Mathematics Objective Questions Part 14

8/18/2019 Mathematics Objective Questions Part 14

1/10

w w

w . e x a

m r a c e

. c o m

I .

.

3.

:

I ol l t1

M THEM TICS

n

Wbi('

h one

of

the follo,Hng

c m ~

is

a l w ~ correct

for

IU'bitr:tl')

B

:md

Cl

:o

. If

A e B

and

B

C . .

h

en

Ae C

h.

I f

A e B and B ~ C ben Ae C

r.

If

~

:md

B tl .

. ~ ,

= {2k: k e

A)

x, =(3k :k e

. 4,-.

.

complement

of

UX, in A eq

ual

Jo'/

,.,

:o.

A fin

ue non-empty set

h. 0

e. Theset

of

primes

11 The

set or 'OmJ

lO

stte nttmbers

What

are rhe

four

1

l ~ e s

of

I I )' '

l2+2H 'I

1L

( ~ . k ±

b.

l±

:c

JH

v2

i

c.

±1 fi

tl . JclJc J3f

IJ a. b

und

c OJ'« 1 r e e

non·t.ero r

eal

number.; and

a?:c. then

wh

ocb one

of Jhe

foUowin

g

is nlw


2/10

w w

w . e x a

m r a c e

. c o m

d is commulalive and

: J lS 35SO"CUJhYO

.

What

'" the least number of clements in •

non nbeli•n

grnup

•II of whose

proper

subgroups""'

cyclic:

'I

a

_

6

c. 7

.._

8

13. What

Is

the numberof

propor

subgo·ou ps of

tho

group (Z, ; ) ofintcgcrs1

' '· 0

b.

•. 2

d. infinite

14. Comider the following

slntemcnllS

:

L £vel)' cyclic group is

obclinn

.

: . Bv.::ry

nl>clian group i:.

c:yeli.::

.

J.

Titere

is

a.t

t e n ~ t

one

abclfon group

of

ordern. ·rorevery nE IN

4, I':V'ery

group of cydic.

\\'hidt

no elemcut• ofurdet 4

b.

the gro up

llll'i on clemculoro.rdcr 3

l· 1l\c group is non·nbolin:n

18.

t9.

l l

l J .

2 ill 10

l

l O . . .

.

0

f) o

S own

C I ' ~ e

Supp

011e

tllJlt H

llotd

K are

u b g r o u p ~


3/10

w w

w . e x a

m r a c e

. c o m

n. S 3ndT are both

b. S

iH

hut T 11

01

bnsi•

,.

, S i• nola basi.

bul

T is a bosi•

d.

N'ei

therS n.or T is • b:1

sis

2 1. C'ntu ider the mappings:

t.

T R

1

R o T ( < . ) ' . ' l l J

S + ~ y

1 z)

l . T . R ' - . R ~ x . y ) ~ x y

3. T · R ' - > R ' ~ T ( ~ . y - 7 ) = 1 1 ~ <

Which

of

tlte nbov. I

p

nd

2.

unly

c. 2 tmd 3, onl,v

d.

No

ne of

th

ese.

25. l.el r: R:' - > R' be a linear transl\mnntion

given by l {x.. y. z)

=

1.' 2. y/2. tl). \VI 13l ia

the rank of T?

•. 4

b. 3

c. 2

R' be a tran

.Conu•tiOJt

given by T(x. y.

z)

-= (x. y, 0). D

um lh

et

null

>pace is generated by wb icb one

of

lhe

fo

llowing 1

n.

(0,

0. I )

b. (0. l. 0)

c.

(1.0.

0)

d. N

nn

euf«• es


4/10

w w

w . e x a

m r a c e

. c o m

d.

x= y= ·z

35

.

What is

the p

ll <

ilicmvector

of th

e c

en

tre of

the •phcre 1 l I

(i

• j

k} 1:\1

d. ;+j- k

b. ( ; ~ ] -

c. J / 2

(- l - j .

k)

.

,

.

''· -·-·-

;:

36. nu: point (4. I) undorsocs the foUowing

two successive. tran.tJformat ions;

1. Rell

ec

tion u

bo

ut

the lin

e y =x.

l .

Transla

tio

n tltrough •

dos

tur

ce

l

unit

along U

e psitJve x-axis.

What the final coordinat

es

of lhe puint'l

· •

3

)

b. 11. 4)

e.

(1,

4)

d.

t6

.

J)

J7 Wbeo does the

ilX

1

1\Vt AZ LIX 2:vy .,-2wz+d : f .

, . ~ ) tep rt;:enl •

sphere ?

38

.

.

Y

.

a. uJ

~ w ~

b.

u

1

tv

~ O

c.

u

'

~ V

•

w

- ~

tl.

u·

.,.

,,.,_ w

T-

ad ..;;; tJ

f < J

1

.111

1

. JJ

1

>

, J t ~ . ~ ~

ottl:3

direetion cosin

es

of

lhr

co n t u t u

pc

rpcndicu ;u"

l

in

es

th

en

whot

i.

c

b.

f>•rnbola

t .

Flyperbo

lu

11.

c i r c l ~

A. B. C are lixetl

po

ints nttd P

is

o 1•al'inb le

pomt S

um

of veclon;

PA

:md

PB

always

passes Ut rnuglt C. \\ hnt

th

e mtio In

hic

h PC divide-s AD 7

IL

1 : 2.

b.

2 : 1

c. I : l

II. 1 : 3

.

-

.. ~ · ~

A = B

k . . C '

Jjt 7k

IL 8 J d k

b.

2;

+8j--lk

C

-i

Ts

]T

: k

d. -2J-GjT

k

[ f h


5/10

w w

w . e x a

m r a c e

. c o m

47.

50.

St.

4 -

lf a.l>.c

be

three

unit

vectors

such Utet

_.. - • I -

ax b• c)= - bl . what is rho angle whicll

1

; makes witJa

;

7

••

30

b.

c.

'10

d.

cannot be d e t ( f m i n ~ d

Whar

is

tbe. value

of

lim (sin(I x) +cos I / x)l

/

I ••

•. 0

b. 1/e

c. e

d. I

Let

f ( ~ > +y)= f(x) . f(y)

foqll

x and

y,

and

t15) : . -2, £ '(\1) =3.

Wl,

atl

s

the yalue or

[ (5) 1

· - J

b. I

t .

-6

d. 6

Wlucb

one

ol'

the

rollowlng functjons is

we

ll-

defined?

a. ~ ( 1 - s i n x )

b.

~

( S s c c - 4)

r.

-

d. · ~ • +

Which one of the following graphs is the

correct graph of the functiony ~ x

I

o x?

b.

x•

-:: -v ~ 7 . - - ; ; ; - -

o

I /

tt.o)

•.

II

v•

52.

53.

54.

55

- - - . ------ · j i ol IU

v

d.

••

----::-lt--:::>y _

n. ;:

0 '-----" :I. 01 X

y ·

The

fu

nction f

(JX) =s

in '

m s i n is-defined

0

u

the open

interval

(-'lC

/ 1, /

2) and

it

assumes

onl

y

I maximum value and

only

I

minimum value on this interval Then,

wh

ich one of the fo llowin must be

correct?

a.

O< m

c.

-c < -1

d. xs:- l

www.examrace.co


6/10

w w

w . e x a

m r a c e

. c o m

56-

Let , ~ r . r k . .

JI

dOd ~ . . , :

r -

,O l

$ln 21

II.

n

59

60

.

Wh.1i is Ute v

alu

e of fit + ll)'l

11

:1

- toal

1

b.

- n log

c. ntos2

d.

= ~

1t

- a > < ' - ~ 4

e

1

1-l

1

4

48

\ \ ' h a t • ~

·lbe ' 'alue of a I

Ltkf(x)=f(llJ"-xrX{ll ..x' f'(lll •

x'

f"((ll t .

I

:lf 31

••

11=11 16

h. t t = l l

c.

(A=ll

d.

··= - l / 16

Le

t ll

x:) =

t e l l , ' x d x W

h ~ t i.<

lh

e

volue

curve

= ~ l

x -2

n.

y =

I and x = - 2

b. y = - I and x: = -2

r. ) = I) = -2

d.

y =

I and

x=

2

Let A and B be lil


7/10

w w

w . e x a

m r a c e

. c o m

b. 4. I

c.

4.

4

d. 1. I

66.

What is the

solul on

of the difterent

i:ol

d y d < ''

qu"lion ~ - - · .,y - - 117

'

dx

· •d.<

dx

y'

-

Ainx

- B

h·

v = A . x ~ ~

c.

y=A

inx •B

d.

y = ln:K• B

(o7. Which eqWil

in

n T " f l r e . i < ; 1 1 t ~ the set of •II

v e ~ in the y - p l o n ~ whidtltDI'Cslot>c nt

e

ach point

P equal to

th

e

rodpmcal

of

lh >

slope al

Jl

n 9 ~

Ja•

X

c.

-

t J m

n

d.

_

COS

I

X

a

_

6 ). lor non

-exact

dill'erentm l e q u ~ t i o n

lntegr;a tmg fnctor?

u. I ( 2 . ~ ) '

1

)

1•-

I I ~ Y )

r. J/

(2xll

d. I

( 2 . ~ )

70. noo IIUlerentiaJ c ~ U l l t i

dy - 2Uinoos' y

- ~ x o . - . . ' y

is

• d-.

reduced lo the linear fi'Om :

-1-'1•=

Q,

where P .md

Q a.-..

function

of

x

A l o n

What is the substitution?

n. lanY

-a

V

b;

St C-

:-'

.:v

•• ll

=(

4xry+ tf·l

dx

"·

= 2tlln(2.x-y+

c)

h.

-

y + I = 2Lan(x - 2y

+

e)

t .

I

=

2t

an (2y

- e)

d,

4x

-

y

-

f

=

2

1ru1

(2.'\

+

e)

11.

\Vhni

i.s Uu: solutinn nf the

di\Torenti

31

ctjW11ion E r

~

{(o' - ••)}•

, . ~ · ( e ' - e ' + i ) = C

b.

e (c

o

+

l

) : . t

.

i i

Gk

e I

n ~

d.

c

(o

1

- e' + l)=u

73. \VIonl i• the de81'Ct'

of

lh


8/10

w w

w . e x a

m r a c e

. c o m

d.

or hese

77. f(x)= x' - x -

Lxe

I

Consi

de

r tile

following

statements.

1.

fis increasing on fl,

2],

2.

f has a root in [I . 3j.

J.

fis

decreasingnn[ l,2j

Phns no root in

f

,

2]

Wb1ch of the abuve w rrect 'I

11. l andl

b. I a n d ~

•.

2 Uid3

d. 3 a n d ~

78. Let f(l')

=

b)

(I t

c) be a rea l

val

ued

funct[on where a< b<

c(a. b,

c e

R)

suoh hal r X < > ~ = O i 'hen

•f

a e cc,.c,).

wbic.

h one fo llowing is

C(lrtec

t?

79.

a <

b

C

<

< C

d.

None of

the above (liere c,

'c, )

, \ bi()Ck 1n:tss m rests un a rough

hon7.ontal surface as shown in the figure

given above, Tbc coetlicient of friction

bet

wee

n

lh


9/10

w w

w . e x a

m r a c e

. c o m

85

.

86.

87.

88 .

b.

IQO J3 N,

100

J3 N

~ O O N I O O ~ N

d. l

Oll

J N, lOON

Wbat

s

Um work

done by

lhe

force

l

.

dl ,.

I •

f =

- - - /

- - j.

Wl1ere V

= l ~ n (x/y),

1n

ex t;•

tak

i

ng

a

pa11iclu froru

t t

point

(0

.

1)

to

•

point ( I.

O)?

u

7t:

b. n/2

c. rr/4

d. Tt/6

Wbat [s the moment of

50

N Jbrce directed

along the diagonal

or .a cube

{shown

above) abom 1hc corner A of the

cu

be

'

(Side ofthe cube.is

·a

· m)

•.

soa(*-

J

iV

- m

b .

soa i

- i)N -m

c. ~ k

-

J)N -

d. . E ~ { i -

N - m

If a particle is m

ovrfl l

a\:tording to the lnw

Y2

= 2(x

sin

cos where Y ls

U1e

Velocity

and lC is

. U

1e disranc

e

de

scribed.

what

is

its

accelero ti

on?

X

CO

X

b. xsi r x

.I

CO S .<

r.

,.xsinx

tl.

,.

By wha

t percent Appr

oxima

tely n l d

be

velocrty

of m

oon

in i

ts

orbit be increased

so Uat il escapes7

u. 20.7'r.

b. 41.4%

c.

82.8

d. 100%

89.

90.

91.

92.

.,

or Ill

A partitle is moving

on

x-y plaue

wi

th

velotity at any

in

stant L given

ii = •;11(11tuCOS/lJI)} W[jaL is u.e

eq

uation to tro)ecto(Y

of

U

1c particle

i f the

particle stans from origin wbeli ti me

1

=

07

• · y = a

cos

(oo xlvo

b. y

z

a sin (CIX vt,)

c.

y z

x f a cos (ro x

IVc

1

d. y = x + a sin(w x/v

)

Set J gc1 n

Comment

St

ep

2

StepJ

Step4

St

ep

5

Step 6

Step

7

o

is

a rrataral number

p i i

y i - 2 2 *x - l )

p


10/10

w w

w . e x a

m r a c e

. c o m

b. ll

c.

13

· 5

93

,

A

ROM chip has n y 1024 x •I

Consioerthe following:

I. 4

data

i n p u t ~ are required

2.

4 dat;,

Documents

Mathematics Objective Questions Part 14