Bca Assignment 1st Sem.2012 Maths

May- 2012 Bachelor of Computer Science (BCA) Semester- I BC0033- Basic Mathematics – 4 Credits
(Book ID: B0675 )

Assignment Set – 1 (60 Marks)

Answer All Questions

6 X 10 = 60 Marks

1. Prove that the intersection of any two subgroups of a group is a group. 2. Prove that the sum of the degrees of the points of a graph G is twice the number of lines. 3. Find the mean, median and mode for the following: Mid value Frequency 15 2 20 22 25 19 30 14 n+1 35 3

40 4

45 6

50 1

55 1

4. Prove that nC r + nCr-1 =

Cr

5. If birth to a male child and birth to a female child are equiprobable, what is the probability that at least one of the three children born to a couple is male?

6.

Simplify:

tan ( 180  A ) sec ( 180   A ) cos ec ( 90  A ) sec (  A ) cot ( 90  A )

May- 2012 Bachelor of Computer Science (BCA) Semester- I BC0033- Basic Mathematics – 4 Credits
(Book ID: B0675 )

Assignment Set – II (60 Marks) Answer All Questions 6 X 10 = 60 Marks

 x lim  a  1 1. Show that x 0  x  

    log e a  

2. Find the angle of intersection of the cardiodes r = a(1+cos ), r = b(1 – cos ). 3. Show that



 /2

0

sin 6  cos 3  

2 63
  .  

  a ib 4. Show that tanh 2x = cos  ilog    a ib 

5. Apply Crout’s method to solve the equations : 3x+2y+7z = 4, 2x+3y+z = 5, 3x+4y+z = 7
2 4 6    ......... to  3! 5! 7!

6. Show that