BSc Sem IV 2014 2015 2015 Math L Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 All questions are compulsory 2)For Q.1, Q.2, Q.3, attempt any one subquestion (each 8 mks)from part (a), an y the subquestions (each 4 mks) from part(b)
2. Q3 For Q.4 Attempt any three.(each 5 mks)
   • (a) Attempt any one [Each 8]
3. Q2 Define an exact differential equation and solve following
4. Q1 (b) Attempt any three. [Each 4] ) Define an order and degree of differential equation and Write order and d each of following differential equation
5. Q2 Solve (y = + =<) using separation of variable
6. Q3 Prove that The Bernoulli Differential equation + Py = es to differential equation by transformation Z =
7. Q4 Define linear differential equation and solve ylogy dx + (x
8. Q2 (a) Attempt any one {Each 8}
9. Q1 Define double integral and write properties of double
10. Q2 Write the note on application of double integral to find ree of | ost region R and find area of the region R bounded by y = 2x,y an
11. Q2 (b) Attempt any three. [Each 4]
12. Q1 Evaluate the triple integral SS, E is bounded by the parabolic z
13. Q2 Find mass and center of massof a triangular lamina with vertices (0,0),(1,0),(0,2) if the density function is p(x, y) = 1+ 3x + y
14. Q3 Find the average value of F =
15. Q4 Sketch the region and write an equivalent double integral with order of integration
16. Q3 (a) Attempt any one [Each 8} Define Potential function and Find Potential function for
17. Q2 Define circulation around the curve, flow along the curve and Find the circulation and flux of the field F = —yi + xj around and across the closed semicircular path that consists of the semi circular arch = (acost)i+(asint)j, 0< t < by line segment
18. Q3 (b) Attempt any three. [Each 4]
19. Q1 Define the gradient field of a differentiable function f and find gradient of
20. Q2 F = (x + xkis the velocity field of a fluid flowing through a region in space. Find the flow along the curve r = (cost)i+ (sint)k,
21. Q3 Define work done over a smooth curve by force F and find the work done by F = 3x*i + (2xz — y)j — zk over the curve
22. Q4 Evaluate y?dx — x? dy where C is the positively oriented circle of radius centered at the origin using Green’s theorem 2 marks
23. Q4 Attempt any three [Each 5]
24. Q2 Using Rule 3 to find an integrating factor , Solve following
25. Q4 Use polar coordinate to find volume of given solid Under the cone + y? and above the
26. Q6 Determine whether or not the vector field F(x, y,z)

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