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

FOR KARNATAKA CLASS 11 PREPARATION

Karnataka 1st PUC
Model Question Paper
2027 for Basic Maths
(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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GOVERNMENT OF KARNATAKA
DEPARTMENT OF SCHOOL EDUCATION (PRE-UNIVERSITY)
I PUC ANNUAL EXAMINATION 2026-27
MODEL QUESTION PAPER 2
SUBJECT CODE: 75
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BASIC MATHEMATICS
TIME : 3 Hours
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c Max. Marks: 80
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Instructions:
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i) The question
s paper has 5 Parts A, B, C, D and E. Answer all the Parts.
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a - D carries 20 marks and Part - E carries 10 marks.
ii) Part - A carries 20 marks, Part - B carries 12 marks, Part - C carries 18 marks,

iii) Write the question number properly as indicated in the question paper.

PART-A
I. Answer ALL the multiple-choice questions: 10 x 1 = 10
1. The real and imaginary part of the complex number 4 − 7𝑖 is
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a) 4 𝑎𝑛𝑑 − 7 b) −4 𝑎𝑛𝑑 − 7 c) 4 𝑎𝑛𝑑 7 d) −4 𝑎𝑛𝑑 7𝑖
.
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2. If 𝐴 = {𝑎, 𝑏} and 𝐵 = {𝑐} then 𝐵 × 𝐴 is
a) {(𝑐, 𝑎)} b){(𝑐, 𝑎), (𝑐, 𝑏)} c) {(𝑐, 𝑏)}
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d) {(𝑎, 𝑐), (𝑏, 𝑐), (𝑏, 𝑑)}

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0
3. The value of (50 )2 + (5)2 in its simplest form is
a) 4 b) 5 c) 1 d) 6
4. The value of log 25 625 is
a) 0 b) 1 c) 2 d) 3
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5. The 11 term of the A.P. 3, 5, 7, 9,….. is
a) 21 b) 22 c) 23 d) 24

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6. The roots of the quadratic equation x 2 − 4x + 3 = 0 are

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a) 3,1 b) 2,3 c) 1,4 d) 2,2
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7. The solution of 4𝑥 − 2 < 8 is

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la 8. The effective rate of interest at 9% compounded quarterlya is
5
b) (−∞, 4) c) (2, ∞) d) (−∞,

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a) 9.3% b) 8.1% c) 3.9% d) 1.9%
9. The radian measure of 450° is
π 7π 5π 19π
a) b) c) d)
36 2 2 2
𝜋
10. The slope of the line with inclination is
3

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1
a) 3 b) √3 c) d) 1
√3

II. Match the following 5x1=5
11. A B
10
a) If 𝑛(𝐴) = 4, then 𝑛[𝑃(𝐴)] is i)
√5
4
b) What percent is of 125 ? ii) 25,000
5
c) The average marks of 5 students are 88, 71, 35, 30, 46 iii) 16
d) The present value of perpetuity of ₹ 2000 at 8% p.a is ₹ iv) 0.64
e) Distance between two parallel lines x + 2y + 3 = 0 and v) 54
x + 2y − 7 = 0 is vi) 17,000

𝑰𝑰𝑰 Fill in the blanks by choosing appropriate answer from given options: 5 x 1 = 5
𝟖
(𝟒, 𝟓 , 𝟕𝟐, 𝟔, 𝟓, 𝟏𝟎 )

12. The least integer divisible by 18 and 24 is
13. If 𝑓(𝑥) = 2𝑥 + 1, then 𝑓(2) is
3 13
14. If , k , are in A.P., then the value of k is
5 5
15.The sum of 4 times a number and 3 times the number is 70, then the number is
16. The distance of the point (4, 6) from x-axis is

PART-B
IV Answer any SIX questions. 6 X 2 =12

𝟏𝟕. Find the number of positive divisors of 768.
18. If 𝑓(𝑥) = 𝑥 and 𝑔(𝑥) = 𝑥 3 + 1, find i) 𝑓𝑜𝑔(1) ii) 𝑔𝑜𝑓(−1)
1 1
19. Find the sum to infinity of the G.P. 3, – 1, , − ,………
3 9
1 1
20. Insert 3 harmonic means between and .
4 12
21. The cost of an article is ₹ 80.If a profit of ₹ 20 is made by selling the article, find the profit
percentage.

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22. Solve 7x + 3 < 5x + 9, x ∈ R and represent the solution on the number line.
23. Samarth bought a walkman for ₹1800.If it depreciates at the rate of 15% per year,
what is its worth after 3 years?
1
24. Prove that = sec A − tan A
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sec A + tan A

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25. Find the intercepts made by the line 3𝑥 + 4𝑦 − 12 = 0 on the coordinate axis.

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lSIX questions. 𝟔 ×a
PART-C
V. Answer any
a g 𝟑 = 𝟏𝟖
26. If 𝑈 = {a, b, c, d, e}, 𝐴 = {a, b, c} and 𝐵 = {𝑐, 𝑑, 𝑒}, then verify (A ∩ B) = A′ ∪ B ′
′

8 32 16
27. Find the HCF of , ,
9 81 27

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73−2x
= 493x−14
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28. Solve
77−5x

em2 − 6𝑥 + 4 = 0. Find the values of the
29. If α and β are the roots of the equations3𝑥
a 𝛼 𝛽
(i) α 2 + β2 gl (ii) +
following:
a 𝛽 𝛼

30. Solve the inequality 3x + 4y ≥ 12, 4x + y ≥ 8, x ≥ 0, y ≥ 0.

31. The population of a town was 2,50,000 three years ago.If the population increased
by 4% , 3.5% 𝑎𝑛𝑑 6% respectively in the last three years, find its present

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population.

m average age of 10 students is 14 years. Among them the average c o
. of 5 students
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. is 12 years. Find the average age of the remaining students. se m
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ag 33. Find the equation of the locus of the point which moves such that it lies on the
perpendicular bisector of the line joining the points (3, −2) and (4, 1).

34. The angles of a triangle are in A.P. and the greatest is 5 times the least. Find the
angles in degrees and in radians.

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PART-D
VI. Answer any FOUR questions. 4 × 5 =20

35. In a group of 65 people, 40 like cricket, 10 like hockey and cricket both. How many
like only cricket? How many like hockey? Show the result using Venn diagram.
213.781 ×7.434
36. Using logarithmic tables, find the value of
6.321
37. Find an integral root between −3 and 3 by inspection and then by using synthetic
division solve the equation 𝑥 3 − 3𝑥 2 − 28x + 60 = 0.
38. The difference between simple interest and compound interest on a sum of money
invested for 3 years at 6% p.a. is ₹ 110.16. Find the sum.
39. Find the present value of an annuity of ₹ 2500 paid at the end of every 6 months
for 5 years if the rate of interest is 10% semi annually.
40. Venu gives 50% of his salary to his wife, 40% of the remaining he spends on
recreation, 20% of the remaining he gives to his daughter and still saves ₹ 12000.
What is Venu’s income? Also find the amount he gives his wife and daughter.
41. Find the image of the point (2, 4) on the line 𝑥 + 𝑦 − 10 = 0

PART- E
VII. Answer the following questions.
42. Find the sum to ‘n’ terms of the series 7 + 77 + 777 + ⋯ (6 marks)
(OR)
Show that the points (1, 1), (4, 1), (4, 4) and (1, 4) are the vertices of a square and
hence find the area.
43.A company finds that the production cost directly attributed to each book is ₹ 25
and the fixed cost is ₹ 10000. If each book can be sold for ₹ 35, find (4 marks)
(i) Cost function
(ii) Revenue function
(iii) Profit function
(iv) Break even point
(OR)
−3 3π 3 tan θ−4 cos θ 109
If sin θ = and < 𝜃 < 2𝜋, then prove that =
5 2 4 tan θ+3 cos θ 12

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