Model Question Paper Basic Mathematics II Karnataka : www.pue.kar.nic.in Pre University/ PUC
Organization : Karnataka Department of Pre-University Education
Exam : II PU Basic Mathematics
Document type : Question Paper
Website : pue.kar.nic.in
Download Previous/ Old Question Papers :
March 2009 : https://www.pdfquestion.in/uploads/pue.kar.nic.in/5983-m0975.pdf
July 2009 : https://www.pdfquestion.in/uploads/pue.kar.nic.in/5983-j0975.pdf
March 2010 : https://www.pdfquestion.in/uploads/pue.kar.nic.in/5983-m1075.pdf
July 2010 : https://www.pdfquestion.in/uploads/pue.kar.nic.in/5983-j1075.pdf
March 2011 : https://www.pdfquestion.in/uploads/pue.kar.nic.in/5983-m1175.pdf
July 2011 : https://www.pdfquestion.in/uploads/pue.kar.nic.in/5983-j1175.pdf
March 2014 : https://www.pdfquestion.in/uploads/pue.kar.nic.in/5983-m1475.pdf
PUE Basic Mathematics Question Paper
March, 2009 Basic Mathematics
Time : 3 Hours 15 Minutes ] [ Max. Marks : 100
Related / Similar Question Paper : PUC Physics Question Bank
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.
Model Questions
PART – A
Answer all the ten questions : 10 × 1 = 10
1. Write the Inverse of “If it rains then we are happy”.
2. Find the number of words that can be formed using all the letters of the
3. Evaluate –
4. The average age of 42 students in a class is 16 years. Find the sum of
5. Define Banker’s Discount.
6. Find the index of learning for 70% learning effect.
7. Find the radius of the circle x 2 + y 2 + 4x – 2y – 4 = 0.
8. Evaluate : lim x – 2 x 5 – 32 x – 2 .
9. If x 2 + y 2 = a 2 , find dy dx .
10. Evaluate : ) – ( 1 2x + 5 dx.
PART – B
Answer any ten questions : 10 × 2 = 20
11. If p : 2 is an integer q : 2 is an odd number r : 5 is a prime number,
12. Find the number of diagonals of a polygon of sides 8.
13. A bag contains 12 balls out of which 4 are red and 8 are green. 3 balls
14. If two rows or columns of a determinant are identical, prove that the value
15. If A + B = – and A – B = – , find A and B.
16. If 10 men complete a work in 12 days, how many days will it take for
15 men to complete the same work –
17. Find the vertex and focus of the parabola y 2 = 3x – 6.
18. If the function f ( x ) = ( 1 + 2x ) 1/x ‚ x – 0 k ‚ x = 0 is continuous at x = 0, find k.
19. If y = x x then find dy dx .
20. If the sum of two numbers is 20, find the two numbers whose product is
21. Evaluate ) x + 1x dx .
22. If the total cost is C ( x ) = 6x 2 + 2x + 3, find the average cost and
PART – C
I. Answer any three questions : 3 × 5 = 15
23. Prove that ~ ( p – q ) = ( p V ~ q ) V ( q V ~ p ).
24. Resolve into partial fractions x 2 ( x + 1 ) ( x + 2 ) ( x + 3 ) .
25. A committee of 5 are to be formed from 8 Americans and 5 Anglo-
i) exactly two Anglo-Indians ii) at least two Anglo-Indians –
26. If A = – , prove that A . adj A = adj A . A = | A | . I.
PART – D
Answer any two questions : 2 × 10 = 20
35. a) A fair die is rolled. What is the probability that either an odd number
or a number greater than 4 will turn up – 5
b) Evaluate Lim a + x – a – x x . 5
36. a) A point source of light is hung 25 feet directly above a straight
b) Find the coefficient of x 7 in the expansion of – 2x 11 . 5
37. a) Prove that 1 + a b c a 1 + b c a b 1 + c 1 + a + b + c.
March, 2010 :
1. Find the mean proportional to 9 and 16.
2. 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 ?
3. A bill drawn for 3 months was legally due on 06. 07. 2009. Find the date of drawing of the bill.
4. If ( p ∧ ~ q ) → r is a false proposition, find the truth values of p, q and r.
5. In how many ways can the 7 colours of the rainbow be arranged so that the red and the blue colours are always together ?
6. 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.
7. Solve the following equations by Cramer’s rule :
x + 2y = 4
2x + 5y = 9
8. 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.
9. Find the equation of the circle two of whose diameters are x + y = 6 and x + 2y = 4 and radius = 10 units.
10. 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 ?
11. Solve the following equations by matrix method :
x + y – 2z = 0
2x – y + z = 2
x + 2y – z = 2.
12. 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 ?
13. 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 ?
14. 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.
15. Solve the L.P.P. graphically :
Maximize Z = 6x + 8y
subject to the constraints
4x + 2y ≤ 20
2x + 5y ≤ 24
x ≥ 0, y ≥ 0
II. Answer any three questions :
16. Find the equation of the circle passing through the points ( 1, 1 ), ( –2, 2 ) and ( –6, 0 ).
17. A batsman’s average score for a certain number of innings was 21·75 runs per innings. In the next 3 innings, he scored 28, 34 and 37 runs and his average for all the innings was raised by 1·125 runs. How many innings did he play ?