Mathematics Objective Questions Part 7

8/18/2019 Mathematics Objective Questions Part 7

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w w

w . e x a

m r a c e

. c o m

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ol

Il l

M THEM TICS

1

2,

3,

4.

5,

T he number of arbitrary consl

an

t in

lhe

com plete pn1mtive of the

diiTenltl\ial

equ:\IIOn

¢.

{

r,

x

,

tl'

=

0

is

dr

'

2

c.

3

cl

file

dlt.Jerentin

l equallon

of Ute

system

of

circles 1ouclung

lhe x 1 ~ at

origin is

, , dv

0

.

(1C

-y' ) ~ -

2Ay =

(

, '

dl

b >c-y·) 2 ~ =

dx

,

.

d\

o.

(x

- 1 .-) --- +

2xv

=( I

-

tlx

•

d

. r

(x-+y' )

dx

-1 2xy

=

()

The

smgular solution

of the

equauon

4xyp+8p

=c) (p..

:t

27y

= 4x

b =

c. 27y = -lx

cl .n

l

= 4x

r he solutions

\lf

1he diiTerential equa1on

2 y ( y ' + 2 l - ~ ' Y

are the

i't

mction

J_ y=()

2. y =-

-lx

Select

the

correct

ans11

'

er

usillg

the

codes

gh

•

er1

belo .

a

No

ne or I nnd l1s as1ngulnrsolution

b. both I .

nnd

?.arc smgular solullo

ns

~ I is a singular solution but2 is not

cl 2

is a singular so

Ui

ion bu l is not

The o

nhogc)llnl

trajectories of ibe system

ol

curves

1

sm

ffil=K" are

a y cos oa = a

b. y cosO = a

c f cosnO=a

7

d. 1

tun

n9 = a

The equati1111 whose s.olution

fam

il) 1s self

orthogomd

1s

I ,

d1•

a.

p-

p

= - -

p dr

dv

b \'PX+yl(x ,. yp)- J..p= 0. p :

ck

dy

c, (px-y)(' YP)-A.p

=

o, p=-,

u

dy

d.

(px+y-

)(X·)'p)-A.[F0,

dt

Which of the followtog

smtemen

(s

associated with n lirst order non-

li

near

diJrerential equation

llx. y. d) /

dx

) : (I are

correct'

/

l

Its general

so

lution must contain ooly

one arbitrruy cooslrutt.

2 Its singularsolutioo can

be

obtained

by

subsututing partJculnr ' 'alue of U1e

arbitrary

constam in JJS general

solullon

3

It

s stngular solution

ls

an envelope of

hs general sol

uti

on

which also satisfies

tile

equal ion

Select lhe correct answer using the codes

given 11elow:

a. L nd

.3

b I an

d 2

c.

I

and 3

d. 1

and

3

A

particular

integral

d:v dy ,

---"c -

1> b

+ l b,l'

=

Q(.t)LS


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9.

n. ax1by = c

b• • .: - by = I)

cJ

aX:

• b). =1

d. I

t;j -

0

I0. A vari:oble lines p3S$t.."S through the lixcd

0

inJ ' '

b). Th e

locUJ

••

f

Ue

t i d d l ~ t•. -

16

; l

,,.t

c . -

- j

12 t"

d.

- t

l

l n drclo cuts lhc rcctangulnr hyp ·boln

XY -

. _ ~

in points Cx,.. y,) I r = 1, 2.3.4 )

.tl1en

3. X 1 _ l ~ X , j -

h.

X :X3 X,, -

c

j

il.

:il '


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m r a c e

. c o m

20

21.

I f ~ slr.light line lllllk.;, 3ngle.

6fi

45"

ron . - y ~

11 :l

yz +

I izx +

15:<

y= t)

24 . Thd equation bf tho oylinJcr. generated b.)'

llnos

p a ~ ' I I U d

to the l il'ed line

. .,.L

= . .

I

" '

f•

nnd bavintt tl1e ellipse z:

ll

. a.x> by'-=1 • as

the guiding CIUYclS

. . =

a. a(nx - b ( n y J 1 Z )

.

.

'

b,

a(llx h )"

b(n.)'·mz}· n·

c.

a(m

,:: - lzf·bttt

y·

m:>) 'n:

il

.

;l(nx- " ' n ~

25. A unit vect

or

·perpandiculnr to th" two

vc

cto"' i

J j

- In

od 2 i

•3j

l

,i i•

••

s 3j

t

h.

p o ~ i t i o n vectors

are a 3 ; 4 / 4 i • 2 i - j - : t . ~ ; .

3]

-

Si are

a. fin lri


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'35

.

36.

equ

ilibri

um n

that the s

um

oflhe momenu

ofall the

fp

r

ce< :lbou

t

{1, a t) )int i.s 7.ero

b. any 11vo pootts is zoru

c. any three non

-oo

llineru: pointS

IS

zeoo

,

1. ;I

n

ttxi• i&

7,A t"i)

l f

a

p.miclu in

eq

uilibrium i• •

ub

jec

t

ed

to

four f m·ccs viz F

1

2t

- 5 J1

6t . r

3 •

.

"

7 F

3

=

2;

-2J - t :md F., then • egu:ol

to

b ~ t - 4 5

J·


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w w

w . e x a

m r a c e

. c o m

a lirut

of A

c.

A

IS true bu

t R

f ~ l < e

d. A is

fa lse but

R true

44. Ass


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m r a c e

. c o m

- . · · ·

hlhf

x l ll lilctor x: . : ~ x - l l , I ,.,,

value

ora

i$

u. 1)

b. ]

c.

2

d. 3

53. A

q u a d r o 1 i

equation

wilh

rntion 1l

coeflicients and

with

one roo

a M

l-

..fi

i•

u.

- 4 1 1 ~ ~

b. x ~ + 4 : < +

~ 1

c.

x -4, 1=0

• - •

54.

II

' v a l u ~ : o f ( u .

p) .

55 .

56.

57

~ a c

1 - 4ac

h.

d.

b

·Ia•

2

b r T C

2

A r ~ c a t e d cool

of

ll d cquution

3 - . < l

is

;t. 0

b.

- 1

c...

I

d. 2

llto values

ofi

11

• Arc

lr

rr

SU\

T I .:08 - . II I. s 9. 13. 7.

l2 12

2 1

/

l l f

•

r

1 • " I' 17

b C 5 - " - I SU\

.

II - -. l .

12 12

2 1

•

mr

. 111r

0

1

2." ,, "

c. s

ut -

n = , • .,,

...

.

. ,

6 6

it C

A.B aod C wblch one

of

the fo llow inl' stot=ents i.>

U( l'n:(;

t?

.'\ 'Ill

- ~

= = A

B

C

=

Ill

L


7/10

w w

w . e x a

m r a c e

. c o m

m

'

II

In Ia

n

n m

I

q

It>

I n

I n

l d m n

Ia

I a I n 11

m

-

.OJ

II

IP Ia

Ill

IU

Ul Ul I l l

n

m n

m

n

I n

m

I D l l In

lq

m Ia m Ia

Then

wh1ch

one or

the fo l

io

\\

fng

l•

rtc :t•

a.

(R,

~

)

i<

•

group , Inn (R, -t,.J ,. not•

l ing

h. (R,

+,

.1

i•

with

uni

ty

1 .. (R.

•. m m ~ l l l t l \

ring

d.

R

• .) is a non-conuliUiliU

V


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70.

71.

72.

7

.3

.

h, -K

· K

d. - 3K

fA H -;· 1 cn

i o w r s ~ of ~ l r f : <

A

will

b.,

.. l

h. [ - ;,)

- 1 I 0

c.

~

d.

u

J

Co1uidcr the equation ~ B. where A=

( - ~ a l l t ~ u

lhe equ•tlon no so lution

h. solution nf theequorion

c. lhor


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RoUe '$ th

eorem

docs not apply to

f i

n

1·1.

I)

b. Roll

e"s th

eorem

applieo,

to/ in

(·

I, 1]

l l . fis

not eonlinuou;,

x

0

d.

f

(0)

=

0

NQ

The

expansion of

an in

w ~ 11r1' by

Maclaurin

5

theor


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w w

w . e x a

m r a c e

. c o m

1(0, yJ=y

2

sin . .

when

y= n

•

1{0, 0) 0,

then ut (0,

0)

o. ·IX is continuous

hut

not f

b.

I)> continuous

hut

not fs

c. IX

and

J Y ; ~ r e

hotll

coulinu

ous

d. neither

fx. 3Jld

.iJ;

eonlinuoll

91. I he double point on the cucve (x-

2) =

,) () - 1)

2

is

n. t l .

2)

1)

, (3, 4)

c. 3)

d. (2. I )

92.

T he

va

l

ue

M l

;ff J;m;

J.ot

i

~ ~ x z

stnx

93.

?4.

tl 1

/2

b. n/4

c..

n•8

d.

1'hc \'Olue )

IS

£\

1--Ji))

95

.

11ce

:o

oo

of

the crudiod

p

a( H

cosO

I

is

equal

to

iL 4 o t

1

b.

Sli3

c.

)lTD

d.

2n.; :

96

Tha volume of the solid ganerallld by

re\'Oiving d1e curve

:'p

to

the •urn

I

l.

c.

Mathematics Objective Questions Part 7

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