Time : 3 hours
04  Mathematics 
July
2007
Marks : 100
Pg 
1
Instructions :
1.
Answer
all
questions.
2.
Write
your
answers
according
to
the
instructions
given
below
with
the
questions.
3.
Begin
each
section
on
a
new
page.
S E CT I O N

A
•
Given
below
are
1
to
15
multiple
choice
questions.
Each
carries
one
mark.
Write
the
serial
number
( a
or
b
or
c
or
d )
in
your
answer
book
of
the
alternative
which
you
feel
is
the
correct
answer
of
the
question.
15
1.
Find
the
angle
between
the
lines
x
=
3
and
y
=
5.
( a )
2
π
( b )
3
π
( c )
6
π
( d )
4
π
2.
If
the
lines
5x

Ky

7
=
0
and
2x
+
3y
+
5
=
0
are
mutually
perpendicular,
then
the
value
of
K
=
?
10

10
15

15
3.
How
many
tangents
can
be
drawn
from
the
origin
( 0,
0 )
to
the
curve
x
2
+
y
2
=
25 ?
4.
If
x
2
=

16y,
then
find
the
equation
of
the tangent
which
is
perpendicular
to
Y

axis.
5.
Find
the
direction
cosines
of
the
vector
2i
+
2j
+
k.
( a )
3
1
,
3
2
,
3
2
( b )

2,
2,
1
( c )
3
1
,
3
1
,
3
1
( d )
1,
1,
1
6.
Find
the
eccentricity
of
hyperbola
3x
2

12y
2
=
36.
3
3
2
5

5
7.
Find
the
projection
of
vector
( 1,
1 )
on
the
direction
( 3,
4 ).
7
( 1,
1 )
7
( 3,
4 )
7
8.
Find
the
rate
of
change
of
volume
of
a
sphere
having
radius
r
with
respect
to
its
surface
area.
r
r
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