Karnataka 2nd PUC Model Question Paper 2027 for Basic Mathematics (Paper 4)

FOR KARNATAKA CLASS 12 PREPARATION

Karnataka 2nd PUC
Model Question Paper
2027 for Basic
Mathematics (Paper 4)
EXAM YEAR TYPE SUBJECT

Karnataka Class 12 2027 Sample Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

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GOVERNMENT OF KARNATAKA
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
6TH CROSS, MALLESHWARAM, BENGALURU – 560 003
II PUC MODEL QUESTION PAPER – 4 (2026 -27)
SUBJECT: BASIC MATHEMATICS MAXIMUM MARKS:80

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TIME: 03 HOURS NUMBER OF QUESTIONS:42
Instructions: m .co
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The question paper has 5 Parts A, B, C, D and E. Answer all the Parts.
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Part - A carries 20 marks, Part - B carries 12 marks, Part - C carries 18 marks,
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Part - D carries 20 marks and Part - E carries 10 marks.
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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 
1. If  2 x 2  4   3 then x is
 2 
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1 3 3
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(A) (B)  (C) (D) 
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4 4 4 4

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2. The number of ways 9 flowers of different colours
9! 8!
(A) 9! (B) 10! (C) (D)
2 2
3. Two coins are tossed simultaneously. The probability of getting exactly two heads is
1 1 3
(A) 1 (B) (C) (D)
2 4 4
4. The converse of p  q is
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pq (B) p  q (C) q  p q p
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(A) (D)

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5. The fourth proportional of 6, 12 and 15 is
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(D)l2
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(B) 4 (C) 30
l
ag 6. The value of sin 80 cos10  cos80 sin10 is
(A) -1 (B) 1 (C) 0 (D) Not defined
7. The equation of the parabola whose focus  3,0  is
(A) x 2  12y (B) x 2  12y (C) y2  12x (D) y2  12x
dy
8. If x  y  0 then is
dx
1

om .
(A) x (B) (C) 0 (D) 1

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2

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9. The value of  x 5dx is
x5 x4 x6
(A) 5x 4  c (B) c (C) c (D) c
5 4 6
10. The value of  e3 4x dx is
e 3 4 x e 3 4 x
(A) 3e34x  c (B) 4e34x  c (C) c (D) c
4 4

II. Match the following: 𝟓×𝟏= 𝟓

11. A B
x 3
a) If  0 then the value of x is i) 252
12 x

b) The numbers ways a committee of 5 can
be chosen from 10 students is ii) 6
c) The third proportional of 4 and 6 is iii) 6
d) The value of tan  45  A  .tan  45  A  is iv) 2
sin 4x
e) The value of lim is v) 1
x 0 sin 2x
vi) 9

III. Fill in the blanks by choosing appropriate answer from given options: 𝟓 × 𝟏 = 𝟓
( 𝟕, 𝟏, 𝟐, 𝟔𝟎, 𝟐𝟎, 𝟑)

 2a  4 5 
12. If the matrix  is skew-symmetric then the value of ‘a’ is ____.
 5 0 

13. The numbers of 3-digit numbers that can be formed using the digits 1, 2, 5, 6, 8 is____.
14. The antecedent of 7 : 2 is ____.
15. If the length of the latus rectum y2  4kx is 12, then the value of k is____.

2
16. The value of  cos x dx is____.
0

PART-B

IV. Answer any SIX questions. 𝟔 × 𝟐 = 𝟏𝟐
2  x
17. If A    . Find A  A .
 x 7 
18. In how many ways can 6 people can be chosen out of 10 people if one particular person is always
included?
2 1
19. If A and B are mutually exclusive events with P  A   , P  A   . Find P  A  B .
5 7

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gla is 25. Find the quantities.
se 20. A ratio in the lowest terms is 3:8 . If the difference between the aquantities
21. Find the true discount on Rs. 1380, due 1½ years after, at 10% p.a.
22. Find the equation of the parabola given that its focus is (-4 ,0 ) and directrix is x = 4.
dy cos x
23. If y  sin x  sin x  ........ . Prove that  .
dx 2 y  1
24. The total cost function is given by C = q3 – 3q2 + 15q + 27 where q is the output. Find the marginal cost
and fixed cost.
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25. Find the area bounded by the curve x 2  8 y, y axis and the abscissae y  3, y  6 .
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l as PART-C
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V. Answer any
a g SIX questions. 𝟔 × 𝟑 = 𝟏𝟖
26. Solve by Cramer’s rule: 2x + y = 1, x − 3y = 4.
27. Find the number of words can be formed by using all the letters of the word ‘RAINBOW’
a) How many of them begin with R and end with W
b) How many of them end with BOW
28. Two taps can separately fill a tank in 12 minutes and 15 minutes respectively. The tank when full can

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emptied by a drain tap in 20 minutes. When the tank was empty, all the three taps were opened
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29. For ₹512.50 due 6 months at 15% p.a. Find the s
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simultaneously. In what time will the tank be filled up?
e present value and discounted value
la reinvests the proceeds in 9% stock. If Prathik’s income
true
30. Prathik sells out₹6000 of 7.5% stock at 108gand
a
increases by ₹270, at what price did Prathik buy 9% stock?
31. A shopkeeper sells an item at the price of ₹810 including ST of 8%. What should a customer pay for the
same item, if the ST is reduced to 6%.
32. A spherical balloon is being inflated so that its volume is increasing at the rate of 30 cc/min. How fast its
area increasing when its volume is 36π cc.
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33. Evaluate:∫ dx
o m (x+1)(x+2)

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c
. ∫ x e dx 2 𝑥
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34. Evaluate: 1
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PART-D
VI. Answer any FOUR questions. 4× 𝟓 = 𝟐𝟎
35. Solve by matrix method: 3𝑥 + 𝑦 + 2𝑧 = 3, 2𝑥 − 3𝑦 − 𝑧 = −3 , 𝑥 + 2𝑦 + 𝑧 = 4
9
36. Resolve into partial fraction: (x+1)(x+2)2
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37. Verify whether the proposition "(p ∧∼ q) → (p ∧ q)" is a Tautology, contradiction or neither.
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38. XYZ Company supplies water tankers to the Government. The first water tanker takes ₹20,000 labour
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hours. The government auditors suggest that there should be a 90% learning effect rate. The management
expects an order of 8 water tankers in the next year. What will be the labour cost if the company will
incur at the rate of ₹20 per hour.
39. Maximize: Z = 2.5x + y
Subject to the constraints x + 3y ≤ 12, 3x + y ≤ 12 and x ≥ 0, y ≥ 0
sin 5A+sin 4A+sin 2A+sin A
40. Prove that: = tan 3A
cos 5A+cos 4A+cos 2A+cos A

41. If y = log(x + √x 2 + 1) show that (x 2 + 1)y2 + xy1 = 0

PART-E
VII. Answer the following questions.
xn −an
42. a) P.T: lim ( x−a ) = nan−1 , for all rational values of n (6 marks)
x⟶a

(OR)

Show that the points (2, −4), (0, 0) , (3, −1) and (3, −3) are concyclic.

b) The angle of elevation of the top of a tower from the base and top of a building are 60° and 45°
respectively. The building is 20m high. Find the height of the tower. (4 marks)
(OR)
Find the value of (1.02)5 using Binomial theorem, upto 4 decimal places.

PART-F
(Only for visually challenged students)
39. A firm manufactures two types of products A and B sells them at a profit at ₹2 on one unit of A and ₹3
on one unit of B. Each product is processed on 2 machines M1 and M2. Each A requires 1 hour of
on M1 and 2 hours on M2. Each B requires 1hour of time on M1 and 1 hour on M2. The machine M1 is
available for not more than 6 hours and machine M2 is available for 10 hours, per day. Formulate an
LPP to find how many units of the 2 products must be produced so that the profit is maximized.

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