Guru Nanak Dev University 2007-2nd Sem B.Sc Chemistry MATHEMATICS - II (CHEM-204) (-2k7) - Question Paper
2057
B.Sc. (H.S.) in Chemistry II-Semester
CHEMISTRY
Paper - Chem-204
(Mathemetics - II)
Time allowed : 3 Hours
Maximum Marks : 75
Note :- Attempt ALL ques. in Section-A, 8 ques. in Section-B, and any 2 ques. in Section-C
(PLEASE REFER TO ATTACHMENT beneath FOR THE WHOLE ques. PAPER) 7104
B.Sc. (HS) in Chemistry II-Semester CHEMISTRY PaperChem-204 (MathematicsII)
Time allowed: Three Hours] [Maximum Marks : 75
Note :Attempt ALL questions in SectionA, EIGHT questions in SectionB, and any TWO questions in SectionC.
SECTIONA
( X/ Define a continuous function and discuss various types of discontinuities.
2. If f(x) and g(x) are differentiable functions, prove that
(Wx)--Eioo?-w*
- - cot X X
3. Evaluate:
V
4,/ If a ball, thrown vertically upwards, has equation
Y J
of motion s = ut + at2 in meters and seconds and if
Y a = -9 8 m/s2, find the maximum height reached when u = 30 m/s. /
5. The weight w gm of a liquid in a leaking container is given in terms of time t sec. by the relation
7104 1 (Contd.)
1 (p w = 600 lOt t3. Find the rate at which the liquid is / leaking out when t = 5 secs. -I
y b'Ijistate Rolles theorem. V ( **
U\ * 'Y *. W
1. State Taylors theorem.
Evaluate: J sec 2x dx. IH1">
<-9: Define definite integral and imterpret geometrically.
/ r dx
lpEvaluate: J j + x2 V 4 1 marks each
W SECTION2 1 .
, 1 iJJ</Find J (x ~l)dx as the limit of sum. * 5
0 . ' '
12. Find reduction formula for In=Jsin?xdx and evaluate I3. '
-1
f xtan x
13. Evaluate: f-=dx. > ,,-x ft
1 + X
- - r x*fc "f
1 Evaluate: J (r_T)(x-2)(x-3)N v
y \* v "*
. r- Trace the curve x3 + y3 = 3axy. v Vv
Find the Maclaurins expansion for tan-1 x.
\l\f y = tan-1 x, prove that v
' (1 + x2)2y2 + 2x (1 + x2)y, = 2.
\r'*'
v 1 2 H*h
V''1 J- yjl'
secx + 1
tf-V
sec x -1
18, Differentiate w.r.t. x Ji) ax
(ii)
-i
+ X + X
u-
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dy dx
. If x = a cos3 0, y = a sin3 0, find
. JT Find the area of the region between the curves y2 = 4x and its latus rectum by using integration.
d2u d2u
If u = tan-1 (y/x), prove that: + 2 =
Find the asymptote to the curve:
"ft
y2 (a - x) = x3.
4Vi marks each
dy sin2(a + y)
23. (a) If siny = x sm (a + y), prove that .
(b) Discuss the maxima and minima of the function :
f(x>y) = x +y + ~ + ~-
24. (a) Show that radius of curvature at the point
r \
3a 3a
~2~' ~T
on the curve x3 + y3 = 3axy is equal to
LfrA
X i X 1
(b) Evaluate: f --. 2 , ~ dx
v ' J (x + rr (x + 2)
5c(a)Find the equations of \he tangent and normal at
0 = to the cycloid K)
A t
x = a(0 - sin 0), y = a(l - cos 0).
r r~?--
Evaluate: J /x - 4x + 8 dx.
26. Evaluate:
* x tan x
J
(i)
- secx + tanx ,
* T?- *)
f .3(x + l)(x + logx)2 (ii) j x-dx
1/2 sin-'x
e S>U A.
(iii) I -YUi dx. 12 marks each
<
7104 4 100
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