Differential Calculus and Differential Equations 2023 – BSc Computer Science Part 1

Paper code: 13502
1502
B.Sc. (Computer Science) (Part 1)
Examination, 2023
Paper No. 1.2
Differential Calculus and Differential Equations

Time: Three Hours]

[Maximum Marks: 50

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

Section-A

1. (a) If , then prove that:

        hence find the value of

    (b) Find when

2. (a) Apply Maclaurin’s theorem to to prove that:

    (b) Use Tailor’s Theorem to prove that

3. (a) Evaluate:

    (b) If the normal to the curve makes an angle Φ with the axis of x, show that its equation is :

4. (a) Find the pedal equation of the curve:

    (b) Find the polar sub-tangent for the ellipse:

Section-B

5. (a) Solve the following differential equation:

    (b) Solve the following differential equation:

6. (a) Solve the equation:

    (b) Solve the equation:

7. (a) Solve :

    (b) Solve :

Section-C

8. (a) Evaluate :

    (b) Evaluate :

9. (a) Find the indefinite integral :

    (b) Evaluate :

as the limit of a sum.

10. (a) Evaluate :

by summation.

    (b) Evaluate :

……End……