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