How To Exam?

# Mahatma Gandhi University (MGU) 2007 B.C.A Computer Application First Semester Mathematics - Question Paper

Friday, 17 May 2013 08:55Web

First Semester BC A Degree Examination

BCA 102 Mathematics

Time: 3 hrs

Marks: 75

Part A

(Answer any TEN questions, each question carries 3 marks)

1. Define a)conjugate of a matrix b) hermitian matrix

2. Prove that

1+a

1

1

1

1+b

1

1

1

1+C

= abc(l+l 'a -i-l/b+l/c)

3.    What is a singular matrix ? Give an example.

4.    Derive the partial differential equation

z = (x-a)(y + b)

5.    Find d2y/dx2 whenx=a(t-sint) . y=a(lcost)

6.    Differentiate etan 1 x with respect to cos lx

7.    If y=a cos(logx)+b sin (logx). prove that x2 y>-x yi+y =0

S. State the Drichlets conditions of the Fourier series

2

9.    Find the Laplaces transform of sin 3t

10.    State the convolution theorem

11.    Let A= 1 2 and f(x) = x - 3x+4 Find f(A)

2 2

12.    If L{f(t)}= f(s). then pro\e that L{eatf(t) }=f(s-a)

13. Examine whether the following system of equations are consistent, if so. solve

2x - y - 2z =8 . 3x + 2y - 2z = -1 . 5x + 3y - 3z = 3 (9 marks)

OR

r

5 3 3 2 6-3

14. Find A'1 where A =

and hence solve the equations

V8

(9 marks) (4 marks)

5x3y 3z = 48 .2x - 6y -3z = 18 .8x -3y-2z = 21

15. (a) Find the 11th derivative log(9x2-4)

(b) If y=sin-lx. prove that (1-x") y n+2 - (2n+l)xy n+i - nyn=0 (5 marks)

OR

16.    (a) Find the 11th derivative of (10x-2 l)/(2x-3)(2x+5)    (4 marks) (b) If y=[x+V(l+x2)]m. prove that (1-Hx2)y n+2"K2n+l)xy n+i+(n2-m2)yn=0

(5 marks)

17.    Solve (a) (x2 - y 2-z 2)p+2xyz =2xz

(b) p tanx+q tany = tant

(9marks)

OR

18.    a)Fonn the partial differentiate equation

z = f (xy/z) b)Solve (y + z )p+(z+x)q = x+y

(4 marks) (5 marks)

19.    Find a foiuier series to represent x - x from x = *n to x = n (9 marks)

OR

20.    Explain f(x) = x sinx. 0 < x < 211 .as a foiuier series    (9 marks)

21.    (a) Find the Laplace transform of (l-el )/t    (4 marks) (b) Find the Inverse laplace transform of s/(s+a)" (5 marks)

OR

22.    Using convolution theorem, find the inverse Laplace Transforms

(a)l/s(s2-4) (b) s2 / (s2-4)2    (9 marks)

( 1 Vote )