Differential Calculus and Differential Equation 2014 – BSc Computer Science Part 1

Paper code: 13502
1502
B.sc. (Computer Science) (Part 1)
Examination, 2014
Paper No. 1.2
DIFFERENTIAL CALCULUS AND  DIFFERENTIAL EQUATION

Time: Three Hours] [Maximum Marks: 50

Note: Attempt all the five questions in all section one question from each Section. All questions carry equal marks.

Section-A

1. (a) If , prove that:

    (b) If , find

2. (a) Apply Maclaurin’s theorem to find the expansion in ascending powers of x of to the term containing .
(b) Expend in powers of .

Section-B

3. (a) Find the equation of the normal at the point ‘t’ on the curve:

    (b) Find the length of the polar tangent and polar normal for the curve .

4. (a) Find the equation of the tangent at the point  to the ellipse:

     (b) If , prove that:

Section-C

5. (a) Evaluate:

    (b) Evaluate:

6. (a) Show that:

    (b) Evaluate:

Section-D

7. (a) Solve:

    (b) Solve:

8. (a) Solve:

     (b) Solve:

Section-E

9. (a) Solve:

     (b) Solve:

10. (a) Solve:

       (b) Solve:

……………End……………