SOLUTIONS TO JEE (ADVANCED) – 2019

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JEE(ADVANCED)-2019-Paper-1-PCM-1Note:For the benefit of the students, specially the aspiring ones, the question of JEE(advanced), 2019 are also given inthis booklet. Keeping the interest of students studying in class XI, the questions based on topics from class XI havebeen marked with ‘*’, which can be attempted as a test. For this test the time allocated in Physics, Chemistry &Mathematics are 30 minutes, 21 minutes and 25 minutes respectively.FIITJEESOLUTIONS TO JEE (ADVANCED) – 2019PART I: PHYSICSSection 1 (Maximum Marks: 12) This section contains FOUR (04) questions.Each question have FOUR options. ONLY ONE of these four options is the correct answer.For each question, choose the option corresponding to the correct answer.Answer to each question will be evaluated according to the following marking scheme:Full Marks: 3 If ONLY the correct option is chosen.Zero Marks: 0 If none of the options is chosen (i.e. the question is unanswered);Negative Marks : –1 In all other cases.*Q.1Consider a spherical gaseous cloud of mass density (r) in free space where r is the radial distance from itscenter. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the commoncenter with the same kinetic energy K. The force acting on the particles is their mutual gravitational force.If (r) is constant in time, the particle number density n(r) (r)/m is[ G is universal gravitational constant]3KKA.B.222 r m G2 r m 2 GKKC.D.2226 r m G r m 2 GSol.B1 d(gr 2 )4 Gr 2 drmv 2Because mgr1mgrsomv 2 K 22so from equation (i)1 d 2k K r 24 Gr dr m 2 Gmr 2 Kso, m 2 Gm 2 r 2 Q.2. . . (i)A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential atits surface is V0. A hole with a small area 4 R2( 1) is made on the shell without affecting the rest ofthe shell. Which one of the following statements is correct?FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-2A. The magnitude of electric field at a point, located on a line passing through the hole and shell’s center, V0on a distance 2R from the center of the spherical shell will be reduced by2R V0B. The magnitude of electric field at the center of the shell is reduced by2R1C. The ratio of the potential at the center of the shell to that of the point at R from center towards the21 hole will be1 2 D. The potential at the center of the shell is reduced by 2 V0Sol.C 4 R 24 0 RV0 1 2 V0 0 R 2 V0 (1 2 4 0 R Rso V at R/2 v0 -and V at centre V0 *Q.31 1 V0 0 4 R 2 V0 (1 - )4 0 RRA current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metalrod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changeswith time (t) asT (t) T0 (1 t1/4)where is a constant with appropriate dimension while T0 is a constant with dimension of temperature.The heat capacity of the metal is4P(T(t) T0 ) 44P(T(t) T0 )A.B.4 5 T0 4 T02C.Sol.V0 0R 4P(T(t) T0 ) 2 4 T02D.4P(T(t) T0 ) 3 4 T04DAt equilibrium, CdT PdtdT T0 34 tdt4So heat capacity C 4P 34t T0T t T0From the given equation3So t 4 So C Q.4 T t T T01 t430330 T34PT t T0 4 4 T0In a radioactive sampleyear or into stable40184019K nuclei either decay into stable4020Ca nuclei with decay constant 4.5 10-10 perAr nuclei with decay constant 0.5 10 10 per year. Given that in this sample all theFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-3stable4020Ca and4018Ar nuclei are produced by thesum of stable 4020 Ca and[Given : ln10 2.3]A. 1.15C. 9.240184019K nuclei only. In time t 109 years, if the ratio of theAr nuclei to the radioactive4019K nuclei is 99, the value of t will beB. 4.6D. 2.3CSol.So equivalent decay constant 1 2 5 10 10 per yearN eN0eq tN Nand given that 0 99N 140194020CaK 2So t 9.2 109 year4018ArSection 2 (maximum marks: 32) Q.1This section contains EIGHT (08) questions.Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is(are) correctanswer(s).For each question, choose the option(s) corresponding to (all) the correct answer(s).Answer to each question will be evaluated according to the following marking scheme.Full Marks: 4 If only (all) the correct option(s) is (are) chosen;Partial Marks : 3 If all the four options are correct but ONLY three options are chosen;Partial marks : 2 if three or more options are correct but ONLY two options are chosen and bothof which are correct;Partial Marks : 1 If two or more options are correct but ONLY one option is chosen and it is acorrect option;Zero Marks: 0 If none of the options is chosen (i.e. the question is unanswered);Negative Marks : –1 In all other cases.For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correctanswers, thenchoosing ONLY (A), (B) and (D) will get 4 marks;choosing ONLY (A) and (B) will get 2 marks;choosing ONLY (A) and (D) will get 2 marks;choosing ONLY (B) and (D) will get 2 marks;choosing ONLY (A) will get 1 mark;choosing ONLY (B) will get 1 mark;choosing ONLY (D) will get 1 mark;choosing no option (i.e. the question is unanswered) will get 0 marks; andchoosing any other combination of options will get –1 mark.A conducting wire of parabolic shape, initiallyy y x2, is moving with velocity V V0 ˆi in aBLnonuniformmagneticfield y V V0 iˆB B0 1 k̂ , as shown in figure. If V0 L , B0, L and are positive constants and is0Lthe potential difference developed between theends of the wire, then the correct statement(s)is/are:A. is proportional to the length of the wire projected on the y-axis.xFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-4B. remains the same if the parabolic wire is replaced by a straight wire, y x initially, of length1C. B0 V0 L for 024D. B0 V0 L for 23Sol.A, B, DThese is no change in flux through the loopOABO due to the movement of loop. Sopotential difference developed in curved wireand the straight wire OA is same.yAL Q.2 B V V0 ˆiFor 0, 2B0 V0 LL y2For 2, B0 1 20 L2LB V0 dy 0Lx4B0 V0 L3A thin convex lens is made of two materials with refractive indices n1 and n2, asshown in figure. The radius of curvature of the left and right spherical surfacesare equal. f is the focal length of the lens when n 1 n2 n. The focal length is f f when n1 n and n2 n n. Assuming n (n – 1) and 1 n 2. Thecorrect statement(s) is/are.A. f n fnB. If n f 0 then 0nfn2n1C. For n 1.5, n 10-3 and f 20 cm, the value of f will be 0.02 cm (round off to 2nd decimal place). f nandremains unchanged if both the convex surfaces are replaced byfnconcave surfaces of the same radius of curvature.B, C, DWhen n1 n2 n1 2 n 1 (i)f R When, n1 n and n 2 n nD. The relation betweenSol.1 1 1 n 1 n n 1 f fR R So from equation (i) and (ii)11 1 n f f f R f 1 n 2f R f n nSo f2 n 1 2n (ii)FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-5*Q.3A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T 1 and T2 of differentmaterials having water contact angles of 00 and 600, respectively. The capillary tube is dipped vertically inwater in two different configurations, case I and II as shown in figure. Which of the following option(s) is(are) correct?[Surface tension of a water 0.075 N/m, density of water 1000 kg/m3, take g 10 m/s2]Case-IT2Case-IIT1T1T2A. For case I, if the joint is kept at 8 cm above the water surface, the height of water column in the tube willbe 7.5 cm. (Neglect the weight of the water in the meniscus)B. For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised inthe tube will be more than 8.75 cm. (Neglect the weight of the water in the meniscus)C. For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in thetube will be 3.75 cm. (Neglect the weight of the water in the meniscus)D. The correction in the height of water column raised in the tube, due to weight of water contained in themeniscus, will be different for both cases.Sol.A, C, DWhen T1 is in contact with waterthen h 2T cos 1 7.5 cm 8cm .r gBut in option (B) height is insufficient.When T2 is in contact with waterthen h 2T cos 2 3.75 cm 5 cmr gVolume of water in the meniscus depends upon the angle of contact.Q.4A charged shell of radius R carries a total charge Q. Given as the flux of electric field through a closedcylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of thecylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Whichof the following option(s) is/are correct?[ 0 is permittivity of free space]A. If h 8R/5 and r 3R/5 then 0B. If h 2R and r R then Q/ 0C. If h 2R and r 4R/5 then Q/5 0D. If h 2R and r 3R/5 then Q/5 0Sol.A, B, DFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-6Option (B)Option (A)h 2R3R58R h5r ROption (D)37 h 2R r Q 2 2 1 cos 37 4 03R5*Q.5Let us consider a system of units in which mass and angular momentum are dimensionless. If length hasdimension of L, which of the following statement(s) is/are correct?A. The dimension of energy is L–2B. The dimension of force is L–3C. The dimension of power is L–5D. The dimension of linear momentum is L-1Sol.A, B, D M 0 L0 T 0 ML2 T 1 L2 T Energy MLT 2 L L 2Force MLT 2 L 3Power MLT 2 LT 1 L 4linear momentum MLT–1 L–1FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-7Q.6In the circuit shown, initially there is no charge oncapacitors and keys S1 and S2 are open. The valuesof the capacitors are C1 10 F, C2 30 F and C3 C4 80 F. Which of the statement(s) is/arecorrect?S1PC2C1C4 5V 30 S2C330 10V70 100 QA. The key S1 is kept closed for long time such that capacitors are fully charged. Now key S2 is closed,at this time, the instantaneous current across 30 resistor (between points P and Q) will be 0.2 A(round off to 1st decimal place).B. If key S1 is kept closed for long time such that capacitors are fully charged, the voltage across thecapacitor C1 will be 4V.C. At time t 0, the key S1 is closed, the instantaneous current in the closed circuit will be 25 mAD. If key S1 is kept closed for long time such that capacitors are fully charged, the voltage differencebetween points P and Q will be 10 V.Sol.B, CS1 closed for long time5VP80 F80 F10 FQ 40 V10 F 5 4V 40 10 VP VQ 4V t 0 , key S is closed5i 25 mA70 100 300.5 V4V 70 i1i20V 5V30 i1 i2 30 0.5 V 10 V– 70i1 30 i2 – 6 0– 30i1 – 60 i2 6 0 i2 0.11 AFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-8*Q.7One mole of a monatomic ideal gas goes through athermodynamic cycle, as shown in the volume versustemperature (V – T) diagram. The correct statement(s)is/are:[R is the gas constant]V32V02V041TT0/2T03T0/2 2T01RT025 3A. Work done in this thermodynamic cycle (1 2 3 4 1) is W Q1 2Q 2 3B. The ratio of heat transfer during processes 1 2 and 2 3 isC. The above thermodynamic cycle exhibits only isochoric and adiabatic processes.Q1D. The ratio of heat transfer during processes 1 2 and 3 4 is 1 2 Q3 42Sol.A, BRT02nC p T2 T1 PWcycle P0 V0 Q1 25 5 Q2 3nC V T3 T2 3 3nC p T2 T1 Q1 2 2Q2 3nC V T4 T3 (T0)2P0P014(T0/2)(2T0)23(T0)TV0Q.82V0Two identical moving coil galvanometers have 10 resistance and full scale deflection at 2 A current.One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of1mA full scale current using appropriate resistors. These are then used to measure the voltage and currentin the Ohm’s law experiment with R 1000 resistor by using an ideal cell. Which of the followingstatement(s) is/are correct?A. The measured value of R will be 978 R 982 B. The resistance of the Voltmeter will be 100 k C. If the ideal cell is replaced by a cell having internal resistance of 5 then the measured value of R willbe more than 1000 D. The resistance of the Ammeter will be 0.02 (round off to 2nd decimal place)FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-9Sol.A, DV Ig G R V RVGG R V R V 5 10 4 I IgG Ig G I Ig SS 20 m SGSR ammeter 20 10 3 G S 51 i R A is small 1000R V 5 104 1000 R V Vi1A1000 i 1000 R V i1 i 10001000 i1 1000 R measured 980.4 i SECTION 3 (Maximum Marks: 18) This section contains SIX (06) questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer using the mouse and the on-screenvirtual numeric keypad in the place designated to enter the answer. If the numerical value has morethan two decimal places, truncate/round-off the value to TWO decimal places. Answer to each question will be evaluated according to the following marking scheme:Full Marks : 3 If ONLY the correct numerical value is entered;Zero Marks : 0 In all other cases.*Q.1A block of weight 100 N is suspended by copper andsteel wires of same cross sectional area 0.5 cm2 and,length 3 m and 1 m, respectively. Their otherends are fixed on a ceiling as shown in figure. Theangles subtended by copper and steel wires withceiling are 30 and 60 , respectively. If elongation incopper wire is C and elongation in steel wire is30 60 Copper wireSteel wire1m3mBlock Cis S , then the ratio S[Young’s modulus for copper and steel are 1 1011 N/m2 and 2 1011 N/m2, respectively.]FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-10Sol.2.00TSTS sin 30 TC sin 60 TC CT A Y C C S S 2.00 S A C YC TS S 30 60 100*Q.2A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force F yiˆ 2 xjˆ N , –1where x and y are in meter and – 1 Nm . The work done on the particle by this force F will be Joule.y1.0ABDC0.5F0Sol.E0.5x1.00.751w AB ydx 100.5w BC 2 xdy 110.5w CD ydx 0.2510w DE 2 xdy 0.50.5w EF w FA 0Wnet 0.75A train S1, moving with a uniform velocity of 108km/h, approaches another train S2 standing on aplatform. An observer O moves with a uniformvelocity of 36 km/h towards S2, as shown in figure.Both the trains are blowing whistles of samefrequency 120 Hz. When O is 600 m away from S2and distance between S1 and S2 is 800 m, thenumber of beats heard by O is .[Speed of the sound 330 m/s]108 km/hS2800 m600 m36 km/h* Q.3OFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.S1

JEE(ADVANCED)-2019-Paper-1-PCM-11Sol.8.13 330 10 cos53 f1 120 330 30 cos 37 30 m/sS2S1800 m 330 10 f 2 120 330 f b f1 f2 8.128Hz 8.13 Hz37 600 m10 m/s53 O*Q.4A liquid at 30 C is poured very slowly into a Calorimeter that is at temperature of 110 C. The boilingtemperature of the liquid is 80 C. It is found that the first 5 gm of the liquid completely evaporates. Afterpouring another 80 gm of the liquid the equilibrium temperature is found to be 50 C. The ratio of theLatent heat of the liquid to its specific heat will be C.[Neglect the heat exchange with surrounding]Sol.270.005 s 50 5L C 30 (i)80 s 20 C 30 from (i) and (ii)L 270 CS 270.00Q.5 (ii)A planar structure of length L and width W is made of two different optical media of refractive indicesn1 1.5 and n2 1.44 as shown in figure. If L W, a ray entering from end AB will emerge from end CDonly if the total internal reflection condition is met inside the structure. For L 9.6 m, if the incident angle is varied, the maximum time taken by a ray to exit the plane CD is t 10–9 s, where t is .[Speed of light c 3 108 m/s]n2CAAirWn1 Bn2DLFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-12Sol.50.001.5sin C 1.44sin 90 sin C 1.442425Q.6 1.5 x25 xsin C4total length for light to travel25 9.6 10m4 time 5 10 8 s 50 10 9 sc / 1.5t 50.00xA parallel plate capacitor of capacitance C has spacing d between two plates having area A. The regiondbetween the plates is filled with N dielectric layers, parallel to its plates, each with thickness . TheNm dielectric constant of the mth layer is K m K 1 . For a very large N 103 , the capacitance C is N K A 0 . The value of will be . d ln 2 [ 0 is the permittivity of free space] Sol. 1.00dx1dx dC m k 1 0 A N 1ddxx 0 k 1 0 d K 0 A Ceq d ln 2 1.00 dC xddx m NFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-13PART II: CHEMISTRY *Q.1Sol.SECTION 1 (Maximum Marks: 12)This section contains FOUR (04) questions.Each question has FOUR options. ONLY ONE of these four options is the correct answer.For each question, choose the option corresponding to the correct answer.Answer to each question will be evaluated according to the following marking scheme:Full Marks : 3 If ONLY the correct option is chosen.Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).Negative Marks : 1 In all other cases.The green colour produced in the borax bead test of a chromium(III) salt is due to(A) CrB(B) Cr2O3(C) Cr2(B4O7)3(D) Cr(BO2)3(D)Cr(BO2)3 Na 2 B4 O7 10H 2O Na 2 B4O 7 NaBO 2 B2 O3Cr2O3 B2O3 Cr(BO2 ) 3(green colour bead)Q.2Molar conductivity ( m) of aqueous solution of sodium stearate, which behaves as a strong electrolyte, isrecorded at varying concentrations (c) of sodium stearate. Which one of the following plots provides thecorrect representation of micelle formation in the solution?(critical micelle concentration (CMC) is marked with an arrow in the figuresCMCCMC(A) m(B) mc(C) mcCMC(D) mCMCccSol.(B)Q.3Calamine, malachite, magnetite and cryolite, respectively, are(A) ZnSO4, Cu(OH)2, Fe3O4, Na3AlF6(B) ZnCO3, CuCO3.Cu(OH)2, Fe3O4, Na3AlF6(C) ZnSO4, CuCO3, Fe2O3, AlF3(D) ZnCO3, CuCO3, Fe2O3, Na3AlF6(B)Calamine – ZnCO3Malachite – CuCO3.Cu(OH)2Magnetite – Fe3O4Cryolite – Na3AlF6Sol.FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)-2019-Paper-1-PCM-14*Q.4Sol. The correct order of acid stre

JEE(ADVANCED)-2019-Paper-1-PCM-3 FIITJEE Ltd., FIITJEE House, 29 -A, Kalu Sarai, Sarvapriya Vihar, New Delhi 110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. stable 40 20 Ca and 40 18 Ar nuclei are produced by the 40 19 K nuclei only. In time t 10 9 years, if the ratio of the sum of stable 40 20 Ca and 40 18 Ar nuclei to the radioactive

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