JNTU Kakinada B-Tech 1-1 R161102 MATHEMATICS-I R16 May 2018 Question Paper

JNTU Kakinada (JNTUK) B-Tech First Year First Semester (1-1) MATHEMATICS-I R16 Regulation May 2018 Question Paper

Code No: R161102
I B. Tech I Semester Supplementary Examinations, May – 2018
MATHEMATICS-I
Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Solve the DE 0 dy e dx e xy y
x x
= – + ) ( . (2M)
b)Solve the DE
11 1
2 10 0, y y y – + = given y (0) = 4, y
1
(0) = 1. (2M)

c)If
2 2
x y
u
x y
=
+
then find
u u
x y
x y
? ?
+
? ?
(2M)

d)z y x
f
find then e z y x f If
3
xyz
? ? ?
?
= ) , , (
(2M)
e) Find 3 (2M)
f) Solve z=p(x+1)+q(y+2). (2M)
g)Classify the nature of the PDE
2 2 2
2 2
2 4 0
u u u
x x y y
? ? ?
+ + =
? ? ? ?
(2M)
PART ?B
2. a) A body kept in air with temperature 25
0
C cools from 140
0
C to 80
0
C in 20
minutes. Find when the body cools down to 35
0
C. (7M)
b) An R ? L circuit has an Emf given (in volts) by 10 sin t, a resistance of 90
ohms, an inductance of 4 henries. Find the current at any time t by assuming
zero initial current. (7M)
3. a) Solve the DE (D
2
+ 1)y = cotx by the method of variation of parameters (7M)
b) Determine the charge on the capacitor at any time t > 0 in circuit in series having
an emf E(t) = 100 sin 60 t, a resistor of 2 ohms, an inductor of 0.1 henries and
capacitor of farads, if the initial current and charge on the capacitor are
both zero.
(7M)
4. a)Evaluate

(7M)
b)Using Laplace transform solve


0

(7M)
5. a)Find the minimum value of
2 2 2
x y z + + subject to ax + by + cz = p.

(7M)
1
260
SET – 1
R16
1 of 2

Code No: R161102
I B. Tech I Semester Supplementary Examinations, May – 2018
MATHEMATICS-I
Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Solve the DE 0 dy e dx e xy y
x x
= – + ) ( . (2M)
b)Solve the DE
11 1
2 10 0, y y y – + = given y (0) = 4, y
1
(0) = 1. (2M)

c)If
2 2
x y
u
x y
=
+
then find
u u
x y
x y
? ?
+
? ?
(2M)

d)z y x
f
find then e z y x f If
3
xyz
? ? ?
?
= ) , , (
(2M)
e) Find 3 (2M)
f) Solve z=p(x+1)+q(y+2). (2M)
g)Classify the nature of the PDE
2 2 2
2 2
2 4 0
u u u
x x y y
? ? ?
+ + =
? ? ? ?
(2M)
PART ?B
2. a) A body kept in air with temperature 25
0
C cools from 140
0
C to 80
0
C in 20
minutes. Find when the body cools down to 35
0
C. (7M)
b) An R ? L circuit has an Emf given (in volts) by 10 sin t, a resistance of 90
ohms, an inductance of 4 henries. Find the current at any time t by assuming
zero initial current. (7M)
3. a) Solve the DE (D
2
+ 1)y = cotx by the method of variation of parameters (7M)
b) Determine the charge on the capacitor at any time t > 0 in circuit in series having
an emf E(t) = 100 sin 60 t, a resistor of 2 ohms, an inductor of 0.1 henries and
capacitor of farads, if the initial current and charge on the capacitor are
both zero.
(7M)
4. a)Evaluate

(7M)
b)Using Laplace transform solve


0

(7M)
5. a)Find the minimum value of
2 2 2
x y z + + subject to ax + by + cz = p.

(7M)
1
260
SET – 1
R16
1 of 2

Code No: R161102

b) Check whether the following are functionally dependent or not, then find the
relation between ( )
2
,
x y xy
u v
x y
x y
–
= =
+
+
(7M)
6. a) Find partial differential equation by eliminating arbitrary function
2 2( , ) 0 f x y z xy + – =
(7M)

b)Solve the PDE pq 1
z
p
2
2
– = .
(7M)
7. a)Solve the PDE ( )
2
2 1 1 2
3 3
x y
D D D D z e
–
– – + = (7M)
b)Solve the PDE ( )( )
1 1 3
1 2
x y
D D D D z x e
–
– – – – = + (7M)

R16
SET – 1
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