Name of the Organisation : Department of Pre University Education, Karnataka
Exam : I PUC Basic Mathematics Exam
Subject : Basic Mathematics
Document Type : Model Question Paper
Website : https://pue.karnataka.gov.in
Karnataka I PUC Basic Mathematics Model Question Paper
Department of Pre University Education, Karnataka Basic Mathematics Model Question Paper I PUC for the year 2021-22
Related / Similar Question Paper : Karnataka I PUC Home Science Model Question Paper 2021-22
Karnataka I PUC Basic Mathematics Questions
PART – A
I. Answer any TEN questions
1. Write the imaginary part of the complex number –3–4i
2. Write A = {4, 8, 12 …….} in rule from
3. Simplify (81/256)1/4
4. Solve for x : logx 625 4=
5. Find the 5th element of a H.P : 1/3, 1/5, 1/7 , , ……
6. Solve: 3(x + 5) – 25 = 9 + 2 (x – 7).
7. Find the nature of roots without solving the equation 2×2 + 6x + 3 = 0.
8. What is the simple interest on `650 for 14 weeks at 6% p.a?
9. Define perpetuity?
10. The profit of a business firm for 5 years are `17,598, `20,703, `10,085, `25,375 and `16,315. Find the average profit?
11. Convert the ratio 3 : 5 into percentage.
12. Express 135º in radian measure.
13. If A = 60º, verify cos2A = co2A – sin2A
14. Find the distance between the points (5, 8) and (9, 9)
15. Find the slope of the line 3x – 2y + 1 = 0.
PART – B
II. Answer any TEN questions
16. Find the number of divisors of 672.
17. Find the numbers which when divided by 36, 40 and 48 leaves the same remainder 5.
18. If A × B = {(–1, a), (–1, b), (–2, a), (–2, b)} Find A and B.
20. If the second term of an AP is 4 and tenth term is 20, find the 15th term.
21. Insert 3 GM’s between –4 and –64.
23. Solve by Formula method: 3×2 – x – 10 = 0.
24. Solve 3x – 2 < 2x + 1 (x R). Represent on the number line.
25. What sum will amount to `6525 at 10% p.a. compounded annually for 13 years?
26. The average score of 20 boys is 60% and the average score of 30 girls is 70%. Find the combined average.
27. If the cost price of 10 articles is equal to the selling price of 9 articles, find the gain percent?
28. A shopkeeper buys 50 pencils for `80 and sells them at 40 pencils for `90. Find his gain or loss percent?
30. Find the value of cos 1125º.
31. Find the co-ordinates of the centroid of the triangle whose vertices are (2, 3), (–5, 2) and (1, 7).
32. Find the equation of the line passing through (4, 3) and with slope 2.
33. Find the equation of the line joining the points (–1, –2) and (–5, –2).
PART – C
III. Answer any TEN questions
34. Prove that 2 is an irrational number.
35. If A = {4, 6}, B = {6, 8, 10}, C = {8, 10, 12} then verify A × (B – C) = (A × B) – (A × C).
36. A relation R is defined on set of integers by R = {(x, y) : x – y is a multiple of 5}. Show that R is an equivalence relation on Z.
39. If x y z= = =log , log , log2 9 79 7 4 , show that xyz = 2.
40. Find the three numbers in GP whose sum is 39 and their product is 729.
41. The age of the father is four times that of the son. 5 years ago, the age of the father was 7 times that of his son. Find their present ages.
42. Find all pair of consecutive even integers which are greater than 5 and their sum must be less than 23.
43. Samarth bought a walkman for `1800. If it depreciates at the rate of 15% per year, how much is it worth after 3 years?
44. In what time 800 will amount to ` 882 at 10% p.a. interest compounded half yearly.
45. The average weight of a group containing 25 persons is 70 kg. 5 persons with an average weight 63 kg leave the group and 4 persons with weight 72 kg, 78kg, 70kg and 73 kg joins the group. Find the average weight of the new group.
46. The cost of T.V increased by 20% and then decreased by 5% find the percentage increase in the original cost.
49. If the area of the triangle whose vertices are A(x, y), B(1, 2) and C(2, 1) is 6. Show that x + y = 15.
50. 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 (–1, 5) and (2, 4).
51. Derive equation of the line in the intercept form.
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