Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech MATHEMATICSII  Question Paper
JRN Rajasthan Vidyapeeth University
B.Tech
SEMESTER 2
MATHEMATICSII
Model Question Paper
BF7MATHEMATICSII
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)


Q.2 (a) show that



Q.5 Solve the difference equation
U_{n+2} 16 U_{n} = cos n P/2
Group B (25 Marks)

Q.6 Solve with the help of matrices the simultaneous equation x + y + z =3 ,
x +2y +3z = 4, x+4y+9z = 6


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


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 Y_{n + 1} + ^{2} Y_{n1} = 1 is ____________
2.The backward difference
operator symbol and inverse shifting operator E^{1} is related
by __________________
3.If y is a polynomial of n^{th} degree, then n^{th} differences are ________________
4.On putting x = e^{z}, the transformed differential equation of x^{2} + x + y = x is __________
5.If A is a nonzero column vector (nx1), then the rank of matrix AA^{T} is _____________
Q.11 Multiple choice question. (Each question carry 2 marks)
1. If u = x^{2} y^{2} , then analytic function is
a) t^{2} b) t^{2} +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 skewsymmetric matrix of odd order then the determinant of A is ..
a) 1 b) 0 c) 1 d) a real number
4. The differential equation (ay^{2}+x+x^{8})dx + (y^{8}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)^{2}A^{2} + 2AB + B^{2} , b) (AB)^{2}A^{2}  2AB + B^{2}
c) (A+B) (AB)A^{2} B^{2}
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 nonsingular.
3.
4. E = 1
5. (A^{1})^{1} = (A^{1})^{1}
^{ }
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Earning: Approval pending. 