Mathematics for Gate Objective Questions Part 12

8/11/2019 Mathematics for Gate Objective Questions Part 12

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I

.S.E

Pt,.21l(\4

M THEM TICS

t

L

2.

3.

tf 5[(1C) : ( ( 1

~ ~ l z .

xj'(x).

b ~ n ( ) is eq

u

al to

r- ..r 1

3.

14

b 7

8

c. I

d 11

7

Lei

g(x) be lhe inl'erse of

an

inve.rfible

functJon

f (x) = I t l.r

111en g'(xl

is equal

to

a

I

I l I T]r

b.

I

I+

(/l

JJ

c. I+ Jg(

7\

)j

1

d

+ 1 / ( x l l

A

function from

R

to

R(R

being

th

e

set

of

real

nu

mb

ers) is defined bY

the

following

tonnula;

/(X) = 15 JX I0[

The nwnhcr of poinls 111 \\'bJcb the

functi(lu (")

f l

(x)} is not

diOerentiable ts

a.

v

b. I

c. 2

d. 3

: l

f

y

=

I . - . then

:

is equal1o

II 2

J' m

a

tl

X

c. y

d.

c

' For the funcl10n (x) delined by

/

(X)

{

{

anwmf

1 f l \ f.f INHJII N t/

Which one of 1he following statements i$

corre R ns

fo llows

..(

(x)

=-2x'+

3x+..l

iJ'xe(

x.. J) and.

(x)=Lx

+


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12..

13.

14

.

15.

16.

17

.

31

d. 8

f

(t

.lg"lI

rt>) :(.t))d. s

I:C(Uol O

Ju

' (11

h. / C ~ ) g ( ~ l

c.

.fClilg'(xr/'lx)g(

x}

d.

f'(ll)g(x)-f(x)g'(x)

[he

m a g - ~ of

tit open

interval

( ), I) under

t h ~

tontlnuoos lllllpping

y

x - x

1

i>

' The

open intcrvnl(O.

b 'nte semi-closed interva l (0. ' ]

b.

Thuemi-dosed intcrvnl

LO

, ''fe.

th

e g -.:tl:.


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1.

T. : 4

IL ::i.

7

L

~ :1

,6

26.

nte

c r i ~ t i e

of

the ring

z.

L

n. ()

b.

6

c.

12

d.

24

7.7.

Which one vf llle tollltiVing stntemcnl\

io

no

orr

t?

n, n,e et of rationals

is

a field

b

~ , , .

lhe

rins

of

integefll

modnlo 31

is

field

c.

R[

x).

lite

$C l

of

polynomials QVc-r the

sci

of

N>l numbers is an ntogrnl

do

ma

in but not a field

d. R[xj is not ao iutegra l dom.ain

28. Let R

be

the set of the rea l nu

mbers and

"

r ~ l ) ;

Xt

c R.

1,l>l is

cqunllo

- (a, Zb)

b. (2 . ..,

(- " 2)

d. (a b . b)

32. ifT: v V

is

4 lm.,.lrllnlonnaiion of

vector Spnco V and Uoe C


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3. R

d.

h

1

- h

2

=u' 4g (oos'o. - cosll)

l'wch Qlher. k t W O ~

point

vf in Drsoclion of

be two

n1ds.

Their velochies nt p:>rllculor

time

are v

1

I u(9

v

1

'e"peCCI.ively

,

then they s

hoU

UV\Iid

C


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46 Consider I l l ~ following

sl4

temeniJ

regarding olgorithm vi'a pr

(Jblem:

I. l l begtns wi lh in&lmction 10 accept

iuputs

2. 'fl1c pro

nnd R Is tho

torreut R

'"

1101 A

correct

...

,;-pl

bna

tion

Il

l'A.


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~ ~

b, 25

C

IS i:u

d.

3()"

0

56. I f

co

;

l sin

; 1, r= t. 2.. : .

tbon Xt

. ~ .

.. . . . fupto in:finily) oqu: h

11

.

I

I

i

ll. I

c.. i

.[j

d _ _. _

1

z

S7

.

[he

equation whnse mots are

the

n"'

power> o f the

I Ool.> o f ~ u a l i o n x:2x

cosO I t 0 is

11.

2 . . x cos uO 1 0

bo x

2

f b. n01 I

l

c. xl - '2.'< oos u

l:b

1

0.

u.

x

2

,.

2l . A circle with

C>Jt

p

100

1

is "'lualtu

a. -2

b.

l

"' 0

d. 2

If'

ft... :tnd

y

are the ri>Ol'l

of

the

eC(Ualion

x- ~ 1

._x

~ n=O_thai _. .__ s

equ l

to

.....

f l-1

1l1 n

b. 111/JI

c

3

d -3

T I 1 ~

root ufthc Ct

iU>tiou

.

:oC

- lilt$

"

18x

1

-

3th +25

=I) ore

4 .

- I

2 ~

i

b. 1

:-

2i, -2

i

e. I - 2i, .2 "' i

d, - t 2i..-Hi

In

the group or m ~ e r u

rutitll\nl numhers

under the binary op"ftiou given b,v a

b"''lb/5, the idenlitv element 110\1 lbo

inverse

of I ore l l p e ~ t l v c y

"

5 and

15

1. S and 2518

c.

115

nd 1140

d. 1 and 118

U:t x

1

>


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al11ays

e l l ~

b, an inl'egt111domain

c.. an Interval ring

d. licld

68. '

Ote

rln

g of integers (n1od 6lis

a. finite intcgT3l donlllin

b.

tt11

inlioitc i

nl

cgro llfomo in

e.

alie

ld

d.

1101 311

integral doma in

(i\1,

II'

n

donate,; the number

vF

dcmentll in

n ~ J d . litrintc

of

the

form

~ k 1

c. a d u ~ t ol dislinct ~

d. power ofa prime

70. If

th

e

pair

of Rtruight

l i n ~

x

0

2pxy-

rU

ond X-;; 2qxy- . Y ~ he

s:

uch tho I

eaclt pail' bisects ~ 1 e ougl

b


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n. CA ) - I ,

g'(

p)=4 then lim &I J/ (

JI

) glpl/(O

-r I

equal to

lL 5

b. 10

e. -10

d. 5

8.4. An int"' rating

foe

tor of the dill"erenl

irol

e q o ; ~ t i o n

sinh v 1>: + cosh v d1= II is

4

"

"'

. X

)

d 'Y

85

. l'he degree ol' the differential equahOn

...1.. ......1.

-

Ui

(

J

) ' (d'.

)n

.

rr

u

3

b.

5

'

4

d. 'J

Rur9

.

Ti

tc c u r v ~ In

wldcb the

llluJ ent of the

angle between

the

tllngent and

the

radius

at an y point

i'l

equ;tl

to the tangent

nJthe vccll)rio l angle

ate

b. Sytem o f ~ t r . l i g

l l t l i n . , ;

h. S)'lltem

ofcircles

c.. Systerru of

pnrabl)ltL'

d. System

of

ellipses

87

, rr

e be an

r u r y c()nstunt, the general

wlutlon

of tho dlffo:tcn

tinl

cquolion

.x(x

1

3l):d.>t

3 ~ ) d y

o i5

. ... ..., .

\

..

n. tx

-y)'

b

~ . .

.. 2

. y ~ ~

e; (

.-?+y

1

).

x

1

yl:e

d. (x

2

-

y )

1

+x'l

=

1

88. tf c be au nrbitr:lry ""ustauL

Uu: ~ ; , : n . : r n l

l u t i Qfthe dlffet-enliol

equnlion

l t o r ~ l l x i s

a, xy

(c - log I81J

= I

b. xy(c l

og

lxl)=

I

C;

X}' (C 2 Jog X) 1

d.

X ) ( t .

0 8 X ~

I

89.

Tit

gcrtc'l'lll solution of the di.fftn:ntil

90.

91

.

. .i . \ ,, J

eqmUton ...

,m

~ . I S

,;..

,

a.

l

=.'\cos (3;-:+

B)-

,

\sin

X ~ n 3x

b. Auk.t B -

+ 2

si

n 1< ~ sin

d A

. ( ' BJ 3 . + .t

. " sm ~ X - t - stn x - cos

:n ~ - 1 .

3 1

The

l l n i - v e r t i c a l g l ~ of ~ i g l l l circulor

cone v i n g sebl of' three mutually

Jlerpendlcu

.largeneratol"

Is

given

by

a.

fDn

(

./2)

b. tnnl ..fi)

C.

T

d.

' 2

By mQans ol'

il

~ u h a b l c

tr.ln.limn


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b. i l ' ; t l i e ~ I

Jt oft

21

c. _ ;

=

6c log I

/(11

cl.

111

J -

6 isr

d.

ls

none ~ m

93

A

uniform straight beol

m

A.B < f

eight \\

and

length 2

l.s

111nd.s w

th.:

cn

ll A fi.

(o

d

lo

ground.

AB h

in

e

Inoo at

nn

30'

1

10

the

Tho c

ml

A i

ub

jcctcd

IO

H

a. ~ up

wa

nl f4rct W

b. vertical upw>td force \\' nnd n

horizontn l force

\V"2

"

vertica

l up

ward

fo

rce \V

and 4 co

upl

e

of mo

ment \V

U2

lL cnuple 11f 11C)t11 ~ ~

hod

zo

r$lly on lwo 5upports at c.n whW"d

AB= 2 , AC=B0=/12

'

11J

e

weigh of the

plank is \V and a man

of

w stam

wnlkin

g

from

end

W

th

o:.

oth

dr.

Tb

o plane

d

oll l

no t overl

W11

if

n. w

~

h. w< \V

c w > W

t

l. w

W/2

95,

rwu

Jor

ot.os P

and Q

I J I ~

- < ~ > U J t R.

lf P be

~ < l l , U1e oc\v ro

iiUllllnt i s ~ c b th

o

angle be tw

n

R

nnd

P

Then in

t> is given

by

u. 3R

b. R/2

c.

2.R

d. R

% .

AO)Aeni uf lorc

ply

p.1

n

b

3lan

ces wcighiS W

1

ond

\\1

in the atbcr

pan

. \V is given by

(U a J}IY-l

a.

Ill

b.

(If

.-

w )sr.

w

c.

.l..::.. . .

r z

d.

Wi

ITO )I

:

11 2

tOO. < : o K

clovercd

h) in

lime

t

is given b

yx

= 2 c

os

cit

(2a-

l )t . (a

"' I), .If motion is required to be simple

hannonic. llteo n.sbould be

a. I

.fj

b. I - fi

c.

L

;;: .(;

d - 1 t .f'.

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Mathematics for Gate Objective Questions Part 12