ne par al l el t o x- axi s a n d passi ng t hrough ( - 2, 3) i s
(A) x = 3 (B) x = -2 ( C) y = - 2 (D) y = 3 .
10. T h e l e n g t h of t h e l at us r e c t u m of t h e p a r a b o l a y’ = - 9 x
9
(A) 9 (B) - 9 D);
11. T h e eccentricity of t h e h y p e r b o l a s : 9 16
=1
32
(A) 4
(B) 3
(C) 1 48 (D)
12. S t a t e m e n t 1: T h e perpendi cul ar di st ance f r o m t he poi nt P( 6, 7, 8) t o zx- pl ane i s 7
Statement 2 : The shortest distance of the point (a, b, c) f r o m t h e x - a x i s i s V b 2 + c2

A) S t a t e m e n t 1 is t r u e and Statement 2 is false.
B) S t a t e m e n t 1 is false and Statement 2 is false.
C) S t a t e m e n t 1 is t r u e and Statement 2 is true, Statement 2 is n o t a correct

explanation for Statement 1
D) S t a t e m e n t 1 is t r u e and Statement 2 is true, Statemnent 2 is a c o r r e c t
explanation for Statement 1
13. For the figure given below, consider the following statements 1 and 2

y-fa)
3

2

function limit exists at x =1,x = 2 and x = 4
Statemnent 1: T h e given
Statement 2: T h e given function limit exists at at x = 3

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se A)Statement 1 is t r u e a n d S t a t e m e n t 2 i s f al se l a
B) S t a t e m e n t 1 i s f al se and Statement 2 is t r u e ag
C)Both Statement land 2 are true
D)Both Statement l a n d 2 a r e f al se
14. M e a n deviation about median f o r f i rst 5 natural n u m b e r s is
5
(A) 5 (B) (C) 6 ( D)
m
co
events corresponding to the s a m p l e space "two coins are
T h e n u m b e r of sinple
om .
15.
tossed once" is
. c e m
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s
C) 3 D) 4
g
A) B) 2
l a a
F i l l i n tah eg b l a n k s b y c h o o s i n g the appropriate answer from those given in the
II. 5 X1 = 5
bracket. (0,1, 2, 3, 4, 5, )

I f A = 2 , 4, 6, 8} a n d B = { 6 , 8, 1 0 } , t h e n n( A - B ) . . . . .
16.
number. The number of v a l u e s of x i s
17. If 5 x - 3 < 3 x + 1 , w h e n x is a n a t u r a l

18. If 15C3r = 15C3+r then r

om
(k-5)x-(4-k’)y+k†-7k+ 6 = 0 is parallel to
1 9 . T h e v a l u e s o f k f or w h i c h t h e l i ne
. c
t h e y - a x i s is
e m
20. T h e derivative of f ) = 4 x at x = 0 is
l as
ag
PART-B
6 X 2 = 12
A N S W E R ANY SIX QUESTIONS
9, 1 1 , 13}, C = {15, An(BUC).
17} find
2 1 . I f A = { 3 , 5, 7 , 9 , 11}, B - { 7 , of
of diameter 40 cm, the length o f a c h o r d is 2 0 c m . F i n d t h e l e n g t h
22 In a circle

minor arc of the chord.

(sin3xt sin ) sin x + (cos 3x- c o s x) c o s x = 0 .
m
23. Prove that

m .co
.co
a+ib
x † + y 2 = 1.
em5 b o y s a n d 4
2 4 . If x + iy prove that
a-ib

em g i r l s ?
25. In h o w m a n y ways can a team
o f 3 b o y s a n d 3 girls be selected
las from
s
la 2 6 . U s i n g B i n o m i a l T h e o r e m e v a l u a t e ( 9 9 ) . ag
ag t h e 6th t e r m is 192. F i n d t h e 10th
term.
27. I n a G . P , t h e third t e r m is 2 4 a n d through the point (4, 5).
of the circle with centre (2, 2) and passes
28. Find the equation
and 6 on the other a n d a fair die are both
29. A fair coin with 1 marked on one face
that the s u m of numbers that turn u p i s 12.
tossed find the probability

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PART -C
6x3 = 18.
ANSWER ANY SIX QUESTIONS:

30. I f U = { 1 , 2 , 3 , 4 , 5 , 6 , A= 2 , 3 } a n d B = 3 , 4 , 5 veri f y (AU B)= A n B .
the domain and range of the relation R defined by
31. Determine

R = (, x + 5): x ‹ {0, 1,2, 3, 4, 5} } .

32. S h o w that tan3 x tan 2 xtan x = tan 3x - tan 2 x- tan x.

3 3 . I f (x + i y) 3 = u t i v, t h e n s h o w t h a t + = 4(x2 - y’ ).

odd positive integers both of which are smaller than
3 4 . F i n d al l p a i r s of consecutive
10 such that their s u m is m o r e t h a n 11.

35. Eval uat e(V3 + VZ)’-(V3- V2) .
between two lines is n / 4 a n d s l o p e of one of the lines is 1 / 2
3 6 . If t h e a n g l e
find the slope of the other line.
P s u c h t h a t its d i s t a n c e s from the points
37. Find the equation of the set of points

A ( 3, 4, -5) and B(-2, 1, 4) a r e e q u a l .
of tanx w. r . t x f r o m n f i r s t principle.
38. Find the derivative
PART- D
4 X5 = 20
Answer any F O U R questions

Draw the graph o f it. A l s o w r i t e its d o m a i n and range.
39. Define Signum function.
si n 3 x + s i n 5 x + s i n 7 + s i n 9 x = t a n 6 x .
40. Prove that 9x
Cos 3x+ cos 5x+ cos 7x+cos

arranged if t h e
of t h e w o r d P E R M U T A T I O N S b e
41. In h o w m a n y w a y s c a n the letters
( i i ) v o w e l s a r e al l t o g e t h e r ,
i) w o r d s s t a r t w i t h P a n d e n d w i t h S ,
between P and S?
iii) t h e r e a r e a l w a y s 4 l e t t e r s
distance between a point(x1, y;) a n d a
42. Derive anexpression for the perpendicular

l i n e A x + By + C = 0.
=na-1 and hence
43. P r o v e t h a t , f or a n y p o s i t i v e integer n, l i m

evaluate

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l a
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44. Find the variance and standard devi at i on f or t h e f ol l owi ng data
4 17 30 24 32
3 5 9 5 4 3 1

o m once. Fi nd t he pr obabi l i t y . co
4 5 . T h r e e coi ns are tcossed
t a i l s ( i i i ) n o t ai l .( i v) a t m o s t t w o t ai l s
of get t i ng ( i ) 3 t ai l s ( i ) exact l y t wo
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a g PART-E
Answer the following question.

4 6 . I f si nx = 4, x i n quadrant I I , t h e n f i nd s i n , c o s , t a n ; : 6

OR
y2
Define ellipse and derive the equation of the ellipse in standard form as + =b 21 .
g2
m
4 7 . F i n d t h e deri vat i ve off(x) c. o t o X.
= x 5 -s ci no s x x w i t h r e s p e c t 4

e m
F i n d t h e s u m of t h e s e r i e s u p t o n t elra
s OR

ag
ms 5 + 5 5 +555 +

*******t**********k*******

46. Prore Ces ( zt y)
m
m Si nx si ng .co
m .co s e m
s e g la
la a

m
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s em
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