2nd pu maths jan 2015.pdf
TRANSCRIPT
8/20/2019 2nd PU Maths Jan 2015.pdf
http://slidepdf.com/reader/full/2nd-pu-maths-jan-2015pdf 1/4
\J/
:I
S*&&-
+:= *.=
-PUCPA
.:
District
Level
Preparatory
Examination,
January
2015
il
P.U.C
rrebnpMATrCS
(351
Time
:
3
hours
15
minute
Max.
Marks
:
lOO
Instructions
:
(i)
The question
paper
has
fiue
parts
mamely
A,
B,
C,
D
and.
E.
Ansuter
all
the.
parts.
(i0
Use
the
graph
sheet
for
the
Etestion
on
Linear programming
in
pART
E.
ISiNg
PART
-
A
Answer ALL
the
questions
=30
wsr
.rrr'
L't tlu
1o x
1=1o
1'
Let
"
be
the
binary
operation
on
N
given
by a*b=L.C.M
of a
and b,
find
2.
Which
interval
of
f(x)
:
sin-1x
is called
principal
value
branch?
how
-_--
--
-\--l
l,rurwrpor.
v4ruE
ulal
*
3.
construct
a 3x3
matrix
A
=
(ai;)whose
elements
are given
uv
*,:=
;
&
4.
rrA
=
(:
il*o
trot.
5.
Differentiate
1og (cos
e")
w
r
t to
x .
6.
Evaluate
:-
tar*2x.dx
7.
Find
the
angle
between
the two
vectors
d
and
d
such
that
ld
|
=1
,
lBl
-
1
and
d.i=r
8'
Find
the
equation
of the plane
with
the intercept
2,3
and.4
on
x,
y
and
z axesrespectively.
9.
Define
Linear
objective
function,
in
linear
programming
problem
10.
A fair
die
is
rofled
.
consider
the
events
E={1,3,5}
and
F={2,3}
,
find
P(E
lF)
p
PART
B
Answer
any
TEN questions:
lO x2=2O
i
1.
Find the
gof
and
fog
if
/(x)
=
Bx3
and
g(x)
=
5i
12.
If
sin
(sin-r
]
+ cos-1
x)
=
, thepr
find
the value
of
x
13.
write
the
function
tan-1
(ry=)
x*
0,
in
the
simplest
form.
For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com
8/20/2019 2nd PU Maths Jan 2015.pdf
http://slidepdf.com/reader/full/2nd-pu-maths-jan-2015pdf 2/4
t4'
X'#J:ilH?lf,::"".
passins
through
the
points
(3,2)
and
15
16.
find
Idx
18.
19.
20.
?
3
3
25'
show
that
the
reration
R
in
the
set of arl integers
Z
defined
by
=
{(a'
b):2
divides
*ul
i.
an
equivarence
reration.
26.
Find
the
vatue
of
tani
[r,"_,
(#)*
cos_l
tr)]
lx
I
.1
,
yro
and
xy<
1
22.
If
A=E
f,1,
n"aA-r
by
elementary
operdtions.
28.
If y=
1-r-1(-',",
)
then
prove
thatff:
29.
Differentiate
xtiw
+
(sfn
x)cosx
w.
r.
t.
x
,
30'
Find the absolute maximum value
and
the
absolute
minimum
value
of
he
function
f(x)=sinx+qesx,
xe
[0,n]
41.
(-
1,-3)
by
Find
the
derivative
of
,li
*Ji
=9
at
({,51
If
y=
logz(log),
17.
Evaluate
/
#d"
Evaluate
I
,,
(T)*
;f*:T:"ffi,"jj[TTgent
to
the
cur:ve
y=x3_
3x
*
2
at
the
point
Find
the
order
and
degree
of
the
differentiar
equation
,cy#*.(X)'
-
y#=o
27
'
Find
the projection
of
the
vector
i
+
sj
+
7ft
onthe
vecto
r
7t
_
j+
8[.
22.It
d
is
a
unit
vector
and (i
_
A).(i
+
d1=15,
then
find
lif
23'
Find
the
distance
of
the
point
(2,3,-5)
from
the
plane
i. (e
+ 2i
_
2rt1=g
24.
If
the
probability
distribution
of
X
is
'
PART
C
Answer
any
TEN
questions:
1O
x
3=OO
39
40
42.
43.
X
o
1
k
2
3
4
k
P(x)
0.1
2k
2k
44.
For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com
8/20/2019 2nd PU Maths Jan 2015.pdf
http://slidepdf.com/reader/full/2nd-pu-maths-jan-2015pdf 3/4
31.
Evaluate
I
tl*
J
x(xn+t)
Evaluate
{
e*siruc
d.x
Find
the
area
of
the
circle
xt+yz
=4 bound.ed
by
the
lines
x=0
and
x=2
which
is
lying
in
the
first
quadrant.
In
a
bank, principal
"P"
increases
continuously
at
the
rate
of
5% per
year.
Find
the
principal
interest
of
time
t.
Find
a
vector
perpendicular
to
each
of
the
vectors
d
+i
and,
d
-i
where
d
=
3i
+2i+2ft
and
E
'=
i
+2J-2rt
lf
d=-4t
-6i
-
ffi,
,i
=
-t
+4j+gfr
and
d
=
_Bi
-jfifr,
are
coplanar,
find,tr
Find
the
equation
of
the
line
which
passes
throught
the point
{r,2,Bl
and
is parallel
to
the
vector
3i
+2i-2p
both
in
vector
form
and
cartesian
form.
Bag
I
contains
3
red
and
4
black
balrs
and
while
another
bag
II
contains
5 red
and
6
block
balls.
one
ball
is
drawn
at random
from
one
of
the
bag
and
it
is
found
to
be
red.
Find
tJre
probabilify
that
it
was
drawn
from
bag
II
?
,
PART
D
Answer
any
SIJX
questions:
6 x
S=3O
consider
f
:
R*-+
[5,o)
given
by
f (E
= 9x2+6x-s,
show
that
f is
invertibre
withfl
(y)
=[+]
If
A=[3
+
l]
,
,"riry
A3
-3A2
-10A
+24r=o,
where
o
is
zerom
matrix
oforder3x3
'Solve
the
equations
x-y+
3z=lO,
x-y-z=-Z
and
2x+3
y+42=4
by
matrix
If y
-
Aeru
*
Benx
then
pro]/e
that#
-
(m
*
n)H*
mny
=
g.
A
man
of
height
2
meters
walks
at
a
uniform
speed
of
5 km/hour,
away
from
a
lamp post
which is
6 meters
high
.
Find
the rate
at which
the
length
of
his
shadow
increases
Find
the
integral
of
#w.r.t
x
and
hence
evaluate
t
ffia*.
32.
33.
36.
37.
34.
35.
38.
39.
40.
42.
43.
4L.
44.
For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com
8/20/2019 2nd PU Maths Jan 2015.pdf
http://slidepdf.com/reader/full/2nd-pu-maths-jan-2015pdf 4/4
,.?
/
45.
Find the
area of
the
region enclosed by
the parabola
*:4y
and the line
x=4y-2 and the
x
axis.
46.
Derive
the equation
of
the
plane
in normll
form both in the Cartesian
and vector form.
47.
Find the
particular solution
of
the
differential
equation
*
*
#=
1
when
r
=
o &x: 1
48.
A
die
is
thrown
6
times
,
if
'getting
an
odd number is
success'What is
the
probability
of i)5 success
?ii)atleast
5 success?ii)at most 5 success?.
i
PART
I
:
Answer any ONE
question:
1 x 1O=1O
49.
(a)
A
furniture
dealer deals
in
only two items
-tables
and chairs.
He
has Rs
50,000 to invest and has
storage space of
at most 60
pieces.
A
table
costs
Rs
2500 and
a
chair Rs 500.
He
estimates
that
from
the sale
of one table
,
he can make
a
profit
of Rs
25O
and that from the sale
of
one
chair
a
profit
of
Rs
75. How many tables and chairs
he should
buy
from the
available money
so as
to maximize
his total
profit
assuming
that
he can sell
all the
items
which
he
buys.
lx+y+22
x
y
I
(b)Showthat
z
y*z*2x y
I
=2(x+y+zls
I , x
z*x+Tyl
50.
(a)
Prove that
[i
1(x)dx=ff
f
(a-
x)d"x
and
evalu ate
ff
ffiax
(b)
Find the vatue of K if
-f
(*)={y.: '{^.=]
i"
"onunuous
at
x
=
5.
[3x-5
,f x>5
Inst
il
t.
*********
it.
C,{
For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com