Karnataka 1st PUC Model Question Paper 2027 for Mathematics (Paper 2)

FOR KARNATAKA CLASS 11 PREPARATION

Karnataka 1st PUC
Model Question Paper
2027 for Mathematics
(Paper 2)
EXAM YEAR TYPE SUBJECT

Karnataka Class 11 2027 Sample Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

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

Subject Code: 35
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MATHEMATICS

om No. of questions: 47]
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[Time: 3 Hours] [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
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
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. statement is correct?
(15  1 = 15)

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1. Let A = {1, 2, {3, 4}, 5}. Which of the following
B){3, 4} ∈A la
A){3, 4} ⊂A
2. If (x - 1, y + 2) = (1, 5), then (x,
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C) 3∈A D) 4∈A.

A) (1, 2) B) (2, 3) C) (3, 2) D) (2, 1)

3. The range of f (x) = sin x is

A)[0, ) B) (-, ) C) [-1, 1] D) (-1, 1)].

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4. The square roots of – 1

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A) 1,-1 B) −𝑖 C) 𝑖 D) 𝑖, −𝑖
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5. The solution of 3x + 8 > 2, when x is a real number is
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B) (-, -2) C) (-, -2] D) (-, -1)
6. Match List I with List II

List I List II

a) 5𝐶0 i) 20

b) 5𝑃2 ii) 10

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c) 5𝐶2 iii) 1

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Choose the correct answer from the options given below:
A) a-i, b-ii, c-iii B) a-iii, b-ii, c-i

C) a-ii, b-i, c-iii D) a-iii, b-i, c-ii

7. The number of 2digit even numbers can be formed from the digits 1,
2, 3, 4, 5 if the digits can be repeated
A) 10 B)8 C)120 D)
8. The value of C1 + C2 + C3 + ..... C10 is
10 10 10 10

A)1024 B)1023 (C)1022 (D) 512
9. The 9th term of the sequence defined by 𝒂𝒏 = (− 𝟏)𝒏−𝟏 𝒏𝟑 is
A) 36 B) 39 C) -39 D)-36
10. The angle between the x-axis and the line joining the points (3,–1) and
(4,–2)
A) 450 B) 1350 C) -450 D) -1350
11. Equation of the circle with centre at (-3,2) and radius 4.
A) 𝑥 2 + 𝑦 2 + 6𝑥 − 4𝑦 + 3 = 0 B) 𝑥 2 + 𝑦 2 − 6𝑥 + 4𝑦 − 3 = 0
C) 𝑥 2 + 𝑦 2 − 6𝑥 + 4𝑦 + 3 = 0 D) 𝑥 2 + 𝑦 2 + 6𝑥 − 4𝑦 − 3 = 0
12. The point (-2, -3, -4) lies in the
A) First Octant B)Seventh octant C) Second octant D) Eighth octant
13. lim (x3 – x2 + 1) is
x  1

A) -1 B) 0 C) 1 D) 2
14. The median of 3, 10, 6, 7, 11, 13, 15 is
A) 7 B) 9 C) 10 D) 11
15. Which of the following is incorrect
A) If A and B are any two events then𝑃(𝐴 ∪ 𝐵) = 𝑃 (𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
B) P(A′ ) = 1 − P(A)
C) P(A ∩ B ′ ) = P(A) − P(A ∩ B)
D)𝑃(𝐴′ ∩ 𝐵′ ) = 1 + 𝑃(𝐴 ∪ 𝐵)
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 length of the intervals (-1, 1] is______
17. The solution of −8 ≤ 5𝑥 − 3 < 7 𝑖𝑠a ≤ 𝒙 < 𝒃, 𝒕h𝒆𝒏 𝒂 + 𝒃 is_____
18. The x-intercept of the line 2 x  5 y  10  0 is_____
19. The length of the lotus rectum of the parabola y 2  4 x is_____
20. The derivative of f(x) = 3𝑥 at x =2

PART-B
III. Answer Any Six of the following questions (6 2 = 12)
21. If A= {3, 5, 7, 9, 11}, B= {7, 9, 11, 13}, C= {15, 17} find A∩(B∪C).

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m 22. In a circle of diameter 40 cm, the length of a chord isla20 cm. Find the length of
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minor arc of the chord
23. Prove that (sin3x+ sin x) sin x + (cos 3x – cos x) cos x = 0
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24. Express i    in a + ib form.
18 1
i
25. How many 4-letter codes can be formed using the first 10 letters of the English
alphabet, if no letter can be repeated?

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26. Find an approximation of (0.99)5 using the first three terms of its expansion

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27. The sum of first three terms of a G.P. is and their product is − 1. Find the

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12

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common ratio and the terms
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28. Find the equation of the ellipse whose vertices are (± 13, 0) and foci are (± 5, 0).
29. One card is drawn from a well shuffled deck of 52 cards. If each outcome is
equally likely, calculate the probability that the card will be (i) a diamond (ii)
not an ace card

PART –C
IV. Answer Any Six of the following questions (6 3 = 18)

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30. Let U= {1, 2, 3, 4, 5, 6} A= {2, 3}, and B={3, 4, 5}. Show that (A ∪ B)∁ = A∁ ∩ B ∁

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3 1 . Determine the domain and range of the relation R defined by

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

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32. Show that tan 3 x tan 2 x tan x = tan 3x – tan 2 x – tan x

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33. If (x + iy) 3 = u + iv, then show that 𝑥 + 𝑦 = 4(𝑥 2 − 𝑦 2 ).
34. Solve the inequality and show the graph of the solution on the number line
3x  4 x  1
 -1
2 4
𝑥 2 4
35. Expand using binomial theorem (1 + 2 − 𝑥) , 𝑥 ≠ 0
36. If the angle between two lines is π/4 and slope of one of the lines is 1/2
find the slope of the other line.
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37. If the origin is the centroid of the triangle PQR with vertices P (2a, 4, 6

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Q(4,3b, 10) and R (8,14, 2c) then find the values of a, b, c
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Find the derivative of 𝑡𝑎𝑛𝑥 w. r. t x from first principle.
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38.

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V. Answer Any Four of the following questions (4 5 = 20)
39. Define Modulus function. Draw the graph of it. Also write its domain and
range.
cos 4 x  cos 3 x  cos 2 x
40. Prove that = cot 3x
sin 4 x  sin 3 x  sin 2 x
41. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways

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can this be done when the committee consists of:
(i) exactly 3 girls?
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(ii) atleast 3 girls? (iii) atmost 3 girls?
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42. Derive a formula for the angle between two lines with slopes m1 and m2 . If the
 1
angle between two lines is and slope of one of the lines is , find the slope of
4 2
the other line
𝑥 𝑛−𝑎 𝑛
43. Prove that,for any positive integer n,lim [ 𝑥−𝑎 ] = 𝑛𝑎𝑛−1 , and hence
𝑥→0
𝑥 15−1
evaluate lim [𝑥 10−1].
𝑥→1

44. Find the variance and standard deviation for the following data
xi 4 8 11 17 30 24 32
fi 3 5 9 5 4 3 1

45. One card is drawn from a well shuffled deck of 52 cards. If each outcome is
equally
likely, calculate the probability that the card will be
(i) a diamond (ii) not an ace card (iii) a black card
(iv) not a diamond (v) not a black card.

PART-E
VI. Answer the following question.
46. Prove geometrically that 𝑐𝑜𝑠(𝑥 + 𝑦) = 𝑐𝑜𝑠𝑥 𝑐𝑜𝑠𝑦 − 𝑠𝑖𝑛𝑥 𝑠𝑖𝑛𝑦, and hence
 
evaluate cos   x 
2 
OR
𝑥2 𝑦2
Define hyperbola and derive the equation in the form 𝑎2 − 𝑏2 = 1 . 6

x5  cos x
47. Find the derivative of f  x  
sin x
OR
Find the sum of n terms of the sequence 7,77,777,7777,….tonterms. 4

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