1st PU Maths March 2014.pdf

8/20/2019 1st PU Maths March 2014.pdf

1/4

PUC

FIRST

YEAR

Code

:

35

Date

:

d

DIST.

LEVEL

ANNUAL

EXAM

Subject

:

MATHEMATICS

FEB

/

MARCH

2014

Duration

:

3

Hrs

15

Min.

Max.

Marks

:

1OO

i)

ii)

The question

paper

has

five-.parts-

A,

B, C,

D and

E.

Answer

att

tfre

parts.

Use

the graph

paper

sheet

for

tne quesiion'Jn

Lin. ,

Inequarities

in

part

-

D.

PART

-

A

Answer

ALL

the

following

questions.

1.

\l/rite

the

set

{x:

x

e

R

and

_4

<

x

S

6}

as

interval.

2.

Convert

52Oo

in

radian

measure.

3.

Express

i9

+

119

in

the

form

a

+

ib.

4'

How

many

three

digit

numbers

can

be

formed

by

using

digits

,1

to

g,

if

no

digit

repeated

?

5

Find

the

12th

term

of

a

G.p.

whose

gth

term

is

1g2

and

whose

common

ratio

is

2.

6.

Find

the

distance

between

parallel

lines

1Sx

+

gy

_

34

=

0

and

15x

+

gy

+

31

=

0.

7

Evaruate

*

5_. +#

8

write

the

negation

of

the

statement.

,,Ail

tringres

are

not

equiraterar.,,

9

A

box

contains

1 red,

3

identical

white

balls.

Two

balls

are

drawn

at

random

in

succession

with

out

replacement.

write

the

sampre

space

for

thrs

expirement.

10.

Find

the

domain

of

the

real

valued

function

f

(x)

=

ffi

PART

-

B

Answer

any

TEN

of

the

following

questions.

1Ox2=2O

11

LetA

=

i1,2)

and

B

=

t3,4),

writeAx

B.

How

many

subsets

wi,A

x B

have

?

12.

If

A

=

{

3,

6,

g,

12,

15,

1A,

Z1i,

B

=

{

4,

B, 12,

16,20

}

and

C

=

{

2,

4,

6,

B,

40,

12,

14,

16}

Find

(A

_

B)

u

(C

_

A)

13,

Letf

:R-+

R

andg:R-+

Rarethefunctionsdefined

byf

(x)

=x+ l

and

g

(x)

=

2x

-3.

Find

f

+

g

and

fg.

,.

14.

Show

that

Sin2

*

+

o

15.

Find the general solution

of

cos

4x

=

cos

2x.

16.

Evaluate

lim

x

-->

-2

Determine

n,

if

2nC3

:

nC,

=

12

:

1.

write

the

contra

positive

and

converse

of

,,If

x.is

prime

number

then

x

is

ddd,,.

A

coin

is

tossed

twice-

wt'at

is

the

probabirity

that

at

reast

one

tair,occurs

?

Instructions

:

10x1=10

cos2

f

-tan2

+

=-+

17.

18

19.

(P.T.O.)

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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/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog.com/http://www.pediawikiblog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2/4

MATHEMATICS

P.U.C.

FTRST YEAR

PAGE

NO.

:

2A.

rn

a

triangreABc,

with

vertices

A(2,3),

B

(4,

-

1)

and

c

(1,2).

Find

the

rength

of the

attitude

from

the

vertex

A.

21

.

Represent

the

complex

number 6

*

i

in

the

pclar

form.

22'

write

the

sorution

set

of

-

12

x

>

30.

when

x is

an

integer.

23'

Find

the

equation

of a

line

that

cuts

off

equal

intercepts

on

the

co-ordinate

axes

and passes

through

the

point

(2,

3)

24.

Find

the

co-ordinates

of

the

point

which

divides

the

line

segment joining

the

points

(-2,3,5)

and

(1,

-4,6)

externaily

in

the

ratio

2

:

3.

PART

-

C

Answer

any

TEN

of the

following

qu8stions.

10

x

3

=

30

25.

In

a

group

of 70

peopr.,

,,

,,*.

coffee,

s2

rike

tea

and

each person

rikes

at

reast

one of

the two

drinks.

How

many peopre

rike

both

coffee

and

tea

?

26'

IfA=

{

1,

2,

g,

5I and

B

=

{4,

6,

9}.

Determine

reration

R from

Ato

B

by

R

=

{(x,

y):

the

difference

between

x

and

y

is

odd,

x

eA, y

€ B}

,1

zr.

prove

that

cos

(+

-

-)

-cos

(+

_r)

=

_*

sinx.

28.

Solve

the

equation

*2

.*

x

*

1

^12

=Q.

29'

ttow

n(any

words

with

or witnout

meaning

can

be

formed

using

the

retters

of the word

MoNDAy

assuming

that

no

retter

is

repeated

if.

i)

4

letters

are

used

at

a

time.

ii)

All

letters

are

used

at

a

time,

and

iii)

All

letters

are

used

but

first

letter

is

vowel

?

30. If x+iv - a+ib',

;f

,

Prove

thal

x2

+

y2

=

1.

31.

Find

the

middle.term

in

the

expansion

of

(+

.

nr

ro

32.

How

many

terms

of

A.p.

:6,

+

-5

...............

are

needed

to

give

the

sum

-25

?

2

- '

qre

i

Find

the

mean

deviation

about

the

median

for

data.

13,

17,

16;

tq,11,

13,

10,

16,

.t1,

i8,

12,

12.

Find

the

derivative

of

Sinx

wr.t.x.

from

the

first

principles.

Find

the

focus

length

of

the

latusrectum

and

equation

of

the

directrix

of

the

parabola

x2

=

-gy.

33.

34.

35.



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3/4

-

MATHEMATIGS P.U.C. FIRST

YEAR

PAGE.,NO;.3

Insert three

nunrbers

between 1

and

25Q

s9-

that thd resulting sequence,ig

a G.p.

Show'that

the

statement

P :

If

x

is real number

such that

13

i

+x

=

g,

16s6,:-'

xis.O,istruebythemethodofcontradictioh.]

In class PUC

I

year

of

a

college,

4OP/o of students study

mathematics, and

307o

I

study Biology

and

10%

of class study both Mathematics

and Biology,

If a student

is

selected

at

random from

the class,

find the

probability

that he

will be

studying

Mathematics

or

Biology.

PART

-

D

31

Define Signum

function,

Draw

the

graph

of the

signum function.

Write

the

//

,/- r---

-:- --

domain and range of

the function.

36.

37,

38.

40.

Prove

geometfically

Pt

=

1,

0 being measured

in radian.

'

0

--+

0

o

'-

-: -

41. Prove

by

the method of mathematical

induction.

.aa

13+23+33+

*n3=

n 1n+1;

4

42.

In

a

group

of

7

boys and 5 girls, find

the

number

of

days in which a

team,of 5

members

can be

selected

so

as

to

have atleast

one boy and

one

girl.

43.

For all real numbers

a, b

and

positive

integer

n,

prove

that

(a

*

b)n

=

an.

+

nc.,an-lb

*

nc2an-2

b2

+

.....

*

ngrai=i

br

+

......

*

nCn_,

a

bn-1

+

bn

44. Derive

the

expression

for the

co-ordinates

of the

point

which

divideq

the

line

joining

the

points

A

(x.,

y.,

21)

and

B

(x2yzzr)

inte'rnally in

the

r.atio

m : n. Hence

find

the

co-ordinates

of the mid

point

of the line

joining

A

(1,

*2,

3)

and

45.

Derive

the formula for the angle

between

the

lines

whose slopes are

ml and

m,

and state

the

conditions for two lines

are Parallel

and Perpendicular.

46. Prove

that

Sin5x*2Sin3x+Sinx

=

tanx.

Cos5x

*

Cosx

47.

Solve the

linear inequalities graphically,

3x

+

4y

:

60,

x

+

3y

<

30 and

x>0,y>0.



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4/4

MATHEMATIGS

PU.C.

FIRST

YEAR

48.

Find

the

mean diviation about

the

mean

for the

data.

PART

-

E

Answer'any

ONE

of

the

following

questions.

49.

a)

Prove geometrically

Cos (A

+

B)

=

CosA

CosB

-

SinA

SinB

and

evaluate

Cos

105o.

b) Findthe.sumton-termsof

theseries3xg+6x

11

+9x

14+

PAGE

NO. 4

10

x 1

=

10

t6I

ri\

t4I

50.

a)

Define

hyperbora

as

a

set

of

points

and derive

its

equation

rardform

* *

- 1

a'

bt

b)

Differentiate

j:lll-fl

w.r.t.i.

4Cosx

+

1

t6l

t4j

8*{

Documents

1st PU Maths March 2014.pdf