- The document appears to be instructions for an examination. It details instructions students must follow during the exam, including only reading the question paper during the first 15 minutes and not writing anything during that time.
- The exam consists of 3 sections (A, B, C) with Section A containing 10 one-mark questions, Section B containing 12 four-mark questions, and Section C containing 7 six-mark questions.
- Other instructions include writing identification details on the answer booklet, not using calculators, and that all questions are compulsory. The total marks for the paper are 65.
1. ~~,
65/1
1
P.T
00
1
:
100
-""'",
~;~~~~:;"".;
~t~,~;.,
l1fUffi
.0.
'
.J!
am
I
if
~
,~,c.;t
I
~
qj)
I
f(;r&
tf{
~-~
~
I
~
11
~
not write
~
~
~
~
'qjT
I
~
~
~-~~
fcfaUT
"q:jT
~-~
I
't1
~
~
~,
~
students will read the question paper only and will
on the answer script during this period.
qj)
~-~
~
~
"(fq:)"
~
~
~
~
29
~
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
~
~
10.30
~
~
at
distributed
be
write
I
1~(9.1
"~I
~
-q:;r
if
~
~-~
~
fCfj
~
"qj"{
J
Marks:
tf{
~
~
~
3lT
~
ffl
~
I
I
.,;,.,.;
fiR"?:
15
~-~
~
fCfj
~
"qj"{
.
I
q")1~
~
10.15
~
~
f<-I~-t1
,
IIi
I
~
~
qj)
'qjT
number
Code
I
3:rfi:rq;frif
MATHEMATICS
~-:1I"I'111
~
M
attempting
4.
~
4-
Please
I
q
GI~I'1
~
will
minutes
15
';f
I
Maximum
hours
3
if
~
paper
.
I
f!TJi
~
~
~
.
m
~-~
~
.
~-~
~
.
.
3
"'~
~
.
.
.
~ql~
10.15
.
No.
:
~
.
~
Roll
allowed:
llme
65/1
No.
Code
I
SOS
Series
I
'frirlr
R~
;'
qj)-s ;{.
must write the Code on
0.
";1.
Please check that this question paper contains 11 printed pages.
written on the title page of the answer-book by the candidate,.
Please check that this question paper contains 29 questions.
it.
any answer
~j{
0"
...",.-c'
-.f
3. -
65/1
3
',..
)
.
sm
sm
+
.
cos 75°
-1
I
'~~:
_c"::~~t
,
~
'Q
3
cos
2n)
~
I
~
"j:fR"
(
~
3]
A.
of
-1
~
if
~
cos
0
ue
va
f
~
~
~
-1
terms
.
"q:jT
3
sm
. 2n)
~
sin 75°
m
sin 15°
A
3]
I
~
A
cos 15°
i:I1T
15°
sm-
I
m
[ 2'
1(
A-I
[2
.
~,
sin 75°
wrIte
,
sin
prrnCIpa
..
m
~,
5
+
3)
2n
~
5
e
t
IS
at
W
. h
5
:
~
( cos
if
i
15°
cos
1
=
cos-
=
~
3.
A
"j:fR"
h
3W3lif;
5.
If
I
I
A
~
.
2
~
*
4.
( . 2n)
.
.
3
I
~
arI;rqr
~
f~
~
fqj
~
I
~
~
~
~
B
A~
6)}
(3,
5),
(2,
4),
{(I,
=
f
~
m
7}
6,
5,
{4,
=
B
3},
2,
{I,
=
A
trRT
not.
or
one-one
is
f
whether
State
B.
to
A
from
function
a
be
6)}
(3,
5),
(2,
4),
{(I,
=
f
let
and
7}
6,
5,
{4,
=
B
3},
2,
{I,
=
A
Let
1.
I
-ff
qj7
3iCli
1
~
~
n-q;
10
:if
1
~
~
each.
mark
1
carry
10
to
1
numbers
Question
'
~3:r
~r
SECTION
:
A
";4;!'ii1Y~&
c/fi~1~f(:!
?
Evaluate:
cos 75°
:'"
,.
-2
.
-2
If a matrix has 5 elements, write all possible orders it can have.
P.T.G.
~
~
4. -.c~'-
1:fT";f~
.
dx
b)3
~
f
:
(ax
+ b)3
dx
Evaluate:
In
7.
+
(ax
Evaluate:
f
6.
~
:
In
1:fT";f
~
Write
of the
(1, 0, 0) "(f~ (0, 1, 1) ~
Write
the
points
(1,
~
I
vector
1
- j
i
1
on the vector
4
7
I
~4-iIct>(UI~
~~'1:&r'qjT~
2
z-6
-.
. y+4
=
x-5
-
b
=
.
-
1.
y
0
equatIon
~
=
~
=
~
I
65/1
7
1
i + j.
~~~I
+j
f
.
vector
1
3
3
0, 0) and
1
i
1
'qjT~
1
e
t
W
the
firc;rR "qR;ft '1:&r ~ ~-~~
of the
h
.
rIte
.
projection
i-j
~
1
10
joining
1).
~an
9.
line
gIven
1,
direction-cosines
me
(0,
the
a
8.
2
6. - 2
2x - 3
2x - 9
2x - 27
:
~
~
3x - 16 = 0
x- 8
~
3x - 4
x- 4
~
x
~
RJor1I(.1I~(1
~
m
qjT
""J]um
~
~1fTJl~1
3x - 64
x
14. Find the relationship
between 'a' and 'b' so that the function 'f' defined
by:
{ ax + 1,
if
x:S 3
f(x) =
is continuous at x = 3.
if
x > 3
~,
"qft~
3
>
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
7. -{
(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
dx
(y + 3x 2) -
""
,.
:
~
~
-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).
8. 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<!~~J
~
~
~
~
~
~
~
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
9. 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,-~
,