How To Exam?

a knowledge trading engine...

Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech MATHEMATICS-II - Question Paper

Tuesday, 14 May 2013 02:55Web

JRN Rajasthan Vidyapeeth University





Model Question Paper


Time : 3 hrs Maximum marks : 75



1. Question paper is divided into Group A, Group B and Group C

2. Each Group is 25 Marks

3. Figure to the right in bracket indicates marks.

4. Good Handwriting is expected

5. Assume suitable data if necessary.


Group A (25 Marks)


Answer any three questions (Question 1 is compulsory)




Q.1 Prove that the inverse of a matrix is unique .

Q.2 (a) show that




Q.3 (a) Prove that E = 1 + (b) Prove that E = (1- )-1 ?


Q.4 Derive cauchys integral formula ?

Q.5 Solve the difference equation

Un+2 16 Un = cos n P/2

Group B (25 Marks)


Answer any three questions (Questions 6 is compulsory)

Q.6 Solve with the help of matrices the simultaneous equation x + y + z =3 ,

x +2y +3z = 4, x+4y+9z = 6


Q.7 Find the inverse of matrix by row transformation method of


A =

Q.8 Evaluate the following i) dz where c is the circle =2 ii)

where C is the circle


Q.9 Determine the analytic function whose real part is


i) log ii) cos x cos h y

Q.10. If f (z) = u + iv is an analytic function them show that u and v

are both harmonic functions.



Group C (25 Marks)

All Questions are Compulsory.

Q.11 Fill in the blanks ( each question carry 2 marks)

1.The order of the difference equation Yn + 1 + 2 Yn-1 = 1 is ____________


2.The backward difference operator symbol and inverse shifting operator E-1 is related
by __________________

3.If y is a polynomial of nth degree, then nth differences are ________________

4.On putting x = ez, the transformed differential equation of x2 + x + y = x is __________

5.If A is a non-zero column vector (nx1), then the rank of matrix AAT is _____________

Q.11 Multiple choice question. (Each question carry 2 marks)


1. If u = x2- y2 , then analytic function is

a) t2 b) t2 +c c) t/2 +c d) None of these

2. w = log t is an analytic function every where except at t =

a) 3 b) 0 c) 2 d) 1


3. If A is a skew-symmetric matrix of odd order then the determinant of A is ..

a) -1 b) 0 c) 1 d) a real number

4. The differential equation (ay2+x+x8)dx + (y8-y+bxy)dy=0 is exact if

a)b=a b) b=2a c) a=1, b=3 d) b2a


5. If A and B are square matrices of the same order explain in general.

a) (A+B)2A2 + 2AB + B2 , b) (A-B)2A2 - 2AB + B2

c) (A+B) (A-B)A2 B2


Q.11 True or false (each question carry 1 marks).


1. The A-1 exist only for singular matrix.

2. The determinant of a matrix is zero, then matrix is non-singular.


4. E = 1-

5. (A1)-1 = (A-1)1








( 0 Votes )

Add comment

Security code

Earning:   Approval pending.
You are here: PAPER Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech MATHEMATICS-II - Question Paper