Download 12754

12754
*12754*
21011
3 Hours/100 Marks
Seat No.
Instructions :
(1) All questions are compulsory.
(2) Answer each next main question on a new page.
(3) Illustrate your answers with neat sketches wherever
necessary.
(4) Figures to the right indicate full marks.
(5) Assume suitable data, if necessary.
(6) Use of Non-programmable Electronic Pocket Calculator
is permissible.
(7) Mobile Phone, Pager and any other Electronic
Communication devices are not permissible in
Examination Hall.
MARKS
1. Attempt any ten of the following :
20
a) Evaluate log214 – log27.
b) Resolve into partial fraction
.
N
!
c) If
#
and
)
-
*
, find 3A – 2B.
!
N
d) Find x, if
&
"
e) Prove that sin A + cot A cos A = cosec A.
!
f) Find 5th term of
.
N
N
g) Find x, if log3(x+6) = 2.
P.T.O.
12754
*12754*
-2-
MARKS
h) If sin
is –ve, then find the quadrant in which
is +ve and cos
s
i) Prove that
i
n
t
c
o
a
lies.
.
n
s
j) Using principal value, find the value of
c
o
s
s
i
.
n
k) Find the value of x, if the distance between the points (x, 2) and (3, 4) is
.
&
l) Find the distance between parallel lines 2x + 3y + 7 = 0 and 6x + 9y – 10 = 0.
m) Find the equation of the circle joining (–3, 4) and (1, – 8) as diameter.
2. Attempt any four of the following :
16
"
a) Resolve into partial fraction
.
N
!
N
N
b) Resolve into partial fraction
N
"
c) Simplify
.
N
N
!
"
N
, using binomial theorem.
N
N
N
d) Expand upto first four terms using binomial theorem
.
N
e) Solve by Cramer’s rule
1
1
1
3
1
x
y
1
4
z
x
l
2
,
o
g
N
o
g
"
y
l
o
z
g
$
"
f) Find x if
.
l
l
o
g
$
9
1
4
x
y
z
,
1
6
.
*12754*
12754
-3-
MARKS
16
3. Attempt any four of the following :
!
find A2 – 3I
a) If
)
!
b) If
, verify that
!
)
,
*
)
"
*
*
)
!
c) Find the adjoint of matrix
"
)
!
#
"
!
$
!
#
d) Solve by matrix method x + y + z =2, y + z = 1, z + x = 3.
e) If
)
,
!
, show that AB is a non-singular matrix.
*
"
-
c
o
s
3
A
!
2
c
o
s
5
A
c
o
s
7
A
f) Prove that
c
c
o
s
A
2
c
o
s
3
A
c
o
s
5
o
s
2
A
s
i
n
2
A
.
t
a
n
3
4. Attempt any four of the following :
c
a) Prove that
o
s
)
s
i
n
a
n
)
)
c
o
t
i
n
)
c
o
s
.
)
)
b) Prove that 4 sinA sin (60°–A) sin (60°+A) = sin3A.
c) Prove that in any
s
d) Prove that
i
n
)
s
i
n
)
t
c
s
e) Prove that
i
o
n
s
)
)
c
s
i
n
o
s
"
a
n
.
)
)
!
)
s
!
)
c
i
n
#
)
s
i
n
%
)
t
c
f) Prove that
ABC tanA + tanB+tanC = tanA.tanB.tanC.
"
o
s
)
c
o
s
o
s
#
)
c
o
"
c
o
s
c
#
o
.
16
s
t
A
A
s
c
!
o
s
%
)
!
!
$
#
s
.
a
n
"
)
.
12754
*12754*
-4-
MARKS
16
5. Attempt any four of the following :
a) If (4, b) is the centroid of the triangle with vertices (a, 5), (6, – 2) and (–7, 3).
Find a and b.
b) In what ratio does C(3, 11) divides the line joining A(1, 3), B(2, 7) ?
c) Find the equation of the line passing through the intersection of the lines
2x – y = 14 and 2x + y = 10 and perpendicular to the line 3x – y + 6 = 0.
d) Find the equation of the line passing through the point (6, 5) and parallel to
the line which makes intercepts 2 and 4 on the coordinate axes.
e) Find the angle between the lines 2y + x = 1, x + 3y = 6.
f) Find the equation of the line making equal positive intercepts on coordinate
axes and passing through the point (– 2, 7).
6. Attempt any four of the following :
16
a) Find the area of quadrilateral whose vertices are (1, 2), (–2, 6), (–3, – 5) and
(2, – 7).
b) Find the equation of the circle passing through the points (0, 0) , (6, 0) and
(0, 8).
c) Find the equation of the circle which passes through (1, – 2), (4, – 3) and has
centre on the line 3x + 4y = 5.
d) Find the unit vector perpendicular to the vectors
and
a
2
i
j
3
k
.
b
3
i
j
4
k
e) Two forces
acting on a point P with position vector
2
i
7
j
,
2
i
1
5
j
6
k
and displaces it to point Q with position vector
4
i
3
j
2
k
. Find
6
i
j
3
k
work done.
f) Find the moment of force
point (2, –1, –4)
about the point (1, 2, 3) acting the
3
i
4
j
5
k
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