National Institute of Technology-Durgapur

Department of Mathematics (M-201)Class Test CxCy Date 24.03.2010

Full Marks: 20 Time: 50 min

Answer any FOUR 4 5

1. If In = sin n

sind, prove that (n 1)(In In2) = 2 sin(n 1).

2. Prove that0 e

x2dx =pi2

using Gamma function. Hence find the value of e

x2dx.

3. Solve (D2 + 1)y = 2 sin3x.

4. Find the rank of the matrix A =

1 1 31 3 32 4 4

.5. Determine the values of for which the following equations have non-zero solutions: x+2y+3z = x,

3x+ y + 2z = y and 2x+ 3y + z = z.

1