Differential Calculus and Differential Equation 2019 – BSc Computer Science Part 1

Paper code: 13502
1502
B.Sc. (Computer Science) (Part 1)
Examination, 2019
Paper No. 1.2
DIFFERENTIAL CALCULUS AND DIFFERENTIAL EQUATION

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) Find nth derivative of:

    (b) If , show that:

\frac{d^{n}y}{dx^{n}} = \frac{n}{2}\left ( n-1 \right )\frac{d^{2}y}{dx^{2}}-n\left ( n-2 \right )\frac{dy}{dx}+\frac{1}{2}\left ( n-1 \right )\left ( n-2 \right )y

2. (a) use Maclaurin’s Theorem to find the expansion in ascending power of x of upto term containing x⁴.

    (b) Use Tailor’s Theorem to prove that

3. (a) Find :

    (b) Show that the condition that the curve and should intersect orthogonally is that:

4. (a) If , find the polar sub-tangent, polar sub-normal and the lengths of polar tangent and polar normal at the point when

    (b) Find the pedal equation of

Section-B

5. (a) Solve the following differential equation:

    (b) Solve the following differential equation:

6. (a) Solve:

    (b) Solve :

7. (a) Solve :

    (b) Solve the differential equation

Section-C

8. (a) Solve the differential equation :

    (b) Solve the simultaneous equations.

9. (a) Evaluate the following :

      (b) Solve the following :

10. (a) Evaluate the as limit of sums.

      (b) Evaluate :

……End……

Thank You!