LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034.
B.Sc. DEGREE EXAMINATION – MATHEMATICS
SECOND SEMESTER – APRIL 2003
MT 2500 / MAT 501 – ALGEBRA ANALYTICAL GEOMETRY, cALCULUS – II
23.04.2003
9.00 – 12.00 Max : 100 Marks
PART – A (10´ 2=20 marks)
Answer ALL questions. Each question carries TWO marks.
- Prove that
- Evaluate
- State cauchy’s root test for convergence of a given series.
- Show that
- If Y= show that
- Solve
- Solve where
- Evaluate
- Find the equation to the plane through the point (3,4,5) and parallel to the plane
- Find the equation of the sphere with centre (-1, 2, -3) and radius 3 units.
PART – B (5´ 8=40 marks)
Answer any FIVE questions. Each question carries EIGHT marks.
- If n = prove that .
- Evaluate .
- Sum the series .
- Sum the series .
- Solve .
- Solve .
- Test for convergence of the series .
- Find the perpendicular distance from P (3, 9, -1) to the line .
PART – C (2´20=40 marks)
Answer any TWO questions. Each question carries TWENTY marks.
- a) Evaluate I = (10)
- b) Find the reduction formulae for In = (10)
- a) Solve by variation of parameter method. (10)
- b) Solve (10)
- a) Sum the series (10)
- b) Sum the series (10)
- a) Show that the series is convergent when k is greater than unity and
divergent when k is equal to or less than unity. (10)
- Find the equation of the sphere which passes through the circle
and touch the plane (10)