Karnataka 1st PUC Model Question Paper for Basic Maths

SAMPLE PAPER

Karnataka
Board
Model Paper

Model Question Paper

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
1. The conjugate of 𝑧 = −1 − 𝑖 is
a) 1 − 𝑖 b) −1 + 𝑖 c) 1 + 𝑖 d) −𝑖
2. If 𝐴 ⊂ 𝐵 𝑡ℎ𝑒𝑛 𝐴 ∪ 𝐵 is
a) 𝐴 b) ∅ c) 𝐵 d) 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒𝑠𝑒
0
3. Simplify : 5(5 ) + (52 )0 .
a) 6 b) 0 c) 26 d) 2
4. 𝑇ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 log 5 125 𝑖𝑠
a) 1 b) 0 c) 2 d) 3
5. Geometric mean of 2 and 8 is
a) 5 b) 4 c) 3 d) 2
6. If 𝛼 𝑎𝑛𝑑 𝛽 are the roots of the quadratic equation 3𝑥 2 − 6𝑥 + 4 = 0, 𝑡ℎ𝑒𝑛 𝛼 + 𝛽 =
a) −2 b) −4/3 c) 2 d) 4/3
7. The solution of 2(𝑥 − 1) < 𝑥 + 5 is
a) (7, ∞) b) (−7, ∞) c) (−∞, 7) d) (−∞, − 7)
8. If 𝑅 = 12%, 𝑤ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑑𝑜𝑢𝑏𝑙𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑 𝑎𝑠 𝑝𝑒𝑟 𝑟𝑢𝑙𝑒 𝑜𝑓 72
a) 6 𝑦𝑒𝑎𝑟𝑠 b) 7 𝑦𝑒𝑎𝑟𝑠 c) 8 𝑦𝑒𝑎𝑟𝑠 d) 5 𝑦𝑒𝑎𝑟𝑠

1

𝜋
9. If 𝜃 = 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 𝑖𝑠
4
1
a) 1 b) 0 c) 2 d)
2

10. (cos 𝐴 + sin 𝐴)2 + (cos 𝐴 − sin 𝐴)2 =
1
a) 1 b) 0 c) d) 2
2

II. Match the following: 𝟓×𝟏=𝟓
11. A B
a) If 𝐴 = ∅ then 𝑛[𝑃(𝐴)] is i) 11
−
5
b) 𝑃∞ 𝑜𝑓 ₹3000 𝑎𝑡 15% 𝑝. 𝑎 𝑖𝑠 ii) 3
10
c) If the average age of 10 boys is 13, then sum of their age iii) 1
d) 𝐸𝑥𝑝𝑟𝑒𝑠𝑠 30% 𝑖𝑛 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 iv) 30000
e) x-intercept of the line 5𝑥 − 7𝑦 + 11 = 0 is v) 20000
vi) 130

III. Fill in the blanks by choosing appropriate answer from given options : 𝟓×𝟏=𝟓

(16, 5, 4, 2, 168, 8/5)
12. LCM of 12, 21 and 24 is
13. If 𝐴 = {2,3} , 𝐵 = {3,4}, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑓𝑟𝑜𝑚 𝐴 𝑡𝑜 𝐵 𝑖𝑠 _______
3 13
14. 𝐼𝑓 , 𝐾, 𝑎𝑟𝑒 𝑖𝑛 𝐴𝑃, 𝑡ℎ𝑒𝑛 𝐾 = ________
5 5

15. The sum of 6 times a number and 5 times the number is 55, then the number is ________

16. Distance between the parallel lines 5𝑥 + 12𝑦 + 7 = 0 𝑎𝑛𝑑 5𝑥 + 12𝑦 − 19 = 0 is _____

2

PART-B

IV. Answer any SIX questions. 𝟔 × 𝟐 = 𝟏𝟐
17. Find the numbers of positive divisors of 960
18. Give an example of a relation which is symmetric but not reflexive and not transitive
19. If 𝑓: 𝑍 → 𝑍, 𝑓 = {(1,1), (2,3), (0, −1)} defined by 𝑓(𝑥) = 𝑎𝑥 + 𝑏, 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 𝑎 𝑎𝑛𝑑 𝑏
20. How many terms of AP -3, -5, -7,…… amount to -120?
1 1
21. Insert 3 H.M’s between 𝑎𝑛𝑑
4 12
22. The sum of three consecutive numbers is 186. Find the numbers?
23. Find all pair of consecutive even integers which are greater than 5 and their sum must be less
than 23
24. If sin 𝑥 + sin2 𝑥 = 1, 𝑡ℎ𝑒𝑛 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡: cos 2 𝑥 + cos 4 𝑥 = 1
25. Find the slope and x-intercept of the line 5𝑥 − 7𝑦 + 11 = 0

PART-C

V. Answer any SIX questions. 𝟔 × 𝟑 = 𝟏𝟖
26. Find the greatest integer which divides 42, 52, 86 leaving remainder 6, 4, 2 respectively.

27. Write all the proper subsets of {2, 3, 4}
2𝑛+1 +2𝑛−1
28. Simplify:
2𝑛 +2𝑛+2
𝛼2 𝛽2
29. If 𝛼 𝑎𝑛𝑑 𝛽 are the roots of the equation 2x2 – 5x + 7 =0 then evaluate + .
𝛽 𝛼
5−2𝑥 𝑥
30. Solve: < − 5, 𝑥 ∈ ℝ, Represent on a number line.
3 6
31. A person deposits ₹10000 in a bank. If the bank offers compound interest at the rate of 5% for
the first 3 years, 7% for the next 2 years and 8% from the sixth year onwards. What is the
amount after 10 years?

32. The average height of 12 girls in a class is 4 feet and the average height of 8 boys is 5 feet.
Find the combined average height of the class.

33. P.T: sec 6 𝑥 − tan6 𝑥 = 1 + 3 tan2 𝑥 sec 2 𝑥

34. Find the equation of the locus of points such that the sum of its distance from (0,3) and (0,-3)
is 8.

3

PART-D

VI. Answer any FOUR questions. 𝟒 × 𝟓 = 𝟐𝟎
35. In a certain college with 500 students, 300 take milk and 251 take tea. Assuming that every
student takes at least one of the two, find how many will take both milk and tea, milk only
and tea only. Represent through a Venn diagram
√6.43×0.5789
36. Using log table find 3
(13.46) ⁄2
37. A certain two digit number is 4 times the sum of the digits. If 18 is added to the number, the
digits get interchanged. Find the numbers
38. A machine depreciates at 10% of its value at the beginning of the year. The cost and the scrap
value realized at the time of sale being ₹23240 and ₹9000 respectively. For how many years
the machine was put to use?
39. A person repaid his loan in 10 equal annual installments starting from the beginning of the
first year. If each installment was ₹6000 and compound interest charged was 12% p.a. What
was the amount borrowed.
40. Ram Singh purchased two camels for ₹18000 and ₹15000 respectively. He sold them at a loss
of 15% and gain of 19% respectively. Find the selling price of each of the camels. Also find
the overall loss or gain percent in the transaction.
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 4 + 44 + 444+……. (6 marks)
(OR)
Show that the points (2, −2), (8, 4) , (5, 7) 𝑎𝑛𝑑 (−1, 1) the vertices of a rectangle.

43. If the sale price per unit is ₹3, the variable cost per unit is ₹2 and the fixed cost is ₹4500 find
the Cost function, Revenue function, Profit function and Break Even Point. (4 marks)
(OR)
12 3 𝑠𝑖𝑛 𝐴−2 cos 𝐴
If tan 𝐴 = 𝑎𝑛𝑑 2700 < 𝐴 < 3600 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓
13 9 cos 𝐴+4 𝑠𝑖𝑛 𝐴

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