8/20/2019 2nd PU Maths July 2014.pdf

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>\,

i

l:r.E

,(f,nglish

Verdion)

,'

;

r:

The

question paper has

five

parts

namely A, B,

C, D

arrd E. Answer

all

the'parts.

Use

the

graph

sheet

for the

qudstion

on Linetrr

Prograrnrning

problem

in

I3,

Inst

s';.

(i)

:

,

(ii)

Parl

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<

nl\l

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Alrswer alt

tlrc questions :

i

I0

x

I

=

l0

'r'

l,

'L"t

*

be a binary operation defined orr

iElre

set:of rational

tlumbers

Q

defined by

a

*b=

ab+

1,

Provethat*

isacommutatiyg.,

.',.

Find the

principal

value

of

cor-'

(-i)

i

'

i

I

.1

I-

r

21

lf

A:

L

; i

l.

tuen

find the value

of

l2Al.

-dv.^

.

'

.t

16,

17.

18.,

,

14.

15.

19.

20.

21.

{

)

a

4.

.6.

7,

8.

I

Evaluate

I

(2"-3

cos.r+ e')

dx.

J

Define a unit

vector.

If

a

line

makes angle

90o. 60o and,30o

with'lpsitire

direction of x.

respeelively.

find its direction cosines.

,:

9.,

ln tineAr

prdgraruming

problems, defineulinear

oU.lective'flrnstion.

l0; IfP(A)

=

0.6, P(Bt

=

0.3 and P(AnB)

*8.2,

find'F1

ts).

':

ll. Answeranyten'questions: i ,

l0x2=20

11.

Show'thatthe

functionf

:

N

*r

N,giv$nby{,{)=f(2)= I

andtl.t)=x- I;.for

-J

- ir

:'

fr

lZ.

prove

that

tan_lx+ cot_ls=i r.elR.

.

:-

PAR.T

-

B

y

ano z axrs

))

23.

24.

Ilt.r

Answ,

15.

(

2a, I

ti

cffldrfirb.35

(Ns)

.,

I,.

.ia

.il

:J ":_

tr.

ld'

Code

No.3

*=*l*l

Second PUC Mathematics July, 2014 Question Paper

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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/

8/20/2019 2nd PU Maths July 2014.pdf

2/5

3

17.

18.

Write

the

simplest fbrm

of

14,

Find

the equation

of a line passihg

through (3,

I

)

and

(9,

3) using

determinants.

Approximate

a@

by using

differential.

Integrate

sin

r

.

sin(cos

"r)

with

respect

to

-r-.

I

.fr

Evaluate

, ;7

dr.

J

l

-rf-

0

20.

Find

order

and degree

of differential

equation

/a3v\2 /cl2v\3 /dv\

tAtl

*[#J

*[C*v=0.

21.

Find

the

area

of

parallelogram

whose

adjacent

sides

determine

by the vectors

a:?*i-Qand6=?-i*t

22.

obtain

the

projection

of

the

vector

d:

zi

+

:i

+

zt

on the

vector

d:

I *

zf

+

t.

23.

Find,the

equation

of

the plane

througlr

the

intersection

of

planes

3.,

-

y

+

2z- 4:0

and

;r

*

y

-

z

-2

=

0.and

the

point

(2,

Z,

l).

24.

A

die is

thrown.

If

E is the

evetrt

'the

number

appearing

is

a

multiple

of

3'

alclF

be

the event 'the

number

appearirrg

is

even',

then

prove

that

E and

F

are

indepeldent

events.

19.

z 

axis

2=20

-

1.

for

10x3=30

{(x,y):2clivides

PART

-

C

25.

Show

that

the relation

R

i'

the

set

Z of

integers given

by

R

=

(x

-

y)

|

is

an equivalence

relatiorr.

/ .l- \ /;

1\

26.

provetrrattan

r(x)+tan-r

(*".,:ra'-r

(-*)

Li.t.

lode No.35

(NS)

tln,:'

p]I.61,'

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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/

8/20/2019 2nd PU Maths July 2014.pdf

3/5

For

any

square

matrix

A with

real

numbersjprove

that

A

-

A'

is

a

skew-symrnetric

Ifx:

a

(0 +

sin

0)

ancl

y

=

a (l

-

cos

0)

.

dy

f0\

t,rove

thatt:

tan

(.iJ.

verify

Mean

value

theorem,

if

f(x)

=

.tr2

-

4x

-

3

in the

interval

[a,

b],

where

Find

two positive

numbers;r

snd

)

such

that

r

*

y

=

60

and

xy3 is

maximum.

f

31.

Evaluate

I

sin

3r

.

cos

4x dx

J.

I

33.

Detennine

the area'of

the

region

bounded

by

y2,

=

x and

the lines

x

:

I

and

.r

=

4

34.

Fonn

the differential

equation

of

the

fbmily'ofcircles

touchirigther-axisat

origin.

':

35.

If

two

veetors

d

and

6suchthat

ldl=2,

16l=3

and

d.6=4,

find

E-61.

36.

Find

a unit

vector perpendicular

to

each

of

the vectors

(d +

By anct

(a

_

6),

where

d=t+i*t,B=?+zi+1fr.

37.

Fincl

the

shortest

distance

between

the

lines

I,

anal4

whose

vector

equations

are

r=r+1+),12i-1*tl

r'

'l

't''.:'

,.

38.

Bag'l

c.,tains

3.red

and

4

black balls

while

another

Bag.ll

contains

5 red and

6

black

balls.

Oue

ball

is drawn

at random

from

one

of

the

bags

and

it

is found

to

be

red.

Find

the

probability

that

it

was

drawn

from

Bag-ll.

27.

28.

29.

30.

4

4

4

4

Code

No, 35

(NS)

"

.'

-. -

r0

Code

I

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8/20/2019 2nd PU Maths July 2014.pdf

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39.

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function

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=.t'

where

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equatio's

by

matrix

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ta

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ector

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6

e

Code

No.35

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8/20/2019 2nd PU Maths July 2014.pdf

5/5

PART

*

E

and

henge evaluate

: :..-:

.1.i.

,.. ,,'

V.

Answer

any one

question

:

b-b

a9.

1a1

Frsve

that

J

*,

*

=

J

l

J

I

I

6

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.:,

:i

i.

i

i

f,

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l

.:.

.:.

:j

tIa+b-r'

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Determine

the

value

of k,

if

/.

tkcosx

n

t-

)

tr-Zx'

''

*

?

t(-t)

=

1

l^TC

IJ,I:T

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iscontinuousatx=3.

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50,

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and

Maximise

:

Z

=

r.

+

2y,:,

.t:

','

Subjected

to,Constraints

-

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.

2t-y