JEE Advanced 2014 Question Paper Solutions - Paper 2

Part I : Physics Section - 1 : (Only One option correct Type) multiplee choice choice question questionss. Each This This secti section on conta contains ins 10 multipl Each ques questio tion n has has four four choi choice ce (A), (A), (B), (B), (C) (C) and and ONLY ONE optio (D) (D) out out of whic which h ONLY option n is corre correct. ct.

Q.1

A tenn tennis is ball ball is drop droppe ped d on a hori horizo zont ntal al smoo smooth th surf surfac ace. e. It boun bounce cess back back to its its orig origin inal al posi positi tion on afte afterr hittin hitting g the the surfa surface ce.. The The force forceon on the the ball ball durin during g theco the colli llisi sion on ispr is prop oport ortion ional al to thele the leng ngth thof ofco comp mpre resi sion on of  theba the ball. ll. Which Which one one of the the follow followin ing g sketch sketches es desc describ ribes es theva the varia riatio tion n of its kinet kinetic ic ener energyK gyK with with time time t most most appro appropria priately tely.. Thefig The figure uress are only only illustra illustrative tiveand andnot not thesca the scale. le.

K

K (A)

(B) t

t

K

K

(C)

(D) t

t

Ans.

[B]

Q.2

A wire wire,, whic which h pass passes es thro throug ugh h the the hole holein in a smal smalll bead bead,, is bent bent in the the form form ofqu of quar arte terr of a circ circle le.. The The wire wire is fixe fixed d vert vertic ical allyon lyon grou ground ndas assh show own n in the the figu figure re.. The The bead beadis is rele releas ased edfr from omne near arth thee top top ofth of thee wire wirean and d it slid slides es alon along g the the wire wire with withou outt fric frictio tion.As n.As the the bead bead move movess fromA fromA to B, the the forc forcee it appl applie iess on the the wire wire is A

90°

Ans.

B

(A) always always radially radially outwards outwards (B) always alwaysradia radially lly inwards inwards (C) radially radiallyoutw outward ardss initially initiallyand andradi radially allyinwa inwards rds later later (D) radiallyinward radiallyinwardss initially initiallyand andrad radiallyoutwar iallyoutwards ds later later [D]

[2]

Q.3

Duri During ng an expe experi rime ment nt with with a metre metre brid bridg ge, the the galv galvan anom omet eter er show showss a null null poin pointt when when the the jock jockey ey is press pressed ed at 40.0 40.0 cm usin using g a stan standa dard rd resis resista tanc ncee of 90 , as show shown n in the the figu figure re.. The The leas leastt coun countt of the the scal scalee used used in the the metr metree brid bridge geis is 1 mm. mm. The The unkn unknow own n resi resist stan ance ce is

R

90

40.0cm Ans.

Q.4 Q.4

(A) 60 ± 0.15  [C]

(B) 135 ± 0.56

(C) 60 ± 0.25

(D) 135 ± 0.23

Char Charge gess Q, 2Q and and 4Q are are unif unifor orml mly y dist distri ribu bute ted d in thre threee diel dielec ectr tric ic soli solid d sphe sphere ress 1, 2 and and 3 of radi radiii R/2, R/2, R and and 2R resp respec ecti tive vely ly,, assh as show own n in figu figure re.. Ifma If mag gnitud nitudes esof of the the elec electri tricc fiel fields ds at poin pointt P at a dist distan ance ce R from rom the the centre tre of spheres res 1, 2 and 3 are E1, E2 and and E3 respectively respectively,, then

P

P

P R

R

R

Q

4Q

2Q R/2

2R Sphere 1

Ans.

Q.5 Q.5

(A) E1 > E 2 > E 3 [C]

Sphere 2

Sphere 3

(B) E3 > E 1 > E 2

(C) E2 > E 1 > E 3

(D) E3 > E 2 > E 1

A point oint sourc ourcee S is plac placedat edat the the botto ottom m of a tra transp nsparen arentt bloc lock of heig heigh ht 10 mm andrefra ndrefract ctiv ivee inde index x 2.72 2.72.. It is imme immers rsed ed in a lowe lowerr refr refrac acti tive ve inde index x liqu liquid id as show shown n in the the figu figure re.. It is foun found d that that the the ligh lightt emer emergi ging ng from from the the bloc block k to the the liqui liquid d form formss a circ circulabrig ulabright ht spot spot of diam diamet eter er1 11.54 1.54 mm on the the top top of the bloc block. k. The The refr refrac activ tivee inde index x of the the liqui liquid d is Liquid

Block  S Ans.

(A) 1.21 [C]

(B) 1.30

(C) 1.36

(D) 1.42

[3]

Q.6

Ans.

Q.7

Ans.

Para Parall llel elra ray ys ofli of ligh ghtt ofin of inte tens nsit ity y I = 912Wm 12Wm–2 areincide areincident nt on a sphe spheric rical al blac black k body bodyke kept pt in surro surroun undin dings gs –8 –2 –4 of temperatur temperaturee 300 K. Take StefanStefan-Boltz Boltzmann mann constan constantt  =5.7×10 Wm K and and assu assume me that that the energyexcha energyexchangewith ngewith thesur the surrou roundin ndings gs is only only throug through h radiati radiation. on.The Thefin final al steadystate steadystate temper temperatu ature re of the blac black k bodyis bodyis clos closee to (A) 330 K (B) 660 K (C) 990 K (D) 1550 K [A] A meta metall surf surfac acee is illum illumina inate ted d bylight bylight of two two diffe differe rent nt wave wavele leng ngth thss 248 248 nm and and 310 310 nm. nm. The The maxim maximum um speed speedss of the photoel photoelect ectron ronss corres correspon ponding dingto to these these wavele waveleng ngths ths areu are u 1 and u2, respec respective tively ly.. If the ratio ratio u1 : u2 = 2 : 1 and hc = 1240 240 eV nm, nm, the the work work func functi tio on of the the meta etal is near nearly ly (A) 3. 3.7 eV (B) 3. 3.2 eV (C) 2.8 eV (D) 2. 2.5 eV [A]

Ans.

If    Cu  is the the wave wavele leng ngth th ofK of K X-ray X-raylin linee of coppe copperr (atom (atomic ic numbe numberr 29) 29) and and Mo is the the wave wavele leng ngth th of the the K X-ray X-raylin linee of moly molybd bden enum um (atom (atomic ic numb number er 42), 42), then then the ratio ratio Cu / Mo is clos closee to (A) 1.99 (B) 2.14 (C) 0.50 (D) 0.48 [B]

Q.9 Q.9

A planet of radius R =

Q.8

depth

Ans.

Q.10 Q.10

1

×(ra ×(radi dius us of Earth Earth)) has has thesa the same me mass massde dens nsityas ityas Earth Earth.. Scie Scient ntis ists ts dig dig a well well of 

on it and and lowe lowerr a wire wire of the the same same leng length th and and of line linear ar mass mass dens densit ity y 10–3 kgm–1 into into it. it. If the the

5 wire wire is not not touc touchi hing ng any anywher where, e, the the forc forcee appl applie ied d at the the top top of the the wire wire bya pers person on hold holdin ing g it in plac placee is 6 –2 (tak (takee the the radi radius us of Eart Earth h = 6 × 10 m and and the the acce accele lera rati tion on due due to grav gravit ity y on Eart Earth h is 10 ms ) (A) 96 N (B) 108 N (C) 120 N (D) 150 N [B]

A glas glasss capi capill llar ary y tube tube is of the the shap shapee of trun trunca cate ted d cone cone with with an apex apex angl anglee a so that that its its two two ends ends have have cros crosss sect sectio ions nsof of diff differ eren entt radi radii. i. When Whendi dipp pped edin in wate waterr verti vertica call lly y, wate waterr rise risess in it to a heig height ht h,wh h, wher eree the the radi radius us of its its cros crosss sect sectio ion n is b. If the the surf surfac acee tens tensio ion n of wate waterr is S, its its dens densit ity y is , and and its cont contac actt angl anglee with with glas glasss is , the the valu valuee of h will will be(g be (g is the the acce accele lera rati tion on due due to grav gravit ity y) (A)

(B)

(C)

(D) Ans.

R

1

2s b g 2s b g 2s b g 2s b g

cos(   ) cos(   ) cos(    / 2) cos(    / 2)

[D]

[4]

SECTION -2 : Comprehension Type (Only One Option Correct) This section contains 3 paragraphs, each describing theory, experiments, data etc. Six questions relate to the three paragraphs with two questions on each paragraph. Each ques qu esti tion on ha has s on only ly on one e corr correc ectt an answ swer er am amon ong g the the four four giv given op opti tion ons s (A), (A), (B), (B), (C) (C) an and d (D). (D). Para Paragr grap aph h For For Qu Ques esti tion onss 11 & 12 In thefig the figur uree a cont contain ainer er is show shown n to have have a mova movabl blee (witho (without ut frict frictio ion) n) pisto piston n on top. top. The The conta contain iner er and and the piston piston are all made made of perfe perfectl ctly y insula insulating ting materi material al allowi allowing ng no heat heat transf transfer er betwee between n outsid outsidee and insi inside de the the cont contai aine nerr. The The cont contai aine nerr is divi divide ded d into into two two comp compar artme tment ntss by a rigi rigid d part partit itio ion n made made of a therma thermally llyco cond nduc uctin ting g mater material ialtha thatt allow allowss slow slow transf transfer er of heat. heat.Th Thee lower lower comp compart artmen mentt of theco the conta ntaine inerr is fill filled ed with with 2 mole moless of an idea ideall mona monato tomi micc gas gas at 700 700 K and and the the uppe upperr comp compar artm tmeent is fill filled ed with with 2 mole moless of an idea ideall diat diatom omic ic gas gas at 400 400 K. The The heat heat capa capaci citi ties es per per mole mole of an idea ideall mona monato tomi micc gas are are

CV =

Q.11 Q.11

Ans.

Q.12 Q.12

Ans.

3 2

R, CP =

5 2

R, and and thos thosee for for an idea ideall diat diatom omic ic gas gas are are CV =

5 2

R, CP =

7 2

R.

Cons Consid ider erth thee part partit itio ion n to berigid berigidly lyfi fixe xed d soth so that atit it does doesno nott move move.. When Wheneq equi uili libr briu ium m isac is achi hiev eved ed,, the the fina finall tempe tempera ratur turee of the the gase gasess will will be (A) 550 K (8) 525 K (C) 513 K (D) 490 K [D] Now Now cons consid ider er the the parti partitio tion n to be free free to mov movee with withou outt fric frictio tion n so that that the the pres pressu sure re of gase gasess in bot both h comp compar artm tmen ents tsis is thesame. thesame. Then Thento tota tall work workdo done nebythe bythe gase gasess till till thetime theyachi theyachiev evee equil equilibr ibrium iumwil willl be (A) 250 R (8) 200 R (C) 100 R (.D) –100 R [D] Para Paragr grap aph h For For Qu Ques esti tion onss 13 & 14 A spra spray y gun gun is show shown n in the the figu figure re wher wheree a pist piston onpu push shes esai airr out out of a nozz nozzle le.. A thin thin tube tubeof of unifo uniform rm cros crosss sect section ionis is conn connec ecte ted d to the the nozz nozzle le.. Theot The othe herr end end of ,the ,the tube tube is in a smal smalll liqui liquid d conta containe inerr. As the the pisto piston n pushe pushess airthr air throu ough gh the the nozzl nozzle, e, theliq the liqui uid d from from theco the conta ntaine inerr rises rises into into theno the nozzl zzlee and and is spray sprayed ed out. out. For For the the spra spray y gun gun show shown, n, the the radi radiii of the the pisto piston n and and the the nozz nozzle le are are 20mm 20 mm and and 1 mm resp respec ecti tive vely ly.. The The uppe upperr end end of the the cont contai aine nerr is open open to the the atmo atmosp sphe here re..

[5]

Q.13 Q.13 Ans.

Q.14 Q.14

If the the piston ton is pus pushed at a speed of 5 mms–1, the the air comes mes out out ofthe nozzl ozzlee with ith a spee peed of  –1 –1 –1 –1 (A) (A) 0.1 ms (8) (8) 1 ms ms (C) 2 ms (D) 8 ms [C] If the the density ity of air is a and and that that of the the liqui liquid d , then thenfo forr a given iven pist piston on spee speed d the the rate rate (vol (volum umee per per unit unit time) time) at whic which h the the liquid liquidis is spra spray yed will will be prop propor ortio tiona nall to (A)

Ans.

a 

(B)

a 

(C)

 a

(D) 

[A] Para Paragr grap aph h For For Qu Ques esti tion onss 15 & 16 The The figu figure re show showss a circ circul ular ar loop loop of radi radius us a with with two two long long para parall llel el wire wiress (num (numbe bere red d 1 and and 2) all all in the the plan planee ofth of thee pape paperr. The. The. dist distan ance ceof ofea each chwi wire refr from om the the cent centre reof of the the loop loopis is d.The loop loopan and d the the wire wiress are are carry carrying ing the same same curr curren entt I. The The curre current nt in the loop loop is in the coun counte terc rcloc lockw kwise ise direc directio tion n if seen seen from from above.

Q Wire 1

d

d a

Wire 2

P

Q.15 Q.15

Ans.

Q.16

R

Whe When d a but but wire wiress are not touc touchi hingth ngthee loop loop,, it is foun found d tha that the the net net magn magneetic tic fie field on the the axis xis ofthe loop loop is zero zero at a heig height ht h abov abovee the the loop loop.. In tha that case case (A) (A) curr curren entt in wire wire 1 and and wire wire 2 is the the dire direct ctio ion n PO and and RS, RS, resp respec ecti tive velyand lyand h    a (B) (B) curr curren entt in wire wire 1 and and wire wire 2 is the the dire direct ctio ion n PO and and SR, SR, resp respec ecti tive velyand lyand h    a (C) (C) curr curren entt in wire wire 1 and and wire wire 2 is the the dire direct ctio ion n PO and and SR, SR, resp respec ecti tive vely ly and and h    1.2a (D) (D) curr curren entt in wire wire 1 and and wire wire 2 is the the dire direct ctio ion n PO and and RS, RS, resp respec ecti tive vely ly and and h    1.2a [C] Cons Consid ider er d >> >>a, a, and and the the loop loop is rota rotate ted d abou aboutt its its diam diamet eter er para parall llel el to the the wire wiress by30° from from the the posi positi tion on show shown n in the the figu figure re.. Ifth If thee curr curren ents ts in thewires thewires are are in the the oppo opposi site te direc directio tions ns,, the the torq torque ue on the the loop loop at its new new posi positi tion on will will be (ass (assum umee that that the the net net fiel field d due due to the the wire wiress is cons consta tant nt over over the the loop loop)) (A)

Ans.

S

 0 I2a 2 d

(B)

 0 I2a 2 2d

2 2

(C)

3 0 I a

2 2

(D)

3 0 I a 2d

[A]

[6]

Section - 3 : Matching List Type (Only One Option Correct) questions,  each having two matching lists. Choices for the This section contains four contains  four questions, each corr correc ectt comb combin inat atio ion n of elem elemen ents ts from from List List-I -I an and d List List-I -III are are give given n as op opti tion ons s (A), (A), (B), (B), (C) (C) an and d (D), (D), ou outt of wh whic ich h on one e is corr correc ect. t. Q.17 Q.17

Four Four char charg ges Q1, Q2, Q3 and Q4 of same ame mag magnitu nitude de are are fixe fixed d alon along g the the x axis axis at x = –2a, –2a, –a, –a, +a and and +2a, +2a, resp respec ectiv tivel ely y. A posi positiv tivee char charge ge q is place placed d on the the posi positiv tivee y axis axis at a dista distanc ncee b > 0. Four Four optio options ns of the the sig signs of thes thesee char charg ges are are give given n in Listist-I. I. The The dire direct ctio ion n of the the forc forces es on the the char charge ge q is give given n in List-I List-II. I. Match Match ListList-II with ListList-II II and and selec selectt the correc correctt answe answerr using using the code code given given below below the lists. lists. q(0, b)

Q1 (–2a, 0)

Ans.

Q2 (–a, 0)

List-I P. Q1, Q2, Q3, Q4 all positive Q. Q1, Q2 positive positive;; Q3, Q4 negative R.   Q1, Q1, Q4 posi positi tive ve;; Q2, Q3 negative S.   Q1, Q1, Q3 posi positi tive ve;; Q2, Q4 negative Code Code : (A) P-3, Q-1, R-4, S-2 (C) P-3, Q-1, R-2, S-4 [A]

Q3 (+a, 0)

1. 2. 3. 4.

Q4 (+2a, 0)

List-II +x –x +y –y

(B) P-4, Q-2, R-3, S-1 (D) P-4, Q-2, R-1, S-3

[7]

Q.18

Ans.

Four Four comb combin inat atio ions ns of two two thin thin lens lenses es are are give given n in List List-I -I.. The The radi radius usof of curv curvat atur uree of all all curv curved ed surf surfac aces esis is r and and the the refr refrac activ tivee inde index x ofal of alll the the lens lenses es is 1.5. 1.5. Matc Match h lens lensco comb mbin inat atio ions nsin in Listist-II with with thei theirr foca focall leng length th in List-I ist-III andse and sele lect ct the corre correct ct answ answer er using usingthe the code code give given n below below thelis the lists. ts. List-I List-II

P.

1.

2r

Q.

2.

r/2

R.

3.

–r

S.

4.

r

Code Code : (A) P-1, Q-2, R-3, S-4 (C) P-4, Q-1, R-2, S-3 [B]

(B) P-2, Q-4, R-3, S-1 (D) P-2, Q-1, R-3, S-4

[8]

Q.19 Q.19

A block of mass m1 = 1 kgano kganothe ther mas mass m2 = 2kg, 2kg, are are plac placed ed toget togethe herr (see (see figur figure) e) on aninc an inclin lined ed plane plane with with angle angleof of inclin inclinati ation on . Various arious values values of  are are given given in ListList-I. I.The Theco coef effic ficien ientt of fricti friction onbe betwe tween en the block block m1 and and thepl the plan anee is alwa alway ys zero. zero.Th Thee coef coeffic ficie ient nt of stat static ic and and dyna dynamic mic frict friction ionbe betwe tween en theblo the block  ck  m2 and and the the plan planee are are equa equall to µ = 0.3. 0.3. InLi In List st-I -III expr expres essi sion onss for for thefrictio thefriction n on bloc block k m2 aregi are given ven.. Match Match the corre correct ct expre express ssion ion of the the fricti friction on in ListList-II II with with the the angl angles es give given n in ListList-I, I, and and choo choose se the corre correct ct optio option. n. The The acce accele lerat ration ion due to grav gravity ity is deno denoted ted by g. [Usef [Useful ul infor informa matio tion n : tan tan (5.5° (5.5°)) 0.1; 0.1; tan tan (11. (11.5° 5°))    0.2 ; tan tan (16. (16.5° 5°))    0.3]

m1 m2



List-I  = 5°  = 10° 10°  = 15° 15° 20°  = 20°

Ans.

Q.20 Q.20

Ans.

P. Q. R. S. Code Code : (A) P-1, Q-1, R-1, S-3 (C) P-2, Q-2, R-2, S-4 [D]

1. 2. 3. 4.

List-II m2gsin  (m1 + m2)g sin sin  µm 2gcos  µ (m1 + m2)g cos cos 

(B) P-2, Q-2, R-2, S-3 (D) P-2, Q-2, R-3, S-3

Apers Apersonin onin a lift lift is hold holdin ing g a wate waterr jar jar, whic which h has has a sma small hole hole at the the lowe lowerr end of its its side ide. When When the the lift lift is at res rest, the the wate waterr jet jet comi comingout ngout of the the hole hole hits hits the the flo floor of the the lift lift at a dist distaance nce d of 1.2 m fro from the the pers person on.. Inth In thee foll follow owin ing, g, stat statee of the the lift lift's 's moti motion on is given iven in List List-1 -1 and and the the dist distan ance cewh wher eree the the wate waterr jet jet hits hits the the floo floorr of the the lift lift is give given n in List List-I -II.Matc I.Match h the the stat statem emen ents ts from fromLi List st-I -Iwi with th thos thosee inL in Listist-IIand IIand sele select ct the corr correc ectt answ answer er using usingthe the code code give given n below below the lists. lists. List-I List-II P.   Lift 1. Lift is accele acceleratio ration n vertica vertically llyup. up. d = 1.2 m Q.   Lift is accel 2. accelera erating tingver vertica tically llydow down n d > 1.2 m with with an acce accele lera ratio tion n less less than than the the gravitational acceleration R.   Lift 3. Liftis ismov movingverti ingvertica cally llyup upwit with h d < 1.2 m constant constant speed. speed. S.   Liftis 4.   No wate Lift isfal falling lingfree freely ly.. ater lea leaks out out of the the jar jar Code Code : (A) P-2, Q-3, R-2, S-4 (B) P-2, Q-3, R-1, S-4 (C) P-1, Q-1, R-1, S-4 (D) P-2, Q-3, R-1, S-1 [C]

[9]

Part II : Chemistry Section - 1 : (Only One option correct Type) multiplee choice choice question questionss. Each This This secti section on conta contains ins 10 multipl Each ques questio tion n has has four four choi choice ce (A), (A), (B), (B), (C) (C) and and ONLY ONE optio (D) (D) out out of whic which h ONLY option n is corre correct. ct.

Q.21

The The acid acidic ic hydr hydrol oly ysis sis of ethe etherr (X) (X) show shown n belo below w is fast fastes estt when when

OR

acid       

OH + OH  + ROH

[X]

Ans.

Q.22

(A) (A) one one phen pheny yl grou group p is repl replac aced ed bya meth methy yl grou group. p. (B) (B) one one phen phenyl yl grou group p is repla replace ced d bya by a para para-me -metho thoxy xyph phen enyl yl grou group. p. (C) two pheny phenyll group groupss are are repla replace ced d bytwo by two parapara-me metho thoxy xyphe pheny nyll group groups. s. (D) (D) no stru struct ctur ural al chan change ge is made made to X. [C] Iso Isome mers rs of hexa hexane ne,, base based d on their their bran branci cing ng,, can can be divid divided ed into into thre threee distin distinct ct class classes es as show shown n in the figure. and

I

and

II

Ans.

The The corre correct ct orde orderr of their their boili boiling ngpoi point nt is (A) I > II > III (B) III > II > I [B]

Q.23

The The majo majorr prod produc uctt in the the follo followi wing ngre reac actio tion n is

O

(C) II > III > I

CH3

2. aq. acid

OH

O

(C) Ans.

O

CH3

CH2

(D) III > I > II

1. CH 3MgBr , dry ether , 0 C                    

Cl

(A) H 3C

III

CH3 CH3

(B) H C 2

(D)

CH3 O

CH3

[D] [10]

Q.24

Ans.

Q.25 Ans.

Q.26

Hydr Hydrog ogen en pero peroxi xide de in its reac reactio tion n with with KIO KIO4 and and NH2OH respec respectiv tivel ely y, is actin acting g as a (A)redu A)reduccing ing agent, oxid xidisi isingagen ngagentt (B) (B) red reducin ucing g agent, nt, reduc ducing ing agent (C) (C) oxid oxidis isin ing g agen agent, t,ox oxid idis isin ing g agent (D) (D) oxid oxidis isin ing g age agent, nt, redu reduccing ing agen agentt [A] The The prod produc uctt form formed ed in the the reac reacti tion on of SOCl SOCl2 with white white phosph phosphorou orouss is (A) (A) PCl PCl3   (B) (B) SO2Cl2   (C) (C) SCl SCl2   (D) (D) POCl POCl3 [A] Unde Underr ambi ambien entt cond conditi ition ons, s,th thee tota totall numb number er of gase gasess rele releas ased edas as prod produc ucts ts in thefinal thefinal step stepof of the the reac reacti tion on scheme schemesho shown wn below below is

XeF6

Complete Hydrolysis

P

+

other product

OH¯¯ / H2O OH

Q slow disproporti disproportionatio onation n in OH¯ /H 2O

Products Ans.

Q.27

Ans.

Q.28 Q.28

Ans.

Q.29 Q.29

Ans.

Q.30 Ans.

(A) 0 [C]

(B) 1

(C ) 2

(D) 3

For For the the iden identi tifi fica catio tion n of -naph -naphtho tholl using using dye dye test, test, it is nece necess ssar ary y to use use (A) dichloro dichlorometh methane anesolu solution tion of -na -naphth phthol ol (B) (B) acid acidic icso solu luti tion on of -naphthol (C) neutr neutral al soluti solution on of -naphthol (D) alkalineso esolutionof -naphthol [D] For For the the elem elemen enta tary ry reac reactio tion n M  N, the the rate rate of disa disapp ppea eara ranc ncee of M incr increa ease sess by a fact factor or of 8 upon upon doub doublin ling g the the conc concen entra tratio tion n of M. The The orde orderr of the the reac reactio tion n with with resp respec ectt to M is (A) 4 (B) 3 (C ) 2 (D) 1 [B] For For the the proc proces esss H2O ( l)   H2O (g) at T = 100° 100°C C and and 1 atmo atmosp sphe here re pres pressu surr, the the corr correc ectt choi choice ce is (A) Ssystem  > 0 and  Ssurroundings > 0 (B)  Ssystem  > 0 and  Ssurroundings < 0 (C) Ssystem  < 0 and  Ssurroundings > 0 (D) Ssystem  < 0 and  Ssurroundings < 0 [B] Assuming Assuming2s2s-2p 2p mixing mixingin in NOT opera operativ tive, e, thepa the param ramag agne netic tic specie speciess among amongthe thefol follow lowing ingis is (A) (A) Be2   (B) (B) B2 (C) C2 (D) N2 [C]

[11]

Section - 2 :Comprehension Type (Only One Option Correct) paragraphss each questions relate This section section contain containss 3 paragraph each describ describing ing theory theory,, experim experiment ent,, data data etc. etc. Six questions only one one corr correct ectans answe werr to three three parag paragrap raphs hs with two questio questions ns on each each parag paragrap raph. h. Each Each questio question n has only amon among g the the four four choi choice cess (A), (A), (B), (B), (C) (C) and and (D). (D). Para Paragr grap aph h For For Qu Ques esti tion onss 31 to 32 Scheme Schemess 1 and and 2 desc describ ribee seque sequenti ntial al transf transform ormati ation on of of alkyn alkynes es M and N. Consid Consider er only only the major major prod produc ucts ts form formed ed in each each step step for for both both the the sche scheme mes. s.

Scheme–1

Scheme–2

Q.31 Q.31

Theprod heproduc uctt X is (A)

(B)

(C )

(D)

Ans.

[A]

Q.32

The The corr correc ectt stat statem emen entt with with resp respec ectt to prod produc uctt Y is (A) (A) It give givess a posi positiv tivee Tollen ollenss test test and and is funct functio iona nall isome isomerr of X (B) (B) It give givess a posi positi tive veT Tolle ollens ns test test and and is a geom geomet etri rica call isom isomer er of X (C) (C) Itgi It give vesa sa posi positiv tivee iodo iodofo form rm test test and and is func functio tiona nall isome isomerr of X. (D) (D) it give givess a posi positi tive ve iodo iodofo form rm test test and and is a geom geomet etri rica call isom isomer er of X. [C]

Ans.

[12]

Para Paragr grap aph h for Qu Ques esti tion onss 33 to 34 Anaq An aque ueou ouss solut solutio ion n of meta metall ion ion M1 reacts reacts separately separatelywith with reagents reagents Q and and R in exces excesss to give give tetrah tetrahedr edral al andsqu and square arepla planar narcom comple plexes xes,, respec respective tively ly.. An aqueo aqueous us soluti solution on of anoth another er metal metal ion M2 always always forms tetrah tetrahedr edral al compl complexe exess with these these reage reagents nts.. Aqueou Aqueouss solutio solution n of M2 on reacti reaction on with reage reagent nt S gives white white precip precipita itate te which which diss dissolv olves es in exces excesss of S. The The reac reactio tions ns are are summ summari arize zed d in the the sche scheme me give given n belo below w: SCHE SCHEME ME :

Tetrahedral

R Q                M1   excess excess

Square Square planar planar

R

         M2    Tetrahedral     excess  Tetrahedral excess Q

S, stoichiom stoichiometric etric amount amount S

     precipitate White precipitate precipitate   excess precipitate dissolves dissolves Q.33 Q.33

Ans.

Q.34 Q.34 Ans.

M1, M1, Q and and R resp respeective tivelyare lyare 2+ (A) (A) Zn , KCN and HCl (C) Cd2+, KCN and HCl [B]

(B) Ni2+, HCl HCl and and KCN KCN 2+ (D) Co , HCl and KCN

Reagents S is (A) K4[Fe(CN)6] [D]

(C) (C) K2CrO4

(B) Na2HPO4

 

(D)KOH

Para Paragr grap aph h for Qu Ques esti tion onss 35 to 36 X and Y are are two two vola volati tile le liqu liquid idss with with mola molarr weig weight htss of 10 g mol mol–1 and40 g mol–1 respectively. respectively. Two cotto cotton n plugs plugs,, one one soak soaked ed in X and and the the othe otherr soak soaked ed in Y, are are simu simulta ltane neou ousl sly y place placed d at theen the ends ds of a tube tube of length length L = 24 cm, cm, assh as show own n in the the figu figure re.. The The tube tubeis is fill filled edwi with than an iner inertt gas gas at 1 atmo atmosp sphe here re pres pressu sure re and and a temp temper erat atur uree of 300 300 K. Vapou apours rs of X and Y reac reactt to form form a prod produc uctt whic which h is firs firstt obse observ rved ed at a distance d cm from from the the plug plugso soak aked ed in X. Take X and Y to have have equal equal molecul molecular ar diamete diameters rs and assume assume ideal ideal beha behavio viour ur for the inert inert gas gas and and the two vapo vapour urs. s.

Q.35 Ans.

Q.36

Ans.

The The valu valuee of d in cm (sho (shown wn in the the figu figure re), ),as as estim estimat ated ed from from Grah Graham am's 's law law, is (A) 8 (B) 12 (C) 16 (D) 20 [C] The The expe experi rime ment ntal alva valu luee of d is foun found d to besm be smal alle lerr than thanth thee esti estima mate te obta obtain ined edus usin ing g Grah Graham am's 'sla law w. This This is due due to (A) (A) lar larger mean mean free free path path for for X as comp compar ared ed to that that ofY (B) (B) larg larger er mean mean free free path path for for Y as comp compar ared ed to that that of X. (C) (C) incr increa ease sed d coll collis isio ion n requ requen encyof cyof Y with with the the iner inertt gas gas as comp compar ared ed to that that of X with with the the iner inertt gas. gas. (D) (D) incr increa ease sess colli collisi sion on freq freque uenc ncy y of X with with the the iner inertt gas gas as comp compar ared ed to that that ofY with with the the iner inertt gas. as. [D] [13]

Section - 3 : Matching List Type (Only One Option Correct)

Q.37

This This section sectioncon contai tains nsfou fourr questio questions, ns,ea each ch having havingtwo twomat matchin ching g lists. lists. Choice Choicess forthe for thecor correc rectt combina combination tion of elements from List-I and List-II List-II are given as options (A), (B), (C) and (D), out of which one is correct. Diffe Differe rent nt poss possibl iblee therma thermall deco decompo mposit sition ion pathw pathway ayss for perox peroxy yester esterss are are shwo shwon n belwo belwo.. Match Match each each pathw pathway ayfro from m List List I with with an appr approp opria riate te struc structu ture re from from List List IIan II and d selec selectt the the corr correc ectt answ answer er usin using g the the code code give given n below belowthe thelis lists ts.. P –CO2

Q

O O

R

O

–CO2

R + R'O

R + R'O

R + X + carbonyl compound

R'

(Peroxyester)

R

S

RCO RC O2 + R' R'O O

RCO RC O2 + R' R'O O

–CO 2

–CO2

List-I P.

 

R + X' + carbonyl compound

R + R'O

List-II O 1.

Pathwa Pathway yP

O

C6H 5CH2

O

CH3

O Q.   Pathway PathwayQ Q

2.

O

C6H5

O

CH3

O R.

3.

  Pathway PathwayR R

O

C6H5CH2 O

S.

 

4.

Pathwa Pathway yS

Codes:

Ans.

(A) (B) (C) (D) [A]

P 1 2 4 3

Q 3 4 1 2

R 4 3 2 1

C6H5

O

O

O

CH3 CH3 CH2C6H5

CH3 CH3 C6H5

S 2 1 3 4

[14]

Q.38

(P, Q, R,S) given Matc Match h the the four four star startin ting g mate materia rials ls (P, given in List List I with the corre correspo spondi nding ng reacti reaction on scheme schemess (I, (I, II, II, III, III, IV) IV) prov provid ided ed in List List II and and sele select ct the the corr correc ectt answ answer er using usingth thee code code give given n below belowthe thelis lists ts.. List- I List-II H H P. 1. Scheme Scheme I 

(i ) KMnO 4 ,H O ,heat ( ii ) H  ,H 2O (iii ) SOCl2 ( iv ) NH3

?                         C7 H 6 N 2 O3

OH Q.

2. Scheme II

OH (i ) Sn / HCl ( ii ) CH 3COCl (iii ) conc. H 2SO 4 (iv ) HNO ( v ) dil.H SO , heat ( vi ) HO 

3 2 4 ?                                C 6 H 6 N 2O 2

NO2 R.

3. Scheme III (i ) red hot iron ,873 K ( ii ) fu min g HNO3 ,H 2SO 4 ,heat (iii ) H 2S. NH3 ( iv) NaNO2 ,H 2SO 4 ( v ) hydrolysis

?                                   C6 H 5 NO3

NO2 S.

4. Scheme IV

CH3 (i ) conc.H 2SO 4 ,60C (ii ) conc.HNO3 ,conc.H 2SO 4 (iii ) dil.H 2SO 4 ,heat

?                                 C6 H 5 NO4 Code:

Ans.

(A) (B) (C) (D) [C]

P 1 3 3 4

Q 4 1 4 1

R 2 4 2 3

S 3 2 1 2

[15]

Q.39

Ans.

Q.40 Q.40

Match Match each each coordin coordinat ation ion compo compound undin in ListList-II with with an approp appropria riate te pair pair of chara characte cterist ristics icsfro from m List-I List-III and sele select ct the corre correct ct answ answer er usin using g theco the code de give given n below belowthe thelis lists. ts. {en {en = H2NCH2CH2NH2; atom atomic ic numb number erss : Ti = 22; 22; Cr = 24; 24; Co = 27; 27; Pt = 78} 78} List-I List-II P.   [Cr(NH3)4Cl2]Cl 1. Paramagne Paramagnetic tic andexhibi and exhibits ts ionisation ionisation isomerism. isomerism. Q.   [Ti(H2O)5Cl](NO3)2 2. Diamag Diamagnet netic ic andexh and exhibit ibitss cis-tran cis-transs isomer isomerism. ism. R.   [Pt(en)(NH3)Cl]NO3 3. Paramag Paramagnetic neticand andexh exhibits ibits cis-tran cis-transs isomeris isomerism. m. S.   [Co(NH3)4(NO3)2]NO3 4.   Diamagn Diamagnetic eticand andexhib exhibits its ionisation ionisationisome isomerism. rism. Code: P Q R S (A) 4 2 3 1 (B) 3 1 4 2 (C) 2 1 3 4 (D) 1 3 4 2 [B] Matc Match h the the orbi orbita tall over overla lap p figu figure ress show shown n in Listist-II with with the the desc descri ript ptio ion n give given n in List List-I -III and and sele selecct the the corr correc ectt answ answer er using using theco the code de given given below below thelis the lists. ts. List-I List-II P.

1.

p – d  antibonding

Q.

2.

d – d  bonding

R.

3.

p – d  bonding

S.

4.

d – d  antibonding

Code:

Ans.

(A) (B) (C) (D) [C]

P 2 4 2 4

Q 1 3 3 1

R 3 1 1 3

S 4 2 4 2

[16]

Part III : Mathematics Section - 1 : (Only One Option Correct Type) multiple le choice choice questi questions ons. Each This section section contains contains 10 multip Each ques questio tion n has has four four choi choice cess (A), (A), (B), (B), (C) (C) and and (D) (D) out out of whic which h ONL ONLY ONE ONE optio option n is corr correc ect. t.

Q.41

The function function y = f (x) is the solution solution of differe differential ntial equation equation

dy dx



xy x

2

1



x 4  2x 1 x

2

in (–1, (–1, 1)

sati satisf sfy ying ing f (0) (0) = 0. Then Then (A) Ans.

 3



3

(B)

2

 3



3 4



(C)

6



3

(D)

4

 6



3 2

[B]  2

Q.42

The The follo followi wing ngin inte tegr gral al

 (2 cosec  x)

17

dx iseq is equa uall to

4



log 1 2

(A)



 2(e

u

e

u



16

) du

(B)

0



(C)

 (e

 e  u )17 du

0



log 1 2 u

 (e



log 1 2 u

e

u



log 1 2 17

) du

0

(D)



 2( e

u

 e  u )16 du

0

Ans.

[A]

Q.43 Q.43 Ans.

Coef Coeffi fici cien entt of x11 in the the expan xpansi sio on of (1 + x 2)4 ( 1 + x3)7 ( 1 + x4)12 is (A) 1051 (B) 1106 (C) 1113 (D) 1120 [C]

Q.44 Q.44

Let f : [0, 2]  R be a func functi tion on whic which h is conti ontinu nuou ouss on [0, [0, 2] and and is diff differ eren enti tiab able le (0, (0, 2) with with f (0) (0) = 1. x2

Let F (x) (x) =

 f   t dt

for for x  [0, [0, 2]. 2]. If F'(x) '(x) = f ' (x) (x) for for all x  (0, 2), 2), then then F (2) equals equals

0

Ans.

Q.45

Ans.

(A) e2 – 1 [B]

(B) e4 – 1

(C ) e – 1

(D) e4

The The comm common on tang tangen ents ts to the the circ circle le x 2 + y2 = 2 and the the parab arabol olaa y2 = 8x touc touch h the the circ circle le at the the poin points ts P, Q and and the the para parabo bola la at the the poin points ts R, S. Then Then the the area area of the the quad quadri rila late tera rall PQRS PQRS is (A) 3 (B) 6 (C ) 9 (D) 15 [D]

[17]

Q.46

Ans.

Q.47 Q.47

For x  (0, ) the the equa equati tion on sin sin x + 2 sin sin 2x – sin sin 3x = 3 has has (A)in )infinitelyma ymanyso ysolutions (B) threesol esolutions (C) one solution (D) no solution [D] In a tria triang ngle le the the sum sum of two two side sidess is x and and the the prod produc uctt of the the same same two two sid sides is y. If x 2 – c2 = y, wher wheree c is the the thir third d side side of the the tria triang ngle le,, then then the the ratio ratio of the the in-r in-rad adiu iuss to the the circ circum um-r -rad adiu iuss of the the tria triang ngle le is (A)

3y 2 x ( x  c)

(B)

3y 2c ( x  c )

(C)

3y 4 x ( x  c)

(D)

3y 4c ( x  c )

Ans.

[B]

Q.48 Q.48

Six Six cards rds andsix enve envelo lope pess are are numb numbeered red 1, 2, 3, 4,5, 6 and and cards ards are are to beplac beplacedin enve nvelope lopess so tha that each each enve envelop lopee cont contai ains ns exac exactlyone tlyone card card and and no card card is place placed d in the the enve envelo lope pe bear bearingthe ingthe same same numb number er and and more moreov over er the the card card numb number ered ed 1 is alwa alway ys plac placed ed in enve envelop lopee numb number ered ed 2. Then Then the the numb number er of way ways it can can be done done is (A) 264 (B) 265 (C) 53 (D) 67 [C]

Ans.

Q.49

Thre Threee boy boys and and two two girl girlss stan stand d in a queu queue. e.Th Thee prob probab abili ility ty,, that that the the numb number er of boy boys ahea ahead d of ever every y girl girl is at leas leastt one one more more than than the the numb numbeer of girls irls ahea ahead d of her her, is (A)

1 2

(B)

1

(C)

3

2 3

(D)

3 4

Ans.

[A]

Q.50

The The quad quadra ratic tic equa equatio tion n p(x) p(x) = 0 with with real real coef coeffic ficie ients nts has has pure purely ly imag imagin inar ary y roots roots.. Then Then the the equa equatio tion n

Ans.

pp( x )   0 has (A) onlypu ypurelyim yimaginaryro yroots (C) (C) two two real real and and two two pure purelyimag lyimagin inar ary y root rootss [D]

(B) all real roots (D) (D) neit neithe herr realnor realnor pure purelyima lyimag ginar inary y root rootss

Section - 2 : Comprehension Type (Only One Option Correct) This This secti section on contai contains ns 3 parag paragra raph phs, s, each each descr describi ibing ngthe theory ory,, experi experimen ments, ts, data data etc. etc. Six ques questio tions ns relat relatee to the the thre threee para paragr grap aphs hs with with two ques questio tions ns on each each para paragr grap aph. h. Each Each ques questio tion n has has only only one one corre correct ct answ answer er amon among g the the four four give given n opti option onss (A), (A), (B), (B), (C) (C) and and (D). (D). Para Paragr grap aph h For For Ques Questi tion ons s 51 and and 52 2 2 Let a, r, s, t be nonz nonzer ero o real real numb number ers. s. Let P(at P(at ,2at ,2at), ), Q, R(ar R(ar ,2ar ,2ar)) and and S(as S(as2,2as ,2as)) be dist distinc inctt poin points ts on 2 the para parabo bola la y = 4ax. 4ax. Supp Suppos osee that that PQ is the the foca focall chor chord d and and line liness QR and and PK are are para parall llel el,, wher wheree K is the the poin pointt (2a, (2a, 0). 0).

Q.51 Q.51

The value lue of r is (A)

Ans.

1 t

(B)

t2 1 t

(C )

1 t

(D)

t2 1 t

[D] [18]

Q.52 Q.52

If st = 1, then then the the tang tangen entt at P and the the norma ormall at S to the the para parab bola ola mee meet at a poin pointt whoseord hoseordin inaate is (A)

Ans.

( t 2  1) 2 2t

(B)

3

a ( t 2  1) 2 2t

(C)

3

a ( t 2  1) 2 t

3

(D)

a ( t 2  2) 2 t

3

[B] Para Paragr grap aph h For For Ques Questi tion ons s 53 and and 54 1 h

Give Given n that thatfo forr each eachaa  (0,1), Lim

h  0

exists ts.. Let Let this this limi limitt beg be g(a). (a). Inaddit Inadditio ion, n,it it is give given n  t  (1  t )  dt exis a

a 1

h

that that thefun the functio ction n g(a) g(a) is differ different entiab iable le on (0,1). (0,1).

Q.53 Q.53

 1  is   2 

Thevalu hevaluee of  g  (A) 

(B) 2

Ans.

[A]

Q.54 Q.54

The value lue of  g ' 

 2

(D)

 4

 1  is   2 

(A) Ans.

(C)

 2

(B) 

(C)

 2

(D) (D) 0

[D] Para Paragr grap aph h For For Ques Questi tion ons s 55 and and 56

Box Box 1 cont contai ains ns thre threee card cardss bear bearin ing g numb number erss 1, 2, 3; box box 2 cont contai ains ns five five card cardss bear bearin ing g numb number erss 1, 2, 3, 4, 5; and and box box 3 cont contai ains ns seve seven n card cardss bear bearin ing g numb number erss 1, 2, 3, 4, 5, 6, 7.A card card is draw drawn n from from each each of  th the the boxe boxes. s. Let x i   be be the the numb numbeer on the the card card dra drawn from from the the i box, i = 1, 2, 3. Q.55 Q.55

The The prob probab abil ilit ity y that that x1 + x2 + x3  is odd, odd, is (A)

29 105

(B)

53 105

(C)

57 105

Ans.

[B]

Q.56

The The prob probab abil ilit ity y that that x1, x2, x3 are are in an arith arithme metic tic progr progres essio sion, n, is (A)

Ans.

9 105

(B)

10 105

(C)

11 105

(D)

(D)

1 2

7 105

[C]

[19]

SECTION -3 : Matching List Type (Only One Option Correct) This This section sectioncon contai tains nsfou fourr questio questions, ns,ea each ch having havingtwo twomat matchin ching g lists. lists. Choice Choicess forthe for thecor correc rectt combina combination tion of elements from List-I and List-II List-II are given as options (A), (B), (C) and (D), out of which one is correct. Q.57 Q.57

 2k    i sin  2k      ; k = 1, 2, …….,9.   10     10  

Let zk  = cos  P. Q.

R.

List-I For each z k  ther theree exist xistss a z j such such that that zk  · z j = 1

List-II 1. True

There exists a k   {1, 2, ……., 9} such that z 1 · z = z k  has has noso no solu luti tion on z in the the set set of comp comple lex x numb number erss

2.

False

3.

1

4.

2

| 1  z1 | | 1 z 2 | . | 1  z9 | 10

  cos    10   equals 9

S.

1–

2k 

equals

k  1

Codes:

Ans.

(A) (B) (C) (D) [C]

P 1 2 1 2

Q 2 1 2 1

R 4 3 3 4

S 3 4 4 3

[20]

Q.58 P.

List-I Thenum enumberofpo rofpolynomialsf(x sf(x)wit )withno hnon-negativeint einteger

1.

List-II 8

1



coefficien coefficients ts of degree degree  2, sati satisf sfy ying ing f(0) f(0) = 0 and and f ( x ) dx =1,is 0

Q.

The number of pointsin intsin the the inte interrval [ 13 , 13 ] at which f(x) f(x) = sin (x2)+cos(x2) atta attains insits its maxim maximum um valu value, e, is 2

R.

3x

2.

2

3.

4

4.

0

2

 (1  e ) dx equals x

2

S.

  1   2  1  x      cos 2x log   dx   1 x  1         2    1   2   1 x       cos 2x log   dx   1 x 0          

equals

Codes:

Ans.

(A) (B) (C) (D) [D]

P 3 2 3 2

Q 2 3 2 3

R 4 4 1 1

S 1 1 4 4

[21]

List-I

Q.59 P.

Let y(x) (x) = cos (3c (3cos–1x), x  [–1, 1], x  ±

Then Q.

List-II 3 2

.

1.

1

2.

2

 2 d 2 y( x ) dy( x )    ( x 1 ) x   equals 2 y( x )  dx  dx 1

Let A1, A2, …….,An (n > 2) be the vertices of a regular polygon of n side sidess with with its cent centre re at the the orig origin in.. Let Let a k  be the the posi positi tion on vect vector or of  n 1

the poin pointt Ak , k = 1, 2, ……., n. If 

 (a

k 

 a k 1)

n 1

=

k  1

 (a

k 

· a k 1 ) ,

k  1

then thenth thee minim minimum umva valu luee of n is R.

S.

If the normal fro from the point int P (h, 1) on the ellip llipsse

x



y2

6 3 isperp isperpeendic dicula ular to the the lin line x + y = 8,thentheva 8,thenthevalu luee ofh is Nu Number of of po positive so solutions sa satisfying th the eq equation

  1    tan 1  1       2x  1   4 x  1 

tan 1

  2     x 2 

1 = tan 

=1

3.

8

4.

9

is

Codes:

Ans.

(A) (B) (C) (D) [A]

P 4 2 4 2

Q 3 4 3 4

R 2 3 1 1

S 1 1 2 3

[22]

Q.60 Q.60

Let f 1 : R  R, f 2 : [0, )  R, f 3 : R  R and and f 4 : R  [0, ) be defi define ned d by

| x |, f 1(x) =  x e ,

if  x  0 if  x  0

f 2(x)=x2, f 3(x) =

sin x , x , 

if  x  0 if  x  0

and and f 4(x) =

f 2  f 1( x ) , f   f  ( x )   1, 2 1

if  x  0 if  x  0

List-I

Ans.

P. f 4 is Q. f 3 is R. f 2of 1 is S. f 2 is Codes: P (A) 3 (B) 1 (C) 3 (D) 1 [D]

1. 2. 3. 4. Q 1 3 1 3

R 4 4 2 2

List-II onto but not one-one neither co continuous no nor on one-one differentiable bu but no not on one-one continuous and one-one

S 2 2 4 4

[23]