Download DBATU B-Tech 1st Year 2019 Mid Semester BTBS101 Engineering Mathematics I Question Paper

Download DBATU (Dr. Babasaheb Ambedkar Technological University) B.Tech First Year 2019 Mid Semester BTBS101 Engineering Mathematics I Question Paper

SVKM INSTITUTE OF TECHNOLOGY, DHULE
Mid Semester Exam 2019-20
Course: Common to All Branches Div: A/B/C/D/E Sem: I
Subject Name: Engineering Mathematics I Subject Code: BTBS101
Max Marks: 20 Datez-3/10/2019 Duration:? 1 Hr.
Instructions to the Students:
1. All Questions are Compulsory
2. Use of Non-Programmable calculator allowed
(Level/CO) Marks
Q.1 Write a correct option of following questions 6
1. The Product of Eigen values of Matrix A equal to Understand
(a) IAI (b) 0 (c) 1 ((1) None
2. Eigen values of triangular matrix are Understand
(a) Non Principle diagonal (b) Principle Diagonal (c) Zero ((1) None
3. The Eigen values of A and A? are always Understand
(a) Different (b) Same (0) Cannot be decided ((1) None
4' If 2 = exy then 3?: = ..... Apply
(a)exy (b) 9? y (c) 9? x (d) exy xy
5- Ifu = xythen 3?: =. .. Apply
(a) xylogx (b) xylogy (c) yxy'1 (d) 0
6- Ifu=x2+2xy+y2,thenx:?:+y:?:=--- Apply
(a) u (b) 0 (c) 3u (d) 2u
Q.2 Solve Any Two of the following. 3 X 2
(A) 1 ?1 2 ?3 Apply
Reduce the Matrix A to Normal form and find its Rank A = 3 31, (1) i
0 1 0 2
B _ _ _ _ E Q E ? Evaluate
( ) Ifu ? f(x y,y 2,2 x) then showthat ax+ ay+ az ? 0
C a_f % E ? a_f @- ? _ Understand
( ) Prove that ay' 62 .dx ? 6x '03? |ff(x,y) ? 0 and ?(y,z) ? 0
0.3 Solve Any One of the following. 8
(A) Verify Cayley?Hamilton theorem to A = E _i] and hence find A?1 also Apply/
deduce that A8 = 6251 Evaluate
(B) 96%?; Apply
_ ?1
If u ? cosec ? prove that . /Evaluate
x3+y3
232?11 "2?1? 2 32?11 _ tan? 2 i 2
x 6x2 + zxyaxay + y ay2 _ 12 12 + 12tan u