mathematics objective questions part 15

8/18/2019 Mathematics Objective Questions Part 15

1/10

w w

w . e x a

m r a c e

. c o m

cS. t;.

p

. 2D0

7

I ol ICI

MATHEMATICS

r

J

Let

X=

l u • n

IS

a

po

s

ili1

·e mteger. n.s

50}

,

If A -

ln

e

:<

,n

is

evcrnf

and.

B= fue X:n mu tuploof7J , then what is

the number

of

elemen

ts

in

lhe smallest

su

bset of

cQn

t

ntning

bo

th

A

and B?

~ 28

b. 2 1

c. 32

d. 35

2 Let A

=

[t

e N.

Il and l are

rela tn•

el)

pcimel and

B = 1t.: N. t s

241

. Wtmtis lhe

numbe

r

of

elements in

A("' B

I

a. [()

b. H

c. 7

cL 4

3

t.et

7, c o s : r + f 1 t / and

A=

rz

u e

NJ which

011e

of

the

follo\\1li

J;

is correct

n. A

is

1101

a

linim

set

b. A contams

12

non-real comple'

n

umbe

rs

o. The

number of

elements in A 1S

16

d.

A con tains no mlegers

1 Which

ooe of

the fo llou

ing is correct? The

e q n ~ 221ox

1

(2Ml

' { 2 6 1 ~ ~

u

Has

no

mull

1ple roots

.

b, Has

one

rea l

ro

ot.

c. as no non-real

roots

,

d. Has

no

integral roots

5.

\Vl\a

t

is

the sum of the roots

of

the equnnon

((•-2 )

H}(tN

-3f >=l)'/

n. 5

b. JO

0.

l3

d. 18

6 Let rn be positive intege

r,

m ~ l . If

, ~ ,

...

_


2/10

w w

w . e x a

m r a c e

. c o m

11.

~

u m i t l e r the group

(R•

R• t, where<

R*=R-10} illld

ro.

b) • (c,d

) (ac,

bc - d)

\Vhnt an. th•

id

entity element nnd the

in,,._,., of

(n,

b) resp<

-c

tive ly'l

a.

(l.O)

nnd(a

1

.b n

1

l

b. (

0.

J) rutd

(a

1

• ba

1

1

c. (0. l) nnd (o

1

• •

bn

·t)

d

(1

.

U)

ond

(al.

·

b

'

1)

l3

.

Wh

lc

h one

of foll

QIIlng.

•Ui

tetnenls is

euttet:t'

a

..

AbclU.n groups _may ha

vt.: u o u - ~ a b c - l i n n

subgroups.

b. N011-abclfan groups may have abelian

c.

Cyclic

gtQU

Jl"

ma

y havg non•eycJic

;, ubgJ

'O

UilS·

d. Noq-.:yclic gmups C311MI ho1e C)'ll

lic

sub gro ul -

14. U:t

o - = - ( 1 , 3 , 5 .

) 1 2 . .

Wh.tl

the

s m o

e c ~ l

11ositive int

eger

n. •uci•

that

ri =

rs ?

n. 3

b. 5

the nUtllber of

lnwrtibel ulcm.,uts

un

ttr nutltiplfcallon

In

R'

l

1 l

b

. It

c. u

1

d. (n.'2 ] whcrt:H l. 1lte brnckct

.l

lmctiou

19. If Q. R.

C

ore rcspoc tivdy lh t litlds of

rational numbcf>l , rc•l

n u m b c ~

3nd m

nnrnbers,

which

cme

of

tl)

e fo

ll

owing

olg*ruicSl{\lttur"s ill nvt yeciqr p : t c ~

n,

R ClVe

r

th

e field Q.

h Rov

erthdi

eld R,

"· CJ over

lh• tiold R.

•I

(' Qver the fie

ld

C,

20. Let "' = (

3. 2.

·

1)

. y

=

(2,

4,

1). z = (4, \),

ond

11 10.

-1

, ·3) be vectors in R:\. il rtill

1

cclot p a c e \Vl•i

c

li on of tho

fo

ll

o11 iog Is

correct?

o. 2't z

\v y

t

z -- w

b.

2x

y

z .

y

.. ._

2z

•

w

c.

:t •z • w.2. Cty z.

d

. y

f

2z \ \T X

z_

21.

lf

V

rool

vector

spoc.:

of m> pp ings

from

R

to

R, : ( f ~ V I r t · x ) : f ( . ' < ) l and

V,= -{ f « V I f.

: < ) - f l ~ ) } .

l

hon

which one

of

l h ~

following

i.s

Cf)m:cl?

IS. Nelther V

1

God V, h a Sltbsapce of V.

b. V

1

i.•

n

a c c

o f

V. hu

t.

V:

;., not G

Rl:>,

apa

ce

ofV

.

c.

V

1

' no

t

o

s

ub

s

pa

ce of

V.

hut

\1

1

;

,,

suln pact:

orv.

d.

Botl• Vt

and v:

ace

subs5t>ces .,rv.

22. l.el F[xI he the

rin

g or pOI)'nu rnial. m One>

variab le

J(

11\'Cl' O li'c:Jd F wilh Ue

rc

la

li


3/10

w w

w . e x a

m r a c e

. c o m

23. Which nne of

th

e

fo llowing i•

co•

1'e

ct 7 l he

st:t S

= {a

~ ih, c

+

ul} L• o b

asi

s

tb

•·

th

e

v J J u

c

nvcrR

to

'

a. e ~

b. ad +be - 0

R by T(x,y,?.)=(y

iJ 2)'

1

I l.

b, 2

c. 1

d.

()

29

Comider Lh e vcctor•

pn

ce C uwr R und lot

T C C be n linenr r t r u ~ f n

n n r o t i o n

given

by 1'(z) = 1 . fh en w

hi

ch one

1.1f

the

fo

lluwing is

cotre


4/10

w w

w . e x a

m r a c e

. c o m

given

by

xu -

2

b

Yl • - 3h)

=

:o b

p:tt: unply

e

;1

cb

oibet.

\VItal

is ibe angl

co

between

tl1

e

tw

o

drawn from ( L 0) to

tl1c

eurvo: y - 4:t

OJ

3. 30°

b.

4 '"

)

c.

60•

d.

< 0

•

I f ~

cu·

de

ami lhe

reewugubr hypel'bola xy

c

meet in f-our poi.nt8 lt - t

3

and

4 th..:u

what ;, t

1

t

1

(3t.. equal to?

:1

I

b. - J

"- 2

d. 2

l

fP. Q. A.

B

lire\

I, 2, 5), (·2.

1.3).(4

,

-1

.

2)

,

(2. I, respect

ive ly

. then

wha t

ill

lh

e

projt:


5/10

w w

w . e x a

m r a c e

. c o m

~ " b

c'

=- . - . are

non coplonar.

Jnbcl

Which one

of

th" fo

ll

owins L Orrcct?

u. S

1

impli

es S1

b u t ~ docs

nOl

imply S

t,

I),

s ,

d

oe;;

n

ot

im11ly St hut

S1

mpli ts s,.

.::. S, implies S, and lh impliCll S,,

d. 5

1

docs

M l

imt ly

St

and

S

1

dn

os

lUI

imply

s.

\Vhnt is the

vol

um

e of

the

lctrahetlron witlt

vurticcsat(O, U

O).(L 1.1), 2 Ll):tnd

( L

2, I)?

• . 1/6

b, 113

c.

1

:

47

. I f

r ••ti;>lies the e q u ; l l i ~ n

f

i ~ 2 j L

) =

i - t <

then

for

an

y

.Cll

lar

m.

what is

;

l l j

to•

a. i-m(i-2)+ k)

h. j 1m(1.zj' k)

:

k

· mti +

l]-k)

d. i- k+m(lT 2+- k)

48. For the triangle OB('. one '""""" 0

i•

the

or

igin l\nd the position vector.. of

Ute

o

Ut


6/10

w w

w . e x a

m r a c e

. c o m

5

3.

>< < -lorx " 6

. - 2

c;

~

6

o

d s i

.\ B

c D

b.

4

2

]

3

c.

3 1

2 4

d. 3

2

1

4

c.

4 1 ?

3

f

.t.

2b 0 0. ih


7/10

w w

w . e x a

m r a c e

. c o m

b, 12 n

c. Sn

d.

Gn

o7

. Jr

u l l - : f . r l -

xl ' then whot

•

••

68.

i&p equn l t

o?

a. 2n

b.

I l l

C..

l-i

tt

d.

W h ~ t 1S 1 1 ~

area

of the region b o u n d ~

t

he curve 2y - - l y'

•nd he

l ·n.'l.is

'J

a. 12

514$

uph

b. 4 unit

c..

3 uni

t

d.. 2 ~ / U sq

un11

. x -

y•

G9.

\Vha11s t h e ~

e o h

1

.-yJt"-y'

7 l.

h ln v

1- In'"

b

1- lny

I

r lny

"-

- + loy

l+lny

d.

1 · loy

I lny

s3n

COS.X

rf f C ~ < ) - (I - 1 u where I

p p· p·

constaut.. Ute:n ' ' bal

i5

Ute

val

ue of ~ {f(x))

nt x : O']

p

b.

p • p'

c. p - p·

d.

[ndepcndent of

p

71

. Whot ore

Ute

order and cl" 9"'e respective )

ol

' the

dilferentiaJ l CjUOt

tO

n nf

t

he f.1mi lv of

u r v e ~ ~ :

J c b < +

where

c ; , ·an

;trhitr:u- · conslanrl

n. I, 1

b 1, 2

c.

I.

3

d. '2, I

7

ul

Ill

72.

\VJ1ot is the

oofutiou o

lh

e

73

.

d-)

dv

ditlerentiat eqnotion - .

-2

- · " " ~ Y "'"·

d,

·

~ ~ .

.

with tho< g

ivc1

1 conditimu ) (tl) - 0 ond

y

O)

= 1?

11.

V= i

•

CmiX

b y ~

c.

o o s x

-

. .

d. y :S fn :<

Wh31 iii lhc o l u t i o n of

equa tion

(1• e' )dx•e

'(

l

••

X y e ~ " '

= ~

h. Y t-Xe

:tJ

c

1 .

X J fi'f C

d.

n < J n ~

11f th

esc

Ute differential

~ \ y e

,.

74, 1'hc

smgulor

$(llu

t

1o

n

or

lhe

dinerenlial

cquat

ioll

y pll +

f1p)

will bo QblJJined b)•

elirniunting p

between

he equation ) :

l' p)

and wl ich

one

of

the 19

11nwing

U l l . • o n

df

tt.

J t + - - 1 1

dp

dv

elf

b. - · -

• t

-

dp dp

c. dy - p

d.

Jy


8/10

w w

w . e x a

m r a c e

. c o m

76.

Whol

arc

the urthogonal trajectories or

d•

e al A s lh,,l Ue new centre

or

grovi ly

d i

\ll de.

median

through A

in

til e mt lo 3 :

47

•.

'4

b. 3g

1 ,

d.

S&

82 Two p h e r c s of radti 6 m 3 em •ro finnly

uniled.

11•o two e o an: to lid

3nd

of

lll

e

same mnt,.,.;al.

What

i

;.

the

d

is

tnnce of the

centtc or

of l1e wlwl•

bo

dy lrom

lhe

centre nf 11c la•·ser

' J ' l h c u

a,

I

em

b. 1cou

t:..

~ t u

d. -1

· ~ n

83.

U

h . < > a n g l

of

friction

IS

:t.

lh

cn w

ho

I is

Ue

ycntcsl

hcigbl nl wlticll iU I

Q tes

t

inside • hollow sphereofrnd

i\J$

a7

::t t s

i n

).

b. o(l cos1..)

c. trul ?..

d. •0 - liiJl.).l

14

. B

1\

w poinl$ A and

B

hn

ve

velociti

el<

u1

nod u1

ns

shc111n ill

he

f i g u

obl)

ve, lf AB= d, whal U c 11ng

ular

of A n:

JatiVQ 111

11'1

3.

< > : ; ~ L )l d

b. tu

1

co• .l

; u

•O>


9/10

w w

w . e x a

m r a c e

. c o m

SS

1'wo

p ; ~ r t i c l

ure projected v c r G c a l l ~

UpWaT

i

l<

Jrum a

pfaee

:ll

an tnlC Vaf

of 2

socottds. I f

Utt .Gn H

1

and

n situultaooousty, tblltl whkb ouu of tltu

foUowing

;.

con:cct

?

a. .pi;=(

. j t { .

,fi8)

h.

foL

-t

./H

./2i

)

e; m ~ -

:.zs

d. JH I I i

l

86. A rarticte or unit mass 1S U1)05tmined to

move in a smooth clrcul3.r pAth ul' ,ndim> a

witlt

ronsi.Ont spoerojection

. Whllt L'

U1o

greatest

hct

gbt (h) a l l ~

inctl

tlunug ~ 1 0 paih uf Ihe

pfojtctilu 7

v•r

rgRJ])

. h = - 1-

.,

1 -

-lg

v•

b + ~ J I J

=

l f J

89

.

~ 1 .

92

9nl lll

A paniole Is executing s

impl

e ham.onic

motion and its

tli splncetnent Irotn i ts

mean

position

S

giv n

.,.<

~ c a s { r u . k ) . .

wh r

l denotes the Urn.: and n,

n.

k at (< pasili""

con•tants.

Und

er

w

hat

co

ndilion

wi

ll

th

e

speed oflbe por1itle be m a x i m u m

a. t

=l2p+

l)lr :n. tl befug,an mtegor

n

t

=('lp+l)

ni

Zn

- (1; n)

p

1ein8 :m

integer

c.

1"

(2

p • 1 an

' a} r

being

:t11

integer

d.

t

p1r/ n (k n

).

p bcmg :uuntcgcr

A. portkle who,e w ~ i g h t OJJ

IJ1

d

s u r f • ~

of

the earth is \V. falls to the surfoce of t l ~

earth

fmm

a

heigh

Xll13llo

th

e

dinmeter

2R

of tlte e.1rth. What is the work dnoe by U1e

eatth

••

iltlJ'Ol


10/10

w w

w . e x a

m r a c e

. c o m

Comment l : f

'

(i ,

J)

is the product matnx

AB

of

o

rd

er m •

p.

Wltnt is

X

in the obovc

l g o r i t h m

a. C'(i. j) I A(i, k

)"B(

k,J)

b. C Lj) r

A(l.

k)• B(J,k

J

c.

A(t,k

)•

B(l;.j)

d,

C ' ( t . j ) ~

A(i

,J) •B(t.J)

94.

What

is tltc decimal

equ

iv

alent

of

t

ile

hexacl

ecimo

I numbc:r FF ?

.•. 225

b.

u

255

d 256

95

W

Wch ouc of tlt

cnllcd

"eo

inciden

ce

deteo1 l

••

OR gotc

b.

NAND

l-

''

""

NOT

gato

d. AND ga te

96. Let n ::.3.n be odd.

A.S>I rtiou (A):

For

01uy 1-l, ..

.

"n l i f

u,,c..,

..,a

,,

""'

the

t

tlol.s of the

cqu•tiotl

x" ~ - :IJ then

(I

1 «, '(l

1.

.

. I

Rt•asun (R.)

:

l f 11

,

rt,

ore the m1•1Jri'th.:

cq u:itiun.•, .,.• - '< - I : ) , ant

io

n

nr

A

b.

Botlt

A and R a r ~

indh

dduo lly true bul

R iR tc

n . , e t

Cl

nnatiun

nrA

c.

A ls

tru but

R

i >

f:ilie

d.

. U s

fal c bu t R iu.ruc.

9 8.

Asse

rti

on

(A):

Tho

l\mc6on f (>.) - - - is

1

lxl

nm difforcntiabl" 111 s

=

0,

Rt•

uson {R)

t

lsi

nnd hcnQc; (J

I lX)

i . ~

n-wlue to c m the gc

ncm

l so lution

• · BoUt /1 .end R .ere individu•lly

true

und

R

iR

the

~ o i 1 ' < ' C t explonnlion orA

b. Hoth A Md R ore

d

a l l v

~ bul

R '" he

.:om;ct

eXp

lanation

of

A

c: A is true bul R til be

d. A is fnl lc

bLLl

R

is

'" '

""

10(). Assertion

(A)

:

r·05 •

- oolxdx

' ,,

Rea•on (R) : 'Tho inlcgr:md i$ on oven

functio .

"' Jloth A and R nre individually true

nod

R the .:ot

we

t l o n 1 1 t i orA

b. Bot.h A :md R ure

md

ividunltv true but

R

r. lbc .:orrect cxplnnnlion

of

A

tl.

A

i•

true

but

-a [

fn

L

mathematics objective questions part 15

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