Sri Chaitanya s Solutions to

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1 .A.P. :: IIT JEE 0 Paper - II :: Sri Chaitanya s Solutions to IIT JEE - 0 (PAPER ) Time: Hours Maximum Marks: 7 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose A. General : INSTRUCTINS. The question paper CDE is printed on the right hand top corner of this sheet and also on the back page (page no of this booklet). No additional sheets will be provided for rough work. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed 4. Write your name and registration number in the space provided on the back page of this booklet 5. The answer sheet, a machine - gradable bjective Response Sheet (RS), is provided separately. 6. D NT TAMPER WITH/MULTILATE THE RS R THE BKLET. 7. Do not break the seals of the question paper booklet before instrucuted to do so by the invigilators. 8. The question paper contains pages having 60 questions 9. n breaking the seals, please check that all the questions are legible. B. Filling the bootom half of the RS : 0. The RS has CDE printed on its lower and upper Parts.. Make sure the CDE on the RS is the same as that on this booklet. If the Codes do not match, ask fora change of the Booklet.. Write your Registration No., Name and Name of centre and sign with pen in appropriate boxes. Do not write these anywhere else. Darken the appropriate bubbles below your regis tration number with HB pencil. C. Question paper format and marking scheme :. The question paper consists of Parts (Chemistry, Mathematics and Physics), and each part consists of four Sections 4. In Section I (Total Marks : 4), for each question you will be awqrded marks if you darken NLY the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all othe cases, minus one ( ) mark will be awarded. 5. In Section II (Total Marks : 6) for each question you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) NLY and zero marks otherwise. There are no negative marks in this section. 6. In Section III (Total Marks : 4) for each question you will be awarded 4 marks if you darken NLY. the bubble corresponding to the correct answer and zero marks otherwise. There are no negative marks in this section. 7. In Section IV (Total Marks : 6), for each question you will be awarded marks for each row in which you have darkened ALL the bubble(s) corresponding to the correct answer(s) NLY and zero marks otherwise. Thus each question in this section carries a maximum of 8 marks. There are no negative marks in this section., Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

2 .A.P. :: IIT JEE 0 Paper - II :: IIT JEE 0 (PAPER - II) PART - I CHEMISTRY CHEMISTRY SECTIN I ( Total Marks : 4) ( SINGLE CRRECT CHICE TYPE ) This section contains 8 multiple choice questions. Each question has four choices A,B,C and D out of which NLY NE is correct.. Among the following complexes K P, K Fe CN 6 K, Co NH L, Na 6 Co oxalate M, Ni H Cl 6 N, K Pt CN 4 and Zn H N 6 P the diamagnetic complexes are a) K,L,M,N b) K, M,, P c) L, M,,P d) L, M, N, Ans : C Sol : (K) K FeCN [ ]-diamagnetic 6 d sp (L) Co CN d sp Co NH Cl 6 diamagnetic d 6 NH (M) Cooxalate same as above Co + = d 6 - due to chelation d SP hybridisation takes place Hence dia magnetic (N) Ni H Cl 6 8 H Ni d Paramagnetic (P) K Pt CN d sp 4 d sp Zn + =d 0 - dia Magnetic dsp, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

3 .A.P. :: IIT JEE 0 Paper - II ::. Passing H S gas into a mixture of Mn, Ni, Cu solution precipitates Ans : A and Hg ions in an acidified aqueous a) Cus and HgS b) MnS and CuS c) MnS and NiS d) NiS and HgS Sol : H S in acidic Medium is group reagent for nd group cation Hence only CuS, HgS are precipitated. Consider the following cell reaction : Fe 4H Fe H 0 E.67V s g aq aq At Fe M P 0, 0. atm and ph =, the cell potential at 5ºC is a).47 V b).77 V c).84 V d).57 V Ans : D Sol: E Cell = E 0 Cell Fe Log 4 P. H =.67 Log = The freezing point (in ºC) of a solution containing 0. g of K FeCN Mol Wt 00 g of water K f.86k kg mol is..9 6 in Ans : A a).0 b) 5.70 c) 5.70 d).0 Sol: T ik m, where i 4 f f = 0.06 T f = -.6 X 0 - = -. X 0-5. Amongst the compounds given, the one that would form a brilliant colored dye on treatment with NaN in dil. HCl followed by addition to an alkaline solution of naphthol is N(CH ) b) NHCH C) NH CHNH a) d) H C Ans : C, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

4 .A.P. 4 :: IIT JEE 0 Paper - II :: NH N + H NaN - HCl + CH H C Sol : N = N CH H 6. The major product of the following reaction is Ans : B Sol : RCH H (anhydrous) H a) c hemiacetal b) an acetal c) an ether d) an ester H H H - CH - R H -H + CH - R acetal 7. The following carbohydrate is Ans : B a) a ketohexose b) an aldohexose c) an furanose d) an pyranose H H CH H Sol : H H H H H H H, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

5 .A.P. 5 :: IIT JEE 0 Paper - II :: 8. xidation states of the metal in the minerals haematile and magnetic, respectively, are Ans : D a) II, III in haematite and II in magnetic b) II, III in haematite and II in magnetic c) II in haematite and II, II in magnetic d) III in haematite and II, III in magnetic Sol : Haematite : Fe (+) Magnetite : Fe 4 Fe (+)+Fe (+) (Mixed oxide) SECTIN II ( Total Marks : 6) ( MULTIPLE CRRECT ANSWER TYPE) This section contains 4 multiple choice questions. Each question has four choices A,B,C and D out of which NE or MRE may be correct. 9. The equalibrium Ans : BCD in aqueous medium at 5ºC shifts towards the left in the presence of 0 Cu ' Cu Cu '' a) N b) Cl c) SCN d) CN Sol : Because in Aq. Medium Cu + is Highly unstable and undergoes disproportionation. Cu + is stable only with insoluble Cu Cl, Cu (CN), Cu (SCN) in aq. medium hence with these liginds. Equilibrium moves to left side 0. For trhe first order reaction Ans : ABD N g 4N g g 5 a) The concentration of the reactant decreases exponentially with time b) The half-life of the reaction decreases with increasing temperature c) The half-life of the reaction depends on the initial concentration of the reactant d) The reaction proceeds to 99.6% completion in eight half-life duration. Sol: ac C0. e kt 0.69 bt / k Since k increases with incresing of temperature t/ decreases 0 ct a / d t t /, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

6 .A.P. 6 :: IIT JEE 0 Paper - II ::. The correct functional group X and the reagent/reaction conditions Y in the following scheme are (i) Y X (CH ) 4 - X (ii) C (CH ) 4 C H heat H condensation polymer a) X CCH, Y H / Ni / heat b) X CNH, Y H / Ni / heat c) X CNH, Y Br / NaH d) X CN, Y H / Ni / heat Ans : BCD Sol : A) H /Ni/ Heat H CC - (CH ) 4 - CCH (B) H N - C - (CH ) 4 - C - NH H /Ni H CC - (CH ) 4 - CCH no effect on ester group C) H N - C - (CH ) 4 - C - NH heat Br /NaH H N - CH - (CH ) 4 - CH - NH H N - (CH ) 4 - NH D) NC - (CH ) 4 - CN H /Ni/Heat H N - CH - (CH ) 4 - CH - NH. Reduction of the metal centre in aqueous permanganate ion involves Ans: A,D a) electrons in neutral medium b) 5 electrons in neutral medium c) electrons in alkaline medium d) 5 electrons in acidic medium Sol: Mn - H 4 Mn Mn - H + 4 Mn - - H Mn Mn, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

7 .A.P. 7 :: IIT JEE 0 Paper - II :: SECTIN III ( Total Marks : 4) ( INTEGER ANSWER TYPE ) This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkned in the RS.. The volume (in ml) of 0. M AgN required for complete precipitation of chloride ions Ans : 6 present in 0 ml of 0.0 M solution of [Cr (H ) 5 Cl]Cl, as silver chloride is close to Sol: m. moles of AgN = X m.moles of [Cr(H ) 5 Cl] Cl 0. X V ml = X 0. V ml = 6 4. In L saturated solution of AgCl [K sp (AgCl)=.6 X 0-0 ], 0. mol of CuCl [K sp (CuCl)=.0 X 0-6 ] is added. The resultant concentration of Ag + in the solution is.6 X 0 -x. The value of x is Ans: 7 Sol: K sp(agcl) = [Ag+]. [Cl - ] [Cl - ] = 0 - from K sp (CuCl).6 X 0-0 = [Ag+] 0 - [Ag+] =.6 X 0-7 x 7 5. The number of hexagonal faces that are present in a truncated octahedron is Ans : 8 Sol : Truncated octahedron. It is an archimedean solid. It has 4 faces (8 regular hexagonal and 6 square) 6. The maximum number of isomers (including stereoisomers) that are possible on monochloriantion of the following compound, is CH C CH CH H CH CH Ans : 8, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

8 .A.P. 8 :: IIT JEE 0 Paper - II :: CH CH Cl CH Sol : CH - CH - C - CH - CH Cl / h Cl - CH - CH - C - CH - CH + CH - CH - C - CH - CH + H H H CH CH Cl CH - CH - C - CH - CH + CH - CH - C - CH - CH Cl H 7. The total number of contributing structures showing hyperconjugation (involving C-H bonds) for the following carbocation is Ans : 6 Sol : H C CH CH H C CH CH six hydrogens are present 8. Among the following, the number of compounds than can react with PCl 5 to give PCl is, C, S, H, H S 4, P 4 0 Ans : 4 Sol : PCl5 H PCl HCl PCl5 S SCl PCl 6PCl P 0PCl 5 4 0, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

9 .A.P. 9 :: IIT JEE 0 Paper - II :: SECTIN IV( Total Marks : 6) (MATRIX-MATCH TYPE) This section contains questions. Each question has four statements A,B,C and D given in Column I and five statements p,q,r,s and t in Column II. Any given statement in Column I can have correct matching with NE or MRE statement(s) given in Column II. For example, if for a given question, statement B matches with the statement given in q and r, then for the particularquestion, against statement B, darken the bubbles corresponding to q and r in the RS. 9. Match the reaction in colum I with appropriate types of steps/reactive intermediate involved in these reactions as given in column II Column - I Column -II A) P) Nucleophilic substitution B) Q) Electrophilic substitution C) R) Dehydratiion D) S) Nucleophilic addition Ans :Arst; B pst; C rs; Dqr T) Carbanion CH - H C Sol : A) H H H H H H, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

10 .A.P. 0 :: IIT JEE 0 Paper - II :: - Cl CH - CH - CH - Cl + CH MgI CH Cl - Nu. sub B) CH C) 8 CH - CH - CH - H H S 4 + H 8 CH - CH - CH - H Nucleophilic addition H H 8 - H 8 - H + 8 H dehydration D) H H H H electrophelic sub., Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

11 .A.P. :: IIT JEE 0 Paper - II :: 0. M atch the transf ormati ons i n column I with appropriate options in column II Column I A) C s C g Column II (P) phase transition B) CaC s Ca s C g (Q) allotropic change C) H H g (R) H is positive P P D) white,solid red,solid (S) S is positive Ans: Ap,r,s;Br,s; Ct; Dq,t Sol : Conceptual (T) S is negative, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

12 .A.P. :: IIT JEE 0 Paper - II :: PART II : PHYSICS ============================================================== SECTIN I (Total Marks : 4) ( SINGLE CRRECT CHICE TYPE ) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) for its answer, out of which NLY NE is correct. A satellite is moving with a constant speed V in a cirular orbit about the earth. An object of mass m is ejected from the satellite such that it just escapes from the gravitation pull of the earth. At the time of its ejection, the kinetic energy of the object is Ans : B Sol : a) mv b) mv c) mv d) mv P. E. KEi mv Gm pei r finally KE PE r 0 KE PE r Gm r mv. A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius ' ' and outer radius b. The spiral lies in the X - Y plane and a steady current I flows through the wire. The Z - component of the magnetic field at the center of the spiral is r v 0NI b ln b a a a) 0NI b a ln b a b a b) c) d) Ans : A 0NI b ln b a 0NI b a ln b b a, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

13 .A.P. :: IIT JEE 0 Paper - II :: N dn Sol :...() b a dr db C 0 dni r db c 0I N dr r b a B c 0IN b ln b a a. A point mass is subjected to two simultaneous sinusoidal displacements in x - direction, and x t Asin t x t Asin t. Adding a third sinusoidal displacement x t Bsin t brings the mass to a complete rest. The vaules of B and are a) Ans : B Sol : A 4 A, b) 4 4 A, c) 5 A, d) A, 6 A A A; / B A; at 4 4. Which of the field patterns given below is valid for electric field as well as for magnetic field? a) b) c) d) Ans : C Sol : Induced electric field may be cd a closed loop, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

14 .A.P. 4 :: IIT JEE 0 Paper - II :: 5. A ball of mass 0. kg rests on a vertical of heights 5 m. A bullet of mass 0.0 kg, travelling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The hits the ground at a distance of 0 m and the bullet at a distance of 00 m from the foot of the post. The initial velocity V of the bullet is Ans : D a) 50 m/s b) 50 m / s c) 400 m/s d) 500 m/s Sol : time of fall = t gt 5 t = sec V 0; V 0 m / s ball ball V 00; V 00 m / s bullet bullet m V m V m. V bullet bullet bullet ball ball 0.0v m m = 0. mb v 4 5 v 500 m / s 6. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is.5 mm and that on the circular scale is 0 divisions. If the measured mass of the ball has a relative error of %, the relative percentange error in the density is Ans : C a) 0.9% b).4% c).% d) 4.% Sol : msd = 0.5mm csd has 50 division 50csd = msd 50 csd = 0.5 mm...() least count = 0.0mm, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

15 .A.P. 5 :: IIT JEE 0 Paper - II :: diameter = d ; 0.5 d.5mm 0 mm 50 d.7 mm 4 d m. 8 d now max dm m d d d d d 0.0 d.7 90 % value. d 00.. max 7. A wooden block performs SHM on a frictionless surface with frequency, v 0. The block carries a charge +Q on its surface. If now a uniform electric field E is switched - on as shown, then the SHM of the block will be a) of the same frequency and with shifted mean position b) of the same frequency and with the same mean position c) of changed frequency and with shifted mean position d) of changed frequency and with the same mean position Ans : A Sol : +Q E due to new constant force mean position is shifted but frequency of oscillation will not change, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

16 .A.P. 6 :: IIT JEE 0 Paper - II :: 8. A light ray traveling in glass medium is incident on glass - air interface at an angle of incidence. The reflected (R) and transmitted (T) intensities, both as function of, are plotted. The correct sketch is a) b) Ans : C c) d) Sol : 00% reflection or transmission not possible SECTIN II (Total Marks : 6) ( MULTIPLE CRRECT ANSWER(S) TYPE ) This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) for its answer, out of which NE or MRE may be correct 9. A series R-C circuit is connected to AC voltage source. Consider two cases ; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is / are true? Ans : BC a) I A B R IR b) I A I B A B c) V V A B d) VC VC R R C C Sol : z R wc CA CB Z A ZB, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

17 .A.P. 7 :: IIT JEE 0 Paper - II :: A B I I (B) is correct R R V C C. wc R wc X I R wc C C V V A B A B C C c is correct 0. Which of the following statement(s) is/are correct? Ans : CD a) If the electric field due to a point charge varies as.5 r instead of r, then the Gauss law will still be valid. b) The gauss law can be used to calculate the field distribution around an electric dipole. c) If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same. d) The work done by the external force in moving a unit positive charge from point A at potential V A to potential V B is V - V Sol : Surface area r So,, if and only if E r, E. ds will be independent of r (A) is false B A Around a dipole, E. ds q in, net = zero So, for any type of Gausian surface, RHS = 0 The equation will not be useful to calculate E. (B) is false q kq E. ˆ. ˆ net k r v r 0 r Therefore, rˆ r A rˆ ( in between the charges) B q & q must have same sign (c) is correct A B From the definition of work done by electric field, W q V V B A (D) is correct, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

18 .A.P. 8 :: IIT JEE 0 Paper - II ::. A thin ring of mass kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity m/s. A small ball of mass 0. kg, moving velocity 0 m/s in the opposite direction, hits ring at a height of 0.75 m and goes vertically up with velocity 0 m/s. Immediately after the collision. Ans : A,C a) the ring has pure rotation about its stationary CM. b) the ring comes to a complete stop c) friction between the ring and the ground is to the left. d) there is no friction between the ring and the ground. Sol : F dt = - x F dt y for the ring, N Mg Fy Fy F dt M V V x V V 0 dt : F dt 0.5 F dt 0.5 x y Li MR MVR 0.5 L L dt f W f i 0. Tw o solid spheres A and B of equal volumes but of different densities d A and d B are connectd by a string. They are fully immersed in a fluid of density de. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if a) d A - d F b) d B > d c) F d A > d d) F d A + d B d F, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

19 .A.P. 9 :: IIT JEE 0 Paper - II :: Ans : ABD Sol : Equilibrium : B + B = W + W df V + Vg = Vg d A + db d d + d () F A B If db d F, the string becomes black To keep the string tight, d A < d and F d B > df Ans : ABD SECTIN III (Total Marks : 4) ( INTEGER ANSWER TYPE) This section contains 6 questions. The answer to each of the questions is a single -digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the RS.. A block of mass 0.8 kg is attached to a spring of force-constant N/m. The coefficient of friction between the block and the floor is 0.. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06m and comes to rest for the first time. The initial velocity of the block in m/ s is V = N/0. Then N is Ans : 4 Sol : mv µmgx + kx 0.8 V x V = 08 x x V = V = 0 - N V = 0.4 ms = 0 N = 4, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

20 .A.P. 0 :: IIT JEE 0 Paper - II :: 4. Two batteries of different emfs and different internal resistance are connected as shown. The voltage across AB in volts is Ans : 5 Sol : ε r + ε r V AB = r + r 6 = Water (with refraction index = 4 ) in a tank is 8 cm deep. il of refractive index 7 lies. n 4 water making a conves surface of radius ov curvature R = 6 cm as shown. Consider oil to act as a thin lens. An object S is placed 4 cm above water surface. The location of its image is at x cm above the bottom of the tank. Then x is Ans : Sol : = - V -4 6 V = apporent depth = 4 x = 6 distance = 8-6 = cm 6. A series R-C combination is connected to an AC voltage of angular frequency radian/s. If the impedance of the R-C circuit is, the time constant (in millisecond) of the circuit is, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

21 .A.P. :: IIT JEE 0 Paper - II :: Ans : 4 Sol : - w = 500 rad s z = R + wc R 5 = R 4 wc wc R R X C c RC 0.4 x 0 w 500 4ms 7. A silver sphere of radius cm and work funtion 4.7 ev is suspended from an insulting thread in free-space. It is under continuous illumination of 00 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of Ans : 7 photoelectrons emitted from the sphere is 40 Sol : W0 4.7 ev, E 6.ev 00 k = =.5ev Where < A < 0. The value of Z is z x 0 neqe W 4 r 0 hc n n n n 4 8. A train is moving along a straight line with a constant acceleration ' '. A body standing in the train throws a ball forward with a speed of 0 m/s, at an angle of 60 to the horizontal. The boy has to move forward by.5m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s, is Ans :5, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

22 .A.P. :: IIT JEE 0 Paper - II :: vy 0 sin 60 Sol : T a 0 y ˆ ˆ.5i 5 i a iˆ a 5ms Section IV( Total Marks : 6) (Matrix-Match Type) This section contains questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p,q,r,s and t) in Column II. Any given statement in Column I can have correct matching with NE or MRE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for the particular question, against statement B, darken the bubbles corresponding to q and r in the RS. 9. Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible nature frequency of a system is called its fundamental frequency, whose wavelength is denoted as. Match each system with statements given in f Column II describing the nature and wavelength of the standing waves. Column I (A) Pipe closed at one end Column II (p) Longitudinal waves (B) Pipe open at both ends (q) Transverse waves (C) Stretched wire clamped at both ends (r) f L (D) Stretched wire clamped at both ends and at (s) f L mid-point Ans : A P, t ; B P, s ; C q, s ; D q, r (t) f 4L, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

23 .A.P. :: IIT JEE 0 Paper - II :: Sol : Longitudinal waves can only e rist n gases white transverse waves can only rist in stretched strings A P, t ; B P, s ; C q, s ; D q, r 40. ne mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P.V. diagram. Column II given the characteristics involved in the cycle. Match them with each of the processes given in Column I Column I (A) Process A B (B) Process B C (C) Process C D (D) Process D A Ans : A r, t, p ; B p, r ; C s, q ; D t, r Column II (p) Internal energy decreases. (q) Internal enengy increases. (r) Heat is lost (s) Heat is gained. (t) Work is done one the gas. Sol : p k, V, T both are decreased, so dv decreases, dwalso ve so, dq is ve V = K, P, T dq is also -ve because dw = 0 P = K, V, Tincreased, dv is +ve, dq is also +ve. T = K isothermal process, v is decreased, dq is -ve, dq is -ve because, dv = 0, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

24 .A.P. 4 :: IIT JEE 0 Paper - II :: IIT - JEE 0 PART III : MATHEMATICS SECTIN I (Total Marks : 4) (Single Correct Answer Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which NLY NE is correct 4. A value of b for which the eqautions Ans : B have one root in common is x + bx = 0 x + x + b = 0, a) b) i c) i 5 d) Sol : c a c a a b a b b c b c b bb b b 0 b 0, i 4. Let be a cube root of unity and S be the set of all non-singular matrices of the form a b c, where ech of a, b, and c is either or. Then the number of distinct matrices in the set S is a) b) 6 c) 4 d) 8 Ans : A Sol : c c a c b 0 0 a c c a c ac c = 0, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

25 .A.P. 5 :: IIT JEE 0 Paper - II :: 4. The circle passing thorugh the point (, 0) and touching the y-axis at (0, ) also passes through the point a), 0 b) 5, c) 5, d) ( 4, 0) Ans : D Sol : x + y + gx + fy + c = g + c = 0 f = c f f + c = c = 4 c 6 + c + 8c = 6c f = c 8c + 6 = 0 c = If x a) Lt x b b b x0 ln sin, 0 and (, ], then the value of is b) 4 c) d) 6 Ans : D x ln Sol : Lt x b x0 Lt l nb x 0 e = + b = b sin b b sin + = 0 b> 0 sin = b = 0 b =, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

26 .A.P. 6 :: IIT JEE 0 Paper - II :: 45. Let f : [, ] [0, ) Let R = be a continuous function such taht f(x) = f( x) for all x[, ]. x f x dx, and R be the area of the region bounded by y = f(x), x =, x =, and the x-axis. Then a) R = R b) R = R c) R = R d) R = R Ans : C Sol : R = x f x dx, R f x dx R f t dt t f t dt R R R R = R 46. Let f(x) = x and g(x) = sin x for all x. Then the set of all x satisfying Ans : A f g g f x g g f x, where f g x f g x a) n, n0,,,... b) n, n,... c) n, n...,,,0,,,... d) n, n...,,,0,,,... Sol : f x x, g x sin x f g gf x g g f x f g g x g g x sin sin f g x g x sin sin sin sin f x x x x sin sin, sin sin 0, is sin x n sin x 0 sin 0 No roots x n x n, n 0,,,..., Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

27 .A.P. 7 :: IIT JEE 0 Paper - II :: 47. Let (x, y) be any point on the parabola y = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio :. Then the locus of P is a) x = y b) y = x c) y = x d) x = y Ans : C at at, x, y 4 4 t t x, y t y 4 y x y x x y 48. Let P(6, ) be a point on the hyperbola. If the normal at the point P intersects the a b x-axis at (9, 0), then the eccentricity of the hyperbola is a) Ans : B 5 a x b y a b x y a x b y a b b a a a b b b) c) d) e SECTIN II (Total Marks : 6) (Multiple Correct) This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which NE or MRE may be correct 49. Let E and F be two independent events. The probability that exactly one of them occurs is 5 Ans : AD and the probability of none of them occuring is. If P(T) denotes the probability of 5 occurence of the event T, then a) P E, P( F) b) P E 5 5 c) P(E) = P E, P( F) d) P E, P( F) 5 5 4, P( F) 5 5, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

28 .A.P. 8 :: IIT JEE 0 Paper - II :: 5 5 c c Sol : P E F x y c c P E F P E F x y x y 5 x y xy 5 5 x y xy Let L be a normal to the parabola y = 4x. If L passes through the point (9, 6), then L is given by a) y x + = 0 b) y + x = 0 c) y + x 5 = 0 d) y x + = 0 Ans : ABD Sol : y = mn am am y = mx m m m m + 6 = 0 m = y = x y = x + y = x 5. Let f : (0, ) be defined by f x b x, bx where b is a constant such that 0 < b <. Then a) f is not invertible on (0, ) on (0, ) and f ' b b) f f f ' 0 c) f = f on (0, ) and f ' b d) f is differentiable on (0, ) Ans : CD f ' 0, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

29 .A.P. 9 :: IIT JEE 0 Paper - II :: Sol : b x f x y bx b x = y yb x b y b y = x ( yb) x = by b y f f, f y by f ' x b bx bx b xb bx b 0, f ' x 0 f is invertible b f b f b b b ' ' 0 f ' b f ' 0 5. If f x x, x cos x, x 0 x, 0 x ln x, x, then a) f(x) is continuous at x = b) f(x) is not differentiable at x = 0 c) f(x) is differentiable at x = d) f(x) is differentiable at x =, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

30 .A.P. 0 :: IIT JEE 0 Paper - II :: Ans : ABCD Sol : x x Lt f x Lt f x 0 0 x x Lt f x Lt f x 0 f s continuous at x = x sin x x 0 f ' x 0 x x x f is not diff at x = 0 Lf ' 0 0, Rf Lf ' Rf ' f is diff at x = f is diff at x = ' 0 SECTIN III ( INTEGER ANSWER TYPE) This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which NLY NE is correct 5. The number of distinct real roots of 4 x 4x x x 0 is Ans: Sol : 4 f x x 4x x x 0 f x x x x 4 4 If it is strictly increasing x f 0 has only one root f 0 0 f 0, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

31 .A.P. :: IIT JEE 0 Paper - II :: 54. Let y ' x y x g ' x, y 0 0, x R, where f ' Ans : 0 x denotes non constant differentiable function on R with g g Sol : y ' x y x g ' x g x g ' x ye g x g ' xe ' ' g x dx g x dx gx gx ye g x g ' x e dx df x dx and g(x) is a given 0 0. Then the value of y() is = g x g x ' g x e g x dx t g ' x dx dt t te dt g x y x g x ye g x e e c y 0 0 c c y e g e e g g x g y Let M be a matrix satisfying 0 M, 0 0 M, and 0 0 M 0 Ans : 9 Then the sum of the diagonal entrices of M is Sol : 0 M 0 0 M 0, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

32 .A.P. :: IIT JEE 0 Paper - II :: M 0 a b c M d e f g h i a b c 0 d e f g h i 0 b e = h = a b c d e f g h i 0 a b a 0 g h g a b c 0 d e f 0 g h i g h l l 7 a + e + l = = Let a i k, b i j and c i j k be three given vectors. If r is a vector such that r b cb and r. a 0, then the value of r. b is Ans : 9 Sol : r cb 0, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

33 .A.P. :: IIT JEE 0 Paper - II :: r c b r c tb r. a 0 c. a tb. a c. a t b. a a. c r c b a. b 4 i j k i j i+j+k-4i+4j = i+bj+k r. b The straight line x y divides the circular regeion x y 6 into two parts. If Ans : 5 S,,,,,,,, then the number of points in S lying inside the smaller part is Sol : (0,0) lies at side smaller put 0 0 x y, 4 5, 4, 4 4, Number of points =, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

34 .A.P. 4 :: IIT JEE 0 Paper - II :: i 58. Let e, and a,b,c,x,y,z be non zero complex numbers such that a b c x a b c y a b c z then the value of x y z a b c is Ans : Doesn t get the integer 59. Match the statements given in Column I with the intervalus/union of intervalus given in column II Column I Column II iz A) The set Re : Z is a complex number, z, z z B) The domain of the function f x f C) If tan tan tan tan x 8 sin x, then the set f : 0 p),, is q), 0 0, is r), D) If f x x x 0, x 0, then f(x) is increasing in s),, t),0, i iz ie Sol : A) z e i i ie cos i sin i cos isin sin isin cos i cos i sin sin sin i cos, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

35 .A.P. 5 :: IIT JEE 0 Paper - II :: sin sin (, ] [, ) sin Ans : A s ; B) Let x = a sin 8. x x defined for x 8. x 8a let x = a 9 a x (, 0] [, ) B t ; C) f tan tan 0 tan sec 0 sec [, ) C r ; f ' x x x 0 x D) x x 0 x 0 5x 0 x 0 x 0, x D r, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

36 .A.P. 6 :: IIT JEE 0 Paper - II :: 60. Match the statements given in Column I with the values given in Column II Column I Column II A) If a j k, b j k and c k p) 6 form a triangle, then the internal angle of the triangle between a and b is b B) If a f x x dx a b then the value of f 6 is q) 5 6 C) The value of sec x dx ln is r) 7 6 D) The maximum value of Arg z for z, z is s) given by t) a b A) cos a b. As A q ; B) () f(b) b = b f(b) = b B p ; f sec x tan x C) ln ln ln ln C s 7 6, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :

37 .A.P. 7 :: IIT JEE 0 Paper - II :: D) arg arg z 0 arg cos i sin sin cos tan tan cot As D t ;, Plot No 5, Ayyappa Society, Madhapur, Hyderabad : , Website :