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/