Karnataka Second PUC Basic Mathematics of March, 2010 Question Paper
Below is The Karnataka Second PUC Basic Mathematics Question Paper of March 2010 & Download This Question Paper in PDF Format.
Karnataka Second PUC Basic Mathematics of March, 2010
Time : 3 Hours 15 Minutes Max. Marks : 100
English Version
Instructions :
i) The question paper consists of five Parts – A, B, C, D and E. Answer all the Parts.
ii) Part – A carries 10 marks, Part – B carries 20 marks,
Part – C carries 40 marks, Part – D carries 20 marks and
Part – E carries 10 marks.
iii) Write the question numbers properly as indicated in the
question paper.
PART – A
Answer all questions : 10 × 1 = 10
1. Write the converse of the proposition ‘ If x ( A ∩ B ) then x A and x B ’.
2. Find n if € n P3 = 24.
3. Evaluate : € 2003 2005
2006 2008 .
4. Find the mean proportional to 9 and 16.
5. The average marks of 65 students is 60. Another group of 15 students
have an average marks of 65. What is the average marks of 80 students ?
6. A bill drawn for 3 months was legally due on 06. 07. 2009. Find the date
of drawing of the bill.
7. If the length of the latus rectum of the parabola € x2 = 4 ky is 8, find k.
8. Evaluate : € lim x → −3 x3 + 27 x + 3.
9. If € y = e x , find € dy/dx.
10. Evaluate : € x x + 4 dx ∫ .
PART – B
Answer any ten questions : 10 × 2 = 20
11. If ( p ∧ ~ q ) → r is a false proposition, find the truth values of p, q and r.
12. In how many ways can the 7 colours of the rainbow be arranged so that
the red and the blue colours are always together ?
13. One ticket is drawn at random from a bag containing 30 tickets numbered
1 to 30. Find the probability that it is a multiple of 3 or 5.
14. Solve the following equations by Cramer’s rule : x + 2y = 4 , 2x + 5y = 9
15. Find A and B if € 2A + B = 2 3 1 1 4 0 & € 3A + B = 2 3 2 1 9 −5
16. 2 numbers are in the ratio 3 : 5. If 7 is added to each of them, the new ratio will be 4 : 5. Find the numbers.
17. Find the equation of the circle two of whose diameters are x + y = 6 and x + 2y = 4 and radius = 10 units.
18. If the function € f x ( ) = 1 + 3x ( ) 1 x , x ≠ 0 k, x = 0 is continuous at x = 0, then find the value of k.
19. If € y = x + x + x + ... ∞ , then prove that € dy/dx = 12y − 1.
20. If € s = t 3 − 6t 2 + 9t + 8, where s is the distance travelled by a particle in t seconds, then find i) the initial velocity and & ii) when the body will be at rest momentarily.
21. Evaluate : € x2 ∫ . log x dx
22. Evaluate : € x2 + 2x + 3 ( ) 2 x + 1 ( ) dx 0 1 ∫ .
PART – C
I. Answer any three questions : 3 × 5 = 15
23. Verify : ( p ↔ q ) ≡ [ ( p → q ) ∧ ( q → p ) ]
24. In how many ways can a committee of 2 teachers and 3 students be
formed out of 10 teachers and 20 students ? How many of these will
i) include one particular teacher
ii) exclude one particular student ?
25. Resolve into partial fractions : € x + 3 x − 1 ( ) x2 − 4 ( ) .
26. Solve the following equations by matrix method :
x + y – 2z = 0
2x – y + z = 2
x + 2y – z = 2.Code No. 75 12
II. Answer any two questions : 2 × 5 = 10
27. The expenses of a hostel are partly constant and partly varying with
the number of boys. The expenses were Rs. 55,000 when there are
50 boys and Rs. 64,800 when there are 60 boys. If the hostel admits
80 boys, then what will be the expenses ?
28. How much must be invested in 14·25% stock at 98 to produce the
same income as would be obtained by investing Rs. 9,975 in 15%
stock at 105 ?
29. A company requires 150 hours to produce the first 10 units at
Rs. 50 per hour. The learning effect is expected to be 80%. Find the
total labour cost to produce a total of 80 units.
30. Solve the L.P.P. graphically :
Maximize Z = 6x + 8y
subject to the constraints
4x + 2y ≤ 20
2x + 5y ≤ 24
x ≥ 0, y ≥ 0
III. Answer any three questions : 3 × 5 = 15
31. Find the equation of the circle passing through the points ( 1, 1 ),
( –2, 2 ) and ( –6, 0 ).
32. Find the maximum and minimum values of the function € f x ( ) = x3 − 9x2 + 15x − 3.
33. If € y = ex . log x, then prove that € xy2 − (2x − 1) y1 + (x − 1) y = 0.
34. a) Integrate € 2x + 3 x − 1 w.r.t x. 3
b) Evaluate : € log x . dx 1 2 ∫ . 2
PART – D
Answer any two questions : 2 × 10 = 20
35. a) Prove that € nCr + nCr−1 = n + 1 ( ) Cr and verify the result for n = 5, r = 2. 5
b) Evaluate € lim x → 3 x2 − 9 , 3x − 4 − x + 2 . 5
36. a) A 15 ft ladder leans against a vertical wall. If the top slides
downwards at the rate of 2 ft/sec, find how fast the lower end is
moving when it is 12 ft from the wall. 5
b) Find the coefficient of
€
x−7
in € x − 4x3 21 . 5
37. a) Solve for x :
€ x + 1 x + 2 3
3 x + 2 x + 1
x + 1 2 x + 3 = 0 5
b) Find the focus, directrix and length of the latus rectum of the parabola € x2 − 4x − 32y − 28 = 0.5
8. a) Find the area enclosed between the parabolas € y2 = 6x and € x2 = 6y. 5
b) The Banker’s gain on a certain bill due after 6 months, discounted at 6% p.a. is Rs. 27. Find the true discount, banker’s discount, face value of the bill and discounted value of the bill. 5
PART – E
Answer any one question : 1 × 10 = 10
39. a) Expand € 098 ( ) 5 using Binomial theorem up to 4 decimal places. 4
b) A manufacturer produces 2 products P and Q. Each P requires 4 hours on machine € M1 and 2 hours on machine € M2 . Each Q requires 2 hours on machine € M1 and 5 hours on machine € M2 The available total time on € M1 is 20 hours and on € M2 is 24 hours. Profit per unit of P is Rs. 6 and that of Q is Rs. 8.What quantities of each should be produced and sold to maximize profits ? Formulate the L.P.P.
c) If the marginal cost function of a firm is € f x ( ) = x2 + 7x + 6 and the fixed costs are Rs. 2,500, then determine the total cost for producing 6 units ( x = producing units ). 2
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Kannada Version
Click Here, To Download Basic Mathematics March, 2010 Question Paper of Both Kannada & English Version in PDF Format. Download Question Papers, karnataka 2nd puc question papers, Karnataka Second PUC, Karnataka Second PUC Basic Mathematics Question Paper, Karnataka Second PUC Model Question Papers
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