Jawaharlal Nehru Technological University Hyderabad 2010-1st Year B.Tech -\\Computer Science & Engineering\ regular\MATHEMATICs I set 3 - Question Paper
Code No: 09A1BS01 R09 Set No. 3
I B.Tech Regular Examinations,June 2010
MATHEMATICS-1
Common to ME, CHEM, BME, IT, MECT, MEP, AE, BT, AME, ICE,
E.COMP.E, MMT, ETM, EIE, CSE, ECE, EEE,CE
Time: three hours Max Marks: 75
ans any 5 ques.
All ques. carry equal marks
Code No: 09A1BS01 R09 Set No. 3
I B.Tech Regular Examinations,June 2010 MATHEMATICS-1 Common to ME, CHEM, BME, IT, MECT, MEP, AE, BT, AME, ICE, E.COMP.E, MMT, ETM, EIE, CSE, ECE, EEE,CE Time: 3 hours Max Marks: 75
Answer any FIVE Questions All Questions carry equal marks
Solve the differential equation (D4 2D3 + 2D2 2D + 1)y = cos x Solve the differential equation (D3 3D 2)y = x2
1. (a (b
2. (a (b (c
[7+8]
Form the differential equation by eliminating arbitrary constants y = ex (ACos x + B Sin x)
Solve the differential equation ex-ydx + ey-xdy = 0
If the air is maintained at 150C and the temperature of the body drops from 700 C to 40 in 10 minutes. What will be its temperature after 30 minutes.
[4+5+6]
If u3 + xv2 uy = 0 , u2 + xyv + v2 Find the shortest distance from the point (1,0) to the parabola y2 = 4x [8+7]
0 find du dv_
0 fin r. , r\ , r\ , r\
dx 5 dx 5 oy1 dy
3. (a (b
4. (a (b
5. (a (b
6. (a (b
7. (a (b
8. (a (b
Find the directional derivative of f(x,y,z)=xy2+yz3 at the point (2,-1,1) in the direction of the vector i+2j+2k.
Evaluate by stokes theorem f (exdx + 2ydy dz) where c is the curve
C
x2 + y2 = 9 and z = 2 [8+7]
Find the volume of the solid generated by cycloid x = a (9 + sin#), y = a (1+cos9), when it is revolved about its base.
Evaluate f log z f f x+log y ex+y+z dzdydx [8+7]
Find the Laplace transform of periodic function f(t) with period T, where f (t) = 4Et E, 0 < t < T/2 = 3E 4Et, T < t < T
Find the inverse Laplace transform of (s3(-6s2+1+5-6)
Test the convergence of the series | + 14 + 3.4.9 + 3~6'9~i2
Prove that the series 23 33 (1 + 2) + 43 (1 + 2 + 3) 53 (1 + 2 + 3 +4).....to
is conditionally convergent. [7+8]
The radius of curvature at any point P on the parabola y2 = 4ax and S is the focus, then prove that p2a (SP)3
Find the equation of the circle of curvature of the curve x = a(cos 9 + 9 sin 9), y = a(sin 9 + 9 cos 9) [7+8]
[8+7]
+
-k -k -k -k -k
5
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| Earning: Approval pending. |
