Download PTU B.Tech 2020 March Automation-And-Robotics Question Paper 3rd Sem BTAR 301 Mathematics Iii

FirstRanker.com

Roll No. [T T Total No. of Pages : 02

Total No. of Questions : 09

--- Content provided by FirstRanker.com ---

B.Tech.(Automation & Robotics) (2012 & Onwards) (Sem.-3)

MATHEMATICS - II

Subject Code : BTAR-301

M.Code : 63001

Time : 3 Hrs. Max. Marks : 60

--- Content provided by⁠ FirstRanker.com ---

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

--- Content provided by‌ FirstRanker.com ---

1. Write briefly :
   1. Find Laplace Transform of e^t (t + 2)²
   2. Find Inverse Laplace Transform of ^{2s +18}/_s²+1
   3. Define a singular point and regular singular point.
   4. Express f (x) = 2x³ — x + 1 in terms of Lagendre function.
   5. Show that | z |² is not analytic at any point.

   --- Content provided by FirstRanker.com ---

   6. Define error function.
   7. Define a conformal mapping.
   8. Evaluate ? (dz,C:| z|=1.) / (z—2)
   9. Define poles and find the same for ^z+1/_z²(z-2)
   10. Show that sinh z is analytic function.

   --- Content provided by​ FirstRanker.com ---

FirstRanker.com

SECTION-B

Solve the differential equation using Method of Laplace transform

y''+4y'+3y=e^-3t, y(0)=1,y'(0)=1

--- Content provided by​ FirstRanker.com ---

Prove that P_n (x) = xP'_n-1(x) + nP_n-1(x)

Find the real part of the analytic function whose imaginary part is tan^-1 (y/x). Also find the analytic function.

Expand f(z)= ¹/_(z+1)(z+3) in Laurent’s series, valid for | z |> 3

Find the image of w=¹/_z under the mapping |z—3|=5

SECTION-C

--- Content provided by‍ FirstRanker.com ---

1. a) Define unit impulse function and find its Laplace transform
   b) Prove that J_-1/2 (x)= v(²/_px) cosx
2. Solve in series : x² d²y/dx²+(1+x)dy/dx+2y=0
3. Evaluate ?₀^{2p d?}/_{1—2acos?+a²} , 0 < a <1 using Contour integration.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

--- Content provided by‌ FirstRanker.com ---

FirstRanker.com