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Birla Institute of Technology & Science, Pilani

Work-Integrated Learning Programmes Division

Second Semester 2009-2010

Mid-Semester Test (EC-1 Regular)

Course No. : MATH ZC161

Course Title : ENGINEERING MATHEMATICS I

Nature of Exam : Closed Book

Weightage : 40%

Duration : 2 Hours

Date of Exam : 06/02/2010 (AN)Note:1. Please follow all theInstructions to Candidates given on the cover page of the answer book.2. All parts of a question should be answered consecutively. Each answer should start from a fresh page.3. Mobile phones and computers of any kind should not be used inside the examination hall.4. Use of any unfair means will result in severe disciplinary action.Q.1. If A = (4 8 10)T and B = ( 2 4 5), find (AB + B T )T [4]Q.2. Transform the given matrix into a row reduced echelon form

1 2 2

1 1 1

1 3 1

X

=

[5]

Q.3. Evaluate the determinant of the following matrix

2 2 2

1 1 1

X a b c

a b c

=

[4]

Q.4. Find the Eigen values and Eigen vectors of the matrix [8]

=

342

476

268

A

Q.5. If kjiba 634 += rr and kjic 42 +=r , then find cba rrr )( . [3]Q.6. Find parametric equations for the line of intersection of 1432 =+ zyx and

5= zyx . [3]

Q.7 (a). Solve the following differential equation by using the method of separation of

variables

2 21 1 , (0) 3 / 2y dx x dy y = = [3]

(b). Find the solution of linear differential equation given by2(1 ) 2 ( ), (0) 0

dyx x y f x y

dx+ + = =

where, 0 1

( ), 1

x xf x

x x