TEST SERIES FOR IIT-JEE (FULL SYLLABUS) Name : Roll No. : Date : Instructions to Candidates

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1 TS-I-XIII--M-( TEST SEIES FO IIT-JEE (FULL SYLLUS Time : : Hrs. MX MKS: Name : oll No. : Date : Instructions to Candidates. GENEL :. Please read the instructions given for each question carefull and mark the correct answers against the question numbers on the answer sheet in the respective subjects.. The answer sheet, a machine readable Optical Mark ecognition (OM is provided separatel.. Do not break the seal of the question-paper booklet before being instructed to do so b the invigilators.. MKING SCHEME : Each subject in this paper consists of following tpes of questions:- Section - I. Multiple choice questions with onl one correct answer. marks will be awarded for each correct answer and mark for each wrong answer.. Multiple choice questions with multiple correct option. marks will be awarded for each correct answer and No negative marking.. Passage based single correct tpe questions. marks will be awarded for each correct answer and mark for each wrong answer. Section - III. Numerical response (single digit integer answer questions. marks will be awarded for each correct answer and No negative marking for wrong answer. nswers to this Section are to be given in the form of single integer onl ( to C. FILLING THE OM :. Fill our Name, oll No., atch, Course and Centre Space of for Eamination rough work in the blocks of OM sheet and darken circle properl.. Use onl H pencil or blue/black pen (avoid gel pen for darking the bubbles.. While filling the bubbles please be careful about SECTIONS [i.e. Section-I (include single correct, reason tpe, multiple correct answers, Section II ( column matching tpe, Section-III (include integer answer tpe] Section I Section-II Section-III For eample if onl '' choice is correct then, the correct method for filling the bubbles is C D E For eample if onl ' & C' choices are correct then, the correct method for filling the bublles is C D E the wrong method for filling the bubble are The answer of the questions in wrong or an other manner will be treated as wrong. For eample if Correct match for ( is P; for ( is, S; for (C is Q; for (D is P, Q, S then the correct method for filling the bubbles is P Q S T C D Ensure that all columns are filled. nswers, having blank column will be treated as incorrect. Insert leading zeros (s '' should be filled as '' should be filled as '' should be filled as SEL CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: -, Fa ( info@careerpointgroup.com; Website : CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

2 Section I Questions to are multiple choice questions. Each question has four choices (, (, (C and (D, out of which ONLY ONE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and mark for each wrong answer. Q. mol of a miture of FeSO and Fe (SO required ml of M KMnO solution in acidic medium. Hence, mole fraction of FeSO in the miture is : ( ( (C (D CHEMISTY [k.m - I iz'u ls rd cgqfodyih iz'u gsa iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa, ftuesa ls dso,d fodyi lgh gs OM 'khv esa iz'u dh iz'u la[;k ds le{k viuk mùkj vafdr dhft;s iz;sd lgh mùkj ds f, + vad fn;s tk;ass rfkk iz;sd r mùkj ds f, vad dkvk tk;sk Q. veh; ek/;e esa M KMnO ds ml cukus ds f, FeSO rfkk Fe (SO ds,d fej.k ds mol vko';d gksrs gs vr% fej.k esa FeSO ds eks fhkuu gs - ( ( (C (D Q. For the comple ML, stepwise formation constants for M +L ML ML +L ML are and Hence, overall stabilit constant for M + L ML ( ( (C. (D. Q. ladq ML ds fuekz.k ds f, M +L ML ML +L ML ds f, pj.kc} flfkjkad rfkk gs] vr% M + L ML ds f, lez flfkjrk fu;arkd gksrk gs ( ( (C. (D. Q. Equivalent conductance of acl, H SO and HCl are, and S cm equiv at infinite dilution. If specific conductance of saturated aso solution is of S cm, then K sp of aso is : Q. vuur ruqrk ij acl, H SO rfkk HCl dh rqy;kadh pkdrk, rfkk S cm equiv gs ;fn larìr aso fo;u dh fof'k"v pkdrk S cm gs rks aso dk K sp gs CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

3 ( ( + ( ( + ( ( + ( ( + (C ( + (D + (C ( + (D + Q. C H (g +. O (g CO (g + H O(g S vap (H O,l = cal K (b. p. T H f (H O,l =, H f (CO =, H f (C H = Hence, H of the reaction is : ( + ( + + T (C + T (D T + + Q. Edge length of M + X (NaCl tpe structure is. Å. Find the radius of X ion is (r M+ =. Å: (. Å (. Å (C. Å (D. Å Q. C H (g +. O (g CO (g + H O(g S vap (H O,l = cal K (b. p. T H f (H O,l =, H f (CO =, H f (C H = vr% vfhkfø;k dk H gs ( + ( + + T (C + T (D T + + Q. M + X (NaCl izdkj dh lajpuk dh dksj EckbZ. Å gs X vk;u dh f=kt;k Kkr djs (r M+ =. Å: (. Å (. Å (C. Å (D. Å Q. Intermediate ( changes to chlorohdrin due to attack of H O (nucleophile. Select correct statement about this reaction : Cl ( CH CH + H O α β Q. e/;orhz (, H O (ukfhkdlusgh ds vkøe.k ds dkj.k DksjksgkbfMªu esa ifjofrzr gksrk gs bl vfhkfø;k ds ckjs esa lgh dfku pqfu, % Cl ( CH CH + H O α β CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

4 ( H O attacks α-carbon and bond ( is cleaved ( H O attacks β-carbon and bond ( is c leaved (C H O attacks α-carbon and bond ( is cleaved (D H O attacks β-carbon and bond ( is cleaved Q. ate of hdration of (I CH=CH CH=CHCH, CH C=CH (III will be in order : ( I < II < III (C II < I < III (II ( I < III < II (D III < II < I Q. n olefin on ozonolsis ields a miture of acetone and methl ethl ketone. The possible structure of the olefin is : CH CH C H ( H O, α- dkczu ij vkøe.k djrk gs rfkk ca/k ( dk fonu gksrk gs ( H O, β- dkczu ij vkøe.k djrk gs rfkk ca/k ( fonfr gksrk gs (C H O, α- dkczu ij vkøe.k djrk gs rfkk ca/k (fonfr gksrk gs (D H O, β - dkczu ij vkøe.k djrk gs rfkk ca/k ( fofnfr gksrk gs Q. fueu ds t fo;kstu dh nj dk Øe gksk (I C=CH (III ( I < II < III (C II < I < III CH=CH CH=CHCH, CH (II ( I < III < II (D III < II < I Q.,d vksffqu dk vkstksuhvi?kvu djus ij,flvksu rfkk esffk,ffk dhvksu dk fej.k çkir gksrk gs vksffqu dh lajpuk gs - CH CH C H ( CH C = CCH ( C H C=CH ( CH C = CCH ( CHC=CH CH CH (C (D CH CH = CHCOOH CH C = CCH CH CH CH (C (D CH CH = CHCOOH CH C = CCH CH CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

5 Questions to are multiple choice questions. Each question has four choices (, (, (C and (D, out of which MULTIPLE (ONE O MOE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and no negative marks. Q. Select correct statement (s ( Most alklamines are more basic than ammonia in aqueous solution. ( pk a of Me N H is higher than that of N H (C mmonium ion is stabilized b polarization effect (D pk b of CH NH is higher than that of NH Q. When phenol is reacted with CHCl and NaOH followed b acidification, salicalaldehde is obtained. Which of the following species are involved in the above mentioned reaction as intermediates? O OH H CHCl ( CCl ( (C O H CHCl OH (D O CHCl iz'u ls rd cgqfodyih iz'u gas iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa] ftuesa ls,d ;k,d ls vf/kd fodyi lgh gas OM 'khv esa iz'u dh iz'u la[;k ds le{k vius mùkj vafdr dhft, iz;sd lgh mùkj ds f, + vad fn;s tk;sas rfkk dksbz _.kked vadu ugha gs Q. lgh dfku dk p;u dhft, - ( lokzf/kd,fyd,ehu] th; fo;u esa veksfu;k ls vf/kd {kkjh; gksrh gs ( Me N H dk pk a, N H dh vis{kk mpp gksrk gs (C veksfu;e vk;u /kqzohdj.k çhkko ds }kjk LFkk;h gksrk gs (D CH NH dk pk b, NH dh vis{kk vf/kd gksrk gs Q. tc fqukw] CHCl rfkk NaOH ds lkfk fø;k djrk gs rks veh;dj.k }kjk lsfylsfymgkbm çkir gksrk gs fueu esa ls dksulh Lih'kht mijksdr n'kkzbz bz vfhkfø;k esa e/;oùkh ds :i esa lfeefr gksrh gs - O OH H CHCl ( CCl ( (C O H CHCl OH (D O CHCl CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

6 Q. Select incorrect statement : ( Higher the value of k H (Henr s law constant at a given pressure, the lower is the solubilit of the gas in the liquid ( Solubilit of a gas in a liquid decreases with increase in temperature and pressure (C To minimize the painful effects accompaning the decomposition of deep sea divers, O diluted with less soluble He gas is used as breathing gas (D The solubilit of a gas in a liquid is governed b Henr s law Q. Which are true statements for the following equilibrium? H O(l H O(g ( Increase in Pressure will result in the formation of more liquid water ( Increase in pressure will increase boiling point (C Decrease in pressure will vaporize H O(l to a greater etent (D Increase in pressure will liquef steam Q. Following reaction (s is / are not involved in Thermite process : ( Mn O + l Mn + l O ( Cr O + l l O + Cr (C Fe+ l O l + Fe O (D O + l + l O Q. vl; dfku dk p;u dhft, - ( fn,, nkc ij æo esa Sl dk k H (gsujh fu;e flfkjkad dk eku mpp rfkk fos;rk fueu gksrh gs ( æo esa,d Sl dh fos;rk rki rfkk nkc c<+us ds lkfk?kvrh gs (C gjs leqæh ksrk[kksjksa ds nnz;qdr çhkkoksa dks de djus ds f, O dks vyi fos; He Sl ds lkfk ruqñr djds 'okl Sl ds :i esa mi;ks fd;k tkrk gs (D,d æo esa Sl dh fos;rk gsujh fu;e ds vuqlkj gksrh gs Q. fueu lke; ds f, dksuls dfku l; gs? H O(l H O(g ( vf/kd æoh; t ds fuekz.k ds QLo:i nkc esa o`f gksh ( nkc esa o`f ls DoFkukad c<+sk (C nkc esa deh ls okf"ir H O(l esa vf/kd o`f gksh (D æohñr Hkki ls nkc esa o`f gksh Q. FkekZbZV izøe esa fueu esa ls dksulh vfhkfø;k lfeefr ugh gksrh gs ( Mn O + l Mn + l O ( Cr O + l l O + Cr (C Fe+ l O l + Fe O (D O + l + l O CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

7 This section contains paragraphs; passage- I has multiple choice questions (No. & and passage- II has multiple (No. to. Each question has choices (, (, (C and (D out of which ONLY ONE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and mark for each wrong answer. Passage # (Ques. & lknes undergo acid-catalsed addition of water across the triple bond in the presence of mercuric ion as catalst. miture of HgSO and aqueous H SO is used and addition product follows Markownikoffs orientation. C CH + H O HgSO H SO step I C = CH OH enol step II CCH O ketone Q. Select correct statement (S: ( Enol form in the hdration of alkne is called vinl alcohol ( Conversion of enol to ketone (step II is called tautomerisation and enol and ketone are called tautomers (C HgSO forms vinl cation C = CH with C CH (D ll of the above Hg bl [k.m esa ka'k fn;s ;s gsa] ka'k -I esa cgqfodyih iz'u (iz'u o gsa rfkk ka'k-ii esa cgqfodyih iz'u (iz'u ls gsa iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa, ftuesa ls dso,d fodyi lgh gs OM 'khv esa iz'u dh iz'u la[;k ds le{k viuk mùkj vafdr dhft;s iz;sd lgh mùkj ds f;s + vad fn;s tk,sas rfkk iz;sd r mùkj ds f, vad dkvk tk;sk ka'k # (iz-,oa,ydkbu ds ve mçsjdh esa] mçsjd ds :i eas ed;wzfjd vk;u dh miflfkfr esa f=kca/k ds lkis{k t dk ;qxeu gksrk gs HgSO rfkk th; H SO ds,d fej.k dk mi;ks rfkk ;ksked mikn] ekdkszfudksq vfhkfou;kl dk vuqlj.k djrs gs C CH + H O HgSO H SO step I C = CH OH enol step II CCH O ketone Q. lgh dfku/dfkuksa dk p;u dhft, - (,Ydkbu ds t;kstu esa bzukw #i] okbfu,ydksgkw dgkrk gs ( bzukw dk dhvksu (in II esa :ikurj.k pko;oh rfkk bzukw rfkk dhvksu pko;oh dgkrs gs (C HgSO, C CH ds lkfk foukb /kuk;u C = CH Hg (D mijksdr lhkh cukrk gs CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

8 Q. Hdration of -pentne b a miture of HgSO and H SO ( -pentanone ( -pentanone (C oth ( and ( (D none of these Passage # (Ques. to The most striking difference between the chemistr of alkenes and alknes is that terminal alknes are weakl acidic. When a terminal alknes is treated with a strong base, such as sodium amide, NaNH, the terminal hdrogen is removed and an acetlide anion is formed : C C H + : NH Na + C C : Na + + : NH acetlide anion The acidit of an acetlenic hdrogen arises as a result of sp-hbrid C H bond. cidic hdrogen of an acid (with pk a = can be deprotonated b a base (with pk a = if is greater than. Q. Which can deprotonate hdrogen from acetlene? ( o ( NH (C CH CH (D ll Q. Which acid base reaction is not possible? Θ ( CH CH + NH CH C Θ + NH ( CH CH + O Θ CH C Θ + OH (C CH COOH + O Θ CH COO Θ + OH (D OH Θ NH O Θ + NH + Q. Which is the most stable anion? ( cetlide ( Vinlic (C lkl (D Equal stabilit Q. HgSO rfkk H SO ds,d fej.k }kjk -isuvkbu dk t;kstu gksrk gs - ( -isuvsukwu ( -isuvsukwu (C ( rfkk ( nksuksa (D buesa ls dksbz ugha ka'k # (iz- ls,ydhu rfkk,ydkbu dh jlk;u ds e/; vf/kd vlkeku; (striking vurj gksrk gs ftlesa vurlfk,ydkbu nqcz veh; gksrh gs tc,d vurlfk,ydkbu dks],d çcz {kkj ds lkfk mipkfjr fd;k tkrk gs] tsls lksfm;e,ekbm NaNH, vurlfk gkbmªkstu dks gvkrk gs rfkk,d,lhkbm _.kk;u cukrk gs - C C H + : NH Na + C C : Na + + : NH acetlide anion sp-ladfjr C H ca/k ds ifj.kkelo:i,d,lhfvhfud gkbmªkstu dh veh;rk c<+rh gs,d ve (pk a = dks veh; gkbmªkstu],d {kkj (pk a = ds }kjk foçksvksuhñr gks ldrk gs ;fn, ls vf/kd gs Q.,lhVhhu ls dksulk gkbmªkstu foçksvksuhñr gks ldrk gs? ( O ( NH (C CH CH (D lhkh Q. dksulh ve-{kkj vfhkfø;k lehko ugha gksrh? Θ ( CH CH + NH CH C Θ + NH ( CH CH + O Θ CH C Θ + OH (C CH COOH + O Θ CH COO Θ + OH (D OH Θ NH O Θ + NH + Q. dksulk vf/kd LFkkbZ _.kk;u gs? (,lhfvkbm ( foukbfd (C,Ydh (D cjkcj LFkkf;o CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

9 Section - III This section contains questions (Q. to. + marks will be given for each correct answer and no negative marking. The answer to each of the questions is a SINGLE-DIGIT INTEGE, ranging from to. The appropriate bubbles below the respective question numbers in the OM have to be darkened. For eample, if the correct answers to question numbers X, Y, Z and W (sa are,, and, respectivel, then the correct darkening of bubbles will look like the following : X Y Z W Q. The densit of steam at.ºc and pascal is. kg m. Calculate the compressibilit factor (Z from these data. Give the answer in nearest whole number. Q. mol of CCl vapours at ºC occupies a volume of. L If vander Waals constant are a =. L atm mol. and b =. L mol, calculate compressibilit factor Z under low pressure region. Give the answer in nearest whole number. [k.m - III bl [k.m esa (iz- ls iz'u gas iz;sd lgh mùkj ds f;s + vad fn;s tk,sas rfkk dksbz _.kked vadu ugha gs bl [k.m esa iz;sd iz'u dk mùkj ls rd bdkbz ds,d iw.kk±d gsa OM esa iz'u la[;k ds lar uhps fn;s ;s cqyksa esa ls lgh mùkj oks cqyksa dks dkk fd;k tkuk gs mnkgj.k ds f, ;fn iz'u la[;k ¼ekusa½ X, Y, Z rfkk W ds mùkj,, rfkk gkas, rks lgh fof/k ls dks fd;s ;s cqys,sls fn[krs gsa tks fueuff[kr gs X Y Z W Q..ºC rfkk ij Hkki dk?kuo. kg m. gs bl rf; ls leihm+;rk q.kkad (Z dh.kuk dhft, fudvre iw.kkzzad esa mùkj nhft, Q. ºC ij CCl ok"i ds eks,. L vk;ru zg.k djrk gs ;fn ok.mj ok flfkjkad a =. L atm mol rfkk b =. L mol gs rks U;wu nkc {ks=k esa leihm~;rk q.kkad Z dh.kuk dhft, fudvre iw.kkzzad esa mùkj nhft, CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

10 Q. For the reaction at K : (g + (g C(g + D(g Hº =. kcal, Sº =. kcal K Calculate equilibrium constant. Q. piston eerting a pressure of. atm rests on the surface of water at ºC. The pressure is reduced to smaller etent and as a result g of water evaporates and absorbs. kj of heat. Calculate : heat of vaporization H v ( in KJ. Give the answer b dividing b. Q. gas originall at. atm and K underwent a reversible adiabatic epansion to. atm and K. What is the molar heat capacit of the gas? Q. The enthalp of neutralization for the first proton of H S(aq is. kj mol. Calculate the first acid ionization energ for H S(aq. Q.. mol sample of solid NH Cl was dissolved in. mol of water, the temperature of the solution decreased. small electrical immersion heater restored the temperature of the sstem b passing. from a. V power suppl for a period of s. Determine Hº (in kjmol for NH Cl(s molh O NH Cl (in mol H O Give the answer after multipling b and dividing b. Q. t K, half life of gaseous reactant initiall at KPa is minutes. When the pressure is KPa, the half-life is minutes. What is the order of the reaction? Q. t what ph the oidation potential of hdrogen electrode will be. V? Q. K ij fueu vfhkfø;k ds f, lke; flfkjkad dh.kuk dhft, - (g + (g C(g + D(g Hº =. kcal, sº =. kcal K Q. ºC ij,d filvu t dh lrg ij. atm dk nkc vkjksfir djrk gs nkc dh vyi ek=kk esa deh vkrh gs rfkk ifj.kkelo:i t ds g ok"ihñr gksrs gs rfkk. kj Å"ek vo'kksf"kr gksrh gs ok"iu H v dh Å"ek (fdkstw esa Kkr dhft, ls Hkk nsdj mùkj nhft, Q.,d Sl. atm rfkk K ij oklro esa møe.kh; #}ks"e izlkj dks. atm rfkk K ij leiuu djrh gs Sl dh eksj Å"ek /kkfjrk D;k gs? Q. H S(aq ds çfke çksvkwu ds f, mnklhuhdj.k dh,ufksyih. kj mol gksrh gs H S(aq ds f, çfke ve vk;uu ÅtkZ dh.kuk dhft, Q. ksl NH Cl ds,d. eks uewus dks. eks t esa?kksk tkrk gs] rks fo;u dk rki de gks tkrk gs s ds le; ds f,. V dh 'kfdr vkiwfrz ls. dh /kkjk çokg ls,d NksVs fo qr Å"ed }kjk ra=k dk rki fu;r j[kk tkrk gs NH Cl(s molh O NH Cl (in molh O ds f, Hº (in kjmol Kkr dhft, ls q.kk rfkk ls Hkk nsdj mùkj nhft, Q. K ij vfhkdkjdks dk v}z vk;qdk kpa ij feuv gs tc nkc KPa gs rks v}z vk;qdk feuv gksrk gs vfhkfø;k dh dksfv D;k gs Q. fdl ph ij gkbmªkstu bsdvªkwm dk vkwdlhdj.k fohko. V gksk? CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

11 Section I Questions to are multiple choice questions. Each question has four choices (, (, (C and (D, out of which ONLY ONE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and mark for each wrong answer. MTHEMCTICS [k.m - I iz'u ls rd cgqfodyih iz'u gsa iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa, ftuesa ls dso,d fodyi lgh gs OM 'khv esa iz'u dh iz'u la[;k ds le{k viuk mùkj vafdr dhft;s iz;sd lgh mùkj ds f, + vad fn;s tk;ass rfkk iz;sd r mùkj ds f, vad dkvk tk;sk Q. If f : (, π be defined b f ( = ([ + sin k], k = where [] denotes the integral part of, then range of f ( is - ({n, n + } ( {n, n, n + } (C{n, n + } (D none of these Q. Let f : [, ] [, be a continuous and differentiable function. Then ( f ( + ( f ( + f ( f ( (f ( f ( is equal to ( f (c f '(c (C f (c f '(c where c (, ( f '(c (D none of these n Q. ;fn f : (, π, f ( = ([ + sin k] }kjk k = ifjhkkf"kr gs] tgk [], ds iw.kk±d Hkk dks fu:fir djrk gs] rc f ( dk ifjlj gs - ({n, n + } ( {n, n, n + } (C{n, n + } (D buesa ls dksbz ugha Q. ekuk f : [, ] [,,d lr~r,oa voduh; Qu gs] rc ( f ( + ( f ( + f ( f ( (f ( f ( dk eku cjkcj gs ( f (c f '(c (C f (c f '(c tgk c (, ( f '(c (D buesa ls dksbz ugha n CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

12 Q. If f : is continuous and differentiable function such that - f t dt + f "'( dt = ( t dt f '( t dt + f "( tdt, then the value of f '( is ( f ' ( f " ( ( + f ' ( f " ( (C f ' ( + f " ( (D + f ' ( + f " ( Q. If = c e + c e + c e satisfies the differential equation a ( (C d + b + c abc d + d a + d is equal to - ( (D d b d +c =, then Q. If a, b, c, p, q, r are three non-zero comple numbers p q r a b c such that + + = + i and + + =, the a b c p q r p q r value of + + is - a b c ( ( (C i (D i Q. ;fn f : lr~r,oa voduh; Qu bl izdkj gs fd f t dt + f "'( dt = ( t dt f '( t dt + f "( tdt, rc f '( dk eku gs ( f ' ( f " ( ( + f ' ( f " ( (C f ' ( + f " ( (D + f ' ( + f " ( Q. ;fn = c e + c e + c e vod lehdj.k d d d + a + b +c = dks larq" djrk gs] rc d d d a + b + c abc ( (C cjkcj gs - ( (D Q. ;fn a, b, c, p, q, r rhu v'kwu; lfeej la[;k, bl izdkj p q r a b c gs fd + + = + i,oa + + = gs] rc a b c p q r p q r + + dk eku gs - a b c ( ( (C i (D i CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

13 Q. If n and r are positive integers such that < r < n, then the roots of the quadratic equation n C r +. n C r + n C r + = are ( real and distinct ( rational (C rational but not integer (D imaginar Q. If = z ( z z ( z ( z z and, = ( (C z ( z z ( z ( z z z z z, then = ( ( ( z ( (D None of these Q. circle touches the line = at a point P such that OP =, where O is the origin. The circle contains the point (, in its interior and the length of its chord on the line + = is. The equation of the circle is - ( = ( + + = (C = (D none of these Q. ;fn n,oa r /kuked iw.kk±d bl izdkj gs fd < r < n, rc f}?kkr lehdj.k n C r +. n C r + n C r + = ds ew gs ( oklrfod,oa fhkuuk ( ifjes; (C ifjes; ijurq iw.kk±d ugha (D dkyifud Q. ;fn = z ( z z ( z ( z,oa = ( (C z z ( z z ( z ( z z z z z gs] rc = ( z ( ( ( (D buesa ls dksbz ugha Q.,d o`ùk js[kk = dks,d fcunq P ij bl izdkj Li'kZ djrk gs fd OP =, tgk O ew fcunq gs fcunq (, o`ùk ds vunj flfkr gs,oa js[kk + = ij bldh thok dh EckbZ gs] rc o`ùk dk lehdj.k gs- ( = ( + + = (C = (D buesa ls dksbz ugha CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

14 Questions to are multiple choice questions. Each question has four choices (, (, (C and (D, out of which MULTIPLE (ONE O MOE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and no negative marks. iz'u ls rd cgqfodyih iz'u gas iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa] ftuesa ls,d ;k,d ls vf/kd fodyi lgh gas OM 'khv esa iz'u dh iz'u la[;k ds le{k vius mùkj vafdr dhft, iz;sd lgh mùkj ds f, + vad fn;s tk;sas rfkk dksbz _.kked vadu ugha gs + Q. If d = +, then ( sin + cos cos ( = sin + cos ( = cot (C = ( sin + cos (D = tan d Q. For a certain curve = f( satisfing =, d f( has a local minimum value when = ( Equation of the curve is = + + ( f( has a local maimum at = (C Global maimum value of f( is (D Global minimum value of f( is Q. Let,, C be matrices with entries from the set of real numbers. Define operation, ' ' as follows = ( +, then ( I = ( = (C = (D ( + C = + C + Q. ;fn d = + gs ] rc ( sin + cos cos ( = sin + cos ( = cot (C = ( sin + cos (D = tan Q. d = dks larq" djus oks,d fuf'pr oø d = f( ds f;s f( dk LFkkuh; fufeu" eku gs tcfd = gs ( oø dk lehdj.k = + + gs ( f( dk = ij LFkkuh; mfpp" eku gs (C f( dk lkozf=kd mfpp" eku gs (D f( dk lkozf=kd fufeu" eku gs Q. ekuk,,oa C, dh esfvªdl gs ftuds vo;o oklrfod la[;kvksa ds leqpp; ls gsa lafø;k ' ' fueu izdkj ifjhkkf"kr gs = ( + rc ( I = ( = (C = (D ( + C = + C CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

15 Q.,, C and D are four points such that = m ( ˆ i ˆj + kˆ, C = î ĵ and CD = ( ˆ i + ˆj kˆ. If and CD intersect at some point E, then ( m ( n (C area of CE = (D all of these Q. sin α If sin β = then - cosα and = cosβ π, < α < β <, ( tan α = ( tan α = / (C tan β = / (D tan β = This section contains paragraphs; passage- I has multiple choice questions (No. & and passage- II has multiple (No. to. Each question has choices (, (, (C and (D out of which ONLY ONE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and mark for each wrong answer. Q.,, C,oa D pkj fcunq bl izdkj gs fd = m ( ˆ i ˆj + kˆ, C = î ĵ,oa CD = ( ˆ i + ˆj kˆ gs ;fn,oa CD fdlh fcunq E ij izfrpnsn djrs gs] rc - ( m ( n (C CE dk {ks=kq = (D mijksdr lhkh sin α Q. ;fn = sin β gs, rc -,oa cosα = cosβ π, < α < β < ( tan α = ( tan α = / (C tan β = / (D tan β = bl [k.m esa ka'k fn;s ;s gsa] ka'k -I esa cgqfodyih iz'u (iz'u o gsa rfkk ka'k-ii esa cgqfodyih iz'u (iz'u ls gsa iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa, ftuesa ls dso,d fodyi lgh gs OM 'khv esa iz'u dh iz'u la[;k ds le{k viuk mùkj vafdr dhft;s iz;sd lgh mùkj ds f;s + vad fn;s tk,sas rfkk iz;sd r mùkj ds f, vad dkvk tk;sk CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

16 Passage # (Ques. to person draws a card from a pack of cards. He replaces the card, shuffles the pack and again draws a card. He replaces it and draws again. This he does until he draws a heart. Q. The probabilit that he will have to make at least four draws is ( ( ka'k # (iz-,oa,d O;fDr rk'k dh M~Mh esa ls,d iùkk fudkrk gsa og iùkk okfil j[kdj M~Mh dks QsVrk gs,oa iqu%,d iùkk fudkrk gs og bls okfil j[kdj iqu% fudkrk gs og,slk rc rd djrk gs tc rd dh iku dk iùkk ugha fud tkrk gs gs Q. izkf;drk dh, og de ls de pkj ckj iùkk fudksk, gksh ( ( (C (D None of these (C (D buesa ls dksbz ugha Q. The chance that he will fail in the first two draws is - ( ( (C (D Q. izkf;drk fd, og izfke nks ckj iùkk fudkus ij vlq gksk, gs - ( ( (C (D Passage # (Ques. & f : (, ( π, π be defined as f( = arc tan (ln - Q. The above function can be classified as - ( Injective but not Surjective ( Surjective but not Injective (C neither injective nor surjective (D oth injective as well as surjective ka'k # (iz-,oa π π f : (, (,, f( = arc tan (ln }kjk ifjhkkf"kr gs - Q. mijksdr Qu gs - (,dsdh ijurq vkpnknd ugha ( vkpnknd ijurq,dsdh ugha (C uk rks,dsdh uk gh vkpnknd (D,dSdh,oa vkpnknd nksuksa gh gs CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

17 Q. The graph of f( is - π/ ( ( Q. f( dk vks[k gs - ( ( π/ π/ (C π/ π/ (D π/ π/ (C π/ π/ (D π/ Q. If, and are the point at which g( = [f(] is discontinuous, where [. ] denotes greatest integer function, then + + is - ( Equal to ( Equal to (C Greater than (D Greater than but less than Q. ;fn,,oa og fcunq gs ftuij g( = [f(] vlr~r gs] tgk [. ] egùke iw.kk±d Qu dks fu:fir djrk gs] rc + + gs - ( ds cjkcj ( ds cjkcj (C ls cm+k (D ls cm+k ijurq ls NksVk Section - III This section contains questions (Q. to. + marks will be given for each correct answer and no negative marking. The answer to each of the questions is a SINGLE-DIGIT INTEGE, ranging from to. The appropriate bubbles below the respective question numbers in the OM have to be darkened. For eample, [k.m - III bl [k.m esa (iz- ls iz'u gas iz;sd lgh mùkj ds f;s + vad fn;s tk,sas rfkk dksbz _.kked vadu ugha gs bl [k.m esa iz;sd iz'u dk mùkj ls rd bdkbz ds,d iw.kk±d gsa OM esa iz'u la[;k ds lar uhps fn;s ;s cqyksa esa ls lgh mùkj oks cqyksa dks dkk fd;k tkuk gs mnkgj.k ds CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

18 CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page # if the correct answers to question numbers X, Y, Z and W (sa are,, and, respectivel, then the correct darkening of bubbles will look like the following : X Y Z W Q. lim + +. =... Q. If f( = t cos t dt, then the number of points of discontinuit of f ( in the interval (, π is... Q. If z = + i, then the value of + arg i z i z d, where [.] denotes the greatest integer function, is f, ;fn iz'u la[;k ¼ekusa½ X, Y, Z rfkk W ds mùkj,, rfkk gkas, rks lgh fof/k ls dks fd;s ;s cqys,sls fn[krs gsa tks fueuff[kr gs X Y Z W Q. lim + +. =... Q. ;fn f( = t cos t dt gs, rc (, π esa f ( ds vlkar;rk ds fcunqvks dh la[;k gs - Q. ;fn z = + i gs, rc + arg i z i z d dk eku, tgk [.] egùke iw.kk±d Qu dks fu:fir djrk gs, gksk

19 π/ Q. The value of + ( sin cos d { } d is (where[.] and {.} represent greatest integer and fractional part. Q. If G is the centroid of C having lengths of the sides a, b, c and O is an point, then a + b + c = (O + O + OC k (OG, where k =... Q. Let P (, and Q (, be two given points. Let (, be a point such that ( ( + ( ( + =. If area of PQ is, then the number of possible positions of are - Q. If from an point on the circle + = a, tangents are drawn to the circle + = b (a > b, then the angle between the tangents is ksin b, where k =... a Q. Maimum number of common normals of = a and = b ma be equal to... Q. If sin, cos and tan are in geometric progression, then cot cot =... Q. π/ + ( sin cos d { } d dk eku gs (tgk [.],oa {.} egùke iw.kk±d,oa fhkuuked Hkk dks fuk:fir djrs gs Q. ;fn G f=khkqt C dk dsunzd gs ftldh Hkqtkvksa dh EckbZ a, b, c,oa O dksbz fcunq gs] rc a + b + c = (O + O + OC k (OG, tgk k =... Q. ekuk P (,,oa Q (, nks fn;s ;s fcunq gs ekuk (,,d fcunq bl izdkj gs fd ( ( + ( ( + = gs ;fn PQ dk {ks=kq gs] rc dh lahko flfkfr;ksa dh la[;k gs - Q. ;fn o`ùk + = a ij fdlh fcunq ls o`ùk + = b (a > b ij Li'kZ js[kk, [khaph tkrh gs, rc Li'kZ js[kkvksa ds e/; dks.k ksin b gs, tgk k =... a Q. = a,oa = b ds mhk;fu" vfhkecksa dh vf/kdre la[;k cjkcj] gs... Q. ;fn sin, cos,ao tan q.js. esa gs] rc cot cot =... CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: - Page #

20 Section I Questions to are multiple choice questions. Each question has four choices (, (, (C and (D, out of which ONLY ONE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and mark for each wrong answer. Q. positive point charge is placed at P in front of an earthed metal sheet S. Q & are two points between P & S as shown in figure. If the electric field strength at Q & are respectivel E Q & E and potential at Q & are respectivel V Q & V. Then- P..Q..S PHYSICS [k.m - I iz'u ls rd cgqfodyih iz'u gsa iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa, ftuesa ls dso,d fodyi lgh gs OM 'khv esa iz'u dh iz'u la[;k ds le{k viuk mùkj vafdr dhft;s iz;sd lgh mùkj ds f, + vad fn;s tk;ass rfkk iz;sd r mùkj ds f, vad dkvk tk;sk Q.,d /kuked fcunq vkos'k dks,d HkwlEifdZr /kkfod ifêdk S ds lkeus P ij j[kk ;k gs Q rfkk, fp=k esa n'kkz;s vuqlkj P rfkk S ds e/; flfkr nks fcunq gsa ;fn Q rfkk ij fo qr {ks=k rhozrk, Øe'k% E Q rfkk E gsa] rfkk Q rfkk ij fohko Øe'k% V Q rfkk V. gsa rc& P..Q..S ( E Q > E (C V Q = V ( E Q < E (D V Q < V ( E Q > E (C V Q = V ( E Q < E (D V Q < V Q. The mean lives of a radioactive substance are ear and ear for α-emission and β-emission respectivel. Find the time during which three-fourth of a sample will deca if it is decaing b both α-emission and β-emission simultaneousl. ( ears ( ears (C ears (D ears Q.,d jsfm;kslfø; inkfkz dh α-mltzu rfkk β-mltzu ds f;s ek/; vk;q, Øe'k% o"kz rfkk o"kz gsa og le; Kkr dhft;s tc inkfkz dk rhu&pksfkkbz Hkk {k; gks tk;sk] ;fn ;g α-mltzu rfkk β-mltzu nksuksa }kjk,d lkfk {kf;r gks jgk gs& ( o"kz ( o"kz (C o"kz (D o"kz CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

21 Q. Q. Two containers & contain ideal gases helium and ogen respectivel. Volume of both containers are equal and pressure is also equal. Container has twice the number of molecules than container then if v & v represent the rms speed of gases in containers & respectivel, then - v ( v v (C v v = ( v v = (D v = = Q. The mirror of length l makes revolutions per minute about the ais crossing its mid point O and perpendicular to the plane of the figure There is a light source in point and an observer at point of the circle of radius drawn around centre O ( O = º. What is the proportion /l if the observer first sees the light source when the angle of mirror ψ = º? nks ik=k rfkk vkn'kz Slsa Øe'k% ghf;e rfkk vkwdlhtu j[krsa gsa nksuksa ik=kksa dk vk;ru cjkcj gs rfkk buesa nkc Hkh cjkcj gs ik=k esa Sl v.kqvksa dh la[;k dh rquk esa nqquh gs rfkk ;fn v o v Øe'k% rfkk esa Slksa ds oz ek/; ew pk gksa rks& ( (C v v v v = ( = (D v v v v = = Q. l EckbZ okk,d niz.k blds e/; fcunq O ls qtj jgh rfkk fp=k ds r ds Ecor~ v{k ds lkis{k pø.k izfr feuv dj jgh gs fcunq ij,d izdk'k L=kksr rfkk dsunz O ds pkjksa vksj cuk;s ;s o`ùk ds fcunq ij,d izs{kd miflfkr gs ( O = º vuqikr /l dk eku D;k gksk ;fn izs{kd fcunq L=kksr dks igh ckj rc ns[krk gs tc niz.k ds f;s dks.k ψ = º? CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

22 ψ l O ψ l O l l ( ( / (C (D / Q. massless container is filled with liquid of densit ρ. It contains two holes as shown in figure. Container rests on ground. reas of the two holes are each. Container is filled with liquid upto height H. Then ( ( / (C (D / Q.,d nzo;ekughu ik=k ρ?kuo ds nzo ls Hkjk gqvk gs ;g fp=k esa n'kkz;s vuqlkj nks fnnzksa ls ;qdr gs ik=k /kjkr ij j[kk gqvk gs iz;sd nksuksa fnnzksa dk {ks=kq gs ik=k esa H Å pkbz rd nzo Hkjk gqvk gs rc & H/ H H/ ( Torque produced b normal force between container & ground about center of gravit is ρ gh / into the plane of paper ( Torque produced b friction about center of gravit is ρgh out of the plane of paper (C Net torque produce b thrust force & friction force about center of gravit is ρgh / into the plane of paper (D Torque produced b normal force between container and ground about centre of gravit is zero H/ H H/ ( q:o dsunz ds lkis{k ik=k rfkk /kjkr r ds e/; vfhkec c }kjk miuu ck?kw.kz dkt ds r ds vunj ρ gh / gs ( q:o dsunz ds lkis{k?k"kz.k }kjk miuu ck?kw.kz dkt ds r ds ckgj ρgh gs (C q:o dsunz ds lkis{k mikod c rfkk?k"kz.k c }kjk miuu dq ck?kw.kz dkt ds r ds vunj ρ gh / gs (D q:o dsunz ds lkis{k ik=k rfkk /kjkr ds e/; vfhkec c }kjk miuu ck?kw.kz 'kwu; gs CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

23 Q. L shaped rod whose one rod is horizontal and other is vertical is rotating about a vertical ais as shown with angular speed ω. The sleeve shown in figure has mass m and friction coefficient between rod and sleeve is µ. The minimum angular speed ω for which sleeve cannot slip on rod is ω Q. L vkdkj dh,d NM+ dks n'kkz;k ;k gs ftldh,d NM+ {ksfrt rfkk nwljh Å/okZ/kj gs] tks ω dks.kh; pk ls n'kkz;s Å/okZ/kj v{k ds lkis{k?kw.kzu djrh gs fp=k esa n'kkz;k Lho (sleeve m nzo;eku dk gs rfkk NM+ o Lho ds e/;?k"kz.k q.kkad µ gs U;wure dks.kh; pk ω, ftlds f;s Lho NM+ ij u fqls] gs ω m sleeve m sleeve l l ( ω = (C ω = g µl l µg ( ω = µg l (D None of these ( ω = (C ω = g µl l µg ( ω = µg l (D buesa ls dksbz ugha Q. thin conducting plate is inserted in half wa between the plates of a parallel plates capacitor of capacitance C. Conducting plate Q.,d irh pkd IsV dks C /kkfjrk oks la/kkfj=k dh lekurj IsVksa ds e/; chp esa j[kk tkrk gs pkd IsV What does the value of capacitance, if both the plate of capacitor is shorted? ( C ( C (C C (D C ;fn la/kkfj=k dh nksuksa IsVksa dks?kqiffkr dj fn;k tk,] rks /kkfjrk dk eku D;k gs? ( C ( C (C C (D C CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

24 Q. Consider a usual set-up of Young's double slit eperiment with slits of equal intensit as shown in the figure. Take 'O' as origin and the Y ais as indicated. If average intensit between = λd d λd and = d equals n times the intensit of maimum, then n equal is (take average over phase difference - ( d S S + π D O ( + π (C + (D π π Q.,d lkeku; ;a f}flv iz;ks O;oLFkk o lkfk gh leku rhozrk okh flvsa] fueu fp=kkuqlkj dks] fopkfjr djsa λd 'O' n'kkz,s vuqlkj ew fcunq o Y-v{k gs ;fn = d λd o = ds e/; vkslr rhozrk] vf/kdre rhozrk dh n d quk gks rks n rqy; (dkurj ij vkslr sa gs - d S S ( + ( + π π (C + (D π π D O Questions to are multiple choice questions. Each question has four choices (, (, (C and (D, out of which MULTIPLE (ONE O MOE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and no negative marks. iz'u ls rd cgqfodyih iz'u gas iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa] ftuesa ls,d ;k,d ls vf/kd fodyi lgh gas OM 'khv esa iz'u dh iz'u la[;k ds le{k vius mùkj vafdr dhft, iz;sd lgh mùkj ds f, + vad fn;s tk;sas rfkk dksbz _.kked vadu ugha gs CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

25 Q. liquid of densit ρ filled in the vessel as shown is rotated with constant angular velocit 'ω' about the ais passing through the middle. The radius of clinder is. Then Q. ik=k esa Hkjk gqvk ρ?kuo dk nzo n'kkz, vuqlkj] e/; ls gksdj qtjus okh v{k ds ifjr% fu;r dks.kh; os 'ω' ls?kwf.kzr fd;k tkrk gs csu dh f=kt;k gs] rc H/ O ( The maimum value of 'ω' for which the liquid gh doesn t come out is ( The value of 'ω' for which the base of container is just eposed is H gh (C Volume of liquid remaining in the container in π H case ( is (D Gauge pressure at point in the container in case ( is ρgh H/ O ( 'ω' dk og vf/kdre eku ftl ij nzo ckgj u gh vk tk;ss] gs ( 'ω' dk og eku ftl ij ik=k dk isank hd utj (epose vkus s] H gh (C flfkfr ( esa ik=k esa 'ks"k cps gq, nzo dk vk;ru π H gs (D flfkfr ( esa ik=k esa fcunq ij kwt nkc ρgh gs gs CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

26 Q. stick is tied to the floor of the water tank with a string as shown in the figure. The length of stick is m. rea of cross-section of stick is m. Specific gravit of stick is.. Take g = m/s. Then Q.,d NM]+ t VSad ds Q'kZ ls,d Mksjh }kjk ck /k nh tkrh gs] tslk fd fp=k esa n'kkz;k ;k gs NM+ dh EckbZ m gs NM+ dk vuqizlfk dkv {ks=kq m gs NM+ dk fof'k"v?kuo. gs g = m/s hft, rc & Water ( Tension in the string is N ( uoanc force acting on stick is N (C Length of stick immersed in water is m (D When string is cut initial acceleration of stick is m/s t ( Mksjh esa ruko N gs ( NM+ ij dk;zjr mikou c N gs (C t essa Mwch gqbz NM+ dh EckbZ m gs (D tc jllh dks dkvk tkrk gs rks NM+ dk izkjfehkd oj.k m/s gs Q. bod moves in a circular path of radius with deceleration so that at an moment of time its tangential and normal acceleration are equal in magnitude. t the initial moment t =, the velocit of bod is v then the velocit of bod at an time will be v ( v = at time t v t + S ( v = v after it has moved S meter e (C v = v e S after it has moved S meter (D None of these Q.,d fi.m f=kt;k ds o`ùkh; ifk esa eanhr gksrk gs rkfd fdlh Hkh {k.k ij bldk Li'khZ; rfkk vfhkec oj.k ifjek.k esa cjkcj gks izkjfehkd {k.k t = ij] fi.m dk os v gs rc fdlh Hkh le; fi.m dk os gksk v ( t le; ij v = v + t S ( S ehvj fr djus ds ckn v = v e (C S ehvj fr djus ds ckn v = v e S (D buesa ls dksbz ugha CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

27 Q. clinder block of length L = m is in two immiscible liquids. Part of block inside liquid( is m and in liquid ( is m. rea of cross-section of block is. Densities of liquid ( & ( are ρ and ρ respectivel Q. L = m EckbZ dk,d csukdkj CkWd nks v?kqu'kh nzo esa flfkr gs nzo ( ds vunj CkWd dk m Hkk rfkk nzo ( esa Hkh m Hkk gs CkWd dk vuqizlfk dkv {ks=kq gs nzo ( rfkk ( dk?kuo Øe'k% ρ rfkk ρ gs ρ. Liquid ( ρ. Liquid ( ρ. Liquid ( ρ. Liquid ( ( Densit of block is ρ/ ( Force eerted b liquid ( on block is ρg/ (C lock is depressed so that it is just completel immersed in liquid ( and released. The initial acceleration of block is / g (D In case (C force eerted b liquid ( on block is / ρg ( CkWd dk?kuo ρ/ gs ( nzo ( }kjk CkWd ij vkjksfir c ρg/ gs (C CkWd dks nck;k tkrk gs rkfd ;g hd nzo ( esa iw.kzr;k Mwc tk;s rfkk fqj NksM+k tkrk gs CkWd dk izkjfehkd oj.k / g gksk (D (C flfkfr esa nzo ( }kjk CkWd ij vkjksfir c / ρg gs CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

28 Q. luminous point object is placed at O, whose image is formed at I as shown in figure. Line is optic ais. Which of the following statements are correct? a O a > b b I ( If the lens is used to obtain the image, the lens must be a converging lens and position of its principal focus can be found out. ( If the mirror is used to obtain the image, the mirror must be a conve mirror whose pole will be at point of intersection of line OI with the optic ais. (C Position of principal focus of the mirror cannot be found out. (D I is a real image. Q.,d izfrnhir fcunq olrq O ij j[kh gqbz gs] ftldk izfrfcec fp=k esa n'kkz;s vuqlkj I ij curk gs js[kk izdkf'kd v{k gs fueu esa ls dksuls dfku lgh gsa? a O a > b ( ;fn sul dks izfrfcec izkir djus ds f;s iz;qdr fd;k tkrk gs] rc Sal vo'; gh mùk Sal gksuk pkfg;s rfkk blds eq[; Qksdl dh flfkfr dks Kkr fd;k tk ldrk gs ( ;fn niz.k dks izfrfcec izkir djus ds f;s iz;qdr fd;k tkrk gs rc] ni.kz vo'; gh mùk niz.k gksuk pkfg;s] ftldk /kzqo] js[kk OI dk izdkf'kd v{k ds lkfk izfrpnsnu fcunq gksk (C niz.k ds eq[; Qksdl dh flfkfr dks Kkr ugha fd;k tk ldrk (D I,d oklrfod izfrfcec gs I b This section contains paragraphs; passage- I has multiple choice questions (No. & and passage- II has multiple (No. to. Each question has choices (, (, (C and (D out of which ONLY ONE is correct. Mark our response in OM sheet against the question number of that question. + marks will be given for each correct answer and mark for each wrong answer. bl [k.m esa ka'k fn;s ;s gsa] ka'k -I esa cgqfodyih iz'u (iz'u o gsa rfkk ka'k-ii esa cgqfodyih iz'u (iz'u ls gsa iz;sd iz'u ds pkj fodyi (, (, (C rfkk (D gsa, ftuesa ls dso,d fodyi lgh gs OM 'khv esa iz'u dh iz'u la[;k ds le{k viuk mùkj vafdr dhft;s iz;sd lgh mùkj ds f;s + vad fn;s tk,sas rfkk iz;sd r mùkj ds f, vad dkvk tk;sk CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

29 Passage # (Ques. & ka'k # (iz-,oa E r E r P (watt P (watt Cell emf is fied and internal resistance r is also fied. s value of changes power delivered to circuit b cell also changes. Variation of power delivered with is shown in graph. ls dk fo- ok- c fu;r gs rfkk vkarfjd izfrjks/k r Hkh fu;r gs tsls tsls dk eku ifjofrzr gksrk gs] ls }kjk ifjifk dks nh bz 'kfdr Hkh ifjofrzr gksrh gs zkq esa iznùk 'kfdr dk ds lkfk ifjorzu n'kkz;k ;k gs CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

30 Q. Emf of the cell is Q. ls dk fo-ok- c gs& ( V (C V (. V (D. V ( V (C V (. V (D. V Q. Current through the resistance is nearl (when = Ω (. (. (C. (D. Q. izfrjks/k ls izokfgr /kkjk Hk gksh (tgk = Ω gs (. (. (C. (D. Passage # (Ques. to Equal volumes and different masses of two blocks are in equilibrium on a lever. (case When the blocks are immersed in a liquid then buoanc force acting on blocks are F and F. (case l l m m (case ka'k # (iz- ls leku vk;ru o fhkuu nzo;ekuksa ds nks CkWd hoj (lever ij lke;olfkk esa gsa (flfkfr esa tc CkWdksa dks nzo esa Mqcks;k tkrk gs rc CkWdksa ij dk;zjr mikou c F o F gsa (flfkfr esa l l m m (flfkfr m m (flfkfr m m (flfkfr CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

31 Q. In case ( which of following is true - ( m = m ( m l = m l (C m m = (D l l m + m m l + l = l Q. uoanc force acting on the two blocks F and F satisf the following relation - ( F m = F m ( F = F (C F l = F l (D F l = F l Q. In case ( if the equilibrium is restored at positions and then - ( (C m = ( m = F F (D = F = F mg F m g F Section - III This section contains questions (Q. to. + marks will be given for each correct answer and no negative marking. The answer to each of the questions is a SINGLE-DIGIT INTEGE, ranging from to. The appropriate bubbles below the respective question numbers in the OM have to be darkened. For eample, if the correct answers to question numbers X, Y, Z and W (sa are,, and, respectivel, then the correct darkening of bubbles will look like the following: Q. flfkfr ( esa fueu esa ls dksulk l; gs & ( m = m ( m l = m l m (C m m + m l + l = (D = l l m l Q. nks CkWdksa ij dk;zjr mikou c F o F dksuls fueu lecu/k dks lurq"v djrs gsa & ( F m = F m ( F = F (C F l = F l (D F l = F l Q. flfkfr ( esa ;fn flfkfr;ksa o ij lke;kolfkk iqu% izkir gksrh gs] rc & ( (C m = ( m = F F (D = mg F m g F F = F [k.m - III bl [k.m esa (iz- ls iz'u gas iz;sd lgh mùkj ds f;s + vad fn;s tk,sas rfkk dksbz _.kked vadu ugha gs bl [k.m esa iz;sd iz'u dk mùkj ls rd bdkbz ds,d iw.kk±d gsa OM esa iz'u la[;k ds lar uhps fn;s ;s cqyksa esa ls lgh mùkj oks cqyksa dks dkk fd;k tkuk gs mnkgj.k ds f, ;fn iz'u la[;k ¼ekusa½ X, Y, Z rfkk W ds mùkj,, rfkk gkas, rks lgh fof/k ls dks fd;s ;s cqys,sls fn[krs gsa tks fueuff[kr gs CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

32 X Y Z W Q. block of metal is heated directl b dissipating power in the internal resistance of block. ecause of temperature rise, the resistance increases eponentiall with time and is given b (t =. e t, where t is in second. The block is connected across a V source and dissipates J heat energ over a certain period of time. This period of time is... sec. (Given : ln(. = X Y Z W Q. /kkrq ds,d CkWd dks] mlds vkurfjd izfrjks/k esa 'kfdr ds {k; }kjk lh/ks ez fd;k tkrk gs rki esa o`f ds dkj.k izfrjks/k] le; ds lkfk pj?kkrkadh :i ls c<+rk gs ftls (t =. e t }kjk fn;k ;k gs] tgk t lsd.m esa gs] CkWd dks V ds L=kksr ds fljksa ij tksm+k tkrk gs rks ;g le; ds fdlh fuf'pr vurjk eas J Å"eh; ÅtkZ O;f;r djrk gs le; dk ;g vurjk gksk... lsd.m (fn;k gs : ln(. = Q. thermonuclear device consists of a toroid of total volume. m containing deuterium gas at mm mercur pressure and at room temperature. bank of capacitors of µf is discharged through the tube at kv. If onl % Q.,d rkiukfhkdh; ;a=k,d ifjukfdk ;qdr gs ftldk dq vk;ru. m gs ftlesa mm ikjs ds nkc rfkk dejs ds rki ij M~;wVsfj;e Sl Hkjh gqbz gs µf /kkfjrk okksa la/kkfj=kksa dk la;kstu] kv okh uh }kjk fujkosf'kr dj fn;k tkrk CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

33 of the electrical energ is transformed to plasma kinetic energ, then the maimum temperature attained is... K. ssuming that the energ is equall shared between the deutrons and electrons in the plasma. gs ;fn fo qr ÅtkZ dk dso % gh IkLek dh frt ÅtkZ esa :ikarfjr gksrk gs] rc izkir fd;k tkus okk mppre rkieku gksk... K ;g ekusa Iktek ds Hkhrj miflfkr bsdvªkwuksa rfkk M~;wVªkWuksa }kjk ÅtkZ cjkcj :i ls ck Vh tkrh gs Q. string of length l is fied at both ends and is vibrating in second harmonic. The amplitude at antinodes is mm and the amplitude of a particle at l a distance from fied end is a mm then the value of a is mm. Q. In the arrangement shown in figure, power dissipated b the circuit is... watt. Ω Ω Ω Q Ω Ω Q. l EckbZ okh,d jllh nksuksa fljksa ij c gs rfkk ;g f}ùkh; lauknh esa dfeir gks jgh gs izlianksa ij l vk;ke mm gs rfkk c fljs ls nwjh ij flfkr a d.k dk vk;ke gksk mm. mm gs] rc a dk eku Q. uhps n'kkz;s ifjifk }kjk O;f;r 'kfdr... okwv gs Ω Ω Ω Q Ω Ω P Ω V Ω Ω P Ω V Ω Ω CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

34 Q. With two fingers, ou hold a cone motionless upside down, as shown. The mass of the cone is kg, and coefficient of friction between our fingers and cone is µ =.. What is the minimum normal force (in Newton ou must appl with each finger in order to hold up the cone? Consider onl translational equilibrium. nswer can be written as Newton. Find? (cot θ =. θ Q. vki nks Åaf;ksa dh lgk;rk ls],d frghu 'kadq fp=kkuqlkj idm+s gks 'kadq dk nzo;eku kg gs rfkk 'kadq o vkidh Åaf;k ds e/;?k"kz.k q.kkad µ =. gs 'kadq dks idm+s j[kus ds f, vkidh iz;sd Å h }kjk vkjksfir vko';d vfhkec c (U;wVu esa dk eku D;k gksuk pkfg;s\ dso LFkkukUrj.k lke;kolfkk dks fopkfjr dhft, mùkj U;wVu f[kk tk ldrk gs Kkr dhft;s (cot θ =. θ Q. rectangular plate of mass kg is suspended from points and as shown. If the pin is suddenl removed then the angular acceleration in rad/sec of the plate divided b is equal to (g = m/s Q. kg nzo;eku dh,d vk;rkdkj IsV dks n'kkz;s vuqlkj fcunqvksa o ls Vdk;k ;k gs ;fn fiu dks vpkud gvk f;k tkrk gs] rks IsV dk dks.kh; oj.k (rad/sec eass dks }kjk fohkkftr djus ij izkir eku ff[k, (g = m/s b =.m b =.m l =.m l =.m CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

35 Q. Find the quantum number n corresponding to ecited state of He + ion if on transition to the ground state that ion emits two photons in succession with wavelength. Å and Å. ( =. / m Q. Hdrogen gas in the atomic state is ecited to an energ level such that the potential energ of H-atom becomes. ev. Now the photo-electric plate having work function φ =. ev is eposed to the emission spectra of this gas. ssuming all the transitions to be possible, find the minimum de-roglie wavelength of ejected photo-electrons (in Å (approimatel. Q. capillar of square cross-section with edge. mm is flippest in water at C. The contact angle of water with capillar maternal is, the surface tension of water is N/m. Find vertical rise of water in capillar in mm if angle of capillar with vertical is. Q. He + vk;u dh mùkstu volfkk ls lecfu/kr DokWUVe la[;k n Kkr dhft;s ;fn ew volfkk esa laøe.k djus ij og vk;u Øekr. Å o Å rjans/;z ds nks QksVksu mlftzr djrk gs ( =. / m Q. ijekf.od volfkk Sl dks,d ÅtkZ Lrj esa bl izdkj mùksftr fd;k tkrk gs fd H-ijek.kq dh flfkfrt ÅtkZ. ev gks tkrh gs vc QksVksbsDVªhd IsV ftldk dk;zqu φ =. ev gs dks bl Sl ds mltzu LiSDVªe ds izfr iznf'kzr (eposed fd;k tkrk gs ;g ekfu;s fd lhkh laøe.k lehko gs] mlftzr QksVksbsDVªkuksa dh U;wure Mh-cksXh rjans/;z (Å esa Kkr dhft;s (Hk Q.,d ds'kuh tks okzdkj vuqizlfk lfgr gs o fdukjk. mm lfgr gs dks,d C t esa Mqcks;k ;k gs ds'kuh inkfkz ds lkfk t dk Li'kZ dks.k gs t dk i`" ruko N/m gs ds'kuh esa t dk m/oz muu;u (mm esa Kkr dhft, ;fn ds'kuh dk m/oz ls dks.k gs CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #

36 Time : : Hrs. MX MKS: SEL Name : oll No. : Date : Instructions to Candidates. lkeku; :. Ñi;k iz;sd iz'u ds f, fn,, funsz'kksa dks lko/kkuhiwozd if<+;s rfkk lecfu/kr fo"k;kas esa mùkj&iqflrdk ij iz'u la[;k ds le{k lgh mùkj fpfugr dhft,. mrj ds f,] OM v ls nh tk jgh gs. ifjoh{kdksa }kjk funsz'k fn;s tkus ls iwoz iz'u&i=k iqflrdk dh lh dks ugha [kkssa. vadu ifr: bl iz'ui=k esa iz;sd fo"k; esa fueu izdkj ds iz'u gsa:- [k.m I. cgqfodyih izdkj ds iz'u ftuesa ls dso,d fodyi lgh gs iz;sd lgh mùkj ds f, vad fn;s tk;sas o iz;sd r mùkj ds f, vad?kvk;k tk,k. cgqfodyih izdkj ds iz'u ftuesa ls,d ;k,d ls vf/kd fodyi lgh gsa iz;sd lgh mùkj ds f, vad fn, tk;sas rfkk dksbz _.kked vadu ugha gs. ka'k ij vk/kkfjr cgqfodyih izdkj ds iz'u ftuesa ls dso,d gh fodyi lgh gsa iz;sd lgh mùkj ds f, vad fn, tk;sas rfkk iz;sd r mùkj ds f, vad?kvk;k tk;sk [k.m III..kuked izdkj ds iz'u gsa iz;sd lgh mùkj ds f, vad fn;s tk;sas rfkk r mùkj ds f, dksbz _.kked vadu ugha gs bl [k.m esa mùkj bdkbz iw.kk±d esa nhft, (tsls ls C. OM dh iwfrz :. OM 'khv ds CkWdksa esa viuk uke] vuqøek d] csp] dkslz rfkk ijh{kk dk dsunz Hkjsa rfkk ksksa dks mi;qdr :i ls dkk djsa. ksks dks dkk djus ds f, dso H isful ;k uhs/dks isu (ts isu iz;ks u djsa dk iz;ks djsa. dì;k ksks dks Hkjrs le; [k.mks dks lko/kkuh Space iwozd for ns[k rough sa [vfkkzr work [k.m I (,d p;uked iz'u] dfku izdkj ds iz'u] cgqp;uked iz'u, [k.m II (LrEHk lqesu izdkj ds iz'u, [k.m-iii (iw.kkzd mùkj izdkj ds iz'u½] Section I Section-II Section-III For eample if onl '' choice is correct then, the correct method for filling the bubbles is C D E For eample if onl ' & C' choices are correct then, the correct method for filling the bublles is C D E the wrong method for filling the bubble are The answer of the questions in wrong or an other manner will be treated as wrong. For eample if Correct match for ( is P; for ( is, S; for (C is Q; for (D is P, Q, S then the correct method for filling the bubbles is P Q S T C D Ensure that all columns are filled. nswers, having blank column will be treated as incorrect. Insert leading zeros (s '' should be filled as '' should be filled as '' should be filled as CEE POINT, CP Tower, oad No., IPI, Kota (aj., Ph: -, Fa ( info@careerpointgroup.com; Website : CEE POINT, CP Tower, IPI, oad No., Kota (aj., Ph: - Page #