8
DP,P nAurv pRAffiTtGffi pffiffiffitffif;ws TAffiGHT : n$Y-Jffiffi ffiffi$,m Class : Xll Course Name : VIJETA Batch : P ll,'p *g 3 13to {5 D P t Ns. 1 Jp r were h { 9.4.-Q$ :Q:91-o" 0 $*ES.$ sJ {3 rnark* {4 nra rks tg rnarks s 5 3 I J Tokl,Marks, : 42 (A) y, =i' a,sin ({*}t * kx ' (C)' Yr*'"^,cos,qot i fx (B) V, = a cos (rrri + kx cos ir*t + kx rn in. ) rn in. ) min.) min.) rlrin. ) A standing,wwe'peftern b formed on a string. One of the wavile is qiven bv eouation v then the equationof the offirer wave such that at x = 0 a node is )ormeO. r 1 {. 2" 1t *T) 2n *--- l al J n +-_ \ 3t 4x \ 3/ t;#1fl-xgT'tru il / -.. I i Fl ,rilj, i'li i i',t\ I - .i" / I "i ' ,-\ : I,t: ..:,.. i Fiquge gt*eft$q|$ryi,P$g$F unifor:rnly c-harged, thin rod of tength L and four Column I r. The coordinate(s) of point on circle f*F' where potential is maximum L '1 i '\-- cffi , w#'g tt't6*onfi oc€: wi th llT-J E E lir.1qle .choice objective ('-1' negative marking) e.t to e.? 9unject_ive Ques_ti9ns {'-1' negative marking)-A.g to e.6 c_om:pr€hen,bioq'{'.1' n€gative ,frarking} e,r I; e.g Match the Foilowing -(no negigtr*1"*"iringJ o.io Assertl.onandReafon'itao.nL'iiiivemar:king)Q.11 poihbA;,$1b"*ils'At{& $ffieoii'tand; rrom trne rod, with p;;itilnX ;;!'f-V;, V., V; V;,ar.e their- respective potentials then . 3' |||fpfjffi:fy$-"l Tytq of.ffgq 1 = 't0{!, emitts a pulse of sourid that travets radiany outward frorn the [email protected]**n to,Lo.y_"lfl_T-Ylltit"rygpted by an_a'coustic cytinoiiiai olGcior ot surface area 2..4 cmz, I$Y*nqfffgl*lto]i1.an99 zp from the souice. Thewaves reach perpendicutarty at rhe surface of rhe oeEctor. I he Ftatpower emitted by the source in ihe form of sortnd is 2.2 * 1oaw. (us6 n = 22J7,\ 4. A small cube of mass m slides down 3 ci,rc.utar path of radius R cut into " r"rg* ;ocr of mass M. M rests on a table and both blocis *ove *'itnout friction. LJ ui"Ili i-P .," initially are at rest and m starts from tn" top or in; p;th.'Fi;;]ir" "-jr""t,,';oii;; " i ;*jf cube as it teaves the btock. - i_ " -:i**_ 5. ?991^"L!? enclosed in a cylinder under a piston is transferred quasistaticaly (i.e. stowtyf l'l ,r tPmst?tg.AalprgssurelSatmandvolume4lit.tostateBls.Batmandvotumee.+ilt J. tajr. :lgyl 'lthe figj. (a) Drayv tfre process on the T-V diagram. (b) Find tne maximum ," "L;_ - >s temperatureof thegasduringtheprobess. 561-'- - " 1 . ,ero. .t_-,_s?_*v 6. A uniform square plate of mass m is supported as shown. lf the cable suddenly breaks, tlyy . assuprqlgcentreof massisonhorizontaliinepassingthroughAdeterminei - --":' sU .(a) The angular acceleration of the plate. ,,,n\.r, (b) The acceteration of corner C. +*/ '\g (c)The reaction atA. '\ /:1 comprchension: ".V" A.light inextensible string connects a block of mass m and top of wedge of mass M. The-strihg is paralleito inclin:ed surrace anJille ir"ir"o surface makes an t'[', llgF 9. yltn horizontat as shown. Alt s.urfaces are smooth. No* a constant horizontal force of minimum. magnitude F is applied to wedge towards right such that the.norma,l reaction'on blocR'exerted by wboge just nelo*"s ,eio." .- - -- ' smaoih horizontal su rfa:ce 7. Tfgphdgnitude of acceleratjgfr of wedge is Jrirwl i ' uri4ui ridr sur r?ue ;ffig tan0 lpfg corc (c)g sino (D)g cbso 8. The magnitude of tensionffitring is (A) mgFce ld nrSj .d.."e (C) mg tane (D) mq cotg . . ^ ". F 9. The-g{agni.tudeofnethorizgntal forceonwedqeis: Ie"rt; Ho.' + [ ;' f-"u{'J'lrir-'rt QTMg cote (B) (M + m)g secO ''M (M + mlg c1.rn (D) Mg cosecg i' io. column:Igivesasituationinwhichtwodipolesof dipolemomentpiano n6plare ,,,_,,i \ placed at origin. A circle of radius R with centre at origin is c]rawn as shown tn'frgure - .,' t1l-* - i _ Column II gives coordinates of certain positions on the circte Match tne staterients * 'r .7fT" i---x in Column I with the statements in Column II. 'tlir Max. T{n'le : 4S mlm. [s, s] , ["tr s, 3t}"} [s, 9] [s, s] , fA rrnrJ i,,^5 , "$.i = a oo$ tCIt * kx .+ nr'3) (A) Fgg. $qlg.r" # 'H

resonance Dpp

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Page 1: resonance Dpp

DP,P

nAurv pRAffiTtGffi pffiffiffitffif;wsTAffiGHT : n$Y-Jffiffi ffiffi$,m

Class : Xll Course Name : VIJETA Batch : P

ll,'p *g 313to {5

D P t Ns. 1 Jp r were h { 9.4.-Q$ :Q:91-o" 0 $*ES.$ sJ

{3 rnark*{4 nra rkstg rnarks

s53IJ

Tokl,Marks, : 42

(A) y, =i' a,sin ({*}t * kx

' (C)' Yr*'"^,cos,qot i fx

(B) V, = a cos (rrri + kx

cos ir*t + kx

rn in. )rn in. )min.)min.)rlrin. )

A standing,wwe'peftern b formed on a string. One of the wavile is qiven bv eouation vthen the equationof the offirer wave such that at x = 0 a node is )ormeO. r 1

{.

2"

1t*T)2n*--- lalJ

n+-_ \3t4x

\3/

t;#1fl-xgT'tru il/ -.. I

i Fl ,rilj, i'li i

i',t\ I -.i" / I "i ' ,-\ :

I,t: ..:,.. i

Fiquge gt*eft$q|$ryi,P$g$F unifor:rnly c-harged, thin rod of tength L and four

Column Ir.

The coordinate(s) of point on circlef*F'

where potential is maximum L

'1 i

'\--

cffi, w#'g tt't6*onfi oc€: wi th llT-J E E

lir.1qle .choice objective ('-1' negative marking) e.t to e.?9unject_ive Ques_ti9ns {'-1' negative marking)-A.g to e.6c_om:pr€hen,bioq'{'.1' n€gative ,frarking} e,r I; e.gMatch the Foilowing -(no negigtr*1"*"iringJ o.ioAssertl.onandReafon'itao.nL'iiiivemar:king)Q.11

poihbA;,$1b"*ils'At{& $ffieoii'tand; rrom trne rod, with p;;itilnX;;!'f-V;, V., V; V;,ar.e their- respective potentials then .

3' |||fpfjffi:fy$-"l Tytq of.ffgq 1 = 't0{!, emitts a pulse of sourid that travets radiany outward frorn [email protected]**n to,Lo.y_"lfl_T-Ylltit"rygpted by an_a'coustic cytinoiiiai olGcior ot surface area 2..4 cmz,

I$Y*nqfffgl*lto]i1.an99 zp from the souice. Thewaves reach perpendicutarty at rhe surface of rheoeEctor. I he Ftatpower emitted by the source in ihe form of sortnd is 2.2 * 1oaw. (us6 n = 22J7,\4. A small cube of mass m slides down 3 ci,rc.utar path of radius R cut into "

r"rg* ;ocrof mass M. M rests on a table and both blocis *ove *'itnout friction. LJ ui"Ili i-P .,"initially are at rest and m starts from tn" top or in; p;th.'Fi;;]ir"

"-jr""t,,';oii;; " i ;*jfcube as it teaves the btock. - i_

" -:i**_5.

?991^"L!? enclosed in a cylinder under a piston is transferred quasistaticaly (i.e. stowtyf l'l ,rtPmst?tg.AalprgssurelSatmandvolume4lit.tostateBls.Batmandvotumee.+ilt J. tajr.:lgyl 'lthe

figj. (a) Drayv tfre process on the T-V diagram. (b) Find tne maximum ," "L;_ - >stemperatureof thegasduringtheprobess. 561-'- - " 1. ,ero. .t_-,_s?_*v

6. A uniform square plate of mass m is supported as shown. lf the cable suddenly breaks, tlyy. assuprqlgcentreof massisonhorizontaliinepassingthroughAdeterminei - --":' sU

.(a) The angular acceleration of the plate. ,,,n\.r,(b) The acceteration of corner C. +*/ '\g(c)The reaction atA. '\ /:1comprchension: ".V"A.light inextensible string connects a block of mass m and top of wedge of massM. The-strihg is paralleito inclin:ed surrace anJille ir"ir"o surface makes an t'[',llgF 9. yltn horizontat as shown. Alt s.urfaces are smooth. No* a constanthorizontal force of minimum. magnitude F is applied to wedge towards right suchthat the.norma,l reaction'on blocR'exerted by wboge just nelo*"s ,eio." .-

- -- '

smaoih horizontal su rfa:ce7. Tfgphdgnitude of acceleratjgfr of wedge is Jrirwl i ' uri4ui ridr sur r?ue

;ffig tan0 lpfg corc (c)g sino (D)g cbso8. The magnitude of tensionffitring is

(A) mgFce ld nrSj .d.."e (C) mg tane (D) mq cotg . . ^ ". F

9. The-g{agni.tudeofnethorizgntal forceonwedqeis: Ie"rt; Ho.' + [ ;' f-"u{'J'lrir-'rt

QTMg cote (B) (M + m)g secO ''M (M + mlg c1.rn (D) Mg cosecg i'io. column:Igivesasituationinwhichtwodipolesof dipolemomentpiano n6plare ,,,_,,i \

placed at origin. A circle of radius R with centre at origin is c]rawn as shown tn'frgure - .,' t1l-*

- i _Column II gives coordinates of certain positions on the circte Match tne staterients * 'r .7fT" i---x

in Column I with the statements in Column II. 'tlir

Max. T{n'le : 4S mlm.[s, s]

, ["tr s, 3t}"}

[s, 9][s, s] ,

fA rrnrJ

i,,^5 , "$.i

= a oo$ tCIt * kx .+ nr'3)

(A)

Fgg. $qlg.r" # 'H

Page 2: resonance Dpp

ll-(it u..J,l

[q I

"The ecorr1inateisi cf p*irit *n clr*le where

6rctential is zer*

The cnCIrdinate(m) nt point on cirele where1

{-nasniturde nf electric field intensity is 4ne6 Rg fi*---'-

iL)) -The c*ardlnate(s) cf point an clrcle where

12pmagnitude of electric field intensity ir a* *p :

STATEMENT-{ : Two stones are projected with same initial speed u, onE frorn,top.ot {6Wer (of he{ght H} atan angle 0. with horizontal and other from bottom of a tower at an angle 0r with horizontal. lt rna<irnumheight above ground level attained by both stones is same then 0' + 0z will not be egual to gOs for'anycombinatipn. of u and H. (Neglect air friction)STATEMENT-2 : Two stones are projected with same speeds frorn ground. lf ang{es otgrojebtion with horhgntalfor both arb different and complementary then the maximum helghts above groundbvetrficr both witt,teUifbrent.iNeglect air friction)

,{A) Statrement-1 is True, Statement-2 is True; Statement-2 is a correctexplanationrforStatement- 1

{ B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation:for Statement-l(C)patement-1 is True, Statement-2 is False

"1Df Statement-1 is False, Stratement-2 is True.

Sgew.erp qt&F&j94"C5.D1S" {A) q,s (B) r (C) r (D)

#sgswqrg qf.gPf;fl-f !ffitrmNc nharse vrrill flcw

{A} p,s 1*l

p,s (C)

IT?R @r \4

{ii ;xt ffi *n ADC (ii)

4.85.

( R "l5n)(q) [-2,- , )

( .6n R)(') [T'2)

f.,6nRj(s) [-f'- z)

4p

4.

c4d$

5,

6

7

I

,'rfid

ry'E

lc.{

AAE

4'frn lr4

.rg

f,"

fltr&.f r

gxR[fa

-"tJYe 4

ffiq^f o

rnLJ

tI

r.

A

!-q"

Jr,.""

g"$ei(*

,bqJ'"

&q#o

"R'tf q

d;tr

*$.

q,$ {Lt) r

"h.rJo

ratin 2 : 3

qq/d

s.c 10.

6.

p

D6.A

DA

, fi?,q A

4.CS"A.

V. (a) T*** = |(po

/R)rffi lf " j (b) T*", =:F0 /epR.

'; 10" B 11. D

KffiS?" SY'!.LABU$

ffiffiWffiffiffiS Frmsm Kn petre n SlllUl1 Fleat &

tT]fi

i-*,1 ?- {h)

far\*id t

'\t\/F.

+.. ffitvtm.,\'* ,

-ffi'1"' ? ru"1.i-

", &-t l

1,1, -,".1

L-''',.1.'-"'$*..-'-'

.::Thermodynamics

. ll "i:

: '

:].|.,t,tWf- -flq

rorat Marks : 3z DPP No.2 for week (04.05-09 to 09,:Q5.r,,09t,

!-in.g!e choice Objective {'-{'negative marking) e.1 to e.3 (3 merks 3 min;}Multiple choice objective ('-1' negative marking) e.4 (S marks 4 min.i$ubjective Questions {'-1' negative marking) e.S to e.Z il marfs S'min.i'Match-lhe Following (no negative marking) Q.8 (8 marks 8 min.iAsseltion and Reason (no negative marking) Q,9 (3 marks 3 min.|1, ,' ! Two particles having positive charges +Q and +2Q are fixed at equalF distance x from centre of an conducting sphere having zero net charge' and radius r as shown. lnitially the switch S is open. After. the switch.S is

closecJ, the net charge flowins CIut of $phere is

e : 39 ,min.

'.1

.r

A uniforn r thin rod of ffiass m and length R isshown, "Fhf; fflass of earth is M anrJ its r-a,Cius

i'rirc*: exertecl hy'earth un ttie nod is

GlVTrn/t'\\IH. I\B'rl 4[Q"

(D).ryplaced nCIrmally on surJace of €sr,th;:a$ ., ,,

is R. Then the magnitude of gr:avitatiOnal,,'

,/crumffi -eR'-

firtffi) -;

'rydC" -

Page 3: resonance Dpp

('Y^\1:2.The ratio of intensity atAto that of ts i t& l'-\ ln r

\ uo ,/A s., $,

f*Pf*{nr,l*ut

4--'__rJ

*f{ : ': (B)1/e 'ffi^ (c)o{B) 1re (c) 0ff,cgl$sisns,per unit time of molecules of a gas onlase iflfuHberatr*fe and velume both aFe doubted.!€sg ifttemoerature anrJ volrlrne hn*h rro hehrort

:+ir-' " '': :: t

s; ands4:at*sro-putetent sources of radiations separated by distance 1.0q 2q 1," where L is the wave length ofr,rudffu*:Si$*dSSirin pt"se byr/2.Aand'B arb t*o point, oi,ine rine;qining b,;;JSr;. snorn in figure. The

ratioof ampl,itude,p atA and B of source s, and $, are in ratio. . . _. I

,:.:,,... .i,

A qarticle rnoves in x-y plane with constant acceleration a = 6gginlnlvin$ grdinates,('0,'20 metre) and its initiat vetociiy is-Llu joshntof'tirne when"spegd of the particle is zero wIl be :

(A) l sec W.sec @CaecThe instant of time when the_particle crosses x-axis is .

{A) 3 sec Jpfr sec (Ci s sec

I^t-:nstant of tirqp wtren,the particle crosses y-axis is :(A)3sec ,' .

(D) s

the wall of a c0ntainer per m2 wili :

{l''''-'

{:i,.e

i*gi (in m/:t) At time t = fi, the par"ti*t* is atil,= -12i"+-16j (in m/s)

#/''d'&fl sec

{n} 6 sec

{D) 6 sec

e doubled.

ght H) ataxirnumfor any

orieonhlJifferent.

ent-1

750

39 min.

+2Q- -).

Ly,lif.l* dffldf*?:s M and radys R iies on a fixed rough hori' r vrrr'sr{rr uEr,rrv{ir{u(to}{vr iilltl [aul{.ls i{ lles on.a nxed fough horizOntal suffaCe at time t = 0. lnitial angUlarYi9.9!-gt,",.:S 0igqim-aslitude and sense of rotatiori;

"no

',fi'oriroorat vetocitv v^ of cenrre nr maee ic;;li#,ii;6'.ffii.,.',si []19il'ffi:f[,:ffi1::$:?,lillffi f;1111#i:,11n",13?,SJn"":i"-#f :l,r;i::,':

GoHhnjrion in column-I with the results given ir: *olunrn-trI.ColummrHI

(A) (p) The magnitude of angular speed keep$ frn ci**r*msinE

till the stops slipping.It is givenrthat,vu = ZRaro

It is given that 2uo

(q) After the disc stops slipping, the angulmr

velocity is nonzero and in cloctr<wise sefi$e

itl - ( -J*S,:tt) (1) (r) Arter the disc stops srippins, the verocity

_ fr,_, of centre of disc is towards rightIt is grvtln,that vo = 2RaroFlt$o

(") 4 t*ltf

(B)

rp) $

= R*o

9.

' .' :

(D) ( .l' t ) [ptt i'' i

(s) Arter the disc stops stippins, the

: kinetic energy of disc is less than rts initral value__-tl..gLu_9n that 2vo = RrrioSTATE-MENT-I : Work done by force of kinetic friction acting on a body may be zero.sref'dnrgrlr:'? : Alorce aqts at a point on a body. tf velociv oJinJt point is atways zero or atways perpendicuiarto.ry1qvan force, then work done by this force rn.any time ;r;r;;; is zero.

r,lffitatement-1 is True, Statement-2 is True; Statement-2 is a correct e4planation for Statement_.1@) statement-1 is True,

-statement-2 is True; statement-2 ii Noi

" correct explanati.n for starement-.i(Q) 9Ftement-1 isTrue, Statement-2 is Fatse

\prStatement-1 is False, Statement-2 is True,DPP - 15

Total.Merk6 : 45S-in.gle.choice Objective ('-1'.negative marking) $.! !o A"Z {3 rnarks 3 min,}Mu.ltiple choice objective ('-1' negative marking) e.B .ii *"rlr* 4 min^)subj€ctive euesrions ('-1'negatiG marking) o.d 1o e.12 ii marxs 5 min.)Assertion and Reason (no negative martiiil O.rS - -

ii ^".rr* 3 mifi.)

#2 i:nff ;ir*r; ;tr ;il

Page 4: resonance Dpp

-F+r a particie moving along x-axis, th'e acceleration a of the particle in terms of its x*coordinate x is given. by

fr = -$x, where x is*in meters and a is in ml#.Take acceleration, velocity and displacement in positive x-rriiection as positive. The iniiial velocity of particle at x = 0 is u = +6 m/s. The velocity of particle at.x= 2

iA) + 5",,! m/s (B) - 6n[ nr/s (G) 72 m/s ({ O

2. A swimmer crosses a river in minimum possible time of 10 second. And when he reaches the other end, hestarts swimming in a direction towards the point from where he initially started swimrning. Keeping the directionof his velocity relative to river current fixed, the swimmer crosses the river in 15 sec. The ratio of speed ofswimmer with respect to water and the speed of river flow is (Assume constant speed of river & swimmer) -

', $U:b1ry-*i

l,

:" Tot, S,in,FifI', Suii, Asr

" {.

6.

7.

{0

i l\ \ :1/?\/ iJ'vr,i"e (B) sl4 '(.QJ'ztJs (D) Js rz

Ai&'B ,if th,e air temperatureati teffiperetfure T is,given by

2(,

dlit

#" 'i.

,: v 1#. {-}N"\

"" ''

, ";''-1"'",:'ril.-

-uq*"*',,! h.

itt '

i ""

A force p = lati + S]p.f acts on a particle due to which its position vector varies,as,5, = 1Zt2i'5j).rn'.whete t is

timeinseconds.Theworkdonebythisforcefromt=0tot=2sis: :,, _,

{A) 23 J (B) 32 J (C) zero .(D)cenrt be obtained

i-iow long will it take sound waves to travel a distance / between pointsbetween them varie$ linearly from T. to T, ? (The velocity of sqund in air

v = g.,/T, where u is a constant)/'\ li tL{:

,r ,i\ \ ____t*.tt\''li*,*

ry */ [r'1,U l' d)

iB) *r Jg2(

(c) a (frf+r' 1

(D)

itri*s"iti

d'U3"

flt4axim u nr lreight reached{l\} R/?

by a rocket tiied with a speed equal to 50o/o of the escape(B) 16R1$ (c) R/3 (D) R/8

Two wires each of radius of cross section r but of different rnaterials are connectad.'t€dlilF!'end to end (i.e. inseries). lf the densities of charge carriers in the two wires are in the ratio:1: 4, the dtifr {fun#elections in thetvro wires wilt be in the ratio:

(D) 1 :,4iAil:? {B} 2:''! (c) 4' 1

An infinitely long wire is kept along z-axis from.z = - o to z = * co, having unifOrm linear

10charge density f nc/m. The electric field E at point (6 cm,8 cm, 10 cm) will be:'

{A) (160 i + 1201+ 200 k) N/c tdtzoo k) N/cic) (160 i+ t20 j) N/c (D) (120 i+ 160 j) NiC

S" Acylinder rests in a supporting carriage as shown. The sideAB of carriage makes anangle 3Q" with the horizontal and side BC is vertical. The carriage lies on a fixedhorizontal surface and is being pulled towards left with an horizontal acceleration'a',.The magnitude of normal reactions exerted by sides AB and BC of carriage on,the*vlinder be No, and Nuo respectively. Neglect friction e\renof acceleration 'a ' of the ca{tia$e is increased, pick t4l{A} No* increases.. *-@} Nu. increases

:k uffie correct statement(d) :

"tgT N^u remains constant (l(F) N* rernains GonstantF)Nre

cylinder be Nou and No respectively. Neglect friition everyvvhere. Then as themagnfrld€

A string is fixed at both ends. The tension in the string and density of the strirqg d-e aqqlrlately known butthe length and the radiug of cross section of the string are known with sorne errcr- ffrn+iiwrum errors:madein the meqsurement of length and radius are 1oh and 0.59/o respectively thert whatfu thg'tnaximum possiblepercentage error in the calculation of fundamental frequency of that string, i

10. A man is Stahding on a cart of mass double the mass of the man. lnitially cart is atifeston thpsrnooth ground. Now man jumps with relative velocity'v' horizontally towards right Withrespect to cart. Find the work done by man during the process of jumpingr , , :': , ! .

'lt. The equation of atravelling wave in a uniform string of mass per unitlength'p lsgiVenthsy=Asin (cot'kx). Find

the t*tal energy transferred through the origin

instantaneous pCIwer lf you knowl'$ft" Figure shows the variation of internal energy (U)with the pressure (P) of 2.0 molEge-$

in cyclic process abcda. The temperature of gas at q and d are 300'and'500 K. ,

CaIculatetheheatabsorbedbythegasduringtheprocess.STATEMENT-1 : A larEe block of mass M lies on a smooth horizontal,surfai€ g$d a

'small block of mass m is in contact with larger block as shown" NolV a,hoJ,iiffitalforce of magnitude F = 3t is applied on block towards right at t = 0, where t i*tinb in '

seconds. Then before the smali block reacheb the ho,rizonial surface, the.pa$.-nii[lde, I

of acceleration of small block relative to larger. block increases with tjme. (All l9rfffi.es, o

are frictionless) .

STATEMENT-2 : ln the situation of statement-1, the magnitude of normal reaction'gxerted,:by larger block onsqraller block increases with time Hence nragnitude of acceleration of smallerbloek increqees with time.(e.I6iitement-1 is True, Statement-2 is TruJ; Statement-2 is a correctexRl$atlpn for'${atement-t .

iS) Staterpeht-l is True, Statement-2 is True; Statement-2 is NOT a correct e*pldpatidiirf,b} Siatemqnt-1(C) St#dment-1 is Trr:e, Statement-2 is False : ' "

'':\ :

.lt,) 2.

from e6rth's surface is

in time lnterval from t = O to t= # p, canilse the for:rnula'of

f.p'

{"

3.

{.

1i

.,ii

5:

tip"

i

8.

L'4 q"I q"ll r

1.r

Jrt

f"f f;/./ f f f'/ /.f r f f I f ( r f { f f

smooth horizontal surface

(t;")"Statefi1ent-1 is False, Staten-r.ent-2 is T'rue Pg" N0" # 4

Page 5: resonance Dpp

IFHI.Lrn

resonance with llT;JEE

DPP No. 16 to 1B Class : Xll Course Name : VI:JETA

DPP * t$iro,tat Marksi: .gs , : ,'pP''?'Nb':l forvYeek {1{-05-09 to i6-0S'091

:ilS.l".9trot3.9 $Ule_ctina (':1' negatlve marking) e.1 to e.s (3 marks i min.)llll,jn 11e-plan*sf-1ir:iQ$1tiiie,rpasllln1:g.5 i4. marks + *in.isrbJective Questlons ['-1'negative marking) e-.2 to e.1o '(4

marks s min.1,,Assertion and:'Redsor; (no nogaflve rnarking) e. i'l 1i marks 3 min.)

frorn the_vglobitytime gr.aph of a particte moving atong a straight tine pick up the,ncor:rgcf staFrnent.

-!{da6e, particlb crosses its i n itia I pos iti on(B) therarceleratibn of the particle is constant(C)t!e:force on the particle is constant

gffine sOeed'of flr e particle increa ses con ti nu ou sty.

Rtherrpcdyn-4,{n,nrocessof one mole idealrnonoatomic gas is shown in figure.Tfie effioienc;l,iif cyclic process ABCA wiil be :

f-,{e,n":€#

ivg'.2''

rd, lre)ction

ile,n.

tive;.1,'z-

nd,'ecti

eed]r) -

enf

Irtofo

- enodirecspee{mer)

8:{t,'

, ilT,jff '''I=I

I

I

rer,din

sp€me

DAILY FRACTICH PRffiffiIffiEKTSTARGHT : !$T-iHffi PS#-S

Batch : F'

Max" Time ; 4? n1in.It 5, 15][4,4]{t 6, 20}13,3j

i ..ri ,./1,.i r'''1 ,'i/i./

- *ff*- -*-erY

' I

/,''t-\'t

vhere t is

peraturegriv€il'bf

sul'face is

nd {i.e. in),tls in the

v

---*X

;onstant.

nown butors madeI possible

- kx) Find

lormula of

'rf'l?I

i

og 'Perc

--1-lrnlt- -i

ontal surface .

rr block onh time,nt- 1

msnt-1

im.#4

1.

2. i, ..

'i

(A)25% {,8) 12.5%

A particle initially at rest starts moving from point A on the surface of a fixed smoothhefisj.ftrg of radius r as shown. fne partlite looses its contact *itn n"rnirpf.t"i"

"ipoint B'. e is entre of the hemisphere. The equation relating ., and B is({l lsln o,= | coe p (B) 2 sin cr = 3 cos p*f€ff,sin,$r= 2 cos cr iO1 Z sin p = 3 cos a

ln the givel frg,ur:e, lwo elastic rods A & B are rigidly joined to end supports. Asmail uocK cn rnass I m' is moving with velocity v between the rods. Allcollisions are assumed to be elastic & the surface is given to be smooth. Thetirne period of"oseillation of small mass 'm' will be:(n = area of cross section,Y = young's modulus, L = length of each rod)

(c) 50%,/laa(tr) ^^ %

3.

o.}

ffi'L+2nrl *trr.tzL+2n {eV- (c) u +Tr

?[ .

1r-\\ i:\v/

\tg

Att=0,atransversewavepulsetravellinginthe,positivexdirectionwithaspeedof2m/sinawireisoescribeclby

ffrefunctioh r= $, siventha)X*O. Transversevelocityof aparticteatx= 2m andt=2 seconds is.(A) 3 m/s x-

F{- s k (c) 8 mrs trl_ r r;-"--"A spherical shell of radiy!,fr with uniform charge q has p^oint charge q.o at its ceqtre. The work performed by theelectric:forces during shelt expansion from raoius h, to'R, is rii. {1"! .- .L 1

Three identical balls I ,2,3 are suspended on springs one below *J Ln.,t*f* shown in tirt:uttttttititi:" , ': ''

,--the figure. oA is a weightless thread. The balls are-in equilibriurr r i,,, A . .,i

!fl lrge thread is cut, the system starts falling. Find the acceieration of ail the balts at ,l,i.r*,u ti

the initial instant - .gq - , "e,.q%

rara+ir^^ ^r ^''rL - u -rt- :i (

,. ' 'l' t

J(b),Find:the initial accelerations of allthe balls if we ci,t tt'e spring BC, which is supporting :.ball 3, instead of cutting the thread. gI r r-FC

A billiard ball at rest is.struck horizontally one tentntf the diameter betow the top. tf p he ,n- ,30Tfl* ",the blow find ttre,,initial.kinetic energy of 169 gsl;, the mass ot ftre oatt is tVt.

1l ttg,l3t-"9 conducting sphere has a 10 cm radius. Two wires are connected to it, one caries a current of1.CI00$02 A into it and the other:carries a curient of 1 .000000 Aoui of ii. H;* i"-g *"rrd it take for thes$herd to increaserits potential 'nv g00 Vlai. "orp"rui

toltr iritij value ? (Ans in ms)

6.

7.

5.

ln'10.-?^._"1"i1p|n"ry

star system each star has the same mass as our sun and they revotve about thelr CM. Thedistanqe between them is same as the distance between earth and the sun. wnttiiinliri-r*o'-t'r#irri";

8.

L

11 .

lfi fears,$TATEMENT-1 : A block of mass m kg is kept onshown. The coefficient of friction between bloe kThen the magnitude of minimum horizontal forc*Newton (Take b = 10 n"r/s2)

rough flxed l^inrizcilt;al $Lrrffiilr* r{$ancj'hari;,anii;iii $urJifi,::* iIi li ;:: f,-i "i

{"#qr-itf*d tr.:i i'Trr.;Uf,i 'i..i:ii,, i-;it.,ij|'., titi l:li ' i ...-, i

ffil*

tqY

ll# ri';, iitr,"r, r1f 'll. .:;J " 'i a' cLr'f rr ! tr

Page 6: resonance Dpp

sT $\fr"ffifrb4ffiNT',**

,*';iVefi *y F ,,,' FiN,fr{irn-[qi reactron

tu"tffif Statement-1ifi};stHtennent-1'h{fl) Staten"lent-tr

{UlX Statement-X

: A biock is rept,on fixed rough horizontal surface. The limiting value of triction force fr is

where p = coefficient, of friction (between the block and the horizontal surface) and N ison block due to horizontal surfqce.is True, Stater"nent-2 is True; Statement-2 is a correct explanation for:statement-1is True, Statement-2 is True; Staterrrent-2 is NOT a correct explanation for Statement-1is True, Statement-2 is Falseis False, Statement-2 is True.

Answers of DPP - 13 7"

8.

I,

10,s|d$A ll, +'V/2 * Zfi ; T

'1 ? rnff

=3235K

i:\ { s"

S,nsttr€rs

3q(e) 2.Et (cw)

p {B) r,s (C) p,g (D}tlPp : t4

3,Mg^(b)tsJ(c) fTr,s '11 . D

*un i$ nt ffi

4.

Atlr

(A)

cfftfitrq.,r .tl

It

c7,6.rih

td.

{A\ \..

,#3-8t

tr5"

7.CA

b.&uJ*

{ffi"

{h&,n

$F"

,4ti'.,

ffirf,#"

*tr"AiAi q,t.,$ iffi) p,$ iC) e],r,s

l-,FLr

\"_r

"4 r t\tI . S."/o

r] 4.

) p,E,f',$ . s.&mgwers

BC5.BA0f DpF ' ts

ffi

l-nv 2

,t J

C

$q:c-K

D

13. D

4.DS.{n+3)tt. f = ''---J

24

ffipP * 47

12. dQ. = 400 R/n2

Torar Marks : 3s DPP'l)lo'2 for week (1'1-05'09 to 1S-05-091

$ingle choice Objective {'-1'negative marking) Q.1 to Q.5 (3 mar&s 3 rnin,Jt4 mark$'5 min.)(3 ma'rks 3 min,){4 rnqrks 4 rnin.}(3 rnarks 3 Hlin.)

:

fillax,,Time : 3S min.['t 5, I 5l[4; 5l

'' [9, 9l[4, 4][3, 3]

,ffiubje*t$vs ffiuestions {'*'$ ' nesetive mftrking} 8.6ffimmpnehensicr! {'*t' negative Rnarklng} Q.7 to Q.9ffimtc$] tfne FolNcwing {no nesatlve nnarB{!nE} 8.10Assentfrsrt ffi$ld ffi,easom (nCI nsgatlve rnarking) Q"1'f,

'l. A stone projected at angle '0' with horizontal from top of a tower and it falls on the ground dter three seconds.Two second after the projection the stone was in the horizontal plane passing througfr the point of projectbn.Thenthe.heightofthetowe'}f:(g=10rn/s,)l(A)Srn {FfzSm (C)20m {D)15m:

2. Two blocks each of mass m are placed on a rough horizontal surface and Connectedny a massless inelastic string as shown. The coefficient of friction between.e{chblock and horizontalsurface is p. The string connecting both the'blocks,ir"riti$lty

' has zero tqnsion. The minimum force to be applied on block A ts just rnove the:twoblock system horizontally (without the string getting slack) is :

1'1.

I', r' rJ,'-

\Pfi eF{ffig.6t{

2pmg\*" lrr/' ,'7

t/Mvr

2pirng(c) ffi (D)

{R'{cLJ x Two fixed points A and B are 20 metres apart. At time t = 0, the distance between a third point C and A

is 20 metres and the disiance between C and B is 10 rnetres. The.component.p! gqloctlygpoint C alongboth CA and CB at any instant is sm/s. Then the distance between n and.C;at ihe iodtani all the tlrreepoints are collinear will be

in) s m (B) 10 m (C) 1s m .(p)itrtendbf tngpp

A gas undergoes an adiabatic process and an isothermal process. The tWo:i,1 : '.

processes are plotted on a P-V diagram. The resulting curves intersect at a point:f l \"P. TanBents are drawn to the two curves at P. These rnake angles of 135o & 121o'lp | \-vil|,lda nacif irra \/-avic lf f rn 600 - Cle *hA aac ic lileolr, tn l.ra ' ' I t\.P. Tangents are drawn to the two curves at P. These rnake angles of 135o & 121o'lp I \---witb,thepositiveV-axis lftan59o=5/3,thdgasislikelytobe: I

"\:-*{dmoncatonric ffiatornic{D)amixtureofmonoat#iI[JiuiJmiognsds.,'i'ffln the figure shown the initial velocity of boat (30 kg)+person (15 kg ) is 2 m/s. -'r>vFind vetocity of'person w i.i. ooat sJ t

"i u"rotitv oTtff ;itl'il i r"iJ i" .gh'E- " ,, , *.,jffiiE'r.n(trleglectfriction) : : ;eOrr{\*=j;ffi;

(A) 3 m1s towards right (B) 3 rnls towards le{t {(C) 4 mls tovrards right (D)4 rn/s.towar:ds left

Fg: No.,# 2

.*Ed,i0.

Tot$.irM'uS-u1

GorAsr

1.

Bncxn

s,

Page 7: resonance Dpp

f.t ' ,.t.ii..

I ; .:l.l

feB:';p 'i8,

hnd',.S"ib;

r-1

tent-1

: 36 min.

ieconds.ojection.

blockA

:CandAL C along:he three

\ l2Ec.+r".t

.t-\ +

(c)

The frictional for.ce on

q{v'

block of mass m1

1e

Asolid&,con$'rctilrg block in'theshapeof a cuboid has a cross sectional area of zcml,a front-to-rearbngtr of 18 ctn, an'il a resi*hnce of gob o' rnsbi;k s m-ati-riar contains !l iblr*"onou"tion erectronsrm3.

3,lriltgJfl3,triilEf1fl:rence between its rionia;; ;;;' r";".1"'

"i""iH" tL,o'o,masntude 200 V/m is

7. .A:..!nmg,curr:b:nt.density io Oguaiffo-rm, its magnitude is :'(A) 100A/mz . ,{Wz6 N^' - fdl aoo-'*, (D) 400 A/mz8. The curreDt in the block isgllYA (B)2x1o4A (c)3x10{A (D)4*1alzA9. T,he dlffqOeed of the conduction etectrons is :

ryFfrhts (B) S crn/s (C)7.5 cm/s (D) 15 crn/s10' ln each situation:of column-I, a block.of Tals m, lies on block of mass m2 "no

,, lies over smo6th'horizontal'surifacbi xh"iei" ilm"ieinttriction ?et*r";;;, a.nd m, to preventisripping between both theblocksi tlorje$i:ffitii ro'rces ormaoniiuoe r, anu l;ii;;ilito " T; and m, respectiveiy as shown. Marchthe stateme.o

["Til1; with that in coiumn-ii riiiriT".i t,:1,,"'*:_,i'".t"

ln the air it is vibrating in 3'd overtone with nnexirnurn amplitude ,&,. Findfromclosgdendottnupipg #" t

''r"I'Lv{rtrfr'r'Lt'ru* {? r'

6. A clowd, organ p,ipe has leng th,{, .' : the arnp,titu;e ai,:d';isi;nce of t t7Comprehension :

(A)

The frictio,nal,f,sr** on block of mass m1

The frictional,',forde on block o

&rr(B)

\,f rnass m,

/*F\

(p) has rnagnitude ,+ *t | 5 - L i

ffin r_ r-il2 [ e-n1 mz Jt,\r

rq) has rnasnitud- #fr"[* -fiij

(r) is tolarcts l*fi

(D)

The

{si !s rcwards riqht.

(3 snarks,3 nrin"){3 rnarks 3 nnnri"}

$Jlax" Tssm* : 3if s"r.r$ru.

[s, ffi]

[,s, 43

f,ffi, ,!{

fiffi, ,$ 0]

[$, $]

17"

on block of mass ffi,STATEMENT-I:Ablockismovedonroughhorizontaiflxedsurfacearongacircularpath.Theworkdonebyforceof fribtion on g'iven rough horizonutsurfacl to. fi.'" ori"iio;ilt#; brock compretes a circre is zer*STATEMENT-2 : For a moving body, if net displacement in a tinie iritervar is zero, ,n-,., ilr" iilnro c*n* nya non zero constant force acting on this body is zero.(A) $isfement-1 is True, Staternlnt-2 is Tr:ue; gtatement_2 is a correct explanation for Statemenr_1

ff3gti#J,l;1.,'i,Tftl$5TfiXl#i'p:i3.;.*#"i;''i it1""u".o,,"uct expranation ror starement:-i

.(D) Statement-1 is Fatse; Si"i"*"rt+; iil

Total fVlarks : 31

il'J-nl:;iT:i"::r^:::I:l';.1,n$y,:r:tins)9i ro o.3 (3 marks 3 min.)lt'uliipl.e ehgice o,bjectilv€ {';{' n6gative rn"r1l"'!q'r'!',',e v,rvruE eur'Grrv€ r -1- negatve marking) Q.3 to Q.4 {5 rnarks a min. jll!:Sy. euestio_ns 1'-ri negatii" ,"rLi"gf Oll t"-O.i

-. 'i rn,,k. E *i^{4 ff}arks $ mim"}trH& '{j,,

r::}i 33

?:g$ensio.frf,l. neg.ative ilarki;gf ,O,i io e.eAssertion and Re,as.on {no, negitive marking) e, t 01.

lJ_".y"",:T,X.;::Jn{L:y:t?:**l?^r,flillg!.1:r" from the roof of a verticailyoperatins rilift ;mn{:i 1;*ir,\gi:HlH:13;$ff__:5fj'.'3.'nnj""::llxl,**d[{nli,$l;i;:_".;;:,,:1l8THllil'fi ",i:3,",113L rr rlltl

?^rlrlce'showed 30 kg and 5o kg r€spoctivr

(!) cqntinuously decreasing at a constant rate thr*ur;ht ili; il;;; !i ;,i{ thr* ifi$ient clisnl * s"i r

frictional force

Nq"#2

-w" rlf r/r *." \-'\.,r rqf,rsr rL rcrtff (f IrL"riJL,;iri r.il{:i jil[..{f'tr"1*ii,(D) continuously increasingat,constant rate thrnuilil(-ri.ii +r^;r, ii-i'r.irr;;,,

illlfrfi#t r^lsrll l,s fil"

Page 8: resonance Dpp

fi, There exists a uniform electric field in.the space as shown. Four points A,H, C and D are marked which are equidistant from:the origin. lf V;, V* V.

\

ffiry, Total

, Mult., Subj'. eom' Asst," 1.

Col

find '\,'D #r* their prrt*ntlal$ re$pffictively, theni ,*..) \ft :" V . :* \,/ " > \i'"''l 'f:: "A tt(-; " ot,l

ifi) 'tlr, ''* Vr, ,* Vc * \t,,

;ii;, $\ hir:nk cf mass ? kS is hansins #ver a $rn$CIthil'rhei '*nd of the string is puiled by a constant

r*$t ai$ slrcwri Then iru ihe tinre interval frorn

*-F'

"ffi14oVn"VotV.(il; VntVctVntVn

and light pulley thrnugh a light string Theforce F,= 40 N" At t = 0 the systern is at

2t = 0 ,? 1";f;E6

s.econds, pick up the{r%!" L*?o

(ts) work done by gravity is - 20(D) None of these

J

$"

r*1ilrref;'rstatenient (s) " tS = tr0 n:isl)itsion iri the strinff i$ 4S frU

F=40N) w*rk dorre by t$nsicn on block is 80 J

4" '- [n Resonance tube experiment, if 400 {-lz tuning fork is used, the irst resonance -s,ccursrtfien tength of aircolumn is 19 crn. lf the 4001'{2. tuning fork is replaced by 1600Hztuning forkthe#toge,tresonance, thewater level in the tube should be further lowered by (take end Correction = 1 cm){/\} s nm {B) 10 cnn {C} 15 cm (D) 20 cm

,Electric field in a region is given by E = -4x i + 6 y 3 . f nen find the charge enclosedirr the cube of side 1m oriented as shown in the diagram.

Tlre arrangement shown in figure consists.of two identical unifopn solid cylindas,eaqh of mass m, on which two light threads are wound symmetrically. Find the iensionof each thread,in the process of motion. The friction in the axle of the upper cylinder isassumed to be absent

#*nmglrtrg'rmmsB*,n

Atank of basb area 4 m? is initially filled with water up to height 2m. An object of unifonlr cross-section 2m? andneighi 1 m is now suspended by wire into the tank, keeping distance between base of tank and that of objeot 1m.

T-he rJervunwards force exerted by the water on the top(A) 2f;x'i 05N (fi) 2,Jx105N (C)-l-he tension in the wire is :

14,) fi. t x 1CI5 N

#" Tfim l:uuyant force ont/\i 0.1 H 105 N {C) 0.1 x 105 N (D)04x1:05N

f 0. STATEMENT-1 : The contact force on a rigid spherical body in contactwith anotheririgjg:body ib.always:directed'towardsthecentreoftherigidsphericalbody..:$TATEMENT:Z : Whenevel two smooth rigid bodies are in contact ancl press eaeh o$br, tirby.exert a:contactforceoneachotherindirectionperpendicuiaitosurfaceofcontact..:(A) Statement-1 is True, Statement.2 is True; Statement-2 is a coiiect expiangJio, fo-i,,Stat6fiient-1(B) Statement-1 is True, Statement-2 is True; Statdmentr2 is NOT d,correct explaiati$n f6rl.Sfutement.1(C) Stateggnt-1 is l'rue, Statement-2 is False ':

(Dfffi6ment-1 is False, Statement-2 isTrue : , ,,,1 ,,,' .

,.-'.--/

i,$,

5"

7"

8.

d1)l

A1

[}.

*,-ffiZx '1.il5N (C)

the ob.lqEbs :

:ffiTx 105 ru

surface of the ohjeqt is :

2.2 x 105 N '' (D) 2.9 x fr05'N

0.3 x 105 N tD) 0.4 x 1,105 N,:

10.

W*L E-6lvw,.*4t3{d-'LA IIe

I e-d t'l

"4nsi 1 tulrT

t

*W\"fi.;{.t

ftf'11{- & S ti'l* s\ll ftlu*

Pg.Np. #4