BENGAL INSTITUTE OF TECHNOLOGY & MANAGEMENT, SANTINIKETAN
CONTINIOUS ASSESMENT-III
Advanced Engineering Mathematics
SUBJECT CODE: PGCSE-101
SEMESTER-I
TIME – 1 HOUR FULL MARKS – 25
Group-A (any five) 1x5=5
1. What is the sequence depicted by the generating series 4 + 15x2 + 10x3 + 25x5 + 16x6+⋯?
a) 10, 4, 0, 16, 25, …
b) 0, 4, 15, 10, 16, 25,…
c) 4, 0, 15, 10, 25, 16,…
d) 4, 10, 15, 25,…
2. What is the generating function for the sequence 1, 6, 16, 216,….?
a) (1+6x)x3
b) 1(1−6x)
c) 1(1−4x)
d) 1-6x2
3. What is the generating function for generating series 1, 2, 3, 4, 5,… ?
a) 2(1−3x)
b) 1(1+x)
c) 1(1−x)2
d) 1(1−x2)
4. What is the generating function for the generating sequence A = 1, 9, 25, 49,…?
a) 1+(A-x2)
b) (1-A)-1/x
c) (1-A)+1/x2
d) (A-x)/x3
5. What is the recurrence relation for the sequence 1, 3, 7, 15, 31, 63,…?
a) an = 3an-1−2an+2
b) an = 3an-1−2an-2
c) an = 3an-1−2an-1
d) an = 3an-1−2an-3
6. Can a singular matrix have eigenvalues?
Group-B (any four) 4x5=20
7. State and prove the linear property of FT.
8. State and prove the Change of scale property of FT
9. Find all eigenvalues and corresponding eigenvectors for the matrix A if A=
300
052
032
10. What is the z-transform of the following finite duration signal?
11. What is the ROC of the signal x(n)=δ(n-k), k>0?