LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIRST SEMESTER – NOVEMBER 2012
MT 1101 - MATHEMATICS FOR STATISTICS
Date : 03/11/2012
Time : 1:00 - 4:00
Dept. No.
Max. : 100 Marks
PART – A
Answer ALL questions
dy
dx
1. If y=log(2x+3) then find
2. If y  esin
1
x
with respect to z  sin 1 x ,
3. Define implicit function.
x4  1
4. Find the value of lim
.
x 1 x  1
5. Define Homogeneous function.
6. If u  sin(ax  by  cz ) then find
7. Evaluate:
8. Solve
 tan
2
(10 x 2 = 20)
dy
dz
u u u
.
,
,
x y z
xdx
1
 x log x dx
9. Write the two properties of definite integrals.
10. Evaluate:
 tan
1
xdx
PART – B
Answer any FIVE questions
11. Differentiate:
sin x
.
1  tan x
dy
1  x2 1
with respect to z  tan 1 x , find
dz
x
13. Examine whether the following functions are odd or even functions.
12. If y  tan 1
(a) ax 7  bx5  cx3  dx
(b) ax 6  bx 4  cx 2  d
x
, when x is positive.
1 x
15. State and prove Euler’s theorem.
14. Show that x  log(1  x) 
16. Evaluate:

x
2
 4 x   2 x  3
x3
dx
17. Evaluate the rational algebraic function
lx  m
 ax  bdx .
(5 x 8 = 40)
18. Evaluate:
2x 1
 ( x  3)
2
dx
 3x  1 
19. a). If y  sin 1 

 4 
PART – C
Answer any TWO questions
dy
then find
dx
e x tan 1 x
(2 x 20 = 40)
2
b). Differentiate y 
1  x2
.
(10+10)
20. a). Find the limit of the function lim
x a
x
5
8
1
a
5
8
1
x 3 a 3
b). Determine the maxima and minima of the function f ( x)  x5  5x 4  5x3  10
(10+10)
21. a). Evaluate:
 x
x 1
dx
2
 1  2 x  1
2
b). Using by parts method find out the value of
22. a).Evaluate:

x sin 1 x
3x  4
1  x2
dx
(10+10)
 ( x  7)(2 x  3)dx
b). Evaluate  sin 6 xdx using reduction formula.
***********
(10+10)