Please check that this question paper contains 11 printed pages. . Code number
given on the right hand side of the question paper should be written on the titleĀ ...
~~,
65/1
1
P.T
00
1
100
-""'",
~;~~~~:;"".;
~t~,~;.,
l1fUffi
.0.
'
.J!
am
I
if
~
,~\,c.;t
I
~
~
~
'qjT
I
~
qj)
I
f(;r&
tf{
~-~
~
I
~
11
~
not write
~
fcfa\UT
"q:jT
~-~
I
't1
~
~
~
~
~
~-~~
qj)
~-~
~
~
"(fq:)"
~
~
~,
~
29
students will read the question paper only and will on the answer script during this period.
:
~
~
~
~
~
if
the
a.m.,
10.30
to
a.m.
10.15
From
a.m.
10.15
question
The
paper.
question
this
read
to
allotted
been
has
time
before
question
the
of
Number
Serial
the
down
be
should
paper
question
the
of
side
hand
right
the
on
given
~~~I
~
-
~
m
-~"q)T
3"(R"
~
Q5)s
a:rrtif
~
answer-book.
the
of
page
title
the
I
I
I
I
I
I
I
Candidates
*
I
1~(9.1
"~I
10.30
-q:;r
~
at
distributed
be
write
I
Marks:
tf{ ~
if
~
~-~
~
fCfj
~
"qj"{
J
~
.,;,.,.;
~
~
3lT\
~
ffl
~
I
I
fiR"?:
15
~-~
~
fCfj
~
"qj"{
.
I
q")1~
~
10.15
~
~
f I
x
~
~
~
+ ~
3,
~
3
x:S
~
1,
ax qjT
~
~
'b'
~
'a'
m
bx
~,
{log (x e)}
=
f(x)
~
'f',
~
~
{
+
dx
.
2
log x
-
-
a
ow
s
Y
,
-
x
dy -
t
th
h
e
-
x
Y
If
-
OR
bx + 3,
cosO)
7t] 2
+ cose)
0.03~~F~, I
~
~
F
~I"'~G
.q:
~R~~'1
~
~~~~~9~~~~, ~
65/1
6
m~~
3"{?AaJ
cm, I
~
~
~
~
.q:
its surface area.
2.
~
0.03
of
error
an
with
cm
9
]
~
[
0,
e,
-
e
error in calculating
sin
4
-
=
y
fCfi
~
(2
as
measured
is
sphere
a
of
radius
the
If ~
then find the approximate
.
[0
.
-
t"
,
f
m
.
Ion
.
.
OR
+
unc
- e .
4 sin e (2
(xe)}
mcreasmg
=
an
Prove t h at y
IS
.
{log
.
2
dx
15
X
log
=
~
~
I~
~...~~..' G~II~~
~ (11
~ ~,
y
-
x e
-
Y X
'-11~
-n&
3"{?AaJ
-{
(1 + x2) d2
show
that
d a) -L dx
-
+ (2x
~
m
~,
-d2y
x2)
(1 +
y)
log
(;
tan
=
-
+ (2x
a)
dx2 17. Evaluate: n/2
f
0
dx
:
~
f
n/2
x + sin x dx 1+cosx C
0
x dy
- y dx = .J;i-~7dx
Solve the following (y + 3x 2) -dx
""
,.
:
~
~
-qj)
~1.i1~,UI
,
~~;
"'-': '. "."
dx
equation:
R-~7
=
differe~tial
dx
~
RI'--1I(1~d
19.
y
following . -
the dy
Solve
x
18.
i
~
-dy =
x + sin x dx 1 + cosx
0 1=fr;:r
0
==
,
x
~
dx
fCfi
(; log y ),
= tan
16. If x
differential
-
equation:
=x
'
.
:
~
~1.i1~,UI
~
RI'--1I(1I(9d ~
-qj)
dy
=x
(y + 3x 2dx) -
dy 20. Using vectors, find the area of the triangle with vertices A(1, 1, 2),
5)
3,
B(2,
2),
1,
A(l,
m
~
7
---~
P.T.D.
~
-
65/1
~-
~
~
~
-q)1
~
~ I
'q}""{, ~
5)
m
5,
-q)1 C(l,
~
~
B(2, 3, 5) and C(l, 5, 5).
J"'--
b ~n'l
~"l
--~
:
~11~~
dx ~
~J"t;;
J
n/3
:
--=~~+
the
and
2k)
+
4]
+
(3i
A
+
~
1\ 2k)
+
':' 4J
':'
+
(31
A
+
1\ 2k)
+
':'
In
coins.
I
two
~
~ containing
~ each
~
~
III
and
~~
II
~
I,
5
=
and takes
out a coin. If the coin is of gold, what
box
a
chooses
person
A
coin.
silver
one
and
gold
one
is
there
III,
box
box I, both coins are gold coins, in box II, both are silver coins and in at random
is the
10
~
~ ~
~
~
"G1";1) ~ ~
~
~
-q:;r
I~, m ~ fu"iiiit
fiij
~
~
~
I
~ t,
t
III~,
~ }fll(.f~r:ff
~
~
~ ~
~
'i;fTm-q:;rt?
~
~
~ m
t,
-q:;r
m
~
~I
~
~
~
~
~
~ ~
III
~ ~
~
~
I
"G1";1)
II
I, ~
t
n~,
~ ~
I
t
~
~,
~
-q:;r
~ R~I(.'1ctl
~
m
~
probability that the other coin in the box is also of gold?
65/1
~
6
O.
-
=
=
x
~
~
x-~
~
I
3
+
x
I
=
-
(21
=
r
~
~
1\
~ k)
boxes
+
1\
10)
-
j
1\
5,
identical
(i
.
1\
-
1,
(-
three
r
~
~ ~ Given
28.
to x
= 5.
j + k) 1\
Y
= (2i - ]
J"
-
1\
~
. (i
=- 6
x
(- 1, - 5, - 10), from the point of
point
2k)
of the
+
distance
r
~
'(fP-1T ~
~
above x-axis and between
intersection of the line "1 plane
+ 31 and evaluate the area under the
':'
the
= Ix
y
~
q:jf
I
3
+
Find
-q:;r
x
I
'(f'qj
0
Y
= =
x
27.
31
x +
I
of
ml:fi
=
curve y
dx
--
)(:;":
Sketch the graph
~
26.
7
-5
.J-c:x
~
J
I
~
~
1:Jr;r
3:r~
nl6
",
~
rr
Determine
desktQP
40,000
a computers
Rs.
-
the number
of
demand
and
computers
25,000 monthly
Rs.
personal
cost
of total
will
types
will not exceed 250 units.
the
that
that
two
sell estimates
model
to
plans
portable
a
He
and
merchant respectively.
model
A
-
of units
of each type
of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs. 70 lakhs and his profit on the desktop model is Rs. 4,500 and on the portable
model is Rs. 5,000.
'
~
~
,
~
I
~
"(f4T
.
~
~
~
4,500~.
~W?J1R ~
~
m
~
~ ~
~
m1ft
-;rf:r
'"!iA1m
~
~
~
~
~~ ~
~m~
~
~
~
~ o;f1i't
~ 0
5
2
~
~,
mG-'fq
~
1:{lfuCfi
~
m
~ 70 5,000~.~,
40,000~.
-q;~
~
~ -q;~ 31f~
fC:ti
25,000~.
"5fqjT{
"GT
~
~~
~. ~ "(f4T i-~ifq
~
"qj~~~~~~~?
~~
"(f4T
~ml:fi~~~1
~
r
~~
~
~
Wm'{T
~
W?J1R
~ ~
~
~
~
~
Make an L.P.P. and solve it graphically.
65/1
.
rll.li..iiiiii...iii_..ii~.;;;;;;;;;;;;;
11
~~~~~
'.
t,-~
,