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

First Semester BC A Degree Examination

BCA 102 Mathematics

(2007 Admission onwards

Time: 3 hrs

Part A

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

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

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 e^{tan 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{e^atf(t) }=f(s-a)

PART B (Answer all questions)

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 =

V⁸

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

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

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

OR

16.    (a) Find the 11^th 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)y_n=0

(5 marks)

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

(b) p tanx+q tany = tant

OR

18.    a)Fonn the partial differentiate equation

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

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-e^l )/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)

Attachment: mahatma-gandhi-university--mgu--2007-b-c-a-computer-application-34440-1.JPG mahatma-gandhi-university--mgu--2007-b-c-a-computer-application-34440-2.JPG

Earning:   Approval pending.