Karnataka 2nd PUC Model Question Paper 2024 for Basic Maths

MODEL
QUESTION PAPER
II PUC

2024

II PUC BASIC MATHEMATICS

(English Version)

Instructions: 1. Write the question numbers legibly in the margin.
2. Answer for the questions should be continuous.
3. Only the first written answers will be considered for Part-A

TIME DURATION: 3hr 15 min 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 15 marks, Part - D carries 25 marks and
Part - E carries 8 marks.
iii) Write the question number properly as indicated in the question paper.
PART-A

I. Choose the correct answer (Each question carries 1 mark): 5x1=5

1 2 4 3 −4 −1
1. If A= ( ) 𝑎𝑛𝑑 B= ( ) then, the value of A+B is
−1 3 −2 1 5 −2
4 −2 −3 4 −2 3 4 2 −3 −4 −2 −3
a) ( ) b) ( ) c) ( ) d) ( )
0 6 −4 0 8 −4 0 8 4 0 8 −4
2. If P(A1)=0.63 then the value of P(A) is
a) 0.47 b) 0.47
c) 0.73 d) 0.37
3. The fourth proportional of 4,5,24 is
a) 30 b) 28 c) 32 d) 26
3
4. If SinA=5 then the value of Cos2A is
7 8 6 9
a) 25 b) 25c) 25 d)25
x3 +4 5 2 6 9
5. The value of lim 1+ x is a) 2 b) 5 c) 5 d)5
𝑥→1
II. Match the following
8 2 𝑎
6. (i) The value of | | a) 𝑏
7 −2
(ii) If n C8 =n C12 then the value of n b)12
(iii)If 5:20=3:x then the value of x c)32
Sinax
(iv) lim ( bx ) d)-30
𝑥→0
(v) If S= 𝑡 3 − 6𝑡 2 + 9𝑡 + 8 then the initial velocity. e)9
f)20

III For question numbers 7 to 11 choose the appropriate answer from the answers given below. ( 181440 ,
𝟏
12, (pvr) 𝜦 ~q, (𝒔𝒊𝒏𝟔𝑨 − 𝒔𝒊𝒏𝟐𝑨), (p𝜦r)𝜦 ~q, 720) 5X1=5
𝟐

7. The number of arrangements that can be made with the letters of the word ‘MONDAY’ is ___________
8. The number of of 10 different precious stones be set to form a necklace is_______________
9. There are 4 routes to go from A to B and 3 routes to go from B to C then the number of ways to go from A
to C via B is _______________
10. The negation of “(pvr)→q” is_______________
11. The sum or difference of trigonometric functions of Cos4𝐴. Sin2A is_______________

III. Answer the following questions. (5 X 1 = 5)
12. Find the value of tan750
𝑥 1 0 −1 1
13. If [𝑦] = [2 0 −1] [1] Find x, y, z.
𝑧 0 1 −2 1
14. Write the triplicate ratio of 3:5.
15. 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 ∫ 2x(x 2 + 3)2 dX
1 𝑒 𝑥 +1
16. Evaluate: ∫0 dx
𝑒𝑥
PART-B

IV Answer any SIX of the following questions. (6 X 2 =12)
17. In how many ways can 6 people be chosen out of 10 people if one particular person is always included?
18. Find the number of triangles that can be formed out of 20 points in which 8 are collinear.
19. From a well shuffled pack of 52 cards, one card is drawn at random. Find the probability of getting either a
king or a queen card.
20. Three numbers are in the ratio 2:3:4. If the sum of their squares is 1856. Find the numbers.
21. If 16 men can construct a house in 90 days then how many days will 15 men construct a similar house?
22. BD and BG on a certain bill due after sometime are Rs.1250 and Rs. 50 respectively. Find the face value of
the bill?
23. Find the equation to a parabola with vertex (0,0), focus (0, -3) and directrix is y = 3.
24. Find focus, length of latus rectum of the parabola y2 =16x
𝜋
25. Evaluate: ∫04 𝑠𝑒𝑐 2 3𝑥 dx
2
26. Evaluate: ∫1 𝑙𝑜𝑔𝑥 dX
27. Find the area enclosed by the curve y=𝑥 2 +2x between the ordinates x=0 and x=2
PART-C

V Answer any FIVE of the following questions. (5 X 3 =15)

2 −1
28. 𝐼𝑓 𝐴 = ( ) then show that A2 − 4A+ 3I=0 where I is an identity matrix of order 2x2 & 0 is a null
−1 2

matrix.
1
29. The banker’s gain on a bill is 9 th of the banker’s discount, rate of interest being 10% per annum. Find the
unexpired period of the bill.
30. Sanjana invests Rs.3240 in a stock at 108 and sells when the price falls to 104. How much stock at 130 can
Sanjana buy now?

31. A shopkeeper bought a machine at a discount of 30% on the listed price of Rs. 24000. The shopkeeper
offers a discount of 10% on listed price to the customer. If 10% VAT is levied, find (i) amount paid by the
shopkeeper (ii) VAT to be paid by the shopkeeper.
dy
32. If 𝑥 = 𝑎𝑡2 and 𝑦 = 2𝑎𝑡, then find 𝑑𝑥.
33. The volume of a spherical ball is increasing at the rate of 4𝜋 𝑐𝑐/𝑠𝑒𝑐. Find the rate of increase of the radius
of the ball when the volume is 288𝜋 𝑐𝑐.
3
34. Evaluate: ∫ (𝑥+1)(𝑥+2)dx
PART-D

V Answer any FIVE of the following questions. (5 X 5 =25)

35. Solve the linear equations using the matrix method
3𝑥 + 𝑦 + 2𝑧 = 3, 2𝑥 − 3𝑦 − 𝑧 = −3, 𝑥 + 2𝑦 + 𝑧 = 4
4 21
36. Find the coefficient of x-7 in (√x − x3 ) .
𝑥−1
37. Resolve (𝑥+2)2(𝑥+4) into partial fractions.
38. Verify whether the proposition (𝑝 ∧∼ 𝑞) ∧ (∼ 𝑝 ∨ 𝑞) is a contradiction or not.
39. An aircraft manufacturer supplies aircraft engines to different airlines. They have just completed an initial
order for 30 engines involving a total of 6000 direct labor hours at Rs. 20 per hour. They have been asked
to bid for a prospective contract for a supply of 90 engines. It is expected that there will be 80% learning
effect. Estimate the labor cost for the new order.
40. 55. Solve the LPP graphically: Maximize 𝑍 = 6𝑥 + 8𝑦
Subject to constraints 4𝑥 + 2𝑦 ≤ 20, 2𝑥 + 5𝑦 ≤ 24 𝑥, 𝑦 ≥0
(𝑆𝑖𝑛5𝐴+𝑆𝑖𝑛𝐴)+(𝑆𝑖𝑛4𝐴+𝑆𝑖𝑛2𝐴) =tan3A
41. 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 (𝐶𝑜𝑠5𝐴+𝐶𝑜𝑠𝐴)+𝐶𝑜𝑠4𝐴+𝐶𝑜𝑠2𝐴)

42. Find the equation of the circle passing through the points (1, 1), (-2,2), (-6,0)
𝑥 2 −9
43. Evaluate: lim [ ]
𝑥→3 √3𝑥+7−√5𝑥+1
PART-E

V Answer any TWO of the following questions. (2 X 4 =8)

44. The observer from the top of a cliff, observes the angles of depression of two boats in the same vertical
plane are 300 and 450 . If the distance between the boats is 100 meters,
find the height of the cliff.
𝑚
45. If y = (𝑥 + √𝑥 2 + 1) , show that (𝑥 2 + 1)𝑦2 + 𝑥𝑦1 − 𝑚2 𝑦 = 0.
46. The total revenue(R) and the total cost(C) function of a company are given by
R(Q) =300Q-Q2 and C(Q)=20 +4Q find the equilibrium output.

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