MTH301 Final Term Past Paper July 2013

40 Mcqs each of one mark from past paper 4 question each of two marks

4 question each of three marks 4 question each of five marks

Define the line integral

sin nxdx π

π

Where n is an integer other than zero ---------------------------------------------------------------2 Marks

Q1. Define the line integral

cos nxdx π

π

Where n is an integer other than zero ---------------------------------------------------------------2 Marks

Q2. Find the Laplace transform of the form F (t) that

cos4 t F t e t

Q3. Find the Laplace transform of the form F (t) that

t F t t e−

Q4. Find out the Divergence divF

of a vector function

2 ˆ ˆ ˆ

F x y i xy zj xz k

--------------------------------------------------------------------------5 Marks

Q5. Find the exact change of the equation

y x x when x change from 2 to 2.2

Q6. Find out the curl curlF

of a vector function

2 ˆ ˆ ˆ

F x y i xy zj xz k

--------------------------------------------------------------------------5 Marks

Q7. Evaluate the integral

(3,2)

(0,0) y y xe dx x e dy ------------------------------5 Marks

Q8. Convert Rectangular co-ordinates (

x y z to Spherical co-ordinates ( ρ θ φ

3, π π

--------------------------------------------------------------------------------------------5 Marks