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Institute:
**
JNTUK KAKINADA
**Course:
**
B.Tech
**Specialization:
**Electronics and Communication Engineering**Downloads:
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Set No - 1
Subject Code: R161102/R16
I B. Tech I Semester Regular Examinations December - 2016
MATHEMATICS-I
(Common to all branches)
Time: 3 hours
Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Four Questions should be answered from Part-B
*****
PART-A
1. (a) Find the orthogonal trajectory of r =
2a
1 + cos θ
(b) Find the P.I of ( D + 2)2 y = x 2
et if 0 < t < 1
(c) Find L(f(t)) where f (t ) =
0 if t > 1
2s 2 − 1
−1
(d) Evaluate L 2
2
( s + 1)( s + 4 )
du
(e) Find
If u = sin ( x 2 + y 2 ) , where a 2 x 2 + b 2 y 2 = c 2
dx
(f) Solve the PDE pq (px + qy -z)3 = 1
∂ 2u
∂ 2u
∂ 2u
+4 2 =0
(g) Classify the Nature of PDE 2 + 2
∂x
∂x∂y
∂y
[7 x 2 = 14]
PART-B
dy x 2 + y 2 + 1
=
dx
2 xy
(b) A resistance of 100 ohms, an inductance of 0.5 Henry is connected in series with a
battery of 20 volts. Find the current in the circuit, if initially there is no current in the
circuit
[7+7]
3
2 −x
3. (a) Solve the D.E ( D + 1) y = cos(2 x − 1) + x e
2. (a) Solve the D.E
(b) Consider an electrical circuit containing an inductance L, Resistance R and capacitance
C. let q be the electrical charge on the condenser plate and ‘i’ be the current in the circuit
at any time. Given that L = 0.25 henries, R = 250 ohms, q = 2x10-6 farads and there is no
applied E.M.F in the circuit. At time zero the current is zero and the charge is 0.002
coulomb. Then find the charge (q) and current (i) at any time.
[7+7]
Page 1 of 2
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Set No - 1
Subject Code: R161102/R16
1
s 2 + b 2
4. (a) Evaluate L−1 log 2
2
s + a
2
(b) Solve ( D 2 − 1) x = a cosh t if x (0) = 0, x1 (0) = 0. using Laplace transform method.
[7+7]
5. (a) Find the dimensions of a rectangular parallelopipid box open at the top of max capacity
whose surface area is 108 sq inches.
u , v, w
(b) If u = x + y + z , u 2 v = y + z , u 3 w = z then find J
x, y , z
6. (a) Solve
+
−
+
=
−
2 2
2 2
2 2
2
2
(b) Solve the PDE p q + x y = x q ( x + y )
[7+7]
[7+7]
7. (a) Solve the PDE
(b) Solve the PDE
( D + D −1)( D + 2D
1
1
− 3) z = 4 + 3 x + 6 y
∂2 z
∂2 z ∂2 z
+
2
+
= 2sin y − x cos y
∂x 2
∂x∂y ∂y 2
[7+7]
*****
Page 2 of 2
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Set No - 2
Subject Code: R161102/R16
I B. Tech I Semester Regular Examinations December - 2016
MATHEMATICS-I
(Common to all branches)
Time: 3 hours
Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Four Questions should be answered from Part-B
*****
PART-A
dy
1. (a) Solve the D.E ( x + 2 y 3 ) = y
dx
2
(b) Find the P.I of ( D − 1) ( D + 2) y = e x
(c) Find L(sin 2t sin 3t )
3s + 1
(d) Evaluate L−1
4
( s + 1)
∂u ∂u
(e) Find
+
if u = f(x + y, x-y)
∂x ∂y
(f) Solve the PDE pq = p + q.
∂ 2 z ∂ 2 z ∂z
+ −z=0
(g) Solve the PDE 2 −
∂x ∂x∂y ∂y
[7 x 2 = 14]
PART-B
2. (a) Find the Orthogonal trajectory of the family of confocal conics
x2
y2
+
= 1 , where λ
a2 a2 + λ
is a Parameter.
(b) The number of N of bacteria in a culture grew at a rate proportional to N. The value of N
was initially 100 and increased to 332 in one hour. What was the value of N after 3/2
hours?
[7+7]
2
2
3. (a) Solve the D.E ( D + 1) y = sec x by the Method of variation parameters
(b) Consider an electrical circuit containing an inductance L, Resistance R and capacitance
C. Let q be the electrical charge on the condenser plate and ‘i’ be the current in the circuit
at any time. There is applied E.M.F Esinωt in the circuit. Then find the charge on the
capacitor.
[7+7]
∞
2
sin t
4. (a) Evaluate ∫ e − t
dt using Laplace transform
t
0
(b) Solve ( D 4 − k 4 ) y = 0 if y (0) = 1, y1 (0) = 0, y11 (0) = 0, y111 (0) = 0. using Laplace
transform method
[7+7]
Page 1 of 2
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Set No - 2
Subject Code: R161102/R16
5. (a) Find the point in the plane 2 x + 3 y − z = 5 which is nearest to the origin.
(b) Prove that u = x 1 − y 2 + y 1 − x 2 , v = sin −1 ( x ) + sin −1 ( y ) are functionally dependent and
find the relation between them.
[7+7]
2
2
6. (a) Solve the PDE z ( y − x ) = qy − px
(b) Solve the PDE z 2 ( p 2 + q 2 ) = x 2 + y 2
[7+7]
7. (a) Solve the PDE
(b) Solve
(D
2
− DD − 2D ) z = sin(4 y + 3x)
1
∂2 z
∂2 z
∂2 z
−
6
+
9
= 12 x 2 + 36 xy
∂x 2
∂x∂y
∂y 2
[7+7]
*****
Page 2 of 2
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