### Jntu Btech Maths Previous paper download

Code No: R05010102 Set No. 3
I B.Tech Regular Examinations, Apr/May 2007
MATHEMATICS-I
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. (a) Test the convergence of the following series P 1
(log log n)n [5]
(b) Find the interval of convergence of the series
x + 1
2 . x3
3 + 1
2 . 3
4 . x5
5 + 1.3.5
2.4.6 . x7
7 + ..... [5]
(c) Show that log (1 + ex) = log 2 + x
2 + x2
8 − x4
192 + ..... and hence deduce that
ex
ex+1 = 1
2 + x
4 − x3
48 + ..... [6]
2. (a) Given that x+y+z=a, find the maximum value of xmynzp.
(b) Find the envelope of the circles through the origin and whose centre lies on
the ellipse x2
a2 + y2
b2 . [8+8]
3. (a) Trace the curve : r = a ( 1 + cos θ ).
(b) Find the length of the arc of the curve x = e sinθ; y = e cosθ from θ = 0 to
θ = π/2. [8+8]
4. (a) Find the differential equation of all parabolas having the axis as the axis and
(a,0) as the focus.
(b) Solve the differential equation x2dy
dx = ey − x.
(c) Find the orthogonal trajection of the family of curves x2/3 + y2/3 = a2/3.
[4+6+6]
5. (a) Solve the differential equation: d2y
dx2 + 4 dy
dx + 5y = −2Coshx given that y(0)
= 0, y′(0) = 1.
(b) Solve the differential equation: (2x − 1)3 d3y
dx3 + (2x − 1) dy
dx − 2y = x. [8+8]
6. (a) Evaluate L{et(cos2t + 1/2 sinh2t)} [5]
(b) Find L−1 1
s2+2s+5 [6]
(c) Evaluate the triple integral
1
R
0
1
R
y
1−x
R
0
x dz dx dy [5]
1 of 2
Code No: R05010102 Set No. 3
7. (a) Evaluate ∇2 log r where r = px2 + y2 + z2
(b) Find constants a, b, c so that the vector A =(x+2y+az)i +(bx-3y-z)j+(4x+cy+2z)k
is irrotational. Also find ϕ such that A = ∇φ . [8+8]
8. Verify Stoke’s theorem for the vector field F=(2x-y)i-yz2j-y2zk over the upper half
surface of x2+y2+z2=1, bounded by the projection of the xy-plane. [16]