Download PTU B-Tech EEE 2020 Dec 1st Sem 70970 Engineering Math Iii Question Paper

FirstRanker.com
Firstranker's choice
FirstRanker.com

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

Roll No. | | L LI LTI Total No. of Pages : 02
Total No. of Questions : 08

B.Tech. (EE) PT (Sem.-1)

ENGINEERING MATH-III

Subject Code : BTAM-301

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

Time : 2 Hrs. Max. Marks : 30

INSTRUCTIONS TO CANDIDATES :

1. Attempt any FIVE question(s), each question carries 6 marks.

1. Use the concept of residues to evaluate ?₀^2p dx/(5-3cos?).

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

2. Find a Fourier series to represent, x = x²/4 from x = -p to x = p. Hence, show that
3. Find L^-1 [log(1 + 1/s)] where L^-1 denotes inverse Laplace transform.
4. If f(z) = u + iv is an analytic function of z=x + jy and u –v= (cosx+sinx-e^-y)/(2cosx-e^-y-e^y), find the analytic function f(z), given f(p/2) =0.
5. Solve the equation ?²u/?x²+?u/?y=3u given u=3e^-2x –e^-5x, when y=0.
6. Using the recurrence relation (n + 1)P_n+1(x) = (2n + 1) xP_n(x) – nP_n-1(x). Hence, evaluate P₅(1.5) and P₆(2.1).

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

7. A tightly stretched string has its ends fixed at x = 0 and x = /. At time t = 0 the string is given a shape defined by f(x) = µx (l – x), where µ is constant and then released. Find the displacement of any point x of the string at any time t > 0.
8. Find the power series solution about the origin of the equation : (1–x²)y''–4xy’+2y=0.

Note: Any student found attempting answer sheet from any other person(s), using incriminating material or involved in any wrong activity reported by evaluator shall be treated under UMC provisions.

Student found sharing the question paper(s)/answer sheet on digital media or with any other person or any organization/institution shall also be treated under UMC.

Any student found making any change/addition/modification in contents of scanned copy of answer sheet and original answer sheet, shall be covered under UMC provisions.

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

FirstRanker.com