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I C.S.£ Pre-1.998 I of ltl

MATHEMAT~,_C_S==========~J

3

4.

5

for any two r. se R' with r < $ , lltere· al" nys exists an ne:Z , n> J such that (\\here R and z' staHd for the setS or posith·e rcafs.and integer respcclivoly) s. n r> s b. n r= s c n r< s

d nr ,. s

Cousider the foLia\\ tng statements Assenion (A), 11tere existS a bijection he.t\\eell the set ofnatuml nt1mbers and the set Z of integers

Reason I R): N JS proper subsel of Z Of Ute stalements

a. Both A and R are tn•e and R is the correct e,\-planation of A

b. Bmh A and R are lme and R ts nol the correct e,-plnnarlon or A

t. A is true but R is false

d A 1S f.1Jse but R is tme

If a, b. c. dare four positive renl oumbers and. further tf n b c d = I. tben the least •alue or (I + a)( I + b) (I + c) (I+ dl•s

a 11\ b. 14

c:. 12 d Itt

rf w is nn imaginal)' cube root of w1i l) . x =a b , )' = 36l 1 bro• and z = nco~ I oo _ tbeu xp., eq unls a. a+ b

b o!+ b2

c. o~+b•

d. D~ ,_ b3

l'bo correet polar form ol' the complex number I· 1 ts

., -a. -J1 (''

b .!,

c'

c. ..

...[2 e , .

7,

?.

• _, d. t'

The HCF of two polynomials flx) and g(*)(:<· I) snU lh~•r LCM IS

(x· l)3 (:<· 2) (~<· 1 ) . If f(1() Is (x-l)'. then g(~) IS

a (x- 2)(x-3)

b (,X• 1)7 (>.· 2\

c. ('<-1)1~- 2)(x-3)1

d ("·I )(x·1Xx·3)

Cons1der the [ollowmg p:urs oro umbers:

I -15689_ 456'Xl 2. 6:!9975, 6~9<176

J 8754'Jll. 78458~ -1 I OO!l, I()() I

Tb.e pairs cooststtng of relaJJ ,•ely prhne numbers nre

a·. 1, 2 nnd3

b. t,2snd4 C, 2, 3 and -1

d I Md2

The numbers or candidates appeanng for Hi ndi, English and Mathematics are 60, 84 llnd 108 ~pectil'ely If the same nllmber of candidates have to be sealed tn evel) room and all the candidates in a room should be appeariog for Ote same subjecL then the minimum numb~r of rooms required to seat al l the cand1dntes ts a. 12

b. 21

c. 2!1

tJ ft3

The poJynom1al equai10n x 1 + 3x? - 4s - 7 has over the complex lield

a. 3 roots b. only 2 roots c. only J root d. no root

10 II' the polynomial 8x'·2x3·n.,!~bx·3 IS

divisible b) 2x21"\-3, then the ,-alues of a and b :u-c respecti,·cl)'

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I I,

;1. 10 nnd IJ

b. B '.nd JO

.:.. hnd5

d. - 10 •nd - 13

Consider the following stntements • 1. r-9 is- u fnclor of " j ' 5x: - 9x 45

f "). . 2. I l <I r~ tht rem:rrndc:r wh~n the

polynomr31 flx) Is divided by ax:~ b

3 . l( ~ ) is th" r<:mn inder when the

(l{llyuontiaLQ:<) is divided by 3.'<. I b

-1. 0 i" the rcnntmder when lhe polynomiol 1\x) is diVided by • linear f~ctor x·• ·

Of tb~c ~tatomettts

a... 1.-tnd 2 are con1ec.l

b. I alone is <Wrrecl

c. 3 nlone i• ~orrect cL :> :tnd 4 lire oom:ct

12 Jf k.x1 lind 1,_'1 leave the oe m:Uuders p and

.!.. ll'hon diVided lty '"' 1 h o~nil hx 1 "

" respccliVd y. th<n lht! val~c of kl is

,1. !12 b1

b. b21~2

c. ]

J . - 1

14. Tf v.. p. 'f ond ii are Ill<' t'>nl$ ol' the .:l)tmtion 36.xl- 216:<1 ~40 I l2-13l-.: I 40 I) , th"n a~ .... p1 •{ ·cP equ:tl$

"· 36 247 b.

I ~

15.

l6.

17.

"· 18 1049 d.

18

2 nl lo

rf 3 • n is 11 root of the cquotioo X$·

9<\1 ~32 x 42 "{l.lhen tbercaJ root Qftbe equation is 3 . 3

b. - 3

"· 3- ,fS d. 3T -15 If l is u twit.-.: repealed root ()!'the equntion .. ;;'+bor - "~ - d= ll , t11en • · a ~ -d ~·b

b. - a; d - -b

... • = d =-b

d . • = d = b

lf the polynomiol cqu•tion o:'+px'+'l"-~<1 has the root~ a.. fl . y. then tbe roots of the polynom"1l equation x' -qx'ryrx- r=o are

a /1 r •. p•;'; b. a- P. (3+-y . yt a

c, cxll. fl y. yeo.

p L tt d. a•-· P• -r • -

.,. 0 p Ill. In a sorvey 60'\o of those ~orveycd owned

a car and SO'!tu of O~nse surve~•ed owned • T.V. lf 50'lu owned bolb • c~r oud • T.V. lbon pon:cntasa of !bose surveyed who owned ~ car or • •r. V but not botl• will be

20.

•• 30'1• b. \0 ' -·· "- 25~o

d. 15"•

If i \ : ( l , 2. 3. 4, 5} .then the number of sub*el~ nfo which cnnt.a in 2 bul nnl 4 iN

a. 2 b. 4

c. 6

d. 8 If 'l' be ll1o set of all triangles in • plnne and R means " has twice the ~rea of ' , thilTI IUs

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21

23.

~t- not reflexive-b. rcflc.>:ive but ncithor symmeu:ic nor

trrm~ilh1e

c. t'tlfl~'<i\"c and symmolric

d. t'ell o.!JOve and transit[ve

"fhe m:oppingf; R ->R gi\•<m b)'J (~):xl is ;1, one IQ one J.nd on~o

b. one 10 out but uol onto

~. neither one to one nor ont<1

<L onto hut nQt 11nc 1(1 tme

Let I be the •et of intcgon. tf R lx> • relotion deftned on I by setting (a, b).;d{ if ,,. h ii\ nn cv<:n inttger a. b.:: I. then

a. R os reflexwe bul.ool symmetnc b, R is trnnsit.ivo but neither reOc~a

nor ')rtrunetric:

1:.. R is rdla!tivo ond synunolric but not lransilive

d. R ~on equivolence ,el•lion TI1e inVCI'MC <Jf the pcmtulbtiun

(~ 2 l IS ~ I

(~ 2 ~) 0. ,

b. G 2 ~1

G 2 ~) .:. 1

[ ~ 2 ~) d. 2

24. llt the set Q ofnuounJ uumbct:!l ® do1med

® etfJ oslnllow~ for«, PEQ , n p-3

If C[, Q'1• ~~· r.spectiwly dt!nolc U1e seL• uf po!oili\·c.. ne.gatiw and non-zero r•liQ•nl•. the which one nf tho followina p41rs ill an nbelion group'/

•• !Q .® l b. (Q'1® l c. (Q. ® I d. (()• ® )

25. A 2 2 mntrix which L'Ommut<l!l with .:very 2 ' 2 matrix~ of the (om\

26.

;!7.

28.

29.

.. [: :) l>. (; :)

c. (; ~J

d. (: ~)

3 uf Ill

Pot any two 2 2 ~ymmetri~ matrices A and B consider U1<o foUowlng stnltmc:nt! l. (A+ B) is asymmetric nwtri.~

2. AB os a s;ymmetnc mnuix ;I AB- (Bi \ )'t

4. ATB • ABT

{\\11~= AT denotes the tr>n<posc Q( AI l)f these •llttements

a. 2, 3 and ,4. are COITCCt

b. 1, 3 and 4 ant corr • ..:t

"· I and 2 nrc c<>oTect

d. I. 2. 3 and 4 are correct i" ,, •

-q r _, Tit.u detcnuionnt o.f

' ,, "'JUl1l to fi. , . '1, .. ; +,, b. ( r:+q~+~1+L1)'

c. (r+q2+s,+t12

d. 0 Let o 3 3 mutriK A have dclcruununl 5. II' 11 - 4A 1• tlten Uoe determin•nl of B i> equa l 111 a. 20 b. 100

e. 320

t1 r 61)0 Corulder Ute following >tat.emenv.

As.•ertioo (A): lfM is ann n malrL'< wiUo r.mk n - I, then M c.1n be made non­singll lor by <lhaoging one e lement Ren•on (R): An n • n maiTix with rank n• I ltAs a non-vanishing millOr of order n-1

Of these st~tements

• · BoUt A .>nd R arc true and R is nol • conect e~plan.1tioo ()(A

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30.

b. Doth A and R ore true, but R i3 not • correct e:-:plan~tion of A

c, A .,. 111.e bm R i!; tol~e

d. Ais Julsc buiRis truo:

rue system or ~quntlous 2.'(-y:j

"'{ - 3y - - 1

3X • o.ly k .ls conS;isUmL. when k is

,t, I

b. 2 c. 5

d. 10

31. Por the set of teo I numhc~ rR . Clmside. lho-lollowing. !llotcme•tts:

1. lwery non-empcy subset of I'R wltich is bounded below hllli •n ID.llmum

2. Every 11vn..:mpty subsct of rR wh ich i~ bounded above hllll • supremum

3. Every bounded subset of n~ hn> "'' infimum and a s upremum

Of these stnlomont•

n. .I and 2 arc indep<:ndenl . tatcments

b. 3 implies I but M i tonl'<:~'$ely

c. 3 implies 2 but not coiwerscly d. I. 2 ~nd 3 •re nlh-qui•'lllont

32 Ii' 1 i't[ denotes llum nonrCi!l integer func-tion. then which one of the follow-injl is nol nt'CCI\Smi ly IM!e for nil x nnd Y'l n. r~ t-nJ [xj I IL for w cryintcgoru

b. [x~y]-[x]+[yj

c. 1 2.~ i=rs i - Lx+ll21

d. [3xj=[x[~[ x-113J+[.~+213J

• 1 · -33. hm x 5ln"f - eqUI D ·- . •• b. j)

c. 1

d. ..,;

34. l.<rl f be defined on R br setting/(~)= "'· if x i~ ration~ I Md[ (x)= 1-x if x i~ irrntion.~l thoro

n, [ is continuou~ on R

35.

~6.

37.

'- j" . I I " · IS conLmuous on y at ;( ~ i ,jIll 1\J

c. { is continuous evcrywh.:re e,xcq>l at

:r-.!. 2

d. J is d iscontinuous evorywhcre

I (x) '" ... b. ;r ,.~ ~

" -.'OIIX. ij T ~

Uumf(x) is ditlc renllabkl nl "

u. a =- - i · b I " ,_

7f lt!. b. ·--Jr. b-7f

<:.- · ~ b ~ -'-r: I

d. l1 b -72 Fot fundion.~ f • n•l g e<Jru;ider the lo iJO\\ in& four ~tolcment~.

1. nom: ofjOgand gtifmay be defined

2 only one of f ug and guf may be defined

;\, [Dg nnd 8<1/ mo)' ~olh he delJned h1n may n()( bo cqWll

4. fog and gl!f may be bOth deOnod and equaL

Of these slatenoenls .tbe number of C.OrltCt

stntements ~

a. One h. 'l'wn c. 11uec

d. f'our

lf • in v - ~ sin ("~y) ,then '~. e<fu•l• . . (~

•• fln1(a .. "~ M o

b. f l1.1,a+ 11•! ~Ut i')

c. tiw~ rn +--J'l ..... d. •lo'fo t- yj

unn

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38. The continuity ~nd the dJfferentil!!lilill' of I nnd it~ fiflll few derivatives, as p<.T Toylor's Jhct•rem undct ~uitnblc conditiorm, IJttrc exi.'iiS ~umo l,le (O. I) s•u:h thnt I (o..,h)~ (•J ~ h I '(•)t h: rca)+ 1:.rca+9h) if (x)=sin" .

a= f. then~~ h tends too. the ~lue of B

enllll lo

n. IJ h 114

c. 112

d. 1

::;() l'he &motion [. detined by r (x) = x·'-6x2+ 1~-4 fol'aii ~>;;R i&

a. decrea~ins for" 2- 2 and increning for ll ' 2

h, decrcasin& fnr x ~2 and !nc.rea~in& for :<< 2

c. de~re11.~ing in ewry interv:•l d. inc:rc.Miug in.cnl(!ry inlcrwJ

40. ' llte fwtction l delloed by ll"-)•x1" liltS •

mn.xunum -nl

41.

ll.

h. e c. log 2

" · 2 Mymptotc;~ elf IJ•c c.ur"e (y-x)1y·2.~)-1Y· ~xy·lix) '-.-c· 5y~J=O p.trnUcltr) the line y­x: -: 0 are

n. y· X l • 0 :tnd y • S f 1 ~()

b. y·x ~ 0 and y - x • 4 0

c. y- .11 - 1 = 0 and y- x- .J - (1

d . )'·)( ... . = (I :tnd y- x+ 4 ~0

42 '11te poml nt which the tnngent to the eurve y= s1-:.- 1is pnrnllel to y= :ll' + 9 ;.

43

•• (3 9)

b. (·'2, I)

"· (2.9)

d. (I. 2)

11te ~ubrangentlo the curve y = sin x at the

point r ~ 0 ~1 ha~ '"11!!01

.J4.

-15.

.J6.

47,

.J8.

S ul Ill

•• IT

J

b. ,fi l

c. ,fi

d. 1

11te rndim of ~urvotur<: ,,r the c~•doid given by x~ a (0 ~ ;,in 0) .y - n (]-cos 0) at tbc point ~'G-, is

a . .la~ln 1-)

h. 4o cos ll

c. 4o c-os (0'2)

d. .to $ID(0, 2)

Envelope of one parametcr family of stmighl line.~ x cos a.f y sin a = " , where 0. is a parnmelC'r is

•· xy =~1 ' b. y"' '="' 4 n_x

• • • c. x·_.) ,. n-

' ' ' d. ll'· y· = ••

If . - ... ··( " y J :r; .;r;

a. 2 cos 2u.

b. I . '2 -!fm u ~

o. l wn u I

d. 1 Uw 2u

then a. llo .c "i:' + Y:;: ,.. VJ'

IJ• ·"' . I I ' I 1/; ' z= c: sm y, ~ = 1!£,1 anr )9' I "'" di IS

l!iven bv the cxprosstOn

tl • 1 "· -

1-C<tn y· 21 co• Y)

b e .

21•

, -(SIO y+ • CO$ y} I

d " ( ' I d. - cosy 2L' san y) l •

Fot the curve> '!-(X· 2) (:t· 5)1• tltc ll<)iut

(5, 0) is a a. ~todc

b. single cusp

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c. dO'ublc <:~-p

cL coojugotc Jl<>lnt

49. For ~~~ <:UJVe f- (X· 2)2 (x· S)

a. 16. 4) 1s ~1e only point of inllexlon

b. (6. -4) i$ the only poinr ol' inllexian c. lhcr<> is no point lli inJJ~>.'tioo d. (G, 4) and 16. -41 boUt are point of

inJ1cxion 5(1. Considt:r lbe curvt y=l(2(x· 3a). a~o ~ud

Lbe following •llltcml!llls about its gmplc I. IJ p Q,;JC$SCS no •yrnmctri<.>~

2. It meets lhe y·a.xls 01lly otlhe onf!in ~. y has • maximum al (0. 0) and a

mlnirnuillal (2• . -4a~)

Orthese statemen~•

"· 2 and 3 are conwt b. J ond 3 are coo\:ct c. 1 and 2 are co1n,ct

•L U and 3 are correct I

~1. ~ [ ;f tS"'-!llal to

52.

53.

a~ 0

b. 1 c. C!'

d. lte

• ' • 1 tim r ,...-, ·~ equ.~ to ., __ , lk ,,

• . 0

11. ~ log 2

c. llln' 1 2

d. ~ "mt.tv. r =:.::.&;. cqunl lo b Slli.i'

n. I)

b. 1t

c. ,..,

cL Sn The cw-,·e =·olving around x -a.~JS generating a sphere is :.~ y~ 4nx

J.i v' t., -•- I ,;z b1

C~ ~": I yl - r!

55.

56.

58.

.S!l.

60.

6ul IU d. .('-- y'- r' 11tc area of tbe surfooc of the solid generMed by lhe revolution of the line se&am:nt y =2x from z,; =tl to x = 2.about the >:·axis 1s equal to

a. nE

b. 2nE c. -ln.ft

d. h .fi The are of tho cardioid r = a( 1-om ll) is

a. 3n o1

b. Gn a1

c. 11 > ,

d. l na! !

The IC!ngth of the Me of the curve y ~ lug sec x f1'0m "~o twx : .! i•

3 ., log 12 Ji ) b. log t.fi- 3)

"' log( J.! ' 11

d. IQg( v'3 + I )

TI1e interval uf cunvergc:oce of tbc inlinilc • :1 • serle$ ~~ .. ..t is

' t : '

a. - l <x < I

b. -.1 ~~ l.

c. - 1 s x <. l

d, - l s x < l

The $cri<!s ..!... • ...:.... 2...+ 1 • ill 1.3 J,l J ~

•- J)ivergenl b. Convergent

c. Oscillalln~

d. DI)Dd Of ~1<1 abOVe

Consider the followins stAtements ;

l, ~cquenoe { uu} converges

2. i u.-converges. ... 3, llu, I cnnvqes ... 0 f lh as e • tn tom en 1..1

a. 1 itnllliC• 2 b. 3 inrplie~ I

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c. 1 Implies 3 d. 2 irnpll010 3

G I. lf c l~ nn arbitrary conslnnt. ll1" genernl

solution oftl1e ctJWilion ~'<. I 2y3) : =y is

"-- x =- ey - y: , b. x = cy - y· c._ x -- cy 4- y1

rL x ~ ey -y~

CO.IISi.der lhi! followit>J! s.l:ttemenls: 11le d illeren ti•l eq ua 1 ion 2x y' - 1 f' - dl; + -· <{1>~ 0 i~ yl v•

l • .I>.'CJQl

2. lf omogv-ncou.• 3. l ,lnt:nr Of ihe.•e statements

:~ 1 and 2 ~rc correct

b. l And ~ are eom:cl

c. 2 and 3 a,rc rorrtcl

d. 1, 2-nnd 3 ~J'e <lllmlCI

63. 11•• singular solution of the equation Y"l'~

"- '0' . ~ . ..• l' el' . . + '\J'). p : - IS O,.lnnwu C) 1mmalmg p clx

bctwccn tuigin e.jllaliQn ~nd the ctjli:tllOn

n. x·17 (p) ~ ()

b. x ; I' (V) - o c. y . r(p) = o

cl. .i ' l'(jl/ 0 IH. TI1e ;~ingular sC)lution of lbe difl.'t~,nlial

equation y; px • p1, (p ~ <!!•) is dx

"' 4/- 27 x~~ () b. 4xll 27y3 ~ o

c. 4v! 27 x1 0 . . d. 4x-' - 27yl =tl

6S rhe dlll'erenri•l eq11a1ion y d>t-2x fly = (I l'l:pteSclllS

a. a family of straight lines b, a fomily of parabolas

ll.. a mmily of ~irclcs

tL • f:trully of<llll<m>ri,.;

66.

67.

63.

(>!l.

7 ul ltl 111e orlhoJ!onn l trojeetori~ of the flllllily ot parabol~s y = ax2 3fc gi,·en by the l«llullon of the di1Tcrcoli6l equat·ion

dy 'ly •. - =-( /,'( .~

b. ~= 2y ilx .c

<~' X c. - =-clx. 2}'

d. tly = ... tlt 2y

'11le rote at which bocterb muiJiply L< proporlionnl to the inslllnlllneous numb;:r prcseuL lf U1c orig,lnnl number doubles in 2 hours. then il will triple in

"· 2 log 3 log2

b. 21og2 log3

c. tog3

1ot2

d. luJ!2 log3

The general solution of tl.e dilferenlf31

• tl 'l' . ' - . b cquatton cL~ + 4J' = sm :c ~, g~ y

a. ) C1 C!>r I C'1,)2>< I 2 sin !l 00! !l

b C ~·c· "· 1 ..-. . \" = I COS "" - 1 .810 ~;,._'\ + --- Sin • ~ R 2,~

C , ~z. ~t- ") c. y 1 1- c: cos 2x) e - s Cll!' .. x

I d. ~- C1 """(2>< + C, ) + S A. parlk ulat lntegrn l of l.he diiTcn:nti al C<JWlljon (Dh 4 ))' - X lS a. xe~l'C

b. X CQS 2:(

c. x sin bl

d. lll4

'111c solution of tl1c differential cttualion y"• (3i - 1)y'- 3iy o;.,

a. ) = C ,~· (~i-1 )y' c:l" h. >= c,..,"'-.c:o""

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c. )= Cte""'•c:e·-""

d. )9:tc''l C;:e'·' i<

71 I'll.: an&J<o betwe.:n th~ liDI!!Ilt I )' • 0 3Jid

X-) Oil. a,. ~s'' b. <x)~

c. 135"

d. 180° 12. ·n,c coordioall:$ Ql' the vtrlietli of a

lrinngJc ABC are (0, 0 ). ( 1., -1) ond ( 3, 2) ~$pectively, The lengrh ()f the perpendicUlar drawn rwm t\(0. 0} hl the sidb BC i~

IL s

71 b. 5

7ii c. ' 7i d, -,-

oU

73. If tho equation 2'ly ' 3!1 1 4y I c - 0 repret~enl5 • v•lr or strJight linc. .I hen the ' 'nlue ore is equal lo

a~ 6 b. 0 .:. -2 cl. ~

74 c"onsider tbe following •t•temenl1:

.A.s<•rtiun (,\): 1lu: e<(Untion uf l11c line

lhrousJi IIV() poinL• (2. n ) ~nd r~+) i$ ; -

2sin ti · COB fl R~ason (R): 'l'lle tQilat.irm •helve ;., wrincn in pOlar Cl!lMlirlatcs

lJI' these •L1tements

a, Both A ~nd R are true ond R it the co~n~cl explon.1tion of A

h. Both and R arc true bur R is nqt a c1mect .:xplnn;~tion of A

c. A is tniC but R « fal•e d. A is fobo lJULR io ttu~

75. fba equation of l11e eitclc "ill1 radius 10 and diwnclc"' lt y (i ·ond x ' 2y • 4 is

a. ..r-l-1<>" · ~"~ 32 b. x~+y0 - t(>~ - ~y =n

76.

77.

78.

79.

llO.

8 ul Ill c. x' + y + l6x + 4y = 32

d. xl 'Y • lGx - ~y = 32 Cans.ider a c ircle ,(1-~:Z,fl If 111~ lin.: ax • by 1 t! • 0 ;,. a normal Ia U1c: drdo • lhllll

a. c - o

b, c = r

c. c= -r d. c 1

The lin~ v ~ 2ll •c is a IJ!n{lt:Ol to tho par•bolo .; 16:df c equah

• . 0

l•. - 1 c. -'2

d. 2 If U1a lcnalh or tlu> latus roclum of :tn ollipoc io ;ne·lhitd of its ou itu>r a.-cis, then the:: ccceouicity l)t'!J,e ellip$e is

•• l. J

b. 5 l

c. W J <l ./!1)

'l11e lelli,(UI uJ1 l11e lauos reo;tum of ll1e

bvp•-rhol• .!..- L . 1is • ~ 16

a. I

' b • 1

~

c. la: l

d. :2 M~lcb hst 1 w itb li~l II and select the correct Dnl1WCr using the codes f!IVI:n below the lists:

List r (Eqnation of conics)

A. 3y • 4 f 5 (x<l)1

B. K' - 3f - S r . xy: s 0 . 2~~ .. y~3

Linn (lrs dcscriptjon)

l. • dr~le

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www.examrace.comMI .

82.

83.

2. an ellip~e wifu the two ,..,.es une<[unl 3. 4JMrabola

-L a tl;;claogullir byperl:>olo witll co-ordinnt<> o.xes os asymptotes

5. a non-.r<:<;tnnj!nlar ltyp~·bola witl1 c:.o-c.wdlnAtc axe~ 4S a..x.cs

A 13 c D

~- 2 s 4

b. ~ 1 4 5

.:. ~ s 3 d. 3 2 ~ s l'he value or ), l'or which ihe lines 3x;2y t't.-5=0 ~ x 1 y - 22 - 3 ond 2x - y-AZ 0 ?x I JVy - 8z

... - i 1!. -2 t. 2

"· Con~idet the f<~llmvmg "l!ltemenL• : A••ertion(A): The plane y-rz.- 1=(1 ,. pamtlelto x.-axJs. Rea·son (R): Jllom>alto the plane is parollel tO ~ld lHL~i~ .

I !I' th~e sL,Ic:n,ent•;

n, ·Both A and R ore tn1e and R 1!1 lhe ~rrect e>']llttnntion of A

b. Both ·'- ond R ore lrull bul R is not ~ correct expla~~:~llon Qf A

c. A is lme but R is false

d. A is fol~c b ut R i& true

Tbe SIIIJI1tSt distance hi' the llllln l ( 10. 11. 11) !rom lhe •pbcn: i ~.l'l ... c-a. ' ?.y 2

·~ " · l(j

b. 1-'1

"- IS

" - 19 114, Which of the following are gcnorators of

the cone :iyz- 87X- ~xy= () 'I _, )I ~

I. 1=-z=, 2..x=y=.;-

9 nt Ill Select the =t an•IIC!' u;.ing the cod($ below·

4. 1, J nnd 4

b. L:!and 3

c:. 2. 3 and~

d. 1, 2 and4

85, 1ne equot.ion of .< +4l=5-2y rcJl""enk I he ~urtilce or

~6.

87.

S8.

S9.

a. A =color cylinder

b. A I)Jr~boli.: ~ylind01·

c. An elliptic eylind~'l'

d. _.._cone When we snody the mol ion of the plnnel earth round the ~un in its orbit. the eortb is lreotcd as a. a particle b. • rigid hudy

r:. ••• ob!ntc spheroid

d. • bard"'""" offinite.siZe

If a train pa$lC.• an d c.:lric pulu in 8 •~cond• and l,.icl£c of U1c s•mo JcngU1 o.s ihe troin in 16 ~econds, then lhe Lmin i• moving with a. unifom1 velocity

b. relll!datiou

c. tmitbrm .ux.clcrnliun d, non~ ufth~ 3IIO•'e

J= 3! -2;..-k , Jt=2• --~ ; -3k and 1·~ ­

I -+2 J +2k . then "'"S'Jitude <If 24-3 11 -5 <'

is 3 , ./iii b. .fi20 c. :[tin

d. ,§0

::i~2d ) J - -1~ 3ot1 '8 =5• • 2J-4! tl•cn lhc angle betwo:cn ::i and i is

•. 45° b. 60~ c. 90'1

d. ISO"

'.Ill. f(Jfccs 1'<, I d. 6 kg . w L act along the side!< DC. CA aJid AD of an e<juilateroj lri~mJ!)e

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92.

9+.

l/5.

t\BC. TI1c din.-.:tion of their re~ullanl baJ •lope

a. ~.fi ll

h, ~.fj

c, 2-JS II

d. l!..fi 1

ff a p.1rtlcle Jtadiug with ~ velocity u and subjccttxl to a uniform accc!.,.ation ' u • tr.wel• lor 'n' sec. • tlnm the distance described by it i11 U1e ntl1 second is

4. u- ~(2n-l ) • h. u - !!(2· n)

l

c. u ~ ~(2o - 1) J

d. u - !!.(23 ~ I) 1

A s lonc.• Utro\111 vcr1ic.1JI~ upwMds 11ith ~ vdocity 98 n•cta'S p01 •ccond ~ Its ~.:ltJcil) will be zero oiler tg:-?.~unlsec·)

lL 15 scctlnd>

(1. 20 scccmds

~ I() second~ d. 5 •~conds

A body of mass ~is . ~objected to a force

( i q .. k) N. 1r lhc bod) i> initi•U) ot t'l:!lt • tbon itJ ' 'eloeit}' al\<:r 4 5e~onds will b.:

:1. 2./6 mlsec

b 4./6 ml•e<:

c. S .r. m/~ec

<.l. t (>,fl.. ml•ee

Ncm1on •• third lows. a y

~. lo o:~ery action then:;,"" tlt1<qllil l lllTd oppusile reacLJon

b. to evety <~ction there i< an e<~••l and opposite reacli~o

c. to every oeticm there •~ un equ:rl :oncl ~ama rcuctioo

d. none ur lh.o above

A particle movi•U! in ~.HM has the speeds 8<.m11sec. and 6cn\'second at dis.liluot$ 3 em :tnd 4unl r""peetiwly from

9().

97,

J0 C\1 Jll !l•e center nf its poll~ TI1~ period of Its motion Is

b. 2ot se~

c. n: sec

d ~s·--. } -TI1c ~mpHtude of n porticlc executing S.ftl\t is 20 em nnd time period is I sec. The rnccdmum vdooit> tS

a. I 0 n I!IT1! sec

b. 20 ll cmi•.:c

c. ~0 n cmfscc

d. 411 r. cml!ec

If tl1c gre~tcst heig.ht t9 whicb ~ man c.~n thrOW •wnc ill h. then the ~nte>~t dulllnce lo which he ean thrnW it 11 ill be

ll. h/2 b. h

c. 2b

d . .th

ll$ The ~ngle tlf prnjeetlon C1( a h9dy l'or albtnJI\g maxim urn ru.ngc is

a. ~ -15° b. r45°

t \ -15u

d. 90° 99. Angular velocity ol' the minutes hand or a

wolc.b i3

a.. ~radian rsec 1$00

b. ~ radim lseo ISQ

c ..!.. radian /sec 16£1

d. None oftbe ~bove

I 00. , \ particle mqves in i1 pbne wilh an acceleration wluch is alwilys directed towards o fLxcd point 0 in thu ploue. JL found that ~1c path is given by

r~ u( l+Zsi n 0)

'I he apsi<leol di~t~nceR are equattu

a. 1a and (112

b. ;In uud u

c. .to aud ;lh

d. Sa Md ~.

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