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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