PAPER 2. Time : 3 Hours Maximum Marks : 198

Transcription

1 D NT BREAK THE SEALS WITHUT BEING INSTRUCTED T D S BY THE INVIGILATR PAPER CDE : 7 Time : Hous Maximum Maks : 98 Please ead the instuctions caefully. You ae allotted 5 minutes specifically fo this pupose. INSTRUCTINS A. Geneal:. This booklet is you Question Pape. Do not beak the seals of this booklet befoe being instucted to do so by the invigilatos.. The question pape CDE is pinted on the ight hand top cone of this page and on the back page (page No. 6) of this booklet.. Blank spaces and blank pages ae povided in this booklet fo you ough wok. No additional sheets will be povided fo ough wok.. Blank papes, clipboads, log tables, slide ules, calculatos, cameas, cellula phones, pages and electonic gadgets ae NT allowed inside the examination hall. 5. Answes to the questions and pesonal details ae to be filled on a two-pat cabon-less pape, which is povided sepaately. You should not sepaate these pats. The invigilato will sepaate them at the end of examination. The uppe sheet is a machine-gadable bjective Response Sheet (RS) which will be taken back by the invigilato. You will be allowed to take away the bottom sheet at the end of the examination. 6. Using a black ball point pen, daken the bubbles on the uppe oiginal sheet. Apply sufficient pessue so that the impession is ceated on the bottom sheet. 7. D NT TAMPER WITH/MUTILATE THE RS R THE BKLET. 8. n beaking the seals of the booklet check that it contains 6 pages and all the 60 questions and coesponding answe choices ae legible. Read caefully the instuctions pinted at the beginning of each section. B. Filling the Right Pat of the RS : 9. The RS has CDES pinted on its Left and Right pats. 0. Check that the same CDE is pinted on the RS on this booklet. IF IT IS NT THEM ASK FR A CHANGE F THE BKLET. Sign at the place povided on the RS affiming that you have veified that all the codes ae same.. Wite you name, Registation numbe and the name of the Examination cente and sign with pen in the boxes povided on the ight pat of the RS. Do not wite any of this infomation anywhee else. Daken the appopiate bubble UNDER each digit of you Registation Numbe in such a way that the impession is ceated on the bottom sheet. Also daken the pape CDE given on the ight side of RS (R). C. Question Pape Fomat The question pape consists of pats (Physics, Chemisty and Mathematics). Each pat consists of thee sections.. Section I contains 8 multiple choice questions. Each question has choices (A), (B), (C) and (D) out of which NLY NE is coect.. Section II contains paagaphs each descibing theoy, expeiment, data, etc. Thee ae 6 multiple choice questions elating to thee paagaphs with questions on each paagaph. Each question of a paticula paagaph has choices (A), (B), (C) and (D) out of which NLY NE is coect.. Section III contains 6 multiple choice questions. Each question has fou choices (A), (B), (C) and (D) out of which NE R MRE ae coect. D. Making scheme 5. Fo each question in section I and Section II you will be awaded maks if you daken the bubble coesponding to the coect answe NLY and zeo (0) maks if no bubbles ae dakened. In all othe cases, minus one (-) mak will be awaded in these sections. 6. Fo each question in Section III, you will be awaded maks if you daken ALL the bubble(s) coesponding to the coect answe(s) NLY. In all othe cases zeo (0) maks will be awaded. No negative maks will be awaded fo incoect answe(s) in this section. Wite you Name, egistation numbe and sign in the space povided on the back page of this booklet

2 () Vidyalanka : IIT JEE 0 Question Pape & Solution PART I : PHYSICS SECTIN I : Single Coect Answe Type This section contains 8 multiple choice questions. Each question has fou choices (A), (B), (C) and (D) out of which NLY NE is coect.. A student is pefoming the expeiment of Resonance Column. The diamete of the column tube is cm. The fequency of the tuning fok is 5 Hz. The ai tempeatue is 8ºC in which the speed of sound is 6 m/s. The zeo of the mete scale coincides with the top end of the Resonance Column tube. When the fist esonance occus, the eading of the wate level in the column is (A).0 cm (B) 5. cm (C) 6. cm (D) 7.6 cm. (B) 5 ( e ) 6 ( e) cm cm. Two identical discs of same adius R ae otating about thei axes in opposite diections with the same constant angula speed. The discs ae in the same hoizontal plane. At time t 0, the points P and Q ae facing each othe as shown in the figue. The elative speed between the two points P and Q is v. In one time peiod (T) of otation of the discs, v as a function of time is best epesented by (A) (B) (C) (D)

3 IIT JEE 0 Question Pape & Solution (Pape II) (). (A) v sin v sin V PQ VP V Q v p v cos v cos ( vsin iˆ vcos ˆj) (vsin iˆ vcos ˆj) V PQ vsin i ˆ between 0 to v Q. A loop caying cuent I lies in the x-y plane as shown in the figue. The unit vecto ˆk is coming out of the plane of the pape. The magnetic moment of the cuent loop is (A) ˆ a Ik. (B) M I A (B) ˆ a Ik (C) ˆ a Ik (D) ˆ ( )a Ik A a a a a + a + a a a a a a M a I ˆk

4 () Vidyalanka : IIT JEE 0 Question Pape & Solution. An infinitely long hollow conducting cylinde with inne adius R/ and oute adius R caies a unifom cuent density along its length. The magnitude of the magnetic field, B as a function of the adial distance fom the axis is best epesented by (A) (B) (C) (D). (D) Let cuent be I. Cuent density J R I R Field fo J R B 0 I R I R R/ R Ampeian loop Fo R R Applying Ampee s Law B. I 0 R. R 0I R R B 0I R R At R, B 0 at R field is continuous. Fom the above expession as inceases B inceases. Fo R B. 0I 0 B B At R, 0 B R

5 Fom inside expession at R 0I R 0I B. R R R R This poves the continuity in the gaph at R. Fom the above only coect option is (D) IIT JEE 0 Question Pape & Solution (Pape II) (5) 5. A thin unifom cylinde shell, closed at both ends is patially filled with wate. It is floating vetically in wate in half-submeged state. If c is the elative density of the mateial of the shell with espect to wate, then the coect statement is that the shell is (A) moe than half-filled if c is less than 0.5 (B) moe than half-filled if c is less than.0 (C) half-filled if c is moe than 0.5 (D) less than half-filled if c is less than (A) If wate is half filled M shell g ( V) displaced g V ( V) shell M shell M shell shell liquid V shell liquid V shell liquid R.d. If R.d < Then, the cylinde should be moe than half filled so that it is half submeged and floating. 6. In the given cicuit, a chage of +80 C is given to the uppe plate of the F capacito. Then in the steady state, the chage on the uppe plate of the F capacito is (A) + C (B) +0 C (C) +8 C (D) +80 C 6. (C) Chage on capacito of F Q 80 8 C 7. Two moles of ideal helium gas ae in a ubbe balloon at 0ºC. The balloon is fully expandable and can be assumed to equie no enegy in its expansion. The tempeatue of the gas in the balloon is slowly changed to 5ºC. The amount of heat equied in aising the tempeatue is nealy (take R 8. J/mol.K) (A) 6 J (B) 0 J (C) J (D) 08 J 5

6 (6) Vidyalanka : IIT JEE 0 Question Pape & Solution 7. (D) Since U C V T R 5 and W P V R T R 5 0R so Q U + W 5R + 0R 5R 8 08 J 8. Conside a disc otating in the hoizontal plane with a constant angula speed about its cente. The disc has a shaded egion on one side of the diamete and an unshaded egion on the othe side a shown in the figue. When the disc is in the oientation as shown, two pebbles P and Q ae simultaneously pojected at an angle towads R. The velocity of pojection is in the y-z plane and is same fo both pebbles with espect to the disc. Assume that (i) they land back on the disc befoe the disc has completed 8 otation, (ii) thei ange is less than half the disc adius, and (iii) emains constant thoughout. Then (A) P lands in the shaded egion and Q in the unshaded egion. (B) P lands in the unshaded egion and Q in the shaded egion. (C) Both P and Q land in the unshaded egion. (D) Both P and Q land in the shaded egion. 8. (C) Accoding to poblem paticle is to land on disc If we conside a time t then x component of displacement is R t Rsin t < R t Thus paticle P lands in unshaded egion SECTIN II : Paagaph Type This section contains 6 multiple choice questions elating to thee paagaphs with two questions on each paagaph. Each question has fou choices (A), (B), (C) and (D) out of which NLY NE is coect. Paagaph fo Questions 9 and 0 The -decay pocess, discoveed aound 900, is basically the decay of a neuton (n). In the laboatoy, a poton (p) and an electon (e ) ae obseved as the decay poducts of the neuton. Theefoe, consideing the decay of a neuton as a two-body decay pocess, it was pedicted theoetically that the kinetic enegy of the electon should be a constant. But expeimentally, it was obseved that the electon kinetic enegy has a continuous spectum. Consideing a thee-body decay pocess, i.e. n p + e + v e, aound 90, Pauli explained the obseved electon enegy spectum. Assuming the anti-neutino (v e) to be massless and possessing negligible enegy, and the neuton to be at est, momentum and enegy consevation pinciples ae applied. Fom this calculation, the maximum kinetic enegy of the electon is ev. The kinetic enegy caied by the poton is only the ecoil enegy. 9. If the anti-neutino had a mass of ev/c (whee c is the speed of light) instead of zeo mass, what should be the ange of the kinetic enegy, K, of the electon? (A) 0 K ev (B).0 ev K ev (C).0 ev K < ev (D) 0 K < ev 9. (D) Q ( m)c 6

7 Assuming antineutino to be massless: n p e IIT JEE 0 Question Pape & Solution (Pape II) (7) Q m (m m ) c ecoil enegy of P + + kinetic enegy of e + enegy caied by neutino. Now suppose antineutino had a mass as well of KE of e + KE of ecoiled P + i.e. K K K ev ev e Thus K e is definitely less than 0.8 K 0 since poton is massive p p ev Minimum enegy is possible if momentum ae caied away by P and antineutino 0. What is the maximum enegy of the anti-neutino? (A) Zeo (B) Much less than ev (C) Nealy ev (D) Much lage than ev 0. (C) As pe the situation in Q.9. If (K.E e ) 0 All enegy caied by antineutino only (as poton shae vey less amount of enegy because of its lage inetia) Paagaph fo Questions and The geneal motion of a igid body can be consideed to be a combination of (i) a motion of its cente of mass about an axis, and (ii) its motion about an instantaneous axis passing though the cente of mass. These axes need not be stationay. Conside, fo example, a thin unifom disc welded (igidly fixed) hoizontally at its im to a massless stick, as shown in the figue. When the disc-stick system is otated about the oigin on a hoizontal fictionless plane with angula speed, the motion at any instant can be taken as a combination of (i) a otation of the cente of mass of the disc about the z-axis, and (ii) a otating of the disc though an instantaneous vetical axis passing though its cente of mass (as is seen fom the changed oientation of points P and Q). Both these motions have the same angula speed in this case. Now conside two simila systems as shown in the figue: Case (a) the disc with its face vetical and paallel to x-z plane; Case (b) the disc with its face making an angle of 5º with x-y plane and its hoizontal diamete paallel to x-axis. In both the cases, the dis is welded at point P, and the systems ae otated with constant angula speed about the z-axis. Case (a) Case (b) 7

8 (8) Vidyalanka : IIT JEE 0 Question Pape & Solution. Which of the following statements egading the angula speed about the instantaneous axis (passing though the cente of mass) is coect? (A) It is fo both the cases (B) It is fo case (a); and fo case (b) (C) It is fo case (a); and fo case (b) (D) It is fo both the cases. (D) It is fo both case. as angula velocity of a igid body about any point should be same. v v v P PC C v v P PC C L î d ˆ ˆ d (k j) L.5 ˆi ˆj d d ˆ ˆ c cos 5 j sin 5 k d d ˆ ˆ PC cos 5 j sin 5 k d v ˆ C cos 5 i d ˆ d i (i ˆ j) ˆk î P ˆk d cos 5º ( + d cos 5º) î. Which of the following statements about the instantaneous axis (passing though the cente of mass) is coect? (A) It is vetical fo both the cases (a) and (b) (B) It is vetical fo case (a); and is at 5 to the x z plane and lies in the plane of the disc fo case (b) (C) It is hoizontal fo case (a); and is at 5 to the x z plane and is nomal to the plane of the disc fo case (b) (D) It is vetical fo case (a); and is at 5 to the x z plane and is nomal to the plane of the disc fo case (b). (A) Top View V W Vsin Hee thee is a v el of P and Q (not fo P, Q) (V el ) P Q will be in hoizontal plane must be along vetical Same situation will be thee fo P as mentioned 8 p 0 should be same fo both cases

9 IIT JEE 0 Question Pape & Solution (Pape II) (9) Paagaph fo Questions and Most mateials have the efactive index, n >. So, when a light ay fom ai entes a sin n natually occuing mateial, then by Snell s law,, it is undestood that the sin n efacted ay bends towads the nomal. But it neve emeges on the same side of the nomal as the incident ay. Accoding to electomagnetism, the efactive index of the medium is c given by the elation, n, whee c is the speed of electomagnetic waves in v vacuum, v its speeds in the medium, and ae the elative pemittivity and pemeability of the medium espectively. In nomal mateials, both and ae positive, implying positive n fo the medium. When both and ae negative, one must choose the negative oot of n. Such negative efactive index mateials can now be atificially pepaed and ae called meta mateials. They exhibit significantly diffeent optical behavio, without violating any physical laws. Since n is negative, it esults in a change in the diection of popagation of the efacted light. Howeve, simila to nomal mateials, the fequency of light emains unchanged upon efaction even in meta mateials.. Choose the coect statement. (A) The speed of light in the meta mateial is v c n c (B) The speed of light in the meta mateial is v n (C) The speed of light in the meta mateial is v c. (D) The wavelength of the light in the meta mateial ( m ) is given by m ai n, whee. (B) ai is the wavelength of the light in ai C v C v will be ( )ve fo metal mateials but is (+)ve v C. Fo light incident fom ai on a meta-mateial, the appopiate ay diagam is (A) (B) (C) (D) 9

10 (0) Vidyalanka : IIT JEE 0 Question Pape & Solution. (C) sin sin sin sin sin sin will ( )ve w..t. to nomal. option (C) is coect. SECTIN III : Multiple Coect Answe(s) Type This section contains 6 multiple choice questions. Each question has fou choices (A), (B), (C) and (D) out of which NE o MRE ae coect. 5. Six point chages ae kept at the vetices of a egula hexagon of side L and cente, as q shown in the figue. Given that : K, which of the following statement(s) 0 L is(ae) coect? (A) The electic field at is 6K along D. (B) The potential at is zeo. (C) The potential at all points on the line PR is same. (D) The potential at all points on the line ST is same. 5. (A), (B), (C) q K 0 L q q q q g q Potential at 0 0 L L L L L L Any point on line PR is equidistant fom the chages F & E; A & D; B & C. Each mentioned pai of chages ae of equal magnitudes and opposite signs. Thus I by supeposition pinciple; all points of PR have potential. Consideing the electic field at ; K K K Net field along D K K cos60 K cos60 6K 0

11 IIT JEE 0 Question Pape & Solution (Pape II) () 6. Two spheical planets P and Q have the same unifom density, masses M P and M Q, and suface aeas A and A, espectively. A spheical planet R also has unifom density and its mass is (M P + M Q ). The escape velocities fom the planets P, Q and R, ae V P, V Q and V R, espectively. Then (A) V Q > V R > V P (B) V R > V Q > V P (C) V R /V P (D) V P /V Q 6. (B), (D) Escape velocity fom a planet of mass M and adius R GM v e.g. R R R Fom given infomation : Rp RQ RQ R P VP VR M Q 8M P M R 8M P + M P 9 M P R R v e R [If is same fo all planets) R. 9 / 9.R P Clealy VR VQ V P R P 7. The figue shows a system consisting of (i) a ing of oute adius R olling clockwise without slipping on a hoizontal suface with angula speed and (ii) an inne disc of adius R otating anti-clockwise with angula speed. The ing and disc ae sepaated by fictionless ball beaings. The system is in the x-z plane. The point P on the inne disc is at a distance R fom the oigin, whee P makes an angle of 0 with the hoizontal. Then with espect to the hoizontal suface, (A) the point has a linea velocity R (B) the point P has a linea velocity R i + R k (C) the point P has a linea velocity R i R k (D) the point P has a linea velocity i R i + R k

12 () Vidyalanka : IIT JEE 0 Question Pape & Solution 7. (A) (B) R V (R) i (A) 60 0 (V P) R R R (cos 60)i (sin 60)k R R i k V P VP V R R q V P Ri R k (B) 8. Two solid cylindes P and Q of same mass and same adius stat olling down a fixed inclined plane fom the same height at the same time. Cylinde P has most of its mass concentated nea its suface, while Q has most of its mass concentated nea the axis. Which statement(s) is(ae) coect? (A) Both cylindes P and Q each the gound at the same time (B) Cylinde P has lage linea acceleation than cylinde Q (C) Both cylinde each the gound with same tanslational kinetic enegy (D) Cylinde Q eaches the gound with lage angula speed 8. (D) mg sin f ma f I a mg sin Ia f a t I m g sin k a a

13 IIT JEE 0 Question Pape & Solution (Pape II) () K P K Q a P a Q t P t Q (A) wong K P > K Q a P < a Q mv v v K P > K Q (B) wong K gh Q > P K gh K mgh (K.E) T (D) Coect mgh K both will have diffeent T.K.E. (C) wong 9. A cuent caying infinitely long wie is kept along the diamete of a cicula wie loop, without touching it. The coect statement(s) is(ae) (A) The emf induced in the loop is zeo if the cuent is constant (B) The emf induced in the loop is finite if the cuent is constant (C) The emf induced in the loop is zeo if the cuent deceases at a steady ate (D) The emf induced in the loop is finite if the cuent deceases at a steady ate 9. (A) (C) The Magnetic flux above and below the cicula loop ae equal and opposite due to symmety net 0 emf induced will be zeo x i 0. In the given cicuit, the AC souce has 00 ad/s. Consideing the inducto and capacito to be ideal, the coect choice(s) is(ae) (A) The cuent though the cicuit, I is 0. A (B) The cuent though the cicuit, I is 0. A (C) The voltage acoss 00 esisto 0 V (D) The voltage acoss 50 esisto 0 V

14 () Vidyalanka : IIT JEE 0 Question Pape & Solution 0. (A), (C) I I + I X L X C L (00) (0.5) 50 C Fo inducto cicuit, Z I 0 I 5 A Fo capacito cicuit, 00 I 0 I I 0 A I I I 0. A Voltage acoss 00 I I 0 V Voltage acoss 50 I 50 I V

15 IIT JEE 0 Question Pape & Solution (Pape II) (5) PART - II : CHEMISTRY SECTIN I : Single Coect Choice Type This section contains 8 multiple choice questions. Each question has fou choices (A), (B), (C) and (D) out of which NLY NE is coect.. Using the data povided, calculate the multiple bond enegy (kj mol ) of a C C bond in C H. That enegy is (take the bond enegy of a C H bond as 50 kj mol ) C(s) H(g) CH (g) H 5 kj mol C C H 0 kj mol (s) (g) (g) H H H 0 kj mol (g) (A) 65 (B) 87 (C) 865 (D) 85. (D) C(s) H (g) CH (g)(h C C H) B E(H ) H (C) B E(C H) B E(C C) H Sub xn 0 0 [50 x] 5 x 85. The majo poduct H of the given eaction sequence is (A) CN 95% S Heat CH CH C CH G (B) (C) (D). (A) CN CH CH C CH CH CH C CH CN 95% (G) H S CH CH CH CH C CH CH CH C CH (A) H. NiCl {P(C H 5 ) (C 6 H 5 )} exhibits tempeatue dependent magnetic behavio (paamagnetic / diamagnetic). The coodination geometies of Ni + in the paamagnetic and diamagnetic states ae espectively (A) tetahedal and tetahedal (B) squae plana and squae plana (C) tetahedal and squae plana (D) squae plana and tetahedal 5

16 (6) Vidyalanka : IIT JEE 0 Question Pape & Solution. (C) NiCl P(CH 5) (C6H 5) o 8 Ni(8) : [A]s d In stong ligand Hybidisation is dsp (diamagnetic) Squae plana In weak ligand 8 Hybidisation is sp (paamagnetic) tetahedal. In the cyanide extaction pocess of silve fom agentite oe, the oxidizing and educing agents used ae (A) and C espectively (B) and Zn dust espectively (C) HN and Zn dust espectively (D) HN and C espectively. (B) Ag S NaCN NaAg(CN) Na S Na S 5 H Na S NaH S ox 0 Na Ag(CN) Zn NaZn(CN) Ag 5. The eaction of white phosphous with aqueous NaH gives phosphine along with anothe phosphous containing compound. The eaction type ; the oxidation states of phosphous in phosphine and the othe poduct ae espectively (A) edox eaction ; and 5 (B) edox eaction; + and +5 (C) dispopotionation eaction ; and + 5 (D) dispopotionation eaction ; and + 5. None of these P (white) NaH H PH NaHP PH has and NaH P has +.N. 6. The shape of Xe F molecule is (A) tigonal bipyamidal (B) squae plana (C) tetahedal (D) see saw 6. (D) Shape of Xe F is Hybidisation H V M C A (sp d) 0 F 6

17 IIT JEE 0 Question Pape & Solution (Pape II) (7) 7. Fo a dilute solution containing.5 g of a non volatile non electolyte solute in 00 g of wate, the elevation in boiling point at atm pessue is C. Assuming concentation of solute is much lowe than the concentation of solvent, the vapou pessue (mm of Hg) of the solution is (take K b 0.76 K kg mol ) (A) 7 (B) 70 (C) 76 (D) (A) T L k b m k b Ws Ms Wsolution Ms 00 M s x ns X s n Ws Ms Wsolv M solv x solution The compound that undegoes decaboxylation most eadily unde mild condition is (A) CH (B) CH CH CH (C) CH CH (D) CH CH 8. (B) C H Is a keto acid which undego decaboxylation on slight heating. C H Slight heating C 7

18 (8) Vidyalanka : IIT JEE 0 Question Pape & Solution SECTIN II : Paagaph Type This section contains 6 multiple choice questions elating to thee paagaphs with two questions on each paagaph. Each question has fou choices (A), (B), (C) and (D) out of which NLY NE is coect. Paagaph fo Question 9 and 0 The electochemical cell shown below is a concentation cell. M M + (satuated solution of a spaingly soluble salt, MX ) M + (0.00 mol dm ) M The emf of the cell depends on the diffeence in concentations of M + ions at the two electodes. The emf of the cell at 98 K is V. 9. The value of G (kj mol ) fo the given cell is (take F C mol ) (A) 5.7 (B) 5.7 (C). (D). 9. (D) G I nfe cell kj mol. kj 0. The solubility poduct (K sp ; mol dm 9 ) of MX at 98 K based on the infomation available fo the given concentation cell is (take.0 R 98 / F V) (A) 0 5 (B) 0 5 (C) 0 (D) 0 0. (B) E C log C log0 0 0 C 0 C [M + ] 0 5 M. K sp [M + ] [X ] s (0 5 ) 0 5 Paagaph fo Question to In the following eaction sequence, the compound J is an intemediate. J(C 9 H 8 ) gives effevescence on teatment with NaHC and a positive Baye s test.. The compound K is (A) (B) (C) (D) 8

19 IIT JEE 0 Question Pape & Solution (Pape II) (9). (C) C H I (CHC) CHCNa C H (J) H Pd C (K) AlCl C Cl SCl C H. The compound I is (A) (B) (C) (D). (A) Solution is given with Q. solution. Paagaph fo Question and Bleaching powde and bleach solution ae poduced on a lage scale and used in seveal household poducts. The effectiveness of bleach solution is often measued by iodomety.. 5 ml of household bleach solution was mixed with 0 ml of 0.50 M KI and 0 ml of N acetic acid. In the titation of the libeated iodine, 8 ml of 0.5 N Na S was used to each the end point. The molaity of the household bleach solution is (A) 0.8 M (B) 0.96 M (C) 0. M (D) 0.0 M. (C) No. of moles of bleach solution No. of moles of Na S ( ) 6 0 Molaity Molaity of bleach solution 6 0. M 5. Bleaching powde contains a salt of an oxoacid as one of its components. The anhydide of that oxoacid is (A) Cl (B) Cl 7 (C) Cl (D) Cl 6 9

20 (0) Vidyalanka : IIT JEE 0 Question Pape & Solution. (A) Bleaching powde contains salt of HCl. It is obtained by adding H to Cl. Thus option (A) is coect. SECTIN III : Multiple Coect Answe(s) Type This section contains 6 multiple choice questions. Each question has fou choices (A), (B), (C) and (D) out of which NE o MRE ae coect. 5. Fo the given aqueous eactions, which of the statement(s) is (ae) tue? (A) The fist eaction is a edox eaction (B) White pecipitate is Zn [Fe(N) 6 ]. (C) Addition of filtate to stach solution gives blue colou. (D) White pecipitate is soluble in NaH solution. 5. (A), (C), (D) KI (Excess) + [K Fe(CN) 6 ] + H S KH + I + K [Fe(CN) 6 ] + ZnS I + Stach Blue colo Zn(H) + NaH (Ecess) K [Fe(CN) 6 ] + I + KH (Bownish-Yellow solution) Zn(H) + I (Bown-Yellow Filteate) Na Zn (soluble in alkaline medium) 6. With efeence to the scheme given, which of the given statement(s) about T, U, V and W is (ae) coect? (A) T is soluble in hot aqueous NaH (B) U is optically active (C) Molecula fomula of W is C 0 H 8 (D) V gives effevescence on teatment with aqueous NaHC 0

21 IIT JEE 0 Question Pape & Solution (Pape II) () 6. (A), (C) H C (T) LiAlH H C C H C CH H H H CH CH (U) (CHC) excess CH CH C CH C H C CH H C (CH ) (W) C H + H C CH C H CH CH CH (V) 7. Which of the given statement(s) about N,, P and Q with espect to M is (ae) coect? (A) M and N ae non mio image steeoisomes (B) M and ae identical (C) M and P ae enantiomes (D) M and Q ae identical 7. (A), (B), (C) Factual. 8. With espect to gaphite and diamond, which of the statement(s) given below is (ae) coect? (A) Gaphite is hade than diamond. (B) Gaphite has highe electical conductivity than diamond. (C) Gaphite has highe themal conductivity than diamond. (D) Gaphite has highe C C bond ode than diamond. 8. (B), (C), (D) Gaphite is sp hybidized and contains Vande Wall Foce. While diamond is sp hybidized.

22 () Vidyalanka : IIT JEE 0 Question Pape & Solution 9. The given gaphs/data I, II, III and IV epesent geneal tends obseved fo diffeent physisoption and chemisoption pocesses unde mild conditions of tempeatue and pessue. Which of the following choice(s) about I, II, III and IV is (ae) coect? (A) I is physisoption and II is chemisoption (B) I is physisoption and III is chemisoption (C) IV is chemisoption and II is chemisoption (D) IV is chemisoption and III is chemisoption 9. (A), (C) I : In physisoption, as the tempeatue inceases the amount of gas adsobed deceases. II : In chemisoption, as the tempeatue inceases the amount of gas adsobed inceases (to a cetain ange of tempeatue) III : x /n Fuendlich adsoption isothems fo physisoption kp m (at constant T) IV : H ads 50 KJ is in the ange fo chemisoption. 0. The evesible expansion of an ideal gas unde adiabatic and isothemal conditions is shown in the figue. Which of the following statement(s) is (ae) coect? (A) T T (B) T > T (C) W isothemal > W adiabatic (D) U isothemal > U adiabatic

23 0. (A), (C), (D) Pocess is isothemal implies T T A is coect V V V V T V T V T T IIT JEE 0 Question Pape & Solution (Pape II) () fom the diagam V V V V T < T ption B is incoect Wok done is aea unde the cuve, Clealy the aea unde the cuve fo isothemal pocess is geate. ption C is coect Fo an ideal gas, intenal enegy is a function of Tempeatue. Final tempeatue fo adiabatic pocess is less than its initial tempeatue, while initial and final tempeatue fo isothemal pocess is same. Hence, intenal enegy change fo isothemal pocess is geate than intenal enegy change fo adiabatic pocess ( U iso 0 and U adia < 0) option D is coect. PART III - MATHEMATICS SECTIN I : Single Coect Choice Type This section contains 8 multiple choice questions. Each question has fou choices (A), (B), (C) and (D) out of which NLY NE is coect.. The value of the integal / / x x x n cos x dx (A) 0 (B). (B) is (C) (D) x x cos x dx n cos x dx x 0 x cos x dx 0 [as nd integation, as function is odd] 0 / x sin x x sin x dx 0 / 0 0 x cos x cos x dx 0 sin x / 0 ( )

24 () Vidyalanka : IIT JEE 0 Question Pape & Solution. Let a, a, a, be in hamonic pogession with a 5 and a 0 5. The least positive intege n fo which a n < 0 is (A) (B) (C) (D) 5. (D) a, a, a 0 H.P.,,... A.P. a a a0 9d d T T T5 75. The equation of a plane passing though the line of intesection of the planes x+y+z and x y + z and at a distance fom the point (,, ) is (A) 5x y + z 7 (B) x y (C) x + y + z (D) x y. (A) Equation of family of planes passing though x + y + z 0 and x y + z 0 is (x + y + z ) + (x y + z ) 0 ( + ) x + ( ) y + ( + ) z ( + ) 0 Distance of (,, ) fom equied plane is ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) 7 Hence equation of equied plane is 5 z x y 0 5x y + z 7. Let PQR be a tiangle of aea with a, b 7 and c 5, whee a, b and c ae the lengths of the sides of the tiangle opposite to the angles at P, Q and R espectively. Then sin P sin P sin P sin P equals. (A) (B) 5 (C) (D) 5

25 IIT JEE 0 Question Pape & Solution (Pape II) (5). (C) sin P sin P cos P sin P sin P cos P cos P cos P cos P R P 5/ 7/ Q 5. If a and b ae vectos such that a b 9 and ˆ ˆ ˆ ˆ ˆ ˆ a (i j k) (i j k) b, then a possible value of (a b) ( 7i ˆ j ˆ k) ˆ is (A) 0 (B) (C) (D) 8 5. (C) a b 9 a i j k i j k b a i j k i j k b 0 a i j k b i j k 0 a b i j k 0 a b i j k sin n 0 sin θ 0 It means a b and i j k ae paallel. The angle a b & i j k will fom same angle will be fom by i j k & 7i j k. Let θ is the angle between this pai then cos i j k. 7i j k i j k 7i j k 6 cos Now the possible value of a b. 7i j k a b 7i j k cos

26 (6) Vidyalanka : IIT JEE 0 Question Pape & Solution 6. If P is a matix such that P T P + I, whee P T is he tanspose of P and I is the x 0 identity matix, then thee exists a column matix X y 0 such that z 0 0 (A) PX 0 (B) PX X (C) PX X (D) PX X 0 6. (D) P is a matix P T P + I a b c Let P l m n a l P T b m c n P T a b c P + I l m n a b c l m n a b c l m n a b c l m n a a + a + n n + n b, b. It is possible when b 0 Similaly, c l 0 and m The matix P is So, PX X Coect answe is (D) Let (a) and (a) be the oots of the equation 6 a x a x a 0 whee a >. Then (A) lim a 0 5 and (a) and lim (a) ae a 0 (B) and 6 (C) 7 and (D) 9 and

27 7. (B) IIT JEE 0 Question Pape & Solution (Pape II) (7) 6 a x a x a 0, whee a > (a) (a) 6 a a a 0 + (a) (a) ( a) ( a) lt a 0 ( a) ( a) /6 /6 / / (a) + (a) a (a) a 0 (a) (a) a 0 a a ( a) ( a) / / / / ( a) ( a) ( a) ( a) / / / / (a) (a) / (a) + (a) / By solving (a) / and (a) Coect answe is (B). a 0 a 0 8. Fou fai dice D, D, D and D, each having six faces numbeed,,,, 5 and 6, ae olled simultaneously. The pobability that D shows a numbe appeaing on one of D, D and D is (A) (A) n(s) (6) ne (B) P(E ) P(E) P(E ) 6 6 (C) 5 6 (D) 7 6 SECTIN II : Paagaph Type This section contains 6 multiple choice questions elating to thee paagaphs with two questions on each paagaph. Each question has fou choices (A), (B), (C) and (D) out of which NLY NE is coect. Paagaph fo Questions 9 and 50 Let f(x) ( x) sin x + x fo all x IR, and let g(x) x (, ). x (t ) t nt f (t) dt fo all 7

28 (8) Vidyalanka : IIT JEE 0 Question Pape & Solution 9. Conside the statements : P : Thee exists some x IR such that f(x) + x (+x ) Q : Thee exists some x IR such that f(x) + x(+x) Then (A) both P and Q ae tue (B) P is tue and Q is false (C) P is false and Q is tue (D) both P and Q ae false. 9. (C) P : f(x) + x ( + x ) ( x) sin x + x + x + x ( x) sin x + x x + (x x + ) sin x + x x + x cos x x cos x + cos x + cos x (x x + ) + 0 ( x) cos x + 0 Hence no solution Also Q : f(x) + x + x x sin x x x x Let g(x) x sin x x g(0) 0 g( ) 0 Thee exists a solution of g(x) in [0, ]. Hence statement Q is tue. 50. Which of the following is tue? (A) g is inceasing on (, ) (B) g is deceasing on (, ) (C) g is inceasing on (, ) and deceasing on (, ) (D) g is deceasing on (, ) and inceasing on (, ) 50. (B) g(x) x (t ) t (x ) g (x) n x x we know, f(x) > 0 x. Let h(x) (x ) nx x h(x) nx x h (x) (x ) x n t f (t) dt x (, ) f (x) x (x ) x(x ) 8

29 IIT JEE 0 Question Pape & Solution (Pape II) (9) (x ) (x ) h (x) < 0 h is deceasing x > h(x) < h() (x ) n x 0 x x (, ) (x ) n x 0 x g (x) < 0 x (, ) g is deceasing in (, ) Paagaph fo Questions 5 and 5 A tangent PT is dawn to the cicle x + y at the point P,. A staight line L, pependicula to PT is a tangent to the cicle (x ) + y 5. A common tangent of the two cicles is (A) x (B) y (C) x y (D) x y 6 5. (D) Tangent in slope to x + y is Similaly tangent to (x ) + y is y mx m y m x m () () & () identical m m m m m m Taking (+) sign m m m m m Squaing 9m + m m Taking ( ) sign m m m m m m + m (This is not possible) So put () y mn m y mx m m () P (, 0) 9

30 (0) Vidyalanka : IIT JEE 0 Question Pape & Solution y x 8 y x y x 6 Taking (+) y x 6 x y 6 (only this option given) 5. A possible equation of L is (A) x y (B) x y (C) x y (D) x y 5 5. (A) Equation of tangent at P x y Slope of tangent is So, Slope of L is, to x + y is So, equation of L (is tangent to (x ) + y & slope y x y x Taking (+) sign, y x x y Taking ( ) sign, y x x y 5 Paagaph fo Questions 5 and 5 Let a n denote the numbe of all n digit positive integes fomed by the digits 0, o both such that no consecutive digits in them ae 0. Let b n the numbe of such n digit integes ending with digit and c n the numbe of such n digit integes ending with digit 0. ) 5. Which of the following is coect? (A) a 7 a 6 + a 5 (B) c 7 c 6 + c 5 (C) b 7 b 6 + c 6 (D) a 7 c 7 + b 6 5. (A) a a a a 5 a n is following fibonacci seies. Hence a 7 a 6 + a 5. 0

31 IIT JEE 0 Question Pape & Solution (Pape II) () 5. The value of b 6 is (A) 7 (B) 8 (C) 9 (D) 5. (B) Total no of ways exactly two consecutive two is 5 ways Total no of ways exactly thee consecutive two is ways Total no of ways exactly fou consecutive two is ways So, b SECTIN III : Multiple Coect Answe(s) Type This section contains 6 multiple choice questions. Each question has fou choices (A), (B), (C) and (D) out of which NE o MRE ae coect. 55. If the staight lines x y z k and x y z ae coplana, then the plane (s) 5 k containing these two lines is (ae) (A) y + z (B) y + z (C) y z (D) y z 55. (B), (C) Points (,, 0) & (,, 0) lies on the equied plane. The nomal to the plane equied is i j k k ˆ i k ˆj(k 0) k ˆ ( 5k) 5 k The equation of equied plane containing both the lines is (k ) x + (0 k) y + ( 5k) z d. () Point (,, 0) lies on the plane () (k ) + (k 0) d Equation of plane is (k ) x + (0 k) y + ( 5k) z k + k () k 0 k ± fom () we get, fo k, 6y 6z 6 y z fo k y + z y + z 56. If the adjoint of a matix P is 7, then the possible value(s) of the deteminant of P is (ae) (A) (B) (C) (D) 56. (A), (D) adjp 7 adj P

32 () Vidyalanka : IIT JEE 0 Question Pape & Solution We know, adj P P P P n adj P P (whee n is ode of matix) 57. Let f : (, ) IR be such that f(cos ) fo 0,,, sec value(s) of f is (ae) (A) 57. (A), (B) (B) f cos sec cos cos f cos cos cos cos cos (C) (D) Then the cos f f f and f 58. Let X and Y be two events such that P(X Y), P(Y X), and P(X Y) 6. Which o the following is (ae) coect? (A) P(X Y) (B) X and Y ae independent (C) X and Y ae not independent c (D) P(X Y) 58. (A) and (B) X P(X Y) P Y P(Y) P(Y) P(X Y) P(Y) 6

33 IIT JEE 0 Question Pape & Solution (Pape II) () P(Y) () Y P(X Y) P X P(X) P(X) P(X Y) 6 P(X) () P(X Y) P(X) + P(Y) P(X Y) (A : coect) P(X Y) P(X) P(Y) 6 X & Y ae in dependent (B : coect) X c & Y ae in dependent. P(X c c Y) P X P X P X P Y 6 (A), (B) coect. 59. If f(x) x 0 t e (t ) (t ) dt fo all x (0, ), then (A) f has a local maximum at x (B) f is deceasing on (, ) (C) thee exists some c (0, ) such that f (c) 0 (D) f has a local minimum at x 59. (A), (B), (C), (D) f(x) x 0 t e (t )(t )dt x (0, ) x f (x) e (x )(x ) f is inceasing in (, ) (, ) f is deceasing in (, ) f () f () 0 & f (x) is diffeentiable on (, ) and also continuous on [, ] By Rolle's theoem, at least one c such that c (, ) f (x) 0

34 () Vidyalanka : IIT JEE 0 Question Pape & Solution 60. Fo evey intege n, let a n and b n be eal numbes. Let function f : IR IR be given by an sin x, fo x [n, n ] f(x), fo all integes n. bn cos x, fo x (n, n) If f is continuous, then which of the following hold(s) fo all n? (A) an bn 0 (B) an bn (C) an bn (D) an bn 60. (B), (D) f is continuous on f(n) a n + sin (. n) a n At x n Lt f (x) Lt bn cos x x x n x n bn cos( n) b n + Lt f (x) Lt an sin ( x) n x n a n + sin ( n) a n a n b n + an bn At x n + f(n + ) a n + sin ( (n + )) a n + sin (n + ) a n Lt f(x) Lt an sin x an sin(n ) a n x n x (n ) x n Lt f (x) Lt bn cos x x n bn cos (n ) bn a n b n+ an bn