Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech MATHEMATICS-II - Question Paper
JRN Rajasthan Vidyapeeth University
B.Tech
SEMESTER 2
MATHEMATICS-II
Model Question Paper
BF7-MATHEMATICS-II
Time : 3 hrs Maximum marks : 75
Instruction:
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)
|
(10)
Q.1
Prove
that the inverse of a matrix is unique .
Q.2 (a) show that
(10)
(b)
(10)
Q.3 (a) Prove
that E = 1 + (b)
Prove that E = (1- )-1
?
(10)
Q.4
Derive
cauchys integral formula ?
Q.5 Solve the difference equation
Un+2 16 Un = cos n P/2
Group B (25 Marks)
(5)
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
(10)
Q.7
Find
the inverse of matrix by row transformation method of
(10)
A
=
Q.8 Evaluate the following i) dz where c is the circle =2 ii)
where C is the circle
(10)
Q.9
Determine
the analytic function whose real part is
(10)
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.
3.
4. E = 1-
5. (A1)-1 = (A-1)1
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Earning: Approval pending. |