Mathematics Objective Questions Part 3

8/18/2019 Mathematics Objective Questions Part 3

1/11

w w

w . e x a

m r a c e

. c o m

I

C.S.E Pre-1.995

I ol 11

M THEM TICS

2.

3,

-1

.

5

The last digll io3 is

n.

I

b 3

c. 7

d 9

E

e r y

parr of real ownbers a and b

satislles one and only one, or the

conditions

:1>b

,

a=

b. b


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w w

w . e x a

m r a c e

. c o m

10.

d. A

i ;

fnlse,

hu

t R L'

ltllc

HJ

f iUlgc

of \• ucs of x for wludt t1

funtion x(: dcrHll

B

c

2. ~ ~ A . . B C

Select the correct 0111swer lrom the o o d ~

given bclaw;

Codes

a, I a n ~ 2

h. I ul

on

c. 2 alooo

d.

nrmc

is cnrreel

Considerthc following stotemenls ;

Asser tion

(A)

;

Let.

r 1>e the sol

of

pos

i

tive

integu-s :md J

be

the of flOSilive

oven

Integ...,.. These two seiS are cardinally

equiv•len

t.

Reason tR):

M ere

t ldst. a. Q n ~ - o n c

con..:spondonce

bel\1

cen l and J.

nr bese f • t e m e

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3/11

w w

w . e x a

m r a c e

. c o m

Both A

ruiCl

R

Dre

tnte R rt the

cnrrect explanation of A

b.

Bo

th A

and

R

a t ~ '

true

buJ ~ is not ·a

con·ect explanation of A

c 1 is true

bur R

f•ll fnlse , R is

2] .

•

)

~ C l 5

X

OJ)d

y

and

ru

llr

ro

lati

oll$

f

r.

r,

.n and

~ •re

given •s

fu

ll

ows:

X={l ,2.3 ,4f , Y=tri. l.

r l

fi = l .a),

(2,

n),

(3

. JlJ (4.

y).}

t' 1( I. u}. I , PJ. 2. u),(3, IJ).(4, fll)

f, (< ,

IJ

J.(2.fiM3,f}J.(4 , yl

I

£. l

l . a). (2, IJ), 3

,

y)J

l n p p i

I J ~ fl'flm

X 10 Y

arc delintld

by

a. J , and r,

h.

fJ

and

j

ol. £,a

nd

4

tL

r,

•nd

r.

22 let A be a set and ..:•

on

eqnh·alence

rela.tiou defined oo

A.

.Lcot n. b.c. d be

orbilrl r)' clements of lbe sol A and i f a].

[bl etc denote

cquivalet1ee

M ~ C t i then

wluch

of the Jotlowln& ~ l l l t t m e n ~

lo

Crrec 'l

2J.

l•l =Lbl ifand o

nl

v ifa - h

2. 1•1-"

lbl

is the em pty

if

and only

i f

a

'r

l>

3.

if e.,

la ], de [b]. and [Dl" (b]. thcn.c• d

Se lect the corre , o·

thC: SCt

of Jl

O•ilive

.-.

tionals

d. Z.

'· .

Z.

51;

1of 1lJ

int

egor•

25

.

27

.

3 ui 11

R denoles tltc

s c ~ of real rtumbers

and · • ·

••

M Qp

em

ion on

R

thnl

o ; ~ • f l t l

fl

t- o.fl for all a..P ER.

u·S R

, then

whic-h

' '

of the

following

>a

iD

~ an

Abel nn

group

'l

a.

S

.._s

- R

b. (S. •) . S R\

{0

c. (S. • ). ~ R'l II

d. (S.

•)

.S=RIJ·II

a.

[ llf

b. [;

r

· ll l · " • ]

d

l 10 tl

Coru;ider the

ti))ll "

I n ~ statemenL ;

As.•ertion (A) :

I f

a 2 2 matrix comnmtes

with llVery 2

2

matdx. then it Is

scalar

malri.

L

Rcas ln

(R)

: A 2 2 matrix co

mmutes wi

th

every

2 •2 r\tnttis:

0

1

these

c m e n L

a, Boill A

and

R are irue •nd R is the

c.on-ec(

e.w

lanmi

on

of

A

h, Bc>tb A

•nd

R • ~ tnte , l>nl R i . ~ not

a

co r=t explanution 1>f A

c. ,\

is

true. but R is ml•e

d. J\ f;rl lt,

but R is

tru

e

' file V3 lue of he delenttiunnl

a, U

h.

c.

I

d. Jiluoe of th"

llbOV

28.

IIA

a n d B ' [ ~ : :J thuntbu

~ l 1 02

dcter:utinanl ofA B bas the value

..

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w w

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b. 8

'

16

·

n

l

-

1

9

The

inve-rse ofU1c

m o l ~ L I . o II

os

II

(l J

~

[:j

:

;]

~ :

0 0

c. r

: :J

0 0

- t

d.

.:.=

0 l

:;(), 'l1oe system or

tho equati

on

'C

+

2y

+ t

= 9

2 y ;

37. =7

can be cxpMscd

••

··

-

rm

b.

2

~ J [ } [ ~

c. :]

d. Non u d 1 ~ o v ~

3 L Which one ol' the tollnwing

l'un

clions f R

.

R

is

delinc:d

for

all

rc.1l x?

32.

II. log

.:.

005

log

(Hx

1

)

IJm

.e : f '0. b' 0 > .

-

.\4


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m r a c e

. c o m

C,

cu r

.,,.•

d.

~

•

39.

ff y

=1

111 rwu;

.

then 2:. is

d,

n.

. , ~ ,

1-,p(i. 'J,Rn 1'

l>.

C o t . . . \

I ' .Yl"f.•

"·

.a

I

I

1- ilk

S U

..l

tL None of he abov


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. c o m

so

.

51.

S2

53

.

"- x = l

i>

vertioal asymptote for the

curve

b.

x

~

-1 is

l verti,a l ') nptole

for tha

C\11Ve

c. )= ()

is n

hC ri7onl:lll,

fur

L 'UTVe

d. y = 2 i• o horlzont·al >Symplotc t>r tho

curve

l f

the

f u n c t i o n ~ u. v. w

of

three

Independent variobl.es,

1(,

y.

z ·u-o M l

independent .then the I•cobion of u. '' · \1

1\ itlo espect to

1(

. y.

z

is alwayscquolln

;c I

b.

0

c. the Jacobian

of x

y.

z with respect l.o

u, v . \\'

d. infmity

Ute

r liliU I o£

n l l l t

ol' lto curve v -

t

nt the

point where it

crn>Se$ th

e )

•-o

xh

is

b)

d. 1

Tite

lenglh I [

arc of the curve 6lty- = x•

-'-3 1\'rrm x

=

I t

C

X 2 ii

a.

.

units

b.

11

units

tz

c. . 2 .

unit

s

d. None f t b e < ~ b o v e

57. The scr,h.-s

n<

is

,

..

"· Convorgt)]l

b.

Divergent

c.

co

nditional converg


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w w

w . e x a

m r a c e

. c o m

S9.

GO.

61.

62.

63

c. lxl

"' . .

cL s i ~ .

l

e ~ e t i e o l_

_

2._

+

j

_

_l

3

< w e

tAl

Lu.

be

a

se

.ries or positive

renns.

Given tltal l: u

11

is ccnvergent ltlld •Llo

ilm exlsts. lben lhe

s.aJ

d lim

it is

,, ...

._

u

n. necess•r i Y e


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70.

71

72

L l

01

c pr

im

itiVe

of the diiTcnmt.ial

- q u o

D

2D

5)

1

)•=

o

. w/l

tNO . ..

]u

dx

o

e" l(

t'

1

+C

;:.'\)

cos

2

:


9/11

w w

w . e x a

m r a c e

. c o m81.

83,

84 .

85.

1. R e c t a n ~ u l n r hyperoob

2. Circle

3. St.roiQht l i n ~

P

a r ~ b o l a

5.

El lipse

o d ~ ~ S

A

13

a,

II. 4

e.

cL

I

s

5

4

(

3

3

3

D

2

5

2

z

The

equation of the lnngenl to the

by

perl>ola xy

= e' ot

" p o i n t

(xr. Yt) is

o. xy

1

yx

1

=

b.

~ Y 1

•

y: '+I - l :+2

- ,- =-:s-2

1 ~ i t h lhe

plane r =

S •

n.

15. - 14)

b.

(H

,

SI

.:. ( 1,3. -2)

d. (3.

.

12. -10)

lb

o pl:we

ox

•

by

f

cz

()

ools Uu>cone

xy+y.o; I z:< = 0 • peq>cnclicubr lin""

if

Hb

11:"'

0

>

- . _.1.'

. .:

1)

u

•

c.. ...

0

(L ab-c = 0

.... l- .,

, ole

equ:1t

ion +y t z"+xy;-y-L-zx=9

rtpr.,.cn

ts

Ln

''- a e r e w•O•

x

·+y- T7 - , ,

\·

y +

z=

3

ns

•

~ ~ c i r c l e

. •

cone with K

+y"'+-z'-

9,

X· y ~

f i§

guiding circle

3

eyiincJ; r with x'-y'+z

1

=9.

X·

f 7 . =3

as a guiding cirele

d, None oftheabovc:

11te

equ,tion or.

right

ctr


10/11

w w

w . e x a

m r a c e

. c o m

&.

mngnjl\ld e

of the

other. Tile

111tio of

the

l

aT&er

foree to

th

e smuller

is

• . 3:2,£

b.

:.

. f j 2

1).

3:2

d. 4:3

'1\

vo

Hk

e parullcl brecs P :

md

Q

fl

'

.-.

Q}

net

on

a tigi

il

body. T

~ 1 e l

on:e '

di

splaced

pnr.tllel to iu.clf through • dist lU ct

l It

ma

ximum opecd (in

lon

.ph )

3

Uam

ed h) th

e

lfn in

is

•.

30

h.

J. -IS

\

bollet

of

m•••

0.0 I

kg

is

ftrod

uom

•

nile of ma

s$

20ka with

a •

[l

eed

ol' lOOmis .

Velocj ty ufrecoil of tlte rilk (in m/s )is

I

b. 0.{15

"·

20

d. u.oJ

Th" perio

di

c time of a

pl11

n

el TJlllvi

ng

under b.versc l

ow

Qf

nocelerati


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. c o m

()(j

7.

98.

l f the (lifferentinl equation

of

n particle

< > ~ e c

t i l i n g simple hnmtonic mCition about a

)>oint is

J l

= - I J

'

h

ere i$ some cons

tont

of prnportiunnlity,

tJ••n

n s • ~ • l '

the g ~ ~ m e n t

1.

flrequ•ncy

of oscillation ;,

Jii

2.

Mux.

imum l o ~ i t ) of Ute porticle is

.r ;:;;

whei>; -..•

t

he d i • f n t ~ c e of

tho

mean

JI

O

ibon ii:om the point li'om

where h surns

mo

ving

3. lt

'

lhl: point from whi ch tbe

~ : u t i d

stnrls moving is allered

there

wi ll be

ohaugc in

Ut

e Lime period

u(

osc illoti

otL

Uf

t : j ~ e

t 0 1 o e n t

u

I, 2 nnd are cor=t

b. 1

Md

2

aro co rrect

C. 2and 3 UteOOO'ee

l

d. 1 nnd 3 ure correct

l'wo

bnll

$ ore projected m u l t n n e o u s

with Ute s

ome

velocity frtlm the-

t6Jl

of

tower. one \lortically upw31 ds

and

tho

other downwards. I

titer rea

ch

th grqund in

lm•es

t,nnd 1

2

, then tho

lteit bt

oft

he to"

o;r

is

1L ~ g i l

d.

1 g(tt

I I}

A pllrt{elc fTI

V"" su

thai iiS

fl

sit ion c t o r

~ v e n by r

:c C(Js

<

i

/ +sin lOI 1(where

is

1f

c•m•ln

nt).

n tc

w lo

dl

y

of

the

m ' t i

"- l

)ttpt:

ndicul•r

U) •

b. pnrnllcll to ,

.:. in u direction making :tn :mg le

with

lh

e

di

rec

tion of,

in u dirckin

g

lLD

•n,glc nl4 wilh

the din:ction of

9l).

II ul 11

I f

o p ~ r t k l $Uirts

li'otn

rest the highest

point of • vertical circ

ula

r 1 ~ l r e qf

mtlius •a• then

1. the poniole leaves the wire

a.t

a depth

2n 3

Ii'om

Ute

highest

po

int

2. th

e

ton

gent

ut

ij1c

r •1int m ihe

eire ¢,

wlu:rc

the

particle

~ ~ ~ ~ tha

wire.

m o

wilh tlte

l ) r i z o

n t a l • ~ > l l n

g l e l ) l ) s

1

(2/3)

3. the

&ubsuquont pntnbolk path JtM

lntu< rectum 16/27

4.

th

e vel()l)ity of'

th

o

po1t

tic le '

un

y

h.,1ght ·h fmm tho

lowo•t1'oint is [ ii:

Select the correct an•lver usmg the co de;.

given below

Codes:

:1

4 4 3 •

nll4

b.

l.2nnd

3

:

I and3

d. I and 4

100.

If

• l atellite launclted trolll the s w t ~ c e

earth .then

hiclt of

lhe fo llowing

St

atcmenl . Q(c

CI/Jl't:{ l7

I.

'l'he

yelocity

Qf e s c ; ~ p e IS ten

kilometers per second

2. The S

Mathematics Objective Questions Part 3

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