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B.Tech I Year I Semester (R15) Regular & Supplementary Examinations December 2017

MATHEMATICS - I

(Common to all branches)

Time: 3 hours Max. Marks: 70

PART - A

(Compulsory Question)

*****

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

(a) Define an ordinary differential equation with example.

(b) Find the general solution of

(c) To solve the D.E ( by the method of variation of parameters find ?B? when

P.I = Ax + Bx.

(d)

Transform the Caucy?s homogeneous differential equation into a linear

differential equation with constant coefficients.

(e)

If then find

(f)

If

(g)

Evaluate .

(h)

Evaluate .

(i)

If then find at (1,-1,1).

(j) State the Gauss divergence theorem.

PART - B

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

UNIT - I

2 (a) Solve (

(b) Solve

OR

3 (a) A bacterial culture, growing exponentially increases from 200 to 500 grams in the period from

6 a.m to 9 a.m. How many grams will be present at noon?

(b) If a voltage of 20 Cos 5t is applied to a series circuit consisting of 10 ohm resistor and 2 Henry

inductor, determine the current at any time t.

UNIT - II

4

Solve

OR

5 A horizontal tie-rod is freely pinned at each end. It carries a uniform load w/b per unit length

and has a horizontal pull P. Find the central deflection and the maximum bending moment

taking the origin at one of its ends.

UNIT - III

6 (a) Verify Taylor?s theorem for with Lagranges form of remainder 2 terms in the

interval [0,1].

(b)

If show that

OR

7 (a) Examine for minimum and maximum values of

(b) Find the radius of curvature of the curve at (-2a, 2a).

Continued in page 2

R15

Page 1 of 2

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Code: 15A54101

B.Tech I Year I Semester (R15) Regular & Supplementary Examinations December 2017

MATHEMATICS - I

(Common to all branches)

Time: 3 hours Max. Marks: 70

PART - A

(Compulsory Question)

*****

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

(a) Define an ordinary differential equation with example.

(b) Find the general solution of

(c) To solve the D.E ( by the method of variation of parameters find ?B? when

P.I = Ax + Bx.

(d)

Transform the Caucy?s homogeneous differential equation into a linear

differential equation with constant coefficients.

(e)

If then find

(f)

If

(g)

Evaluate .

(h)

Evaluate .

(i)

If then find at (1,-1,1).

(j) State the Gauss divergence theorem.

PART - B

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

UNIT - I

2 (a) Solve (

(b) Solve

OR

3 (a) A bacterial culture, growing exponentially increases from 200 to 500 grams in the period from

6 a.m to 9 a.m. How many grams will be present at noon?

(b) If a voltage of 20 Cos 5t is applied to a series circuit consisting of 10 ohm resistor and 2 Henry

inductor, determine the current at any time t.

UNIT - II

4

Solve

OR

5 A horizontal tie-rod is freely pinned at each end. It carries a uniform load w/b per unit length

and has a horizontal pull P. Find the central deflection and the maximum bending moment

taking the origin at one of its ends.

UNIT - III

6 (a) Verify Taylor?s theorem for with Lagranges form of remainder 2 terms in the

interval [0,1].

(b)

If show that

OR

7 (a) Examine for minimum and maximum values of

(b) Find the radius of curvature of the curve at (-2a, 2a).

Continued in page 2

R15

Page 1 of 2

Code: 15A54101

UNIT - IV

8 (a)

Evaluate .

(b)

Evaluate

OR

9 (a) Find the whole area of the lemniscates .

(b) Find the volume bounded by the xy plane, the cylinder x

2

+y

2

=1 and the plane x+y+z=3.

UNIT - V

10 (a) Find the angle between the surfaces at the point (2,-

1,2).

(b)

Use divergence theorem to evaluate and S is the

surface bounded by the region

OR

11

Verify stokes theorem for taken round the rectangle bounded by the

lines x = ? a, y=0, y=b.

*****

Page 2 of 2

R15

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This post was last modified on 11 September 2020