Karnataka 1st PUC Model Question Paper 2027 for Mathematics (Paper 1)

FOR KARNATAKA CLASS 11 PREPARATION

Karnataka 1st PUC
Model Question Paper
2027 for Mathematics
(Paper 1)
EXAM YEAR TYPE SUBJECT

Karnataka Class 11 2027 Sample Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

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s GOVERNMENTOF KARNATAKA
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DEPARTMENT OF SCHOOL EDUCATION (PRE UNIVERSITY)
I P.U.C ANNUAL EXAMINATION 2027
SAMPLE MODEL QUESTION PAPER I

Subject Code: 35
MATHEMATICS
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[Time: 3 Hours] [TOTAL No. of questions: 47] [Max. Marks: 80]

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Instructions:
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1. The question paper has five Parts namely A, B, C, D and E. Answer all the
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parts.
2. PART-A has 15 Multiple choice questions and 5 Fill in the blank questions.
3. For PART-A questions, only the first written answers will be considered for
evaluation.
PART - A

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I. Answer ALL the multiple choicequestions (15  1 = 15)
1. The interval form of {x: x  R, - 5 < x  7} is
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A) (-5, 7) B) [-5, 7] D) (-5, 7]

2. The domain of the real functions f(x) = |𝐱 − 𝟏|
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A)(−∞, 0) B)(−∞, ∞) C) (0, ∞) D) [−∞, ∞].
3. Match List I with List II

List I List II
a) 𝑠𝑖𝑛𝑥 is positive i) 1st and 4thquadrant

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m c) 𝑠𝑒𝑐𝑥 is positive c
b) 𝑡𝑎𝑛𝑥 is negative ii) 1st and 2nd quadrant
iii) 2 and 4 quadrant .
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Choose the correct answer from the options given below:

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A) a-ii, b-i, c-iii B) a-i, b-iii, c-ii
C) a-ii, b-iii, c-i D) a-i, b-ii, c-iii
4. The additive inverseof -2+3i
A) 2-3i B)-2-3i C) 2+3i D) -2+3i

5. The solution of the inequality -1 ≥xand x ≥ 1 for real x.
A) [-1, 1] B) (−∞, −1] ∪ [ 1, ∞) C)(−1,1 ) D) (−∞, −1) ∪ (1, ∞)
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1 1 x
6. If   then x =
8 ! 9 ! 10 !
A) 64 B)81 C)100 D) 72.
7. Given 4 flags of different colors, then the number of different signals
can be generated. If a signal requires the use of 2 flags one below the
other
A) 6 B)12 C)24 D) 4.
8. The number of non-zero terms in the expansion of (𝒂 + 𝒃)𝟔 is
A)5 B) 6 C) 7 D) 8
9. The 4th term of the sequence defined by 𝒂𝟏 = 𝟏, 𝒂𝒏 = 𝒂𝒏−𝟏 + 𝟐, 𝒏 ≥ 𝟐 is
A) 3 B) 5 C) 7 D) 9

10. The equations for x and y axes are
A) 𝑥 = 1 , 𝑦 = 1 B) 𝑦 = 1 C) 𝑥 = 0 𝑎𝑛𝑑 𝑦 = 0 D) 𝑥 = 1 𝑎𝑛𝑛 𝑦 = 0.
11. The eccentricity of the hyperbolas: 𝟏𝟔𝒚𝟐 − 𝒙𝟐 = 𝟏𝟔
√17 √15
A) 4 B) √17C) 4 D) √15 .
12. The perpendicular distance from the point P(x, y, z) to xy-plane is
A) x B) y C) z D) √𝑥 2 + 𝑦 2
13. Assertion (A): The derivative of 𝑓 (𝑥 ) = 𝑥 is 0.
Reason(R): The derivative of x −n w. r. t x is − nx −n−1
A) Both Assertion (A) and Reason (R) are true.
B) Both Assertion (A) and Reason (R) are false.
C) Assertion (A) is true and Reason (R) is false.
D) Assertion (A) is false and Reason (R) is true.
14. If the sum of squares of the deviations of 10 observations taken from
their mean is4.9, then their Standard Deviation is
A) 4.9 B) 0.7 C) 0.5 D) 5.3.
15. If sample space 𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔} and events 𝑨 = {𝟐, 𝟒, 𝟔} 𝒂𝒏𝒅 𝑩 = {𝟏, 𝟑, 𝟓}, 𝒕𝒉𝒆𝒏
events A and B are
A)Mutually exhaustive but not exclusive events
B) Mutually exhaustive but not exclusive events
C)Mutually exclusive and exhaustive events
D) Not Mutually exhaustive and not exclusive events
II. Fill in the blanks by choosing the appropriate answer from those given in
the bracket. (0,1, 2, 3, 4, 5) (5  1 = 5)

16. The number of sub set of a set A =φ is______
17. The number of solutions of the inequality 24x < 100,
when x is a natural number is______
18. The slope of the line through the points (3, -2) and (7, -2) is______

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(5,6)is______
 x  2,x  0
20. If f  x    , then lim f  x  is_____
 x  2 ,x  0 x 0

PART-B

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III. Answer Any Six of the following questions (6 2 = 12)

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21. List all the subsets of the set {–1,0,1}.

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22. A wheel makes 360 revolutions in one minute. Through how many radians
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does it turn in one second?
23. Prove thatl 2𝑠𝑖𝑛 a g
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2 3𝜋 2𝜋 2𝜋
+ 2𝑐𝑜𝑠 + 2𝑠𝑒𝑐 = 10
4 4 3
𝑎+𝑖𝑏
24. If x + iy = , prove that x + y = 1. 2 2
𝑎−𝑖𝑏
25. In how many ways can the letters of the word ASSASSINATION be arranged so
that all the S’s are together?
26. Using Binomial Theorem evaluate (𝟏𝟎𝟏)𝟒.
27. In the G.P. 2, 2√2, 4... if an = 128, find the value of n.
28. Find the coordinates of the focus and latus rectum of the parabola 𝑦 2 − 8 = 0x.
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29. A coin is tossed twice, what is the probability that atleast one tail occurs?

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PART
IV. Answer Any Six of the following
a g (6 3 = 18)
30. Let U ={1,2,3,4,5,6,7,8,9}, 𝐴 = {2,4,6,8} and B = {2,3,5,7}. Show that
(𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵′
3 1 . Define a relation R on the set A={1,2,3,4,5,6} by
R={(x,y):y =x + 1,x,y∈ A}. Depict this relationship using roster form.Write
down the domain and the range.
32. Prove that (sin 3𝑥 + 𝑠𝑖𝑛𝑥)𝑠𝑖𝑛𝑥 + (𝑐𝑜𝑠3𝑥 − 𝑐𝑜𝑠𝑥 )𝑐𝑜𝑠𝑥 = 0 .

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(3−2𝑖)(2+3𝑖)

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33. Find the conjugate of (1+2𝑖)(2−𝑖)
m all pairs of consecutive odd positive integers both of whichmare
. smaller
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34. Find

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l 36. Find equation of the line passing through the pointa (2, 2) and cutting off
𝟔
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37. Show that the points (0,7,-10),(1,6,-6) and (4,9,-6) are the vertices of an
isosceles triangle.
38. Find the derivative of sin 𝑥 w. r. t x from first principle.

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PART – D
V. Answer Any Four of the following questions (4 5 = 20)
39. Define Signum function. Draw the graph of it. Also write its domain and
range.
sin 3x  sin 5 x  sin 7 x  sin 9 x
40. Prove that  tan 6 x
cos 3x  cos 5 x  cos 7 x  cos 9 x
41. A group consists of 4 girls and 7 boys. In how many ways can a team of 5
members be selected if the team has
(i) no girl? (ii) at least one boy and one girl?
(iii) at least 3 girls?
42. Derive an expression for the perpendicular distance between a point(𝑥1 , 𝑦1 ) and
a line 𝐴𝑥 + 𝐵𝑦 + 𝐶 = 0.

 sin x 
43. Prove that lim   1 , where x in radian.
x 0
 x 
44. Find the mean deviation about the mean for the following data

xi 5 10 15 20 25
fi 7 4 6 3 5
45. A and B are two events such that P(A) = 0.54, P(B) = 0.69 and
P(A and B) = 0.35.
Find (i) P(A or B) (ii) P(not A and not B) (iii) P(A but not B)

PART-E
VI. Answer the following question.
46. Prove geometrically that 𝑐𝑜𝑠(𝑥 + 𝑦) = 𝑐𝑜𝑠𝑥 𝑐𝑜𝑠𝑦 − 𝑠𝑖𝑛𝑥 𝑠𝑖𝑛𝑦, and hence
evaluate cos 750
OR
𝑥2
Define ellipse and derive the equation of the ellipse in standard form as 𝑎2 +
𝑦2
=1. 6
𝑏2
x  cos x
47. Find the derivative of f  x  
tan x
OR
If A.M. and G.M. of two positive numbers ‘a’ and ‘b’ are 10 and 8, respectively,
find the numbers.
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