Upload
prasad-c-m
View
225
Download
0
Embed Size (px)
Citation preview
8/20/2019 2nd PU Maths Nov 2014.pdf
http://slidepdf.com/reader/full/2nd-pu-maths-nov-2014pdf 1/4
Time
:
31h
Hours
il
P.U.C.
MATTIEMATICS
roN
-
2014
Iil
NC
6ET
Max.
Marks
: 100
DISTRICT
LEVEL
MID-TERM
EXAMINATION
-
2OI4
Instmctions:
The
question
paper
has
five
parts
A B
C
D
and E
Answer
all
the
questions.
PART.A
Answer
all the
questions:
r)
2)
3)
4)
Define
the
equivalence
relation
R
on
a set.
Find
the
principal
value
of
cos-r (-112).
Define
scalar
matrix.
rre{r
olnna
p4
r,_,l
If
51og
a*
find
dy/dx.
r
Evalute
J
(rin^-
1
+l)dx.
If (x):12
and g(x)
I
r
-*
find gof.
If
A:[t
2l
Show
that
(Ar)t
L3U
m
5{iog
x
find
dy/dx.
Evaluate
f
dx
J
x\d\
10x1=10
10
x2= 20
5)
6)
7)
8;
e)
10)
Answer
any
ten
questions:
PART
B
:
i
11)
Let
L
be
the
set
of
all
lines
in
a
planB
.
R
be the
relation
in
L
defined
as
R:{
(Lr
Lz)
: L1
is
perpendicular
to
L2
).Show
that
R symmetric
neither
reflexive
nor
t2)
13)
transitive.
Show
that
Sin-l
x+
cos-l
x:nly
write
the
simplest form
of
tan
,[@
0
<x
< n
[-v
t+cos1J
P.T.O.For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com
8/20/2019 2nd PU Maths Nov 2014.pdf
http://slidepdf.com/reader/full/2nd-pu-maths-nov-2014pdf 2/4
- =,
14)
Find
the
equation
of the
line
passing
through
(2,
l)
(3,1)using
determinants.
15)
If
x2
+y':sinx
frnd
dyldx.
16)
If
1=
x'in*
find
dyldx.
17)
Approximate
Jzx
using
differential
method.
i
18)
Evaluate
f
tan-rx
dx
i
Jft?
ts)
Evatuate
f
(x+r)
dx
-l
Show thattan-|
2/ll
+tan''
7/24:tan-t
yr.
Show
that
the
value
of the determinant
remains
unchanged
if
its
rows
and
columns
are
interchanged
by taking
a
determinant
of
order
3.
Differentiate
sin
(cos
(x2
))
with
respect
to
x.
Find the
maximum
and
minimum
values
of
x+sin2x
on
[0,
2r].
construct
a2x2
matrix
A:[a,j
]
whose
elements
are
given
by
aii=
(iji),
20)
21)
22)
23)
24)
37
38
PART.C
Answer
any
ten
questions:
10x3=30
25)
Show
thatrelation
R in the
setA:{
I
2
3
45
}
givenbv
{a,b)
:
la-bl
is
e'en
}
is
an
eeuivalence
relation.
26)
Prove
that
3
sin-r
x:
sinr(3x-4xr)
,
*€
l_llL,l/21
27)
By
using
elementary
transformation
method
find
the
inverse
of the
matrix
A:
28)
If x:a(
O-sin
g),y:
a(l+cosO)
find
dy/dx.
,
29)
veriff
Mean
value
theorem
if
f(x):
x3-5x'-3x
in
the
interval
[a,b]
where
a:l,
b:3.
30)
Find
the
intervals
in
which
the
function
f
given
by f(x):212-3x
is
(a)
strictly
increasing
and
(b)
strictly
decreasing
31)
Evaluate
/'
xsin-'x
dx
,
u
{6t
32)
Evaluate
/'logx
dx
.
.Je
33)
Find
the
area
of
the
region
bounded
by two
parabolas
5x2
and
t':*.
4t
UX
42
43
44
45
P.T.O.
46
For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com
8/20/2019 2nd PU Maths Nov 2014.pdf
http://slidepdf.com/reader/full/2nd-pu-maths-nov-2014pdf 3/4
34)
Find
gof
and
fog
if
f:R+R
and g:
R->R
are
given
by
f(x)
:sinx
and
g(x):6x
show
that
gof
I
fog.
::3
::
PART
D
35)
Find
X and
y
if
X+y:[Z
Olana
X_y:
[:
O']
L,,J
L,;J
36)
If
x,
y
andzaredifferent
and
A:
lx
x2
1+x, I
ll
't
li,,
f
o
therq
show
that
1*xY2:s'
37)
Find
two positive
number
x
and y
such
that
x+560
and
xy
is
maximum.
38)
Find
f
3x-2
dx
J
o,-Fl)
G+3)
I
inswer
any
six questions:
I
4t)
42)
43)
44)
4s)
46)
6x5=30
3e)
40)
If
f,
A--+
A is
defined
by
(x)
:(4x+3)(6x-a)
where
A:R-{2/3}
.
Show
rhat
f
is
invertible
and
Ffr.
If
A:
[
2'l
B
-
[z
o'lana
cd
r
-)
A
A
I::J
^
.
^
k:
J
calculate
AC,
BC
and
(A+B)
c.
Also
verifr
that
(A+B)
C:aC+bC.-
Solve
the
fotlowing
system
of
equations
by
matrix
method,
x-y+z4,
2x+y-3r0
andx*y*z:)
Y:A
e
*+
B
e*
Show
that
d2
y/dx2-(m+n)
dyldx+mny:Q.
The
length
'x'
of
a
rectangle
is
decreasing
at the
rate
of
5
cm\min
and the
width
'y'
is
increasing
at the
ratg
of
4cm\mirq
when
x=gcm
*o
=ur*
oro
the
rate
of
change
of
its (i)
perimeter
and
(ii)
area,
of
rectangre.
Find
the
integral
of
'_L-
with
respect
to
x
and
hence
evaluate
L,_
a*
rF+az
,r7n
Find
the
area
of
the
region
i., the'first
quadrant
encrosed
by
x-axis,
line
x:{3y
and
the
circle
x2+f:4.
If
x:
a
cos'
e,
y:
asin3
0
find
d2yldx2
P.T.O.For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com
8/20/2019 2nd PU Maths Nov 2014.pdf
http://slidepdf.com/reader/full/2nd-pu-maths-nov-2014pdf 4/4
toir.Ucpl
47)
A ladder
5m
long
is leaning
against
a wall
the
bottom
of
the ladder
is
puller
DIS-]
a
.ow fast
is its
height
on the
wall
decreasing
when the
foot of
the
tadder is
4m away
fro*
I
Ti*t
'
3 F
wall?
Find
J{x'+2x+5
dx.
Answer
any
one
question:
aD
a)
find
the inverse
of
a
matrix
)
48)
hstructions
(i)
r
{ji)
t
Part E
2t
4-l
-7',
2
l,nswer
AII
1. Defir
2.
Prov
3. Wha
I
4.
Find
5. If
y
6.
Find
t
7.
Writ
8.
Find
9.
Defi
10.
If P
(
tA.nswer
an;
11. Are
Ris
12.
Pror
13.
Finc
14.
Finc
ls.If
d
16.
Fin<
17.If tt
calc
18.
Finr
19.Inte
20.
Finr
3
0
1
b)
Determine
the
value
ofk
if
f(x):
is continuous
at
x=rE/z.
50)
a) Find
the
area
enclosed
by
the
ellipse
xzt*+f
rc2:1
by
the
method
of
integration.
b) By
ruingthe
properties
of
determinantsishow
that
:
1l
_x3)2
11
,
*
i
l*,
Ix
l*i*'i
For More Question Papers Visit - www.pediawikiblog.com
For More Question Papers Visit - www.pediawikiblog.com