mathematics objective questions part 13

8/18/2019 Mathematics Objective Questions Part 13

1/22

C.S.f.. MATHEMATICS (Prelim.) - 2005

C.S.E.

MATHEMATICS 2005

(PREUMINARY)

11me Allowed :

wo

lours

I.

2.

3.

4.

J:or what value

on

. arc the the lines x 3y • 3. z

>

y · 6

an


2/22

6.

I

...

tf f

x )

--------

. x >

0

l + x

then

what

is the

least

val ue o

f / {

/(x)}

+ f

{ f l x

}

(a

) I

(b) 2

(c)

3

(d)

0

7.

If

/

(K }

is

-defin

ed Over

j(),

l j then

wha

t

is

the

dom

ain of'

the

8.

f

\mct

io

n

f

(2

x .; 3)

?

a)

.1 ·'2,

I l

(h)

f3, 5

]

(c)

R

{.3i2}

d)

(

312. I )

(

i) /( :<

. , y

x) - f y

)

(n) f

( x) ·

I

•

x

g(x)

\.V

hat

is

d

1

······ f

(x } equ

al to'>

J

X

(a

) g(x)

h ~

(

c) g (

x)

V

· x

g (x )

where

p

o

W h

at is t

he val

ue of

- ..

R

x) a t

x 0

dx

a)

0

(h)

p

p

1

(

C)

; p-

(d )

6p

3

I 0.

I ·

an

g.(x

)

a

rc

two

"uncti

ons

co

minuo

m ev

eryw

he

re

and

. /

X ) I X

1

'g_

(:x)

(x lu

n

· ...

;;;· ·--

·

···--

th

ell F x

) is continu

ou s

ever

ywhere

. . ~

t x.

~

'

' '

' '

of

rollo

wi g

'

'

www.examrace.co


3/22

(a

)

2

(b

) -

2

(

c)

.:: I

{ d )

« l

I I.

L

et f :

R

R

be

a mo

llotc

mic

nlly

d

ec re

as in

g

fun c tio

n

{

dclin

ed

every

wh

ere

()n

the

rea

l

I it le)

an

d le

f

be

di

sco n

tirtu

ous at

.

::e

rta

i n

po

int X

••• a

. W

hm

is

th

e: nat

ure

o r

th i

s

di

scon

tinu

ity•)

( a

)

R

emov

abl

e di

scon

t

in

uity

(b)

Either

removable

d i

iCO

nt·inuity

or

d iscon tin\ li ty

of

2nd

k in d

(c )

Di s

c o

n

l

in

uit

y of 1s

t k in

d

(d

) E

hcr

.

(c ) f

I . ·

l.

·

I )

.(d )

{

l •

I.

+

(a)

1

1)

(b)

{

1 . ·

1

0

13

.

/\

rod

o f le n

gth

o

ne

metr

e

begin s

·nic:al

p lane

p

1-.4

8

-

(a)

·

(b

)

5

(

•

( d)

) irb

>

0

L

www.examrace.co


4/22

B.

y

1

"'

b (

x•+

x·)

i

fb

0

y

3

b(

xz

•

.xJ_ i

fb

> 0

A

B

c

2

.

Cu

sp

3

Co

nj

ug

at

e

po

int

4.

N

ei

th

er a

no

de

no

r a

cu

sp

no

r

a c

on

ju

g<

tte

po

in

t

A

B

C

(

a)

4

3

(b

)

3

4

i

(c)

2 3 (d) 3 2 I

16

.

Re

su

ha

nt

or

a for

ce

j

) a

lo

ng

x

-a

xis

. a

f

or

ce

Q


5/22

21.

.2

2.

2

3 .

2 4

.

25

.

T

w

ha

t

doc

s J

u

1

d t

eq

ua

l

t

o (

u

be in

g

vcit

y o

f

the

m o

tio

n) ?

0

na

'

a·

(c )

T

n

a •

T'

b)

(d

)

l t i

2T

n

1

-

-

··-

T

A particula r is m ov ing und

er

the

i

nl1ucncc

or

l

centra l

fo

rce

alo

ng

th

e

wrv

c r

·

ae

"

0

,

th en

fim:<

? d

irec

ted

tow

ar

d

s

n

i

s p

ro p

ort

ion

al

to

:

(a

}

r

3

(

b

)

r

2

c )

l f

r

(d)

1/ rl

0

If

a

p a r

tic l

e mo

ve

s alo

ng

a s

trai

gh t

iinc

ac

co r

d

i

n

'

s

2

•• at

1

•

. 2

bt ·

· c

wh

ere

s

is th

e

dis

plac

em

en

t a

t a

· i

ns

n

t t.

(a)

A

s

Its

(b)

A

s lis

+

(c) As IN (

d}

As

FQ

r w

ha

t v

a lue

of

(,

m ay

th

e f

orce

s

o

f

ag n

t

d e f

··

1.

f-

I

am

i

f

• 2

.

act

i ng

a t

a p

o in

t b

e i

n

c

qt

t

1

.

(a )

·2

5

·.

(c )

1·7

5

·5

T

hre

e

for

ces

3

.

4

a

nd

1its

ac

ting

a

t

a

po

·in

t

o

f a

b()d

y,

ma

kin

g e

qua

l

an

gle

s ·lh

·h

ot

he1

.

Wh

at

is

t

he r

na

gn itu


6/22

2

6.

Fo

r<

:c

s o

f

m

ag

.n

d

I , 2

.

3,

4

,

5

N

ac

t

a t

an

:an

gu

la

r p

oi

n

t

o

r

a r

eg

ul

ar

h

e

xa

go

n

t

o

w

ard

s th

e

Qt

h

er

an

g

ul

ar

p

o

in

ts.

W

h

a

t

is

t

he

ap

p

n>x

i

ma

tc

va

lu

e

o

f m

a

gni

t

ude

o

f

t

hei

r

r

es

ul

ta

n

t

,,

(a

)

12

N

(

c )

7

·5

N

(

b)

/

SS

N

d)

IS

N

27.

Let

rnl

rn

1 , . • . ,

m"

he

it.

mass partic

le

s

at

p

os

it

io

ns

w

it

h

'to

• )

jl()S

it

io

n

ve

c t

o r

s

r,

,

r

2

, .

.. ,

•·

.,

re

s p

ec

t

ive

)

·

re

fe

rre

d

to

a

p

o

im

;s

o

r

igi

n.

t

f: ea

cl

\

m

o

ve

s

wi

.t

h

ve

lo

c

ity

i\

·.

ti

r (

w

h

er

·

;

.n

d

B

ar

c

con

s

t

an

t

vc

ct

or

s)

at

t

nn

c 1

th

en

wh

tc

h

o

li

l l1o

w

11

1g

is

c-o

r

re

c t

?

,\

J

[a

)

cc

n t

rl

o

r

o

f t

he

p

ar

tic

le

s m

o

v

es

~

o

c

a

y

A

(b

)

ce

n t

re

o

f m

n

's

o

r t

he

p

a1

·ti

c

e

:s

it

c

nc

it

)

1

1.?

r ~

(<

.:) T

h

e

e

'

k

i

(b

)

IO

Ox

"

0>

+

1

0

www.examrace.co


7/22

c) n x ~ · l )

(d) 7x ' 'nx+3

under matrix

multiplication

and

N

·

r

J

y

( )

•\

.

\

'

~ }

where

a,

b.

c.

d

arc

I'c:1l mtmhct·.

(\msidcr

the f(>ll


8/22

35

.

H

=

{a +

ib

(a

1

b

)=

l}

Co

ns

i

d

er

the

fo

llo

wi

n

g

s

tate

m

ent

s :

.

.

H

is

a

subg

ro

up

o

f G

.

l

H

is

A

be l

ian.

W

hi

ch

o

th

e sta

tem

e

nts

g

ive

n

a

b

ove

is

ar

e c

orre

c

t

?

ta

}

l on iy

(

b)

2 ·o

nly

(c)

>h I

ana

2

d)

N

ei

ther

I

nor

2

r:}

Ab

e

lian g

ro

ups

m

ay

ha

ve

n

on

-Abel

i n

su

bg

rou

ps

\b)

No

n

-

A

;

.cli

an

g

rou

p

s

ma

y

have

Ab

elia

n su

bg

ro

ups

c)

Cy

cli

c

grou

ps

m

ay

hav

e

no

n-c

yc

lic

su

bg

ro

ups

i

;i)

No

n

-

}

l ic

gro

up

s

ca

n

n

ot

hav

e

c

yc

lic

su

bg

rou

p

s

1

n

t

he

www.examrace.co


9/22

38.

39.

40.

41

(a) 2

(c)

4

(b)

3

(d) 5

Each

root

of the

equation

v

· 2 2 v ~ ' 1 3 0 v ~ - 2 4 3 y + 6 1 · 0

. '

'

i:; greater by p .tltan each root o f

the

equation

X • 6 x ~ · 38

··

) X 17 ' ()

What

is

the

value

of

p

?

(a) 16 (h)

8

(c)

4

d) 4

If the

mots

of

1hc equation (x a)

(x

b) k ·

c and d, then

x . c) x d) ·

k,

0 ?

(a) a and

·b

(b) a and l>

(c) a and b (d) a and +

What

is

the im:aginar;

pan

of

·

·-·(

:·

.

. .

n\ ;

"

·r

s i n ~ · -

s

)<

Sl

O$c1

(a) sin I 10 h ~

(c) s in i O

.tT(:J IIO

\Vhat rs the angle

a

whicl ~ v r · c. 2cosec 20 intersects

the line 0 '

r 16

?

(a)

0

(c) 2nl: i

42.

What is the n .1 o cal roots lying in the interval ( I, )

forthefun

·

· · · · x ~ ;

15x

.8?

(a) I (b) 2

(c) 3 (d) 4

•

•

·

J

(t

..

I) (t

2)dt

where x > 0 '

, I

0

b)

I /2

(c) :.V2 (d) 5 2

length s - 0 when 0 0) ?

www.examrace.co


10/22

(

a)

(r

+

a)

s

in

o

.

c)

(

r

•

a)

c

os

ec

(b)

(r

..

. a

)

co

s o

.

(d

)

(r

--

a)

se

c

o

.

4

5.

W

ha

t i

s

th

e

ar

ea

bo

w1d

e

d

b

y

tJ

1e

c

ur

v e

y

...

x

s

in x

an

d

th

e

x-

a

xi

s

be

tw

ee

n

x

=

0

a

nd

x

=

2

x

?

u

n

(

c)

3

rt

4 6. W hat

is

(b

)

2

7t

(

d)

7

C

4

7.

L

et

be

a

p

o

sit

iv

e

n u

m

be

r.

D

el

in

e

a f

un

c

ti

on

}

(

····

s

.in

1

a

s

u

ch

th

a

t /

(0

)

f {

a)

.

. 0

. B

y

Ro

lle

's

t

he

·•

h

er

e

ex

is

ts

a

nu

m

be

r

/c ly

in

g

in

th

e

o

pe

n

in

te

rv

e

·

u

h

th

a t

.f

(k

a)

·· 0

.

W

ha

t

is

t h

e

va

lu

e

o

f k

if

a

·)

>

l/

4

(

b)

11 r

(c

}

J

/ 4

4

8.

W

ha

t

is

tl

·

v

al

ue

o f

r•

r

n

r

X

w

he

re

n

E

?

a

-

.

n

.

a

)

n

n

2

.

y

a

1

www.examrace.co


11/22

C

.

x

·

a

(

0

·

s

in

6

)

,

y

'

a

(1

·t ·

co

s

0

)

.

X

a

(0

.

.

s

in

0

),

y

· a

I

c

o

s

0

)

4

.

B

C

D

A

B

C

~

{

a

}

4

2

3

I

(

b

)

I

3

2

~

~

c

)

4

3

2

I

d

)

l

2

3

4

5

0

T

w

o

r

o

d

s

O

A

8

a

r

c

r

ig

i

d

ly

f

ix

e

d

a

t

0

a

t

r

ig

h

t

a

s

}

c

h

o

t

h

e

r

a

n

d

t

h

e

y

r

o

ta

t

e

a

b

o

u

t

0

in

t

h

ei

r

p

la

n

e

w

-

'

'J

l

s

t

a

n

t

a

n

gu

l

a

r

v

e l

o

c

i

ty

w

W

h

a

t

a

re

t

h

e

0

1

¥

'\

)n

e

m

s

o

f

·

a

p

a

rt

i

c l

e

w

h

o

r

.e

c

o

(

)r

(

in

a

t

es

w

i

t

h

re

s

p

e

c

t

,

O

a

re

f

o

r

a ll

t im e

o.

,

>)

where u ,

~

arc

n s ~

a

)

c

o

·

z

u.

al

o

n

g

,,I

a

n

v

e

l

y

b

)

{

w

la

,

w

1

j

3

)

a

lo

n

g

O

a

n

·

c

c

ti

v

c

l

y

(

c

)

w

1

):)

a

lo

n

g

O

A

,

(

'

e

s

p

c

-c

t

i

v

cl

y

d

)

W

2

2

i

a

,

r

o

2

u

2

/

j3

)

a

l

1

a

n

d

o

n

r

es

p

e

c

t

iv

e

l

y

5

1

A

is

la

u

n

c

h

e

d

·

r

c

ti

o

n

p

a

r

a

ll

e

l

t

o

th

e

f

t

h

e

e

a

rt

h

w

i

th

a

~v

I

.8

2

0

m

i

l

f

ro

m

a

n

a

l t

i

tu

d

e

o

f

2

4

0

m

i

le

s

. I

f

th

e

s

c

c

a

c

h

e

s

i

ts

m

ax

i

m

u

m

al

t

it

u

d

e

o

f 2

3

4

0

m

i

le

s

.

w

h

a

t

~

·

s

l

a

x

im

at

c

ve

l

o

c

il

y

f

th

e

S

R

te

ll

it .c

(r

;J

dius

or

e

a

n

h

"'

3

.

)

?

(

a

)

~

r

(

b

)

2

5

5

0

m

il

c

s

/

h

r

c

)

d

)

1

4

,5

5

0

m

i

l c

s

h

r

5

2

.

~

h

i

O l

f

o

f

t

h

e

f

o l

l

o

w

i

n

g

n

u

m

b

e

r

sy

s

1

e

m

s

r

e

s

u

l

ts

in

t

h

e

Ia

t

O

<

ra

g

c

re

q

u

i

r

e

m

e

n

t

s

?

cx

a

d

e

c

i

m

a

l

S

ys t

e

m

b

)

O

c

t

a

l

S

y

s

t

em

D

e

c

im

a

l

S

y

s

t

em

(

d

)

B

in

a

t

y

S

y

st

e

m

8

-

b

i

t

c

o

d

e

r

ep

r

e

s

e

n

ts

?

www.examrace.co


12/22

(a)

1

6

(c)

12

8

(

b)

64

(d

) 2

56

Dir

eetill

IIS : T

he

fo

llo

w

ing

5 (

FIV

E)

item

s. co

nsist

of tw

st

a

m n

t ~

on

e la

bell

ed s

th

e 'A

sse r

t ion

(A )

' and

th

e oth

er

as ' .R

eas

on (

R}'.

You

arc

t.o

ex

am in

e th

ese

tw o

sta

tem e

nts

care

fu ll

y an

d St

:lect

the

an5

wcr

s t

o

i tem

s us

ing tl

tc

cod

es g

iven

bel

ow :

(a) Both A

and

R arc' in divid ually tru e

an


13/22

58

.

5

9.

6

0

.

.(

) 1

.

.

>

to

re

d

in

a

u

x

il

ia r

y

m

e

m

o

ry

(

lr

in

p

u

t

an

d

w

r

it

e

tl1

c

o

ut

p

u

t o

f

th

e

p

r

og

r

a

m

i

n

to

t

h

e

a

u

x i l

ia

r

y

m

em

o

ry

.

~

s c

r

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14/22

(c

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= (

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15/22

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16/22

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3

0

l

2 3)

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Q

2 0

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t\. hat i

s

th e

d eterm

inant

of th

e follo

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matrix

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2 I

3

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2

3

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l

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70.

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system

of e

q

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ns

X i 2y ·

z '' I , (

p · 1 2 )

Z

;

•

is

inco

nsiste

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n wh

(a ) 2

(b)

(c) 0

(d

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7

1. Ir

th e e

quat

on

+ bxy

2

+ y3 '

0

represents

tl ·

two of

wh

i

ch

are perpc

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other

.

is the equ

a

tion

M th e L

hird li

ne ?

a)

y ·

(h )

y -

b

x

•

(

d)

y

·X

n

h

t l ine is

define

d by th

e ime

rscctio

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plan e

paralle

l

l

lane and

a p

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nn

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ratios.

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i ght lir1e

a) (0

,

p,

I)

b)

(p,

0. 1)

1. ;

) l. 0,

p )

(d)

(L

p, 0)

73.

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hat v

alues o

r A an

d B,

a re th

e two

p lane

s repre

sented

by

t

he

equ


17/22

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18/22

79.

80.

81.

82.

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84.

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l

···l>

..

•

···•

.... • •

If p ··· b x c. q c ' a and r ,, a .,

hare three

v ~ c t o r s then

which

'

is parallel

w

q " r

·a pctvcnd

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q

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a is para lcl tc• r

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19/22

a

)

+

s

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;

•

·

y

·

e

8

6

.

www.examrace.co


20/22

C •

. •

s h:

x

·

(d )

y c , e

+ c

1

e ·

- -

2

-

+ · · ··

88 .

Curv

es pa

ssing

through

the p

oint

(0, I

) and

sat is

fying &he

(

dy)

equ

at ion s

in

~

•• c

r

e

gi ve

n b

y

(b)

CQS ;;: l)

; : ~ c

89.

W

hat is

th e s

ingula

r sol ut

ion of

the d

i

ff

eren

tial u

p ···

In

( p x

- y)?

.

r

> •

(

a}

y ·

ex

·

e

(b

)

y

~

(C )

y

·.··

X

h1 X ·

X

(d)

)

C

dy

~

l

T

he di11

c-rem

ial e

qu

atio

n

· c

os

y

i s r

ed

u c

e

d

dv

~

to

li neat lo

rrn

·

r

c P an

d Q

arc. fim

ct io n

of

d

x:

90

.

x

alone.

by ch

angt

c

· r ia b c

as

(a )

sin ·

v

(b )

cos y

::: v

(c)

tan

y

(d )

sin

2y

'

v

9 1

.

.

·

{

-- y (l

n

y

In

x .; l) >

x

e'

b)

y ·:

xc••

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) •

(;e

•

··

0

d)

x

···· e


21/22

a

r

b

it

r

a

r

y

c

o

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n

i

n

g

e

n

e

r

a

l

1

a

)

y

1

+

y

z

i

s

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s

o

l

u

t i

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b

u

t

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y

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s

t

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i

s

it

s

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o

l

u

t

io

n

.

b

u

t

y

1

+

y

2

i

s

n

(

)

t

(

c

)

b

o

t

h

y

1

•

·

y

z

a

n

d

c

y

1

a

r

c

i

ts

s

o

l

u

t

i

o

n

s

(

d

)

n

e

i

E

h

c

r

y

1

+

y

1

i

o

r

c

y

1

i

s

it

s

s

o

iu

t

i

o

n

9

3

.

C

o

n

s

i

d

e

r

th

e

s ta tements regardi ng t

he;

di fferenti

al

e

q

u

a

t

i

o

n

'

\

d

y

;

I

l

d

x

j

y

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0

,

0

l

0

n

~

y

(

O

)

:

I

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r

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.

.

I

t

is


22/22

(

a)

b

·

a

(c

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c

a

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1

/4

(t:)

I

f

(b

) a

···

· b

(d

)

1

c

(b

)

l

/

3

{

d)

l

W

h

at i

s t

he

le

ng

th

of

a

n a

rc

o

r t

he

cu

rv

e

y

=

x

-

1

X

· 2

1

l·i

·om

x

I

to

x

3

?

(a )

J

/

3

(

c)

2

(

b)

1

2

(

d)

3

9

9.

W

hat

a

re

th

e a

sy

m

pt

ote

s

o

f th

e

c

urv

e

(X

' 4

)

'

I· I

)

(

X

···

4y ·

I )

"

4

?

(

a)

y

•·· i4

(

x

I

)

(b

) y

·' ·:

:

4 x

C

J

C

)

X

. . ±

4

y

(d)

X

i =

·

i 4

)'

•

1

00.

At

w

ha p

o

int

o

n

he

c

ur

ve

y

((

e '

c

- )1

2F

, i

s

fn

ur

e

maxim um ?

~

a)

tJ

f2

,

I

1

2

)

(b

)

(0

,

I)

(

C)

(2

, 0

)

(d

)

;t q}

mathematics objective questions part 13

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