Karnataka 1st PUC Mid Term Question Paper 2025 Maths

Government of Karnataka
Karnataka Secondary Education Examination Board

Question Papers
Mid Term

I PUCMID-TERM EXAMINATION, OCTOBER-2025
SUBJECT: MATHEMATICS (35)
Time :3 Hours Max Marks : 80

Instructions :
1) The question paper has FIVE parts namely A, B, C, D and E. Answer all the parts.
2) PART-A has 15 Multiple choice questions. 5 Fill in the blanks of one mark each.
PART-A
Answer ALL the multiple choice questions : 15x1=15
1) IfR is the set of real numbers and Q is the set of rational numbers than R-Q is
a) set of real numbers b)set of rational numbers
c) set of irrational numbers d) set of integers
2) Let A ={a, e, i, o, u} and B = fa, i, u} then
a) A = B b)AcB c) AUB = A d) AnB = A
3) The domain of the real function f(x) = |x-1|
a) (- o,0) b) (-o, o) c) (+o,0) d) [0, o)
4) A ={1, 2} B={3, 4} then Ax(Bo¢)=
a) A b) B c) d) AUB
5) If cos x=0then

a) x-(2n +1)% b) x=2nn c) X= n1 d) x = 0
6) The graph drawn below depicts

a) sine function b) cosine function c)tan function d) cot function

7) If statement 1: sin (2r+Y%)=%
Statement 2: cos
a) Both statements are true
b) Statement 1is true and statement 2 is false
c) Statement 1is false and statement 2 is true
d) Both statements are false

8) Additive inverse of -2+ 3i
a) 2-3i b) -2-3i c) 2 + 3i d) -2 + 3i

9) i++P+i=
a) 2 b) 1 c) -1 d) 0
10) The solution of the inequalityx>0for realx
a) (-o,0] b) [0, co) c) (-o, 0) d) (0, o)
(PIO.)

-2
11) The slope of the line through the points (3, -2) and (- 1, 4) is
a) b) 2 d) not defined

12) Equation of line parallel to x-axis and passing through(-2, 3) is
a) x = 3 b) x = -2 c) y= 2 d) y=3
13) Equation of the line passing through (0, 0) and having slope mis
a) y =mx + c b) x = my + c c) y = mx d) x = my
14) If "C, = "C, then n
a) a b) b c) a-b d) a + b
15) The number of 4 letter words with or without meaning, which can be formed out of the letters
of the word 'ROSE' when repetition of the letters is not allowed
a) 24 b) 12 c) 6 d) 256

II Fillin the blanks by choosing the appropriate answer from those given in the bracket:
5x1=5

[-1, 120, A, B, -2, 1]
16) If AcB then AUB=
17) 6P,
18) The value of sin 37%
1+i
19) The modulus of the complex number 1-i
20) y intercept of the line y-x + 2 = 0 is
PART-B
Answer any SIX questions : 6x2=12

21) U =(1, 2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 3, 4} B= {2, 4, 6, 8}. Find (AUB)'
find the values ofx and y.

23) Find the value of sin 765°.
2tan x
24) Prove sin 2x = 1+ tanx
25) Express (5-3i) in the form a + ib
a +ib
26) Ifx + iy = prove x +y'= 1
a-ib
27) Solve 3x + 8> 2 when
i) x is an integer
i)x is real number
28) Ravi obtained 70 and 75 marks is first two unit test. Find the minimum marks he should get in
the third test to have an average of at least 60 marks.
29) Find the distance between parallel lines 15x + 8y-34 =0and 15x + 8y +31 = 0

(PT.O.)

-3
PART-C
IV Answer any SIX questions : 6x3=18

s0) IfA= {3, 5, 7,9, I} B= (7,9, 11, 13} and C= {l1, 13, 15), Find (ANB)^(Bc)
S2) Define a relation R on the set Nof natural numbers by R = {(x, y) :y=x+5, XIS a natural
number les than 4; x, ye N}. Depict this relationship using roster form write its domain and
Range.
32) Prove sin 5x +sin 3x tan 4x.
cos Sx+ cos3x

33) Prove tan 3x = 3tan x tan° x
1-3tan x
34) Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that
their sum is less than 40.

35) Find the equation of line passing through the point (2, 2) and cutting off intercepts on the axes
whose sum is 9.

36) "P. =42 "P,, n>4 find n.
37) A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how
many ways can this be done ? How many of these committees should consists of 1l man and
2 women.

38) Let f(x) = x* g(x) = 2x +lbe two real functional find
(i)(f+ g) (x)
(i)(f-g) (x)
(ii) (fg) (x)
PART-D
V Answer any FOUR questions : 4x5-20
Define modulus function. Draw the graph of the function. Write the domain and the range of the
39)
function.

3
40) If cot x = x lies in third quadrant. Find the values of other five trigonometric functions.
4

41) Prove cos' x +cos*(x+%)+ cos (x-4)=
Derive an expression for the perpendicular distance from the point
(x,, y.) to the line
42)
0
Ax + By +C=
segment joning the points (3, 4) and (-1. 2)
A3) Find the equation of right bisector of the lne
many ways can a team of5 members selected
44) Aoroup consists of 4 girls and 7 b0ys. In noW
if team has
(i) No girl
girls
(ii) at least 3
boy and one girl
(iii)at least one

(P.T.O.)

-4
from the letters of the word MONDAY
45) How many words with or without meaning can be made
assuming that no letter is repeated if
a) 4 letters are used at a time
b) allthe letters used at a time
c) All the letters are used but first letter is vowel ?
PART-E
(6t4-10)
VI Answer the following questions :
46) Prove geometrically that cos (x + y) = cos x cos y-sin x sin y and hence show that
6M
cos2x = cos'x- sin'x.
OR
What is the number of ways of choosing 4 cards from a pack of 52 playing card ? In how many
of these (1) four cards are of the same suit
(ü) four cards belong to four different suits
(1) are face cards
(iV) two are red cards and two are black cards
(v) cards are of the same colour.
X+y 4M
47) Prove that (cos x +cos y) +(sin x -sin y)´ = 4cos?
OR
Prove "C, + "C,- = *"C,
***k**

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