8/20/2019 1st PU Mathematics March 2015.pdf
1/3
--r
puc
ANNUAL
E>
8/20/2019 1st PU Mathematics March 2015.pdf
2/3
23'
The
mean
and
variance
of
heigrrts
of
crass
Xr
stud.ents
are
162.6
cm
and
27'69
cm2
respectiveryt
iinii',A"
coefficient
of
variation.
24'
t
Ei*"J"?.",t.,.rt;11[
Sjt,T
"
u,
",.".
il.
;"
probabirity
that
the
card
lll
Answer
any
TEN
questions.
33.
The
sum
of
first
3
ierms
of
a
common
ratio.
P4RT-C
G.P.
is
1$
anO
their
product
is
_1.
Find
the
25'
ln
a
group
o,f-6-oo
:judents
in
a
schoot,
150
students
were
found
to
be
taking
l?fu
jf,?f
5ffi;,x;";"1,,,,i1i:,;i::t3,lid',33"un0";ii";:;;;
j-,,t*many
26-
lf
f(x)
=
x2
and
gfrl":
;;;;
'i"
,*o
reat
functions,
find
i)
(f
+
g)
(x)
ii)
(f -
g)
(x)
iii) (f
s)
(x)
27.
lf
sinx -.3.
^-B'"o;v=ff
where
x
and
y
both
rie
in
the
second
quadrant,
find
the
value
of
sin(x
i
y).
28.
Find
the general
solution
of
secz
2x
=
1-tan2x.
29.
Express
1_i
into
polar
form.
30'
[i[S=J[i,"ffH?:
,""1"*,ll:i?T,e,lJ?"
o,
the
retters
or
rhe
word
i)
do
the
words
start
with
p
'
"'
'ir
reoi,
ii)
do
the
words
begin
with
I
and
end
in
p.
:-
'1.
Find
the
coefficient
of
x6 y3
in
the
expansion
of
(x
+
Zyls.
2.
lnsert
3
arithmetic
means
between
B
and
24.
10x3=30
:l
5::1J::r?3ffiHT""li?"i
E:tora
which
is
svmmetric
about
the
y-axis
and
35.
compute
the
derivative
of
tanx
with
respect
to
x
from
first
principre.
36'
Verify
by
the
method
of
contradiction
iir,
:vz
is
irrationar,,.
::
:f,aTd
?i""iffitx)"'"n;;fl":n;r,;;
,"i;}118
and
p(A
and
B)
"
i:" ffi,'1",,i,r1#;f""::#;,',i#fhilfm
2
men
and
2women
what
is
(a)
no
man
(b)
one
man
(c)
two
men
39'
.He:
signum
function.
Draw'th.e
graph
of
it.
Arso
write
its
domain
and
4A.
Prove
that
cqs4x
+
cossx
+
-.
siffi=cot3x
41'
prove
by
the
method
of
mathematicar
induction
that
1
2
+22
+32
+..
.
. .
..
+n2=
n(n+
t)
(zn
+
t),
r,
a
-r-''
"
"
rhically
x+2y=go,
2*+ys
a,
*=0,
y=o
3.
prove
that
nC,.
+
nCr-r
=
1n
*lt
)
C,
6x5=3O
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ediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/
8/20/2019 1st PU Mathematics March 2015.pdf
3/3
44.
For
all
real
a,
b
and
positive
ifieger
n
prove
that
(a
+
b)"
=
nCoan
+
nCran-1
b
+
nCra"-2
b2 +.............
+
nC.bn
45.
Derive
the
formula
for
the distance between
the
paraltel
tines
y
=
ffiX
+ cr
and
y
:
.rrlX
C2
and
hence
find the
distance between
the
faratlel
lines
3x
-
4y
+7
=O
and 3x
-
4y
+ 5
=
0-
Derive
the section formula
in
three dimensions for internal
division.
Prove
geometrically
that
lim
(SUl()
:
1
,
x
being measured in
radians.
x+o\
X
I
Find
the mean deviation
about
the
mean for
the following
data
46.
47.
48.
PART.E
V
Answer any
ONE
questions.
49.
(a)
Define ellipse as
a set of
all
points
in
the
plane
and derive its
equation
in
the standard form
as
4**=1,
a>b
a' b'
(b)
Find
the derivative
ot
fr
-
*
with
respect
to
'x'
50.
(a)
Prove
geometrically
that cos(x
+
y)
=
cos
x
cos
y
-
sin
x
sin
y
(b)
Find
the sum to
n
terms of the series
12
+(1" +2')+(1"
+2'
+32)+
Marks
obtained
10-20
20-30 30-40
40-50 50-60
60-70
70.80
Frequency
2
3
I
14
I
3
2
**rt{.*)tr
1x'lO=1O
4
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ediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/