Mathematics Objective Questions Part 2

8/18/2019 Mathematics Objective Questions Part 2

1/9

w w

w . e x a

m r a c e

. c o m

J

0

_,

3,

s.

1Ot'J

M THEM TICS

J

If the equati

on

of the base of

an

egtillateral

triangle is x + y = Md

the

•·ertex 1s (2. -J)

, then the length or ts side is

11

d. None ol' tbe above

The line(s) passing through

the

intersection

of

4x- 3y- =0 and 2-.- + 3

:{)

3lld

i qually inclined u

>

the axes wiU

huve

.a. )

= ±

x

as

i qurtllons

b,

' =

x, x

+y=

2 as the e ~ J t l a t l o n s

c.

(y- ~ = tl as

the

q u a t i o n s

d. an tndefinite num ber

of

strmgbt lmes

If the three vert1ces

of

a parallelogram

ABCD are

A{

I.

OJ, B(2. 3), C(3,

2)

,

then

the

C O > rd

i

n:He

s

of

the fo

urth Yenex

0

wi

ll

be

a (2. I)

b (2 , -1)

c.

(-1

, '2)

d. none

of

above

Coosider the followmg statements

Assc>nion (A): The tangent and normal at

point I

>

n an e

ll

ipse bis

ect the

e.xtemal and internal angles betwceu the.

focal

distances of P,

Reaso

n(R): The straigbl ltne joining lhe

.foc t

or

tlltl ellip$e subtcnds a rtghl angle at

p

Of

these

statemenlS

a.

Bot

h A

and

R

are

true

and

R

ts

the

correct explanation oJ A

b,

Both

A

nod

R are true

btu

R is not a

CO

II'CCt t Xp

lao.;liion

of

A

t

A is true but Rfs false

d. A 1s false but R IS tme

The condition

th.at

the slrnlghl line l n

r

C


2/9

w w

w . e x a

m r a c e

. c o m

'L of lhe ~ l x l

II

. T he lina I

<

-tmy =n

i•

n normnl to the

.

'

p ~ e . .;+4=

1.

if

n

h

u.

~ = ; ) \ , :

•'

b'

1 ;

lfr

.

. - +

J. , ,,. , -'

c.

mL

T

b

fd'

-b >

d, b

1

f ·a

1

m

=

n'-bi

1

n

1

IZ. Jn the cqu:nion

• b

l '

y ~ · 2 g z x

1 2 f y z 2 w z 1

if

•

~ b ; e '" k ~ constunt nod

J"' g

- h -

O, then

th

e

olwve

eqn.11iun would repn:sent

a. • pn1r ofs l7atght lln..,.

b.

11

pl• no

c

ci

r

cle

d.

a

sphere

13

. I he eqttation nt'

Ot

e

righl

circ

ubt CQ

ne

IVh

QS¢

axis

is

lC

=

y

=

Z • n

iS lhe

ori

f',

ill Jlnd

Uti:

angle i

s.

45

1

' I&

gi

ven

"·

:t +

·•

z' - 0

b.

2 ( x ~

l J - z ~

~ ( x 4

y>z)

1

.,.- '

:

IL . 3 ~ ' < ·

•2(x+y- t )

. ._ ' 2 2 ...., 0

~ x·· y · z

x y J z z x

~

14. The

senor•

I

'(

U3ti

on

of Ute COR

\

which

pa

sses

through the coordinat

-e

ax

e•

;..

II , x ' + - h J ~ < ~ : - 2 f y 7 - 2 g 7 ~ - V > ) = (l

• b '

l . .

b.

ax·-

y--k:z - 0

c.

fYz

- 12"-

h

xy = ()

tL ' t - ' r . . ~ + xy

=

15. fh e equation ofthe

ng

hl circul$r cylinder

whose

md

lusJs.r and .:uds ts U1e z-ax is ill

,

l ..

'

:t .x-

- y

-r"

b.

~ ' r '

C. Xi I

f l

I ZX -

r

d.

~

,

-

-

16, Forces

of nlagtli tuJe. 5

.

L

L

3 3l:l olong

the sid

c.s

u.

iiC

Cii, (iii p o c t i y of

u square

ABC'D

of side

q, II

' AU and AD

nrc

,along the

X -

and

the ' '-aXi$

c t i Y d

Own tlte equut

lo

o

o.r

tt·;c line

oi

uc1i

on

along wh ich

H1

c 8in_glc r

ll8

ul

L1nl

QC

Li

i

• • 2{:(+y)= l l

b. (x-y)= 2q

C. 2(X

·

y ) = q

d.

( ·y) - '2q

J7, A

perscm

weigl1ing 8() kg i• 81nntling

em

A

liti. th

e l

in

move; upw

.:trds

with •

uniform acc

colemli

on of

..1_

9 mls' . The

•PI"'roul weig

ht (

in kg). of the por.son

, .

u.

1

(10

b. 1

20

c.

80

d. -10

Ill. A particle ai P of

~ ~

m

: Ss ol

cscri

bc:s

:w

ellip

se

under an altr.tc

tion ·f •

lo the l

l>c

lJ i

S. ~ n d an nttrac

tion flo th

e f ocus S'. If SP

: r. S'P

=

r' and the . ~ which SP and

S

'P

mnJ.c

W

iOJ t.hc t : ~ n n

at.

P i.< 0 , thctl

llic e

qualiou l l [ mot

ion in Ue direction of

nonnalt

o

theeur

el•

a.

\ ~ l p

~ i n < l f

\).

\ ~

(f •

'

)I

•

c.

\ "l ( f

I

P)

p

COli

cJ

d

~ ·ft"'.,,J.IJ

J;

,n ,J

19. The equal

iO

tl of the pa

th of

n partil:le

moving in • cenlr.l l

o

rb

it "'

' J ['"'' ]. F= tnq•

dti

NCluc of the above

20..

The

periodic limo of

t1

to QloLion described

•

by

Ute

diJ

Jeren

ltal d·

.

o

s

Jr

a, 2

b.

4

ni(L

e. 1nl

[i:

d.

4 5

21. A pan

icle is

projected with a y u •l

an

H

to lhc hOriZO nta

l.

l'lle

tim

e of

Ois

ht

i l"Utu

p 't)jectile is

u • l t

u.

~

•

b.

f ltlf'lt)

I

c.

~ C U f i t i

s

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3/9

w w

w . e x a

m r a c e

. c o m

cl . u

g

2 2

A pat tiele

proj

ected ftom

U

e lowest point

wiU1

velocity

u move-. aiOilJl tl1e iu

side

of

the

nre

of thtr

s

mooth

,,erfical

circle of

radi111<

,• II will oscillate ; ~ b o u t he lowest

point i

a. ~ 2 g r

b. u•

• e < l i•

l l .

75

kg

b. lOO kg

1:. 125 kg

d. 1

50

kg

26. l'hroc forcl3 P. Q. R are acting

al

poml

' plane. lf he antde t>etween P

3nd

(.t nnd

Q n d

R are

tso

and 1

2(1°

respectively.

then for cquiljbrium , forcds P.

Q.

R \1

ill

e

in

tlt

o m

i

o

27

u

I

2:"3

b. b2:Ji

\ .. 3:2:1

d. .{1:2.:I

l ' h r ~ vector<

4.

'i. i ore

capl•nar

if th

e

va

lue ti l

' the

>Cl WJ triple Ji'Qdlult is

•. ll

b. I

c.

2

28 ,

29.

30.

31.

n

33.

3 uf'J

d. 3

If

II is

tbe

•uglo: betwet:n Lhe vector ;; nnd

Ls

uch hal p F~ · t h e n ll

is

• . fl

h.

4,5"

c. Jl0°

d.

TWc) nOn ·'r.erq vecto,_ J •nd 8 are

par;illcl

il

'

a. i • i = o

h

1 1

'i l= t

c.

A D=o

d. i:l l

Ii i

The oispl( l)etnent

of

a poltll mo.vins

in

o

strnight l m ~ £ = St

1

- 3t - 5

s

beln

g me3sured in met

en

and

t

in

seconds. The veJncily when

f h ~

dil plnecment

is

zero.

i5

•· 3ml .s-oc

b. 13m /sec

r:. 16m /st JI

a. L2m ~ e c

Let x.

y.

.:

1.

the

$Ct of ntegC1's. C o n s i ~ c : t

the

following

slllteme

nt

with

regard to

some

propcnies associated

wflh

the 1:

I. c:ither

x

=;· or

x<

y or

x )'

2 X < y X

-t

z

y

't'

:;t,

X )'

.,.Y


4/9

w w

w . e x a

m r a c e

. c o m

c.

Jr

>

I

>p•

d,

p

">r

34. Let l he eq onplex nomber s

11tiAf

ying 7? -

;: + I

=

t lfn

is

not a mulliple o f 3 . 1hen

the vnlue of is

a. 2

b. - 2

c..

I)

d. - 1

35

,

l f 4

w. ll>:

.ue th

e cub.:

o o ~ of

unity .

t h q ~ l h o will"

•>f

· IP

1

)

6

is

12

b. 32

c. 64

(1 128

36. Tite oumbcr of rw l t i o n ( ~

uf th

e

CI

Jilitti

lln liZ 2- 0

•• l

b. 2

1 , 3

iJ

. non e of lhe C

37, C

on

s ider

th

o followmg

t a t c

m c n l i

/ls.cr1ion (A): 11' " i

nt

eg•r iN

divWblc lty 2 ond 3, them

it

i• h l ~ I t ~

(l

Rcasort(R): Jf

:r prn;i livc i

nt

eger

i• i v i ~

by tv.·o positive intcgcB. Dum i1 divisible

by

thdo

·produ

cL

O ~ e

stat ements

Uolh A

•nd

R are but R l• not a

~ , ; m : c t l a n n t i

of A

b. 3oth A and .R are true

but

R Li

not

a

CQn·ect e.sp Bnotion ofA

e. A

is

l.nll:l but R I ; f•lllc:

d. A

is fo)}e l>Ul

R

is lrUc

38. f in o •cmiuar tltc numbor of p•rticip311l i

in l i n d £ngUsb a nd Mathematics "' 6d,

84

and 108 re,;pootively, then Ut.:

minimum number

o

fruoms

n:


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w w

w . e x a

m r a c e

. c o m

7.

5(1

.

51 .

c.

1

28

d.

nona of the

nbovc

Let :\ rond B ba two sets llitvlns Sco

mt

Mn

~ l e m e n t s 'the oumber of alemenli

common

lo

ond

IJ vA,.

4. 0

b 5-:

c,.

2

tl. nOlle tlf the alluvc

[[ ~

be • ••1 wilb u

e l ~ t m : n i S

. whore u. i

,.

;my

futilu cntd

in:tl flUm

bcr.

then lha

c:trdinalnumher of ts

o w e r ~ e l

Pi:\, )

is

n.

:zn·l

b. 2

11

C..

2 u

t l

d. non e ofihe

nbove

T

e

t 'R be • reln

t

.ion In the of integer. I ,

Jdincd b.)' R h ilr • :tnd b both

~ t o t

neither

cw.;n

nor

odtl..

Tl

u:

n R

j$

n

rc:ll

i. ..'

e)(

number

"- 'Inc set uf n 1 J n · 7 ~ r o Tl:lridue . l n ~ S t i S

mod ulo o m p

i t c

~ i t i v e

intcgo:l'

ut

wilb

r

csp


6/9

w w

w . e x a

m r a c e

. c o m

d. M=

57.

Lee

A

be

nn n n

mnlTil.from

che••Cof re.1l

num bers and A=:.3A A GJ

=

0

\Vhere1 is n : n

uni

t mS

tri

x

T .-\'

1

o x i s L • then

n. A

1

=

A-1

h. A

=

A

T

.:.. A = 3A- 61

d, A '

1

-

(A'-3A t

4J)

•

;

SS

Lee

A= t

o a

nd 1 be

3 ·3

unit

0 -1

mnlli <

rn

nkof i -A is

•- 0

b. I

c.. 2

d. 3

59.

t f

A:

:]

t.ltcn A{n

dj

A)

eq

uo

ts

a [ u ,:,]

b.

[ ~ ~

': ]

:

[:

'• :o]

d

.None of

Ow

abo

ve

60

It 3x+

2y

+

z.

=O

+ 4y + z = cl

2 . ~ +

y -

4

>: = C

be

a

OJ'S

Iem

of

eq

ua

tions.

then

n. ills

in

c{l

nsiscent

h.

ic

h•• vnl) ch

e triv

i.l

so

lucio

n

K = 0 .

y: O,t.= O

c. .it

c:w. be

red oo..:

d

co a single

equocion

~ n d

so a sQiution dotS not L .'(ist

d.

u,

e

dcremoinaot of

lbe

mo lri.x Qf

.

.Jt:

ffi

c:

ie

nLi

i.

?. :r

o

61.

If

x

an

dy

are real numbers, lhen

wh1c

h

une

of Uoe follow

in

&

s

a

l\\ayst

ruc?

n.

lx-

Y s

)(

1- lyl

b.

1

<

-

Y

IX

fr IY

c l:


7/9

w w

w . e x a

m r a c e

. c o m

70.

d.

1-los .

x•·····

A

rod 26

m c t ~ r s long leans ag•lnst •

l ' e r t i c wall. The fool

of

the rod

dritl n

c S.,

2- .[ i

cl ,

Su =

:n

73. 1f

• CUI'\ e

io

rleGncd

by

I he J):ir>IIICidc C()

ordinnl x 1J

' z

I)

I

I':

lien -

1s

equal to

r'«

01

"

u v

211

-

v

1

It

,

2uv

7;

76.

77.

78.

79.

7 or9

3 u ~ -. v

e.

2uv

d

11'

- 3v

1

21l

( '

u

=f{y

+ ch;) + ¢(y - dx) , then

a.

f

b

21

¢.

tan

r

d.

sin f

C n n ~ i d c r

the

totln'' in

g

Sl:llcm¢nls

witlt

rugu.rd

to t

be

curve y - 3 (x-2)"

~ < t l i o o A):

t2.

3) is • point of

inflcxion.

p.

Re'ISon

(R)

; - al(2, 3 )

dl:

) f heJc ~ ~ I e m e n

Is

a. Both A

nnd

R are

tru

e nnd R

U

lhc

corre:<

ploootioo o[

A

c. ,-\ tru" b u t ~ is f•bc

d. A

is faille

but R

is

IJiJe

IIJn r-·

--

- - . . . . , . . ; - , - : - +

. . -

,,t 1 n

equal-o

••

1

II

h. 0

c.

r

'I

d.

>

l

..

.

. .

a.. X

: - i ~

XCOS X ..,.. 0 ) ~ - X Sm "

b. x + -

x

CllS

x

c.

,.L

.c _ . .., ....

} 2

)

a. Nouc oftlte above

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8/9

w w

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m r a c e

. c o m

80

.

Sl .

84.

85

.

86.

b. . .r.

c. e

d.

00 /t

,. t '•

f ''"

·:


9/9

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92.

93

.

95.

a.

y;= :<

h, = ~ . : ;

. '

c.

y - x- -

2:<

J.

y

; ~ ? . s

1l10 singul•rso

lution of

p- log1Jl

l .

·y).i•

;L y X ( logx - J)

1-. y ; x l lgx - .1

c. )

- Jog x

- I

d y •

X

. og X

hc differential equation IJf U

ld

fomily of

r

am

bol3

foci

:11

lh

e r•ng1n

and

axlJ

:

li

onJ the

,.;

-

mcis is

a,

>{ rly)' 2r,2- J'

=

I

clx

d.>:

(

ell'J

t

.

,,.

-< -

.. 4 - - - -0

. dt dr

c.

>

fy

)'

.

2xl d;· _ " _ II

r l . ~

t/.,

d. > y )' -

2."

rJy .,. y

-II

dx d.v

Let (v· C)

1

Cx be the prinutjvc

of

the

d i f f e r ; , cq11111ion

"{d) ) ; .

J dy

)-1- 0 he numb,.,. of

d.>: l d.>:

intcgt•l

.:l

urves which will l ass 111roUJ b ( I.

2 ) 1 ~

.l

One

b. Two

~ hree

d. Four

"l11e sol of orlhogo

uo

l trajectories to •

f,1 ntily of curves whose diffarential

equation 9(

r.61. : ~

)=

Oi•

lil

und

b)

1

the

dtirercnt equotion

"•

I J . r d r ) -

rfO

b.

r . I J cUIJ

0

,,,

c. (r.O.-r

) -

d. [

r

.

-; ~ )=

0

9 o

r9

96, Tite .

so

lution of ilie differential .;qu>.lion

tl Y •

y =

) satisl'i'ing the y(Ol

dx

·

=

l 1{ ..) 2 is

•• 2

a. wsx 12sin K

b. ""·'

x

' .sio

x

e. 2cos x t-

si

n x

d.

t t o , ~

X < XI

91.

e"'(C

1

cos ../3x +C, sin

../3

x)

c , e " "

is tbe

generalso

lllli(

IU

al

iou

+

S D 16)) : 0 is given 1

y

a. C

1

olx• t::e'""+Cjo"• C,,,-•

>; c (' ,,,

b. ~

, J ~ •l

1+ 1Jc.

c, (Ca-c,x)cos 2.x

C . . . x ) ~

2 . ~

d. (C ,

.-

C

,x

)

cosh

2x

+

(CJ

+C.)sinh

2"

??. The general solutjon

of

d }'

s m <

b. ~ c C,c '·3cos

c. )=

C

1

c''+C

1

?'-Jx 8in x

d. - r C - 3 c o ~ X - Hin X

Ill()

. Tite

S

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Mathematics Objective Questions Part 2