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* *
4249
*
C14–M–301/C14–CHOT–301/C14–RAC–
301
4249 BOARD DIPLOMA EXAMINATION, (C–14)
42 9
MARCH/APRIL—2016
DME—THIRD SEMESTER EXAMINATION ENGINEERING MATHEMATICS—II
[ Total Marks : 80
42
9
Time : 3 hours ]
PART—A
3×10=30
Instructions : (1) Answer all questions.
9
(2) Each question carries three marks.
42
1. Evaluate :
ò (sec
2
x - e x + sin x ) dx
42
9
2. Evaluate : 1
ò 1 - cos x dx
3. Evaluate :
ò
*
e tan
-1
x
1 + x2
dx
4. Evaluate : 1
1
ò-1 x + 2 dx /4249
1
*
[ Contd...
*
5. Find the mean value of
1 1 + x2
6. Find the differential y = A cos 3x + B sin 3x.
in the interval (0, 1).
equation
of
the
family
of
curves
7. Solve :
42 9
dy 1 + x 2 = dx 1 + y 2
8. Solve :
42
9
dy 2y 1 + = dx x x2
9. Find out the range and coefficient of dispersion of the following data :
42
9
60, 50, 85, 90, 70, 40, 110, 130, 120, 100
10. Find the standard deviation of 16, 13, 17, 12.
PART—B
9
10×5=50
42
Instructions : (1) Answer any five questions. (2) Each question carries ten marks.
11. (a) Evaluate :
ò sin 6x × cos 2x × dx
*
(b) Evaluate : 1
ò 5 + 4 cos x dx /4249
2
*
[ Contd...
*
12. (a) Evaluate :
1
ò
x 2 + 2x + 5
dx
(b) Evaluate : 2
(x + 36)(x 2 + 25)
dx
42 9
1
ò
13. (a) Evaluate :
ò sin
-1
x . dx
(b) Evaluate : p /2
1 + cos 2x dx
42
9
ò0
14. (a) Find the area bounded by the ellipse 4x 2 + 9y 2 = 36 using the method of integration. (b) Prove
sin x p dx = 4 sin x + cos x
9
p /2
42
ò0
15. (a) Evaluate
1
1
ò0 1 + x dx
using trapezoidal rule by taking n = 4
9
intervals.
42
(b) Find the volume of solid formed by revolving the area enclosed by the circle x 2 + y 2 = a 2 .
16. (a) Solve : dy + 2y cot x = 3x 2 cosec2 x dx
* (b) Solve :
(2x - y + 1) dx + (2y - x - 1) dy = 0 /4249
3
*
[ Contd...
17. (a) Solve :
* dy y æy ö = + tan ç ÷ èxø dx x
(b) Solve : dy y 2 + y + 1 = dx x 2 + x + 1
2
3
Marks in Mathematics
60
15
20
Marks in Statistics
10
40
30
4
5
6
7
8
28
12
40
80
20
50
30
20
60
30
42
9
1
Student No.
42 9
18. From the marks obtained by 8 students in mathematics and statistics, compute the rank correlation coefficient and interpret the result :
42
9
42
9
HHH
*
/4249
4
*
AA16—PDF
4249~429.pdf
x e x dx. x. - + ò.
2
. Evaluate : 1. 1 -. ò. cos x. dx. 3. Evaluate : e. x. dx. tan x. -. +. ò. 1. 1.
2
. 4. Evaluate : 1. 1
2
. 1. x. dx. - +. ò. /4249 1 [ Contd... * 4
2
4
9
*. Page 1 of ...
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