Karnataka 2nd PUC Model Question Paper 2025 for Basic Maths

ACADEMIC YEAR

2025

Karnataka
Board
Model Paper

BASIC MATHEMATICS(75) BLUE PRINT MODEL PAPER-1 2024-2025

REMEMBER UNDERSTAND HOTS
CHAPTERS Hours Marks
VSA(1) SA(2) SA(3) LA(5) VSA(1) SA(2) SA(3) LA(5) VSA(1) SA(2) SA(3) LA(4) LA(6)
1.Matrices and Determinants 13 13 1 1 1 1 2
2.Permutations and
8 8 1 1 1 1 1
combinations
3. Probability 5 3 1 1
4.Binomial Theorem 6 4 1
5.Partial Fractions 4 5 1
6. Mathematical Logic 6 6 1 1
7. Ratios and Proportions 10 8 2 1 1 1
8. Bill Discounting 6 5 1 1
9. Stocks and shares 4 3 1
10. Learning Curve 4 5 1
11. Linear Programming
6 5 1
Problems
12. Sales Tax and Value Added
4 3 1
Tax
13.Heights and Distances 4 4 1
14. Compound, Multiple, Sub-
multiple angles & 8 7 1 1 1
Transformation Formulae
15. Circles 6 6 1
16. Parabola 4 4 1 1 1
17. Limits and Continuity of a
8 7 1 1
function
18. Differential Calculus 10 8 1 1 1
19. Application of Derivatives 8 5 1 1
20. Indefinite Integrals 8 5 1 1 1
21. Definite Integrals and its
8 6 1 1 1
application to Areas
TOTAL 140 120 11 4 15 20 4 12 9 15 5 2 3 8 12

BASIC MATHEMATICS(75) BLUE PRINT MODEL PAPER-1 2024-2025

Question Type No. Of Questions Marks
VAS(1) 20/20 20/20
SA(2) 06/09 12/18
SA(3) 06/09 18/27
LA(4) 01/02 04/08
LA(5) 04/07 20/35
LA(6) 01/02 06/12
Total 38/49 80/120

Note: * 6 marks question from circles on concyclic and Theorem 1 from limits.
* 4 marks question from Binomial Theorem and Heights and distances.
* Proof and problems on properties of determinants are excluded.

GOVERNMENT OF KARNATAKA
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
II PUC MODEL QUESTION PAPER-1 (2024-2025)
BASIC MATHEMATICS (75)
TIME: 3 Hours Max.
Marks: 80

Instructions:
i. The question paper has 5 Parts A, B, C, D and E. Answer all the Parts.
ii. Part - A carries 20 marks, Part - B carries 12 marks, Part - C carries 18 marks, Part -
D carries 20 marks and Part - E carries 10 marks.
iii. Write the question number properly as indicated in the question paper.

PART-A

I. Answer ALL the multiple-choice questions: 𝟏𝟎 × 𝟏 = 𝟏𝟎
3 𝑥
1. If | | = −2 then the value of 𝑥 is
4 5
17 17 15 13
a) b) − c) d)
4 4 4 4

2. If nC8 = nC12 then the value of n is
a) 8 b) 12 c) 20 d) 10
3. If 𝑃(𝐴′ ) = 0.65, then 𝑃(𝐴) 𝑖𝑠
a) 1 b) 0 c) 0.35 d) 0.65
4. Negate: ~𝑝 → 𝑞
a) 𝑝 → ~𝑞 b) ~𝑝 ∧ ~𝑞 c) ~𝑝 ∧ 𝑞 d) 𝑝 ∧ 𝑞
5. The mean proportion of 9 𝑎𝑛𝑑 16 is
a) 144 b) 25 c) 12.5 d) 12
6. The value of 3 sin 100 − 4 sin3 100 is
1 1 √3
a) b) c) d) 0
2 √2 2

7. If the focus of the parabola is (0, −6) 𝑡ℎ𝑒𝑛 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑑𝑖𝑟𝑒𝑐𝑡𝑟𝑖𝑥 is
a) 𝑥 = 6 b) 𝑥 = −6 c) 𝑦 = 6 d) 𝑦 = −6
𝑑𝑦
8. If 𝑦 = log 𝑒 𝑒 𝑡ℎ𝑒𝑛 𝑖𝑠
𝑑𝑥
1
a) −1 b) 0 c) 𝑒 d)
𝑒

1

1
9. Evaluate: ∫ 𝑑𝑥
5𝑒 −𝑥
𝑒𝑥 1
a) 𝑒 𝑥 + 𝐶 b) +𝐶 c) 5𝑒 𝑥 + 𝐶 d) +C
5 5𝑒 𝑥
1
10. Evaluate: ∫0 𝑥 2 𝑑𝑥
1 1
a) 1 b) 0 c) d)
2 3

II. Match the following: 𝟓×𝟏=𝟓
11. A B
a) 1 −1 i) √3 + 1
If A = [ ] then the value of |𝐴| is
2 4
2√2
b) The value of 8𝑃3 is ii) 6
c) The value of 𝑥 in 5: 15 = 3: 𝑥 iii) 336
d) sin 15° is iv) 9
e) x3 +4 v)
The value of lim is √3 − 1
𝑥→1 1+ x
2√2
vi) 5
2

III. Fill in the blanks by choosing appropriate answer from given options: 𝟓 × 𝟏 = 𝟓
1
(log 𝑥 + 𝑐, 0, 9, 2, 24, − 2 + 𝑐)
𝑥
12. A square matrix A is a singular matrix if |𝐴| = ________
13. The number of ways 5 people can be seated around a table is ________.
14. The third proportional of 4 and 6 is __________
15. If the length of the latus rectum of the parabola 𝑥 2 = 4𝑘𝑦 𝑖𝑠 8, then the value of k is
___
1
16. ∫ 𝑥 𝑑𝑥 = _______

PART-B

IV. Answer any SIX questions. 𝟔 × 𝟐 = 𝟏𝟐

2 3 1 1 −2 4
17. If 𝐴 = [ ] 𝑎𝑛𝑑 𝐵 = [ ] 𝑓𝑖𝑛𝑑 2𝐴 − 3𝐵
1 −2 0 1 3 2
18. Find the number of parallelograms that can be formed from a set of 6 parallel lines
intersecting another set 4 of parallel lines.
1 1 7
19. If 𝑃(𝐴) = , 𝑃(𝐵) = , 𝑃(𝐴 ∪ 𝐵) = , 𝑓𝑖𝑛𝑑 𝑃(𝐵|𝐴)
2 3 12
2

20. What must be added to the terms of the ratio 2: 3 so that it becomes 5: 6
21. BD and BG on a certain bill due after sometime are ₹1250 and ₹50 respectively.
Find the face value of the bill.
22. Find the equation of the parabola whose vertex is (0, 0) 𝑎𝑛𝑑 𝑑𝑖𝑟𝑒𝑐𝑡𝑟𝑖𝑥 𝑖𝑠 𝑦 = 2
𝑑𝑦
23. If 𝑦 = 𝑥 sin 𝑥 , 𝑓𝑖𝑛𝑑
𝑑𝑥
24. The total revenue function is given by 𝑅 = 400𝑥 − 2𝑥 2 and the total cost function
given by
𝐶 = 2𝑥 2 + 40𝑥 + 4000 find the marginal revenue and marginal cost function
25. Find the area enclosed by the curve 𝑦 = 𝑥 2 + 2𝑥 between the ordinates 𝑥 =
0 𝑎𝑛𝑑 𝑥 = 2

PART-C

V. Answer any SIX questions. 𝟔 × 𝟑 = 𝟏𝟖
2 −1
26. If 𝐴 = [ ] then show that: 𝐴2 − 4𝐴 + 3𝐼 = 0
−1 2
27. Find the number of permutations of the letters of the word ‘MISSISSIPPI’. How
many of these
a) all 4S’s are together
b) Begin with MISS
28. Monthly incomes of A and B are in the ratio 2: 3 and their monthly expenditures are in
the ratio 3: 5. If each saves ₹100 per month, find the monthly incomes of A and B
29. A bill for ₹3500 due for 3 months was drawn on 27 March 2012 and discounted on 18
April 2012, at the rate of 7% p.a. Find the Bankers Discount and discounted value of
the bill.
30. Which is the better investment: 7.5% stock at 125 or 5% stock at 75
31. Bharath bought a shirt for ₹336 including 12% sales tax and a neck tie for ₹110
including 10% sales tax. Find the printed price of shirt and neck tie together.
32. A circular patch of oil spreads on water, the area growing at the rate of 16𝑐𝑚2 /𝑚𝑖𝑛.
How fast are the radius and the circumference increasing when the diameter is 12cms?
1
33. Evaluate:∫ 𝑑𝑥
𝑥(𝑥+2)
1 2𝑥+5
34. Evaluate:∫0 2 𝑑𝑥
𝑥 +5𝑥+3

PART-D

VI. Answer any FOUR questions. 𝟒 × 𝟓 = 𝟐𝟎
35. Solve by matrix method: 𝑥 + 𝑦 + 𝑧 = 5, 2𝑥 + 𝑦 − 𝑧 = 2 , 2𝑥 − 𝑦 + 𝑧 = 2
2𝑥 2 +10𝑥−3
36. Resolve into partial fraction: (𝑥+1)(𝑥−3)(𝑥+3)
37. Verify whether the proposition (~𝑝 ∧ 𝑞) ∧∼ 𝑟 is a Tautology, contradiction or
neither.

3

38. An engineering company has 80% learning effect and spends 1000 hours to produce 1
lot of the product. Estimate the labour cost of producing 8 lots of the product if the
labour cost is ₹100 per hour.
39. Maximize:𝑍 = 5𝑥 + 3𝑦
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑡ℎ𝑒 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠 3𝑥 + 5𝑦 ≤ 15, 5𝑥 + 2𝑦 ≤ 10, 𝑥 ≥ 0, 𝑦 ≥ 0
3
40. Prove that: cos 100 cos 300 cos 500 cos 700 =
16
𝑚
41. If 𝑦 = (𝑥 + √1 + 𝑥 2 ) 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 ∶ (1 + 𝑥 2 )𝑦2 + 𝑥𝑦1 − 𝑚2 𝑦 = 0

PART-E

VII. Answer the following questions.
𝑥 𝑛 −𝑎𝑛
42. P.T: lim (
𝑥−𝑎
) = 𝑛𝑎𝑛−1 , for all rational values of n (6 marks)
𝑥⟶𝑎
(OR)
Show that the points (0, 0), (1, 1) , (5, −5) 𝑎𝑛𝑑 (6, −4) 𝑎𝑟𝑒 𝑐𝑜𝑛𝑐𝑦𝑐𝑙𝑖𝑐

43. The angle of elevation of an object from a point 100m above a lake is 300 and angle
of depression of its image in the lake is 450 . Find the height of the object above the
lake.
(OR)
5
Find the value of (0.99) using Binomial theorem, upto 4 decimal places. (4 marks)

4

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