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Code: 15A54101

B.Tech I Year I Semester (R15) Regular & Supplementary Examinations December 2016

MATHEMATICS ? I

(Common to CE, EEE, CSE, ECE, ME, EIE and IT)

Time: 3 hours Max. Marks: 70

PART ? A

(Compulsory Question)

*****

1 Answer the following: (10 X 02 = 20 Marks)

(a) Find the orthogonal trajectories of the family of parabolas through the origin and foci on the

(b) Find the complementary function

(c) has the general solution

(d)

Find

(e) If then find

(f) Find the radius of curvature at any point of the cardioids .

(g) .

(h) Evaluate .

(i)

(j) Evaluate along the parabola from .

PART ? B

(Answer all five units, 5 X 10 = 50 Marks)

UNIT ? I

2 Solve .

OR

3 Solve

UNIT ? II

4 Solve by the method of variation of parameters.

OR

5 The deflection of a strut of length with one end built-in and other end subjected to the

end thrust , satisfies . Find the deflection of the strut at distance from

the built-in end.

UNIT ? III

6 (a) If then show that .

(b) If then prove .

OR

7 (a) Find the points on the surface nearest to the origin.

(b) Find the radius of curvature at on the curve .

Contd. in page 2

Page 1 of 2

R15

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Code: 15A54101

B.Tech I Year I Semester (R15) Regular & Supplementary Examinations December 2016

MATHEMATICS ? I

(Common to CE, EEE, CSE, ECE, ME, EIE and IT)

Time: 3 hours Max. Marks: 70

PART ? A

(Compulsory Question)

*****

1 Answer the following: (10 X 02 = 20 Marks)

(a) Find the orthogonal trajectories of the family of parabolas through the origin and foci on the

(b) Find the complementary function

(c) has the general solution

(d)

Find

(e) If then find

(f) Find the radius of curvature at any point of the cardioids .

(g) .

(h) Evaluate .

(i)

(j) Evaluate along the parabola from .

PART ? B

(Answer all five units, 5 X 10 = 50 Marks)

UNIT ? I

2 Solve .

OR

3 Solve

UNIT ? II

4 Solve by the method of variation of parameters.

OR

5 The deflection of a strut of length with one end built-in and other end subjected to the

end thrust , satisfies . Find the deflection of the strut at distance from

the built-in end.

UNIT ? III

6 (a) If then show that .

(b) If then prove .

OR

7 (a) Find the points on the surface nearest to the origin.

(b) Find the radius of curvature at on the curve .

Contd. in page 2

Page 1 of 2

R15

Code: 15A54101

UNIT ? IV

8

Evaluate by changing the order of integration.

OR

9 Evaluate taken through the positive octant of the sphere: .

UNIT ? V

10 (a)

Find the directional derivative of in the direction of vector at the point

.

(b)

Find curl where .

OR

11 Evaluate by Green?s theorem where is triangle enclosed the lines

.

*****

Page 2 of 2

R15

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This post was last modified on 11 September 2020