Karnataka Second PUC Basic Mathematics of March, 2010 Question Paper

Download Karnataka Second Pre University Board Basic Mathematics of March, 2010 Question Paper in both English & kannada Version | Karnataka 2nd PUC Annual Question Papers | Karnataka Second PUC Previous Year or Old Question Papers | Karnataka Second PUC Model Question Papers  | Download Second PUC Question Papers in PDF Format.

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
                                                              _______________

                                   Kannada Version







Click Here, To Download Basic Mathematics March, 2010 Question Paper of Both Kannada & English Version in PDF Format.

Subscribe And Get Latest Updates Free !

Follow us!

Tags: , , , ,

About author

Prasad C M is PediaWiki Blog's Founder and Content Manager.