Cochin University of Science and Techology (CUST) 2008 B.Tech engineering mathematics- Question Paper
suitable for all 1st year students
BTS (C) - I&n - 08 - 030 (A)
B. Tech Degree I & II Semester (Combined) Examination
IT/CS/EC/CE/ME/SEB/EI/EE 102 ENGINEERING MATHEMATICS II
(2000Scheme)
BTS (C) - I&n - 08 - 030 (A)
Maximum Marks : 100
Time: 3 Hours
(All questions carry EQUAL maries) Discuss the convergence of
(a)
1
(i)
(ii)
V+Vw+i
l
, x x2 x3
1h---1--H- + .00
2 5 10
cosx cos2x cos3x Prove that the following series converges absolutely ;I----1----I-... .oo.
(b)
(c)
I2 ' 22 ' 32
Find the first three non zero terms ofthe Taylor series expansion of ex sin x about x = 0.
(aT7 Oiscusshe convefgnawi- -
j x x ' ' - - : ' .
(i) 1--+----K...o
2 3 4
(ii) 1 + jc + x2 + .....00
(b) Find the Taylor series expansion of cos x about x = 0.
(c) If y = sm~xx, showthat(l-x2)iy+2-(2+l)1-/22>/H=0.
(a) Solve the following system of equation by Gauss Elimination method:
III.
lx + 6y-5z = 30 3x-4y + z =0 x+2y-3z = 10
(b) Using Cayley Hamilton theorem obtain the inverse of
|
2 |
3 |
4 |
|
3 |
4 |
-1 |
|
1 |
2 |
1 |
OR
8 -6 2
(a) Find the eigen values of A = 6 74
and find eigen vector corresponding
IV.
2 -4 3
to the smallest eigen value.
Express the following matrix as the sum of a symmetric and a skew-symmetric matrix
4 2 -3
1 3 -6 -5 0 -7
V. (a)
(b)
