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

FOR KARNATAKA CLASS 11 PREPARATION

Karnataka 1st PUC
Model Question Paper
2027 for Basic Maths
(Paper 1)
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 1
SUBJECT CODE: 75

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BASIC MATHEMATICS

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Time: 3 hours Max. Marks: 80

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General Instructions:
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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.

SPART - A

I. Answer ALL the multiple choice questions: 10 x 1 = 10

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1. The conjugate of Z = 2+3i is

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. 2-3i
a) -2+3i b) -2-3i
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2+3𝑖

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2. If A = {1} and B= {2} then find B x A
a) {1,2} b) { } a c) {(1,2)} d) {(2,1)}
3 3
3. The value of (2𝑎 ) in its simplest form is
5𝑏

8𝑎9 2𝑎6 2𝑎9
a) b) c)
8𝑎6 d)
125𝑏3 5𝑏 5𝑏3
125𝑏

4. The value of 𝑙𝑜𝑔√3 27 is
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a) 6 b) 3 c) 7 d) 4

c.a) o108
5. The 6th term of the GP 3, 6, 12, … is
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ed)60
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s 6. The value of x in 7𝑥 − 5[𝑥 − {7 − 6(𝑥 − 3)}] = 3𝑥 + 1is ag
b) 96 c) 88

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7. If 5𝑥 − 3 < 3𝑥 + 1 when 𝑥 is real number then 𝑥 ∈
a) (−∞, 2) b) (2,∞) c) (−∞, 2] d) (−∞,−2)
8. The simple interest on ₹600 for 3 years 3 months at 4% p.a is
a) 78 b) 87 c) 67 d) 85

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9. The value of (1 − sin2 𝜃). sec2 𝜃 is
a) 0 b) 1 c)2 d) 3
10. The equation of 𝑥 − 𝑎𝑥𝑖𝑠 is
a) 𝑥 = 0 b) 𝑦 = 0 c) 𝑥𝑦 = 0 d) 𝑥 = 𝑦

II Match the following: 5x1=5

11. A B

a) Value of f(3) when f(x)= 3x-5 (i) -3/5
b) If average age of 10 boys is 13 years, (ii) 1/4
then sum of their Ages is
c) Convert 25% into fraction (iii) 50000
d) Slope of 3𝑥 + 5𝑦 − 11 = 0. (iv) 4
e) 𝑃∞ of Rs 5000 at 5% p.a is (v) 130
(vi)100000

III. Fill in the blanks by choosing appropriate answer from given options: 5x1=5

( 23, 2, 12, 1, 0, 120 )

12. LCM of 8, 10 and 12 is .
13. If (2x + 4, 3x + y) = (8, 0) then value of x is .
14. The 11th term of the A.P 3, 5, 7, 9,….. is .
15. The value of x in 2(x-3) = 9 +3(x-9)is .
16. Find the slope of the line with inclination 𝜋 .
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PART-B

IV. Answer any SIX questions: 6x2=12

17. Find the HCF of 12,15 and 18.
18. If f(x) = x-1 and g(x) = 2x2 -3 find fog(1) and gof(2)
19. If U= {a,b,c,d,e,f,g}, A= {a,b,c} and B = {b,d,f,g} find (A∩B)’
20. Which term of the GP 4, 6, 9, … is 81 ?
4

21. If a = 1, d = 7, Tn = 64, find n and Sn.
𝑥
22. Solve 𝑥+19 − 3 = .
5 4

23. Solve 3𝑥 − 7 > 2(𝑥 − 6) and 6 − 𝑥 > 11 − 2𝑥, 𝑥 ∈ 𝑅.
24. Prove that (1 + tan2 𝜃). (1 − sin2 𝜃) = 1 .
25. Find the equation of the line joining the points (−1, −3) and (6, 11).

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PART-C

V. Answer any SIX questions: 6x3=18

26. Prove that √2 is an irrational number
27. If A={4,6}, B={6,8,10} and C={8,10,12}. Verify Ax(B-C)=(AxB)-(AxC).

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𝑎 𝑎2+𝑎𝑏+𝑏2 𝑏2+𝑏𝑐+𝑐2 𝑐 𝑐2+𝑐𝑎+𝑎2

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𝑏
𝑥 𝑥

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28. Prove that ( )
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𝑥 ( 𝑎) =1
(𝑥𝑐)

29. If 𝛼 𝑎𝑛𝑑 𝛽 are the roots ofco2𝑥 + 3𝑥 + 7 = 0 find the values of + . m
𝑥𝑏 𝑥

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embetween 68°F and 77°F. What is the range in temperature in degree celcius
2 1

30. A solution is to beskept l a(C) if
𝛼 𝛽

la conversion formula is given by F = 𝐶 + 32 ? a g
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the celcius /Fahrenheit
9
5
31. Find the compound interest on ₹6000 for 3 years at 5% p.a if interest is calculated half yearly.
32. A schools runs in morning and afternoon shift and employees 40 teachers. The average salary of 25
teachers working in the morning shift is Rs. 2800/- and the average salary of teachers working the
afternoon shift is Rs. 3000/- find
(i) The average salary of the teachers in the school.

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(ii) The average salary is 5 teachers shifted from morning to afternoon shift.

e m− 4 sec 𝜃 = − .
las from the point (2, 4) and y axis.
5 247
33. If cot 𝐴 = 𝑎𝑛𝑑 𝜃 𝑖𝑠 𝑎𝑐𝑢𝑡𝑒. Show that 2 cosec 𝜃

34. Find the equation of the locus of all points g
12 30

a equidistant

PART-D

VI. Answer any FOUR questions: 4x5 =20

35. In a survey of 100 persons it was found that 28 read magazine A, 30 read magazine B, 42 read magazine

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Find the number of people who read none of the 3 magazines and .also find how many
C, 8 read magazine A and B, 10 read magazine A and C, 5 read magazines B and C while 3 read all the
threeomagazines.
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read only magazine C. Represent the result using Venn Diagram.

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a 37. Find an integral root between -3 and 3 by inspection and then using synthetic division solve the equation
12.567×15.674
using log table
0.5968×19.78

𝑥3 − 2𝑥2 − 29𝑥 − 42 = 0.
38. A person borrowed ₹65000 at 8% simple interest for 4 years and lent out the money for 10% compound
interest for 4 years. How much did the person gain?

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39. A company needs ₹1,50,000 at the end of 10 years from now. It would like to set a side an equal amount
each year from its profit. If the present market rate is 15%. How much should be the annual amount to be
invested?
40. Rohan sold to Raksha cinema tickets at a gain of 10%. Raksha sold it back to Rohan at a loss of 10%. In
the whole process Rohan gain Rs 55 in all . Find the price at which Rohan originally bought the tickets.
41. Find the equations of the medians of the triangle formed by the points (−1, 3), (−3, 5) and (7, −9).

PART-E

VII Answer the following questions:

42. Find the sum to n terms of the series 4 + 44 + 444 + … (6)
(or)

Verify that the points (1,6),(-1,-2),(4,1) and (-4,3) are the vertices of a rectangle.

43. A publishing house finds that the production of each book and the cost of the book are directly attributed.
If the cost of each book is Rs 30 and the fixed costs are Rs 15,000, and the selling price of each book is Rs
45, then determine: (4)
a. Revenue function
b. Cost function
c. Profit function
d. Break-even point function
(or)

cot2 30.sec 60.tan 45
Find x if 𝑥 sin 30 . cos2 45 =
cosec2 45.cosec 30

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