Download JNTUA (JNTU Anantapur) B.Tech R13 (Bachelor of Technology) 1st Year 1st Semester (1-1) 2019 Dec 13A54102 Mathematics II Previous Question Paper || Download B-Tech 1st Year 1st Sem 13A54102 Mathematics II Question Paper || JNTU Anantapur B.Tech 1-1 Previous Question Paper || JNTU Anantapur B.Tech ME 1-1 Previous Question Paper || JNTU Anantapur B.Tech CSE 1-1 Previous Question Paper || JNTU Anantapur B.Tech Mech 1-1 Previous Question Paper || JNTU Anantapur B.Tech EEE 1-1 Previous Question Paper || JNTU Anantapur B.Tech ECE 1-1 Previous Question Paper
Code: 13A54102
B.Tech I Year (R13) Supplementary Examinations December 2019
MATHEMATICS ? II
(Common to EEE, ECE, EIE, CSE & IT)
Time: 3 hours Max. Marks: 70
PART ? A
(Compulsory Question)
*****
1 Answer the following: (10 X 02 = 20 Marks)
(a) Find the Eigen values and the corresponding of ?
5 4
1 2
?.
(b) Show that ?? = ?
2 3 + 4 ?? 3 ? 4 ?? 2
? is Hermitian.
(c) Define algebraic and transcendental equations with example each.
(d) The value of ?
1
?? 2
1
?? ?? by Simpson?s 1/3 rule (taking n = 4) is________.
(e) If
????
????
= ? ?? , ?? (0) = 1, ? = 0.01 then by Euler?s method the value of ?? 1
is _________.
(f) Write the Fourier series of f(x) in [C, C+2L].
(g)
Find the Fourier cosine transform f(x) = e
ax ?
.
(h) Define convolution theorem.
(i) Write the two dimensional Laplace equation.
(j) Form a partial differential equation by eliminating the arbitrary constants a and b from the equation:
z = ax + by.
PART ? B
(Answer all five units, 5 X 10 = 50 Marks)
UNIT ? I
2
Reduce the matrix ?? = ?
2
1
3
6
3
?1
1
3
?1
?2
3
0
?1
?4
?2
?7
? into its normal form and hence find its rank.
OR
3 Reduce the quadratic form 3x
2
+ 3y
2
+ 3z
2
+ 2xy + 2xz ? 2yz into canonical form using orthogonal
transformation and find its rank, index and signature.
UNIT ? II
4 (a) Using Newton-Raphson method compute ?41 correct to four decimal places.
(b) Find the root of an equation 2 ?? ? log ?? = 6 by Regula-falsi method.
OR
5 (a) Evaluate ? ?? 3
?? ?? 1
0
with five sub-intervals by Trapezoidal rule.
(b) Evaluate ?
?? ?? ?? 2
1
?? ?? using Simpson?s
1
3
rule for n = 4.
UNIT ? III
6
Using Euler?s method, solve for ?? at ?? = 0.1 from
????
????
= ?? + ?? + ?? ?? , ?? (0) = 1 taking step size
? = 0.025.
OR
7 Find the Half range cosine series of ?? ( ?? ) = ?? (1 ? ?? ) ???? [0, 2].
Contd. in page 2
Page 1 of 2
R13
FirstRanker.com - FirstRanker's Choice
Code: 13A54102
B.Tech I Year (R13) Supplementary Examinations December 2019
MATHEMATICS ? II
(Common to EEE, ECE, EIE, CSE & IT)
Time: 3 hours Max. Marks: 70
PART ? A
(Compulsory Question)
*****
1 Answer the following: (10 X 02 = 20 Marks)
(a) Find the Eigen values and the corresponding of ?
5 4
1 2
?.
(b) Show that ?? = ?
2 3 + 4 ?? 3 ? 4 ?? 2
? is Hermitian.
(c) Define algebraic and transcendental equations with example each.
(d) The value of ?
1
?? 2
1
?? ?? by Simpson?s 1/3 rule (taking n = 4) is________.
(e) If
????
????
= ? ?? , ?? (0) = 1, ? = 0.01 then by Euler?s method the value of ?? 1
is _________.
(f) Write the Fourier series of f(x) in [C, C+2L].
(g)
Find the Fourier cosine transform f(x) = e
ax ?
.
(h) Define convolution theorem.
(i) Write the two dimensional Laplace equation.
(j) Form a partial differential equation by eliminating the arbitrary constants a and b from the equation:
z = ax + by.
PART ? B
(Answer all five units, 5 X 10 = 50 Marks)
UNIT ? I
2
Reduce the matrix ?? = ?
2
1
3
6
3
?1
1
3
?1
?2
3
0
?1
?4
?2
?7
? into its normal form and hence find its rank.
OR
3 Reduce the quadratic form 3x
2
+ 3y
2
+ 3z
2
+ 2xy + 2xz ? 2yz into canonical form using orthogonal
transformation and find its rank, index and signature.
UNIT ? II
4 (a) Using Newton-Raphson method compute ?41 correct to four decimal places.
(b) Find the root of an equation 2 ?? ? log ?? = 6 by Regula-falsi method.
OR
5 (a) Evaluate ? ?? 3
?? ?? 1
0
with five sub-intervals by Trapezoidal rule.
(b) Evaluate ?
?? ?? ?? 2
1
?? ?? using Simpson?s
1
3
rule for n = 4.
UNIT ? III
6
Using Euler?s method, solve for ?? at ?? = 0.1 from
????
????
= ?? + ?? + ?? ?? , ?? (0) = 1 taking step size
? = 0.025.
OR
7 Find the Half range cosine series of ?? ( ?? ) = ?? (1 ? ?? ) ???? [0, 2].
Contd. in page 2
Page 1 of 2
R13
Code: 13A54102
UNIT ? IV
8
Find the Fourier series for
,0
() , 0
, 0
2
x
fx x x
x
??
?
?
?
?
? ? <<
?
= <<
?
?
?
? =
?
Hence deduce that
1
1
2
+
1
3
2
+
1
5
2
+. . . =
?? 2
8
.
OR
9 (a) Find ?? ( ?? sin ???? ).
(b) Find
( ) ( )
3
1
2
,3
32
z
Zz
zz
?
??
> ??
??
? ?
??
.
UNIT ? V
10
Form the PDE by eliminating arbitrary function
( )
2 22
,0 f x y z xyz ++ = .
OR
11 A bar of length ?? with insulated sides is initially 0 ? temperature throughout the end ?? = 0 is kept at
0 ? for all time and heat is suddenly applied such that
????
????
= 10 at ?? = ?? for all time. Find the
temperature function ?? ( ?? , ?? ).
*****
Page 2 of 2
R13
FirstRanker.com - FirstRanker's Choice
This post was last modified on 11 September 2020