Download PTU B.Tech 2020 March CSE-IT 3rd Sem BTAM304 18 Mathematics Iii Question Paper

FirstRanker.com

Roll No. Total No. of Pages : 02
Total No. of Questions : 18

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

B.Tech.(CSE) (2018 Batch) (Sem.-3)
MATHEMATICS-III
Subject Code : BTAM304-18
M.Code : 76438
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 ---

Solve the following :

1. Evaluate the limit for the function f(x, y) = (2x-y)/(2x+y) if exists as (x, y) = (0, 0)
2. Evaluate the integral ?₀¹ ?₀^1-x ?₀^1-x-y dz dx dy
3. Check the convergence of the following sequences whose nth term is given by a_n = n/(n²+1)
4. State Leibnitz test for convergence of an alternating series.

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

5. Write down the Taylor’s series expansion for ln (1 + x) about x = 0.
6. Define Clairaut’s equation and obtain its general solution.
7. Solve the differential equation dy/dx - y tanx = 3e^x cosx
8. Define Exact differential equation and obtain the necessary condition for M (x, y) dx + N (x, y) dy = 0 to be exact.
9. Solve the differential equation (d²y/dx²) - 4(dy/dx) + 4y = 0

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

10. Find particular integral for (d²y/dx²) - (dy/dx) + y = x²

FirstRanker.com

SECTION-B

11. Find the minimum value of the function x² + y² + z² subjected to x + y + z = 3a.
12. Evaluate ?₀⁸ ?₀⁸ e^-(x2+y2) dydx , by changing into polar coordinates.

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

13. Discuss the convergence of the series : 1/(4*8) + 1/(4*8*12) + 1/(4*8*12*16) +..... to 8
14. Solve the differential equation : (xy² - e^x)dx + (x²y)dy = 0
15. Solve the differential equation (d²y/dx²) - 6(dy/dx) + 13y = 8e^3x sin2x

SECTION-C

16. a) Find the interval of convergence for the infinite series : x - (x³/3!) + (x⁵/5!) - ..... to 8.
    

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

    b) Find the area bounded by the parabola y = x² and line y = 2x + 3
17. a) Solve the differential equation dy/dx + xsin2y = x³cos²y.
    b) Solve the differential equation xp² - 2yp +x = 0, where p= dy/dx
18. a) Apply method of variation of parameters to solve (d²y/dx²) + 2y = e^xtanx,
    b) Solve x²(d²y/dx²) - 3x(dy/dx) + 5y = sin(lnx)

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

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.

FirstRanker.com