This booklet contains 44 printed pages. ß ÈÁSÃ Ê apple ÈÁŒ Ã Îc 44 Ò PAPER - 1 : PHYSICS, MATHEMATICS & CHEMISTRY Ÿ ÈÁSÃ Ê - 1 : ÊÒÁÃ ÁflôÊÊŸ, ªÁáÊÃ Ã

This booklet contains 44 printed pages. ß ÈÁSÃ Ê apple ÈÁŒ Ã Îc 44 Ò PAPER - : PHYSICS, MATHEMATICS & CHEMISTRY Ÿ ÈÁSÃ Ê - : ÊÒÁÃ ÁflôÊÊŸ, ªÁáÊÃ ÃÕÊ U ÊÿŸ ÁflôÊÊŸ Do not open this Test Booklet until you are asked to do so. ß ËˇÊÊ ÈÁSÃ Ê Êapple Ã Ã Ÿ πêapple apple Ã Ê Ÿ Ê Read carefully the Instructions on the Back Cover of this Test Booklet. ß ËˇÊÊ ÈÁSÃ Ê apple Á apple Êfl áê ÁŒ ª ÁŸŒapple ÊÊapple Êapple äÿêÿ apple apple Important Instructions : ûfl ÍáÊ ÁŸŒapple Ê. Immediately fill in the particulars on this page of the Test Booklet with only Black Ball Point Pen provided in the examination hall.. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully.. The test is of hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 60. 5. There are three parts in the question paper A, B, C consisting of Physics, Mathematics and Chemistry having 0 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of each question. ¼ (one-fourth) marks of the total marks allotted to the question (i.e. mark) will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. For writing particulars/marking responses on Side- and Side of the Answer Sheet use only Black Ball Point Pen provided in the examination hall. 9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 0. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom of each page and in four pages ( Page 40-4) at the end of the booklet.. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.. The CODE for this Booklet is B. Make sure that the CODE printed on Side of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet.. Do not fold or make any stray mark on the Answer Sheet. Name of the Candidate (in Capital letters ) : èÿõë Ê ŸÊ ( «apple ˇÊ Êapple apple ) Roll Number : in figures RBS No. :. UËˇÊÊ ÈÁSÃ Ê apple ß Îc U U Êfl ÿ Áflfl UáÊ UËˇÊÊ ˇÊ apple éœ UÊÿapple ª apple fl Ê apple ÊÚ åflêß U appleÿ apple Ãà Ê apple. ûê U òê ß UËˇÊÊ ÈÁSÃ Ê apple ãœ U UπÊ Ò Ê Êapple UËˇÊÊ ÈÁSÃ Ê πêapple Ÿapple Êapple Ê Ê, ÃÊapple ûê U òê ÁŸ Ê U ÊflœÊŸË Ífl Áflfl UáÊ apple U. UËˇÊÊ Ë fláœ ÉÊ appleu Ò 4. ß UËˇÊÊ ÈÁSÃ Ê apple 90 Ÿ Ò Áœ Ã 60 Ò 5. ß UËˇÊÊ ÈÁSÃ Ê apple ÃËŸ Êª A, B, C Ò, Á apple àÿapple Êª apple ÊÒÁÃ ÁflôÊÊŸ, ªÁáÊÃ fl U ÊÿŸ ÁflôÊÊŸ apple 0 Ÿ Ò ÊÒ U Ë ŸÊapple apple ÊŸ Ò àÿapple Ÿ apple Ë ûê U apple Á 4 (øê U) ÁŸœÊ Á UÃ Á ÿapple ªÿapple Ò 6. èÿáõ ÿêapple Êapple àÿapple Ë ûê U apple Á UÊappleÄÃ ÁŸŒapple ÊŸ ÅÿÊ 5 apple ÁŸŒapple ÊÊŸÈ Ê U ÁŒÿapple Êÿapple ªapple àÿapple Ÿ apple ª Ã ûê U apple Á ÿapple Ÿ apple Á ÁŸœÊ Á UÃ È Êapple apple apple ¼ ( -øêòõêß ) Êª ( ÕÊ Ã ) Ê U Á ÿê ÊÿappleªÊ ÿáœ ûê U òê apple Á Ë Ÿ Ê ûê U Ÿ Ë ÁŒÿÊ ªÿÊ Êapple ÃÊapple È Ê#Ê apple Êappleß UÊÒÃË Ÿ Ë Ë ÊÿappleªË 7. àÿapple Ÿ Ê apple fl Ë Ë ûê U Ò apple Áœ ûê U ŒappleŸapple U apple ª Ã ûê U ÊŸÊ ÊÿappleªÊ ÊÒ U UÊappleÄÃ ÁŸŒapple Ê 6 apple ŸÈ Ê U Ê U Á ÿapple Êÿapple ªapple 8. ûê U òê apple Îc U- fl Îc U- U flê Á UÃ Áflfl UáÊ fl ûê U Á Ã UŸapple appleãè UËˇÊÊ ˇÊ apple éœ UÊÿapple ª apple fl Ê apple ÊÚ åflêß UU appleÿ Ê Ë ÿêappleª apple U 9. èÿõë mê UÊ UËˇÊÊ ˇÊ/ ÊÚ apple flapple Ê Ê«U apple ÊflÊ Á Ë Ë Ê U Ë Ê Ũÿ Ê ª Ë, ÈÁŒ Ã ÿê SÃÁ ÁπÃ, Êª Ë Áø ÿê, apple U, Êapple Êß» ÊappleŸ ÿê Á Ë Ë Ê U apple ß appleä ŲÊÚÁŸ UáÊÊapple ÿê Á Ë ãÿ Ê U Ë Ê ª Ë Êapple apple ÊŸapple ÿê ÿêappleª UŸapple Ë ŸÈ ÁÃ Ÿ Ë Ò 0. U» Êÿ UËˇÊÊ ÈÁSÃ Ê apple apple fl ÁŸœÊ Á UÃ ª U Ë ËÁ ÿ ª àÿapple Îc U U ŸËøapple Ë Êapple U ÊÒ U ÈÁSÃ Ê apple Ã apple øê U Îc UÊapple ( Îc U 40-4) U ŒË ªß Ò. UËˇÊÊ ÊåÃ ÊappleŸapple U, èÿõë ˇÊ/ ÊÚ UÊapple«Ÿapple apple Ífl ûê U òê ˇÊ ÁŸ UËˇÊ Êapple fl ÿ ÊÒ Œapple èÿõë Ÿapple ÊÕ ß UËˇÊÊ ÈÁSÃ Ê Êapple apple Ê Ãapple Ò. ß ÈÁSÃ Ê Ê apple Ã B Ò ÿ ÈÁŸÁ øã U apple Á ß ÈÁSÃ Ê Ê apple Ã, ûê U òê apple Îc U- U U apple apple Ã apple Á ÃÊ Ò ÊÒ U ÿ Ë ÈÁŸÁ øã U apple Á UËˇÊÊ ÈÁSÃ Ê ÊÒ U ûê U òê Ë ÅÿÊ Á ÃË Ò ª U ÿ Á ÛÊ Êapple ÃÊapple èÿõë ŒÍ UË UËˇÊÊ ÈÁSÃ Ê ÊÒ U ûê U òê appleÿapple apple Á ÁŸ UËˇÊ Êapple ÃÈ UãÃ flªã UÊ. ûê U òê Êapple Ÿ Êapple«apple fl Ÿ Ë U ãÿ ÁŸ ÊÊŸ ªÊ ŸÈ Ê Êapple apple : in words ÊéŒÊapple apple Examination Centre Number : ËˇÊÊ apple ãœ Ÿê U Name of Examination Centre (in Capital letters) : UËˇÊÊ apple ãœ Ê ŸÊ ( «apple ˇÊ UÊapple apple ) Candidate s Signature :. Invigilator s Signature : èÿõë apple SÃÊˇÊ ÁŸ ËˇÊ apple SÃÊˇÊ. Invigilator s Signature : ÁŸ ËˇÊ apple SÃÊˇÊ Test Booklet Code ËˇÊÊ ÈÁSÃ Ê apple Ã B

PART A PHYSICS ALL THE GRAPHS/DIAGRAMS GIVEN ARE SCHEMATIC AND NOT DRAWN TO SCALE.. A particle is executing simple harmonic motion with a time period T. At time t=0, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like : Êª A ÊÒÁÃ ÁflôÊÊŸ ÁŒ ªÿapple Ë ª Ê» / appleuπê Î ÁÃÿÊ Ê appleuπëÿ Ò ÊÒ U S apple apple ŸÈ Ê U appleuπê Á Ã Ÿ Ë Ò. áê, ÊflÃ Ê T apple U ÊflÃ ªÁÃ U U Ê Ò ÿ t=0 U fl ÊêÿÊflSÕÊ Ë ÁSÕÁÃ apple Ò ÁŸêŸ apple apple ÊÒŸ Ê ª Ê» ÿ apple ÊÕ ªÁÃ Ê Êapple Ë Œ ÊÊ ÃÊ Ò?. The temperature of an open room of volume 0 m increases from 7 C to 7 C due to the sunshine. The atmospheric pressure in the room remains 0 5 Pa. If n i and n f are the number of molecules in the room before and after heating, then n f n i will be :.5 0 5.5 0 5.6 0.8 0. Íÿ Ë Á UáÊÊapple apple πè apple È 0 m ÊÿÃŸ flê apple appleu Ê ÃÊ ÊŸ 7 C apple U 7 C Êapple ÊÃÊ Ò appleu apple ãœ U flêÿè «U Ëÿ ŒÊ 0 5 Pa Ë U ÃÊ Ò ÿáœ appleu apple ãœ U áêè Êapple Ë ÅÿÊ ª ÊappleŸapple apple apple fl ÊŒ apple Ê n i fl n f Ò ÃÊapple n f n i Ê ÊŸ ÊappleªÊ.5 0 5.5 0 5.6 0.8 0 B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

. Which of the following statements is false? A rheostat can be used as a potential divider. Kirchhoff s second law represents energy conservation.. ÁŸêŸÁ ÁπÃ apple apple ÊÒŸ Ê ÕŸ ª Ã Ò? œê UÊ ÁŸÿ òê Êapple Áfl fl Áfl Ê Ë Ã U ÿêappleª U Ãapple Ò Á UøÊÚ» Ê ÁmÃËÿ ÁŸÿ Ê apple UˇÊáÊ Êapple Œ ÊÊ ÃÊ Ò Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude. In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed. 4. The following observations were taken for determining surface tension T of water by capillary method : diameter of capillary, D=.5 0 m rise of water, h=.45 0 m. Using g=9.80 m/s and the simplified r hg relation T = 0 N/m, the possible error in surface tension is closest to :.4% 0% 0.5% Ë US UÊappleŸ appleãè Ë Èª ËÃÊ apple Áœ Ã ÊappleÃË Ò øê UÊapple ÁÃ UÊappleœÊapple Ê Á U ÊáÊ ÃÈÀÿ ÊappleÃÊ Ò ÃÈÁ Ã Ë US UÊappleŸ appleãè apple, apple fl ªÒÀflappleŸÊapple Ë U U Êapple Ê apple Œ Ÿapple U ÊÍãÿ ÁflˇÊapple Á ãœè ÊÁflÃ ÊappleÃÊ Ò 4. ÁŸêŸ appleˇêáêêapple Êapple apple Á Ê Ê ÁflÁœ apple ÊŸË Ê Îc U ÃŸÊfl T ŸÊ Ÿapple apple Á ÿapple Á ÿê ÊÃÊ Ò apple Á Ê Ê Ê ÿê, D=.5 0 m ÊŸË Ê ø Êfl, h=.45 0 m g=9.80 m/s ÃÕÊ U Ë Î Ã ê ãœ r hg T = 0 N/m, Êapple ÿêappleª UÃapple È Îc U ÃŸÊfl apple ê ÊÁflÃ òêèá U Ê ÁŸ UÃ ÊŸ ÊappleªÊ.4% 0% 0.5%.5%.5% B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

5. In amplitude modulation, sinusoidal carrier frequency used is denoted by ω c and the signal frequency is denoted by ω m. The bandwidth ( ω m ) of the signal is such that ω m <<ω c. Which of the following frequencies is not contained in the modulated wave? ω m +ω c ω c ω m ω m 5. ÊÿÊ ÊÚ«ÈU Ÿ apple íÿêfl Ëÿ flê ÊflÎÁûÊ Êapple ω c apple ÃÕÊ Á ÇŸ ÊflÎÁûÊ Êapple ω m apple Œ ÊÊ Ãapple Ò Á ÇŸ Ë Òá«U øêò«êß ( ω m ) Êapple ß Ã U øèÿãapple Ò Á ω m <<ω c. ÁŸêŸ apple apple ÊÒŸ Ë ÊflÎÁûÊ Ê«ÈUÁ Ã Ã Uª apple Ÿ Ë ÊappleªË? ω m +ω c ω c ω m ω m ω c 6. A diverging lens with magnitude of focal length 5 cm is placed at a distance of 5 cm from a converging lens of magnitude of focal length 0 cm. A beam of parallel light falls on the diverging lens. The final image formed is : real and at a distance of 40 cm from the divergent lens. real and at a distance of 6 cm from the convergent lens. real and at a distance of 40 cm from convergent lens. virtual and at a distance of 40 cm from convergent lens. 7. The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l/r such that the moment of inertia is minimum? ω c 6. 5 cm Á U ÊáÊ Ë» Êapple ŒÍ UË apple Ê UË appleã Êapple 0 cm Á ÊáÊ Ë» Êapple ŒÍ UË apple Á Ê UË appleã apple 5 cm Ë ŒÍ UË U UπÊ ÊÃÊ Ò Ê Ã U Ê Ê È Ê UË apple U Ê ÁÃÃ ÊappleÃÊ Ò Á UáÊÊ Ë ÁÃÁ ê ÊappleªÊ B/Page 4 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª flêsãáfl ÊÒ U Ê UË appleã apple 40 cm ŒÍ UË U flêsãáfl ÊÒ U Á Ê UË appleã apple 6 cm ŒÍ UË U flêsãáfl ÊÒ U Á Ê UË apple apple 40 cm ŒÍ UË U Ê Ê Ë ÊÒ U Á Ê UË apple apple 40 cm ŒÍ UË U 7. ÁòÊíÿÊ R ÃÕÊ ê Êß l apple ÊŸ apple Ÿ Ê apple Á ê Ám Ê apple Ê appleˇê «àfl ÊÉÊÍáÊ I Ò «àfl ÊÉÊÍáÊ apple ÁŸêŸÃ ÊŸ apple Á ÿapple ŸÈ ÊÃ l/r ÄÿÊ ÊappleªÊ?

8. An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If λ min is the smallest possible wavelength of X-ray in the spectrum, the variation of log λ min with log V is correctly represented in : 8. X-Á UáÊapple à ãÿ UŸapple apple Á ÿapple ß ÒÄ ŲÊÚŸ Á UáÊ È Êapple Áfl flêãã U V apple àflá UÃ U apple œêãè Ë å apple U U Ê ÁÃÃ Á ÿê ÊÃÊ Ò ß apple ÁflÁflÄÃ (characteristic) fl Áfl UÃ (continuous) X-Á UáÊapple à ãÿ ÊappleÃË Ò ÿáœ X-Á UáÊ S appleä U apple ãÿíÿã fl Ã UªŒÒäÿ λ min Ò ÃÊapple log λ min Ê log V apple ÊÕ Œ Êfl Á ÁøòÊ apple Ë ÁŒπÊÿÊ ªÿÊ Ò? B/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

9. A radioactive nucleus A with a half life T, decays into a nucleus B. At t=0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.. Then, t is given by : t=t log (.) 9. appleuá«uÿêapple ÁÄ Ufl ŸÊÁ -A Á Ë h - ÊÿÈ T Ò, Ê ˇÊÿ ŸÊÁ -B apple ÊappleÃÊ Ò ÿ t=0 U Êappleß Ë ŸÊÁ -B Ÿ Ë Ò ÿ t U ŸÊÁ Êapple B ÃÕÊ A Ë ÅÿÊ Ê ŸÈ ÊÃ 0. Ò ÃÊapple t Ê ÊŸ ÊappleªÊ t=t log (.) T t = log (.) T t = log (.) T log t = log. t = T log. log 0. An electric dipole has a fixed dipole moment p, which makes angle θ with respect to x-axis. When subjected to an electric field E= Ei, it experiences a torque T = τ k. When subjected to another electric field E= E j it experiences a torque T = T. The angle θ is : 60 90 0 45 T log t = log. t = T log. log 0. ÁfllÈÃ Ámœ Èfl Ê ÁSÕ U Ámœ Èfl ÊÉÊÍáÊ p Ò Êapple Á x- ˇÊ apple θ ÊappleáÊ ŸÊÃÊ Ò ÁfllÈÃ ˇÊappleòÊ E= Ei apple UπŸapple U ÿ ÊÉÊÍáÊ T = τ k Ê ŸÈ fl UÃÊ Ò ÁfllÈÃ ˇÊappleòÊ E= E j apple UπŸapple U ÿ ÊÉÊÍáÊ T = T Ê ŸÈ fl UÃÊ Ò ÊappleáÊ θ Ê ÊŸ ÊappleªÊ 60 90 0 45 B/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

. In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be : 5 80 45 90. n-p-n UÊ Á$ S U U apple ŸÊÿapple È ÿáÿc U à flœ Á U Õ apple ÁŸflappleÁ ÊÃ ÃÕÊ ÁŸª Ã Áfl flêapple apple Ëø Ê Ã U Ê ÊŸ ÊappleªÊ 5 80 45 90. C p and C v are specific heats at constant pressure and constant volume respectively. It is observed that C p C v =a for hydrogen gas C p C v =b for nitrogen gas The correct relation between a and b is : a=4 b a=8 b a= 4 b a=b. A copper ball of mass 00 gm is at a temperature T. It is dropped in a copper calorimeter of mass 00 gm, filled with 70 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75 C. T is given by : (Given : room temperature=0 C, specific heat of copper=0. cal/gm C) 50 C 85 C. ÁSÕ U ŒÊ ÃÕÊ ÁSÕ U ÊÿÃŸ U ÁflÁ Êc U c Êÿapple Ê C p ÃÕÊ C v Ò ÊÿÊ ÊÃÊ Ò Á Êß«UÊapple Ÿ apple Á ÿapple, C p C v =a ŸÊß UÊapple Ÿ apple Á ÿapple, C p C v =b a ÊÒ U b apple Ëø Ê Ë ê ãœ ÊappleªÊ a=4 b a=8 b a= 4 b a=b. 00 gm Œ ÿ ÊŸ flê Ê ÃÊ apple apple ªÊapple apple Ê ÃÊ ÊŸ T Ò apple 70 gm ÊŸË apple appleu È 00 gm apple ÃÊ apple apple Ò Êapple UË Ë U U, ÊappleÁ appleu apple ÃÊ ÊŸ U Ò, apple «UÊ ÁŒÿÊ ÊÃÊ Ò Ãà øêã ÁŸ Êÿ Ê ÃÊ ÊŸ 75 C ÊÿÊ ÊÃÊ Ò T Ê ÊŸ ÊappleªÊ (ÁŒÿÊ Ò appleu Ê ÃÊ ÊŸ=0 C, ÃÊ apple Ë ÁflÁ ÊC c Ê =0. cal/gm C) 50 C 85 C 800 C 885 C 800 C 885 C B/Page 7 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

4. A body of mass m=0 kg is moving in a medium and experiences a frictional force F= kv. Its initial speed is v 0 =0 ms. If, after 0 s, its energy is 8 mv 0, the value of k will be : 4. m=0 kg Œ ÿ ÊŸ Ê Á á«u Êäÿ apple Ê U Ê Ò ÊÒ U ÉÊ áê F= kv Ê ŸÈ fl UÃÊ Ò Á á«u Ê Ê UÁê flappleª v 0 =0 ms Ò ÿáœ 0 s apple ÊŒ Ë Ê 8 mv 0 Ò ÃÊapple k Ê ÊŸ ÊappleªÊ 0 4 kg m 0 4 kg m 0 kg m s 0 kg m s 0 kg m 0 kg s 5. When a current of 5 ma is passed through a galvanometer having a coil of resistance 5 Ω, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 0 V is :.55 0 Ω 4.005 0 Ω.985 0 Ω 0 kg m 0 kg s 5. 5 Ω apple È á«u Ë ÁÃ UÊappleœ apple ªÒÀflappleŸÊapple Ë U U apple 5 ma Ë œê UÊ flêá Ã Ë ÊÃË Ò ÃÊapple fl ÍáÊ S apple ÁflˇÊapple Œ ÊÊ ÃÊ Ò ß apple 0 0 V UÊ apple Áfl fl Ê Ë apple Œ Ÿapple apple Á ÿapple Á ÊŸ apple ÁÃ UÊappleœ Êapple ªÒÀflappleŸÊapple Ë U U apple ÊÕ üêappleáêë apple ªÊŸÊ ÊappleªÊ?.55 0 Ω 4.005 0 Ω.985 0 Ω.045 0 Ω.045 0 Ω B/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

6. A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is : 6. Œ ÿ ÊŸ M fl ê Êß l Ë Ã Ë fl ÊŸ U«Ê Á UÊ œè UÊª SÃ Ò Á apple Á fl äflê œ U Ã apple ÉÊÍ ÃË Ò (ÁøòÊ ŒappleÁπÿapple) œè UË Ê ÉÊ áê Ÿªáÿ Ò U«apple ŒÍ appleu Á appleu Êapple œè UË apple U äflê œ U Uπ U UÊapple«ÁŒÿÊ ÊÃÊ Ò U«äfl apple θ ÊappleáÊ ŸÊÃË Ò ÃÊapple Ê ÊappleáÊËÿ àfl UáÊ ÊappleªÊ g cos θ l g cos θ l g sin θ l g sin θ l g cos θ l g cos θ l g sin θ l g sin θ l B/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

7. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r=λ /λ, is given by : 7. áêè apple È U Ê SÃ UÊapple Êapple ÁøòÊ apple ÁŒπÊÿÊ ªÿÊ Ò Ã UªŒÒäÿÊappleZ apple ŸÈ ÊÃ r=λ /λ Ê ÊŸ ÊappleªÊ r= 4 r= 4 r= r= 8. A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of : 8 9 8 9 r= 4 r= 4 r= r= 8. ŸÈcÿ, Áfl ÊÊ Êÿ ÊŸfl apple ß Ê U Á UflÁÃ Ã ÊappleÃÊ Ò Á Ë appleuπëÿ Áfl Êÿapple 9 ªÈŸÊ ÊÃË Ò ÊŸÊ Á apple ÉÊŸàfl apple Êappleß Á UflÃ Ÿ Ÿ Ë ÊappleÃÊ Ò ÃÊapple apple UÊ ª apple ÁÃ Á ÃŸapple ªÈŸÊ Êapple ÊÿappleªÊ? 8 9 8 9 B/Page 0 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

9. In a coil of resistance 00 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is : 9. øèê Ëÿ ç Ä apple Œ Ÿapple apple 00 Ω ÁÃ UÊappleœ Ë È á«u Ë apple appleá UÃ œê UÊ Êapple ÁøòÊ apple Œ ÊÊ ÿê ªÿÊ Ò È á«u Ë apple ªÈ UŸapple flê apple ç Ä apple Œ Êfl Ê Á U ÊáÊ ÊappleªÊ 50 Wb 75 Wb 00 Wb 5 Wb 0. In a Young s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 50 cm away. A beam of light consisting of two wavelengths, 650 nm and 50 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is : 9.75 mm 5.6 mm.56 mm 50 Wb 75 Wb 00 Wb 5 Wb 0. ÿ ª apple ÁmÁ Ê UË ÿêappleª apple, Á ÊÁ UÿÊapple apple Ëø Ë ŒÍ UË 0.5 mm fl Œapple Ë Á Ê UË apple ŒÍ UË 50 cm Ò Ê Ê È, Á apple 650 nm ÊÒ U 50 nm Ë ŒÊapple Ã UªŒÒäÿ Ò, Êapple Œapple U ÿãë UáÊ Á» ã ŸÊŸapple apple ÿêappleª UÃapple Ò ÿáÿc U apple ãœ Ëÿ ÁìÊc U apple fl Á ãœè, Ê ŒÊappleŸÊapple Ã UªŒÒäÿÊappleZ Ë ŒË# Á» ã apple ê ÊÃË ÊappleÃË Ò, Ë ãÿíÿã ŒÍ UË ÊappleªË 9.75 mm 5.6 mm.56 mm 7.8 mm 7.8 mm B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

. A magnetic needle of magnetic moment 6.7 0 Am and moment of inertia 7.5 0 6 kg m is performing simple harmonic oscillations in a magnetic field of 0.0 T. Time taken for 0 complete oscillations is : 6.98 s 8.76 s 6.65 s. øèê Ëÿ ÊÉÊÍáÊ 6.7 0 Am fl «àfl ÊÉÊÍáÊ 7.5 0 6 kg m flê Ë øèê Ëÿ ÈßZ, 0.0 T ÃËfl ÃÊ apple øèê Ëÿ ˇÊappleòÊ apple U ÊflÃ ŒÊapple Ÿ U U Ë Ò 0 Í appleu ŒÊapple Ÿ Ê ÿ ÊappleªÊ 6.98 s 8.76 s 6.65 s 8.89 s. The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R=Earth s radius) : 8.89 s. ÎâflË apple apple ãœ apple ŒÍ UË d apple ÊÕ ªÈL àflëÿ àfl UáÊ g Ê Œ Êfl ÁŸêŸ apple apple Á ª Ê» apple apple Ë Œ ÊÊ ÿê ªÿÊ Ò? (R= ÎâflË Ë ÁòÊíÿÊ) B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

.. In the above circuit the current in each resistance is : 0.5 A U ÁŒÿapple ªÿapple Á U Õ apple àÿapple ÁÃ UÊappleœ apple œê UÊ Ê ÊŸ ÊappleªÊ 0.5 A 0 A A 0.5 A 4. A particle A of mass m and initial velocity v collides with a particle B of mass m which is at rest. The collision is head on, and elastic. The ratio of the de-broglie wavelengths λ A to λ B after the collision is : λa λb λa λb λa λb = = 0 A A 0.5 A 4. Œ ÿ ÊŸ m fl Ê UÁê flappleª v apple áê-a Ë UÄ U Œ ÿ ÊŸ m apple ÁSÕ U áê-b apple ÊappleÃË Ò ÿ UÄ U ê Èπ fl àÿêsõ Ò UÄ U apple ÊŒ Á«U- ÊÚÇ Ë Ã UªŒÒäÿÊappleZ λ A fl λ B Ê ŸÈ ÊÃ ÊappleªÊ λa λb = = λa λb λa λb λa λb λa λb = = = = B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

5. An external pressure P is applied on a cube at 0 C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by : 5. 0 C U Uπapple È ÉÊŸ U Œ Êfl P ªÊÿÊ ÊÃÊ Ò Á apple fl Ë Ã U» apple UÊ U ËÁ«UÃ ÊappleÃÊ Ò ÉÊŸ apple ŒÊÕ Ê ÊÿÃŸ àÿêsõãê ªÈáÊÊ K fl appleuπëÿ Ê U ªÈáÊÊ α Ò ÿáœ ÉÊŸ Êapple ª U apple Í Ê Ê U apple ÊŸÊ Ò ÃÊapple apple ÃÊ ÊŸ Êapple Á ÃŸÊ ÊŸÊ «appleªê? α PK α PK PKα PKα P α K P α K 6. A time dependent force F=6t acts on a particle of mass kg. If the particle starts from rest, the work done by the force during the first sec. will be : 9 J 8 J 4.5 J J 7. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 0 GHz. What is the frequency of the microwave measured by the observer? (speed of light= 0 8 ms ) 7. GHz 5. GHz 0. GHz. GHz P α K P α K 6. kg Œ ÿ ÊŸ Ê áê, ÿ U ÁŸ U (time dependent) F=6t Ê ŸÈ fl UÃÊ Ò ÿáœ áê Áfl UÊ ÊflSÕÊ apple ø ÃÊ Ò ÃÊapple apple s apple mê UÊ Á ÿê ªÿÊ Êÿ ÊappleªÊ 9 J 8 J 4.5 J J 7. appleˇê Ê Ê ªÁÃ Ë ÊœË ªÁÃ apple 0 GHz ÊflÎÁûÊ apple ÁSÕ U Íˇ Ã Uª (microwave) dêappleã Ë Ã U» Ê U Ê Ò appleˇê mê UÊ Ê Ë ªÿË Íˇ Ã Uª Ë ÊflÎÁûÊ Ê ÊŸ ÊappleªÊ ( Ê Ê Ë øê = 0 8 ms ) 7. GHz 5. GHz 0. GHz. GHz B/Page 4 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

8. In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be : 8. ÁŒÿapple ªÿapple Á U Õ apple œê UÊ ÁSÕ UÊflSÕÊ apple È ø ÊÃË Ò ÃÊapple œêá UÃÊ C apple œêá UòÊ U Êflapple Ê Ê ÊŸ ÊappleªÊ r CE (r+ r ) r CE (r + r) C E CE r ( r+ r) 9. A capacitance of µf is required in an electrical circuit across a potential difference of.0 kv. A large number of µf capacitors are available which can withstand a potential difference of not more than 00 V. The minimum number of capacitors required to achieve this is : 4 r CE (r+ r ) r CE (r + r) C E 6 CE r ( r+ r) 9. ÁfllÈÃ Á U Õ apple µf œêá UÃÊ apple œêá UòÊ Êapple.0 kv Áfl flêãã U apple Á ãœè Êapple apple Ëø ªÊŸÊ Ò µf œêá UÃÊ apple ÈÃ Ê appleu œêá UòÊ Êapple Á 00 V Áfl flêãã U Ã fl Ÿ U Ãapple Ò, éœ Ò UÊappleÄÃ Á U Õ Êapple Ê# UŸapple apple Á ÿapple ãÿíÿã Á ÃŸapple œêá UòÊÊapple Ë Êfl ÿ ÃÊ ÊappleªË? 4 6 B/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

0. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? 0. Á á«u Êapple äflê œ U U Ë Ã U»»apple Ê ÊÃÊ Ò ÁŸêŸ apple apple ÊÒŸ Ê ª Ê» ÿ apple ÊÕ flappleª Êapple Ë Œ ÊÊ ÃÊ Ò? B/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

PART B MATHEMATICS. Let k be an integer such that the triangle with vertices (k, k), (5, k) and ( k, ) has area 8 sq. units. Then the orthocentre of this triangle is at the point :, Êª B ªÁáÊÃ. ÊŸÊ k apple Ê ÍáÊÊZ Ò Á ÁòÊ È, Á apple ÊË (k, k), (5, k) ÃÕÊ ( k, ) Ò, Ê ˇÊappleòÊ» 8 flª ß Êß Ò, ÃÊapple ÁòÊ È apple - apple ãœ Á Á ŒÈ U Ò, fl Ò,,,, 4, 4. If, for a positive integer n, the quadratic equation, x(x+)+(x+)(x+)+... +( x + n ) (x+n)=0n has two consecutive integral solutions, then n is equal to : 9 0. The function as x f ( x) =, is : + x f : R, defined neither injective nor surjective. invertible. injective but not surjective. surjective but not injective., 4, 4. ÿáœ Á Ë œÿ ÍáÊÊZ n apple Á, ÁmÉÊÊÃË Ë UáÊ x(x+)+(x+)(x+)+... +( x + n ) (x+n)=0n apple ŒÊapple Á ÍáÊÊZ Ëÿ Ò, ÃÊapple n UÊ U Ò 9 0.» Ÿ f ( x) f :, R, Êapple x x = + mê UÊ Á U ÊÁ Ã Ò Ÿ ÃÊapple Êë UÊŒË ÊÒ U Ÿ Ë Ò Ë Ò ÿèà áêëÿ Ò Ò Ë Ò UãÃÈ Êë UÊŒË Ÿ Ë Ò Êë UÊŒË Ò UãÃÈ Ò Ë Ÿ Ë Ò B/Page 7 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

4. The following statement (p q) [(~p q) q] is : a fallacy a tautology equivalent to ~p q equivalent to p ~q 4. ÁŸêŸ ÕŸ (p q) [(~p q) q] appleàflê Ê (fallacy) Ò ÈŸL ÁÄÃ (tautology) Ò ~p q apple ÃÈÀÿ Ò p ~q apple ÃÈÀÿ Ò 5. If S is the set of distinct values of b for which the following system of linear equations x+y+z= x+ay+z= ax+by+z=0 has no solution, then S is : a singleton an empty set an infinite set a finite set containing two or more elements 6. The area (in sq. units) of the region {(x, y) : x 0, x+y, x 4y and y + x } is : 5 59 5. ÿáœ S, b Ë Ÿ ÁflÁ ÛÊ ÊŸÊapple Ê ÈìÊÿ Ò Á Ÿ apple Á ÁŸêŸ ÒUÁπ Ë UáÊ ÁŸ Êÿ x+y+z= x+ay+z= ax+by+z=0 Ê Êappleß Ÿ Ë Ò, ÃÊapple S Ë flÿfl flê Ê ÈìÊÿ Ò Á UÄÃ ÈìÊÿ Ò Á UÁ Ã ÈìÊÿ Ò Á UÁ Ã ÈìÊÿ Ò Á apple ŒÊapple ÿê Áœ flÿfl Ò 6. ˇÊappleòÊ {(x, y) : x 0, x+y, x 4y ÃÕÊ y + x } Ê ˇÊappleòÊ» (flª ß ÊßÿÊapple ) apple Ò 7 5 59 7 B/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

7. For any three positive real numbers a, b and c, 9(5a +b )+5(c ac)=5b(a+c). Then : a, b and c are in G.P. b, c and a are in G.P. b, c and a are in A.P. a, b and c are in A.P. 7. Á ã Ë ÃËŸ œÿêà flêsãáfl ÅÿÊ Êapple a, b ÃÕÊ c apple Á 9(5a +b )+5(c ac)=5b(a+c) Ò, ÃÊapple a, b ÃÕÊ c ªÈáÊÊappleûÊ U üêapple Ë apple Ò b, c ÃÕÊ a ªÈáÊÊappleûÊ U üêapple Ë apple Ò b, c ÃÕÊ a Ê Ã U üêapple Ë apple Ò a, b ÃÕÊ c Ê Ã U üêapple Ë apple Ò 8. A man X has 7 friends, 4 of them are ladies and are men. His wife Y also has 7 friends, of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting ladies and men, so that friends of each of X and Y are in this party, is : 484 485 468 469 9. The normal to the curve y(x )(x )=x+6 at the point where the curve intersects the y-axis passes through the point :,,, 8. ÿáäã X apple 7 Á òê Ò, Á Ÿ apple 4 Á Ê Ò ÃÕÊ ÈL Ò, Ë àÿë Y apple Ë 7 Á òê Ò, Á Ÿ apple Á Ê ÃÕÊ 4 ÈL Ò ÿ ÊŸÊ ªÿÊ Á X ÃÕÊ Y Ê Êappleß ÿáÿc U (common) Á òê Ÿ Ë Ò ÃÊapple Ÿ Ã UË Êapple Ë ÅÿÊ Á Ÿ apple X ÃÕÊ Y ÊÕ Á Ê Êapple ÃÕÊ ÈL Êapple Êapple Ê UË U È Ê Á X ÃÕÊ Y àÿapple apple ÃËŸ-ÃËŸ Á òê Êÿapple, Ò 484 485 468 469 9. fl y(x )(x )=x+6 apple Á ŒÈ U, Ê fl y- ˇÊ Êapple Ê UÃË Ò, πë øê ªÿÊ Á ÁŸêŸ apple apple Á Á ŒÈ apple Êapple U ÊÃÊ Ò?,,,,, B/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

40. A hyperbola passes through the point P(, ) and has foci at (±, 0). Then the tangent to this hyperbola at P also passes through the point : (, ) (, ) (, ) (, ) 40. ÁÃ Ufl ÿ Á ŒÈ P(, ) apple Êapple U ÊÃÊ Ò, ÃÕÊ Ë ŸÊÁ ÿê (±, 0) U Ò, ÃÊapple ÁÃ Ufl ÿ apple Á ŒÈ P U πë øë ªß S Ê appleuπê Á Á ŒÈ apple Êapple U ÊÃË Ò, fl Ò (, ) (, ) (, ) (, ) 4. Let a, b, c R. If f (x)=ax +bx+c is such that a+b+c= and f (x+y)=f (x)+f (y)+xy, x, y R, 0 then f (n) is equal to : n= 55 0 65 90 4. Let a = i+ j k and b = i+ j. Let c be a vector such that c a =, ( ) a b c = and the angle between c and a b be 0. Then a c is equal to : 8 4. ÊŸÊ a, b, c R ÿáœ f (x)=ax +bx+c apple Ê Ò Á a+b+c= Ò ÃÕÊ Ë x, y R apple Á f (x+y)=f (x)+f (y)+xy Ò, ÃÊapple 0 f (n) n= 5 5 8 B/Page 0 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª 55 0 65 90 UÊ U Ò = i+ j k ÃÕÊ b i j 4. ÊŸÊ a = + Ò =, ÊŸÊ c apple Ê ÁŒ Ê Ò Á c a ( ) a b c = ÃÕÊ c ÊÒ U a b apple Ëø Ê ÊappleáÊ 0 Ò, ÃÊapple a 8 5 5 8 c UÊ U Ò

4. Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP=AB. If BPC=β, then tan β is equal to : 4. ÊŸÊ äflê œ U ËŸÊ U AB apple Ë Ò Á Ê Á UÊ A ÍÁ U Ò ÊŸÊ AB Ê äÿ Á ŒÈ C Ò ÃÕÊ ÍÁ U ÁSÕÃ Á ŒÈ P apple Ê Ò Á AP=AB ÿáœ BPC=β Ò, ÃÊapple tan β UÊ U Ò 4 9 4 9 6 7 6 7 4 9 44. Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is : 0.5 0 5 45. The integral 4 π 4 π 4 dx is equal to : + cos x 4 9 44.»Í Êapple Ë ÄÿÊ UË, Êapple flîûê apple ÁòÊíÿ π «U apple M apple Ò, Ë ÉÊapple UÊ ŒË UŸapple apple Á Ë Ë U U ÃÊ U éœ Ò ÃÊapple»Í Êapple Ë ÄÿÊ UË Ê Áœ Ã ˇÊappleòÊ» (flª Ë. apple ), Ò 0.5 0 5 π 4 45. Ê 4 π 4 dx + cos x UÊ U Ò B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

dy 46. If ( + sin x) + ( y + )cos x = 0 and dx y(0)=, then y π is equal to : dy 46. ÿáœ ( + sin x) + ( y + )cos x = 0 ÃÕÊ dx y(0)= Ò, ÃÊapple π UÊ U Ò y 4 4 47. Let n I n tan x d x, (n > ) =. If I 4 +I 6 =a tan 5 x+bx 5 +C, where C is a constant of integration, then the ordered pair (a, b) is equal to :, 0 5, 5, 0 5, 5 47. ÊŸÊ n I n tan x d x, (n > ) = Ò ÿáœ I 4 +I 6 =a tan 5 x+bx 5 +C Ò, Ê C Ê Ÿ ø U Ò, ÃÊapple Á Ã ÿèç (a, b) UÊ U Ò, 0 5, 5, 0 5, 5 B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

48. Let ω be a complex number such that ω+=z where z=. If 48. ÊŸÊ ω Áê üê ÅÿÊ apple Ë Ò Á ω+=z Ê z= Ò ÿáœ ω ω = k, 7 ω ω ω ω = k 7 ω ω Ò then k is equal to : ÃÊapple k UÊ U Ò z z z 49. The value of ( C 0 C ) ( C 0 C ) + + ( C 0 C ) ( C 0 C ) + 4 4 +... + ( C 0 C ) 0 0 is : 0 0 0 z 49. ( C 0 C ) ( C 0 C ) + + ( C 0 C ) ( C 0 C ) + 4 4 +... + ( C 0 C ) Ê ÊŸ Ò 0 0 0 0 0 0 9 0 9 B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

50. lim cot x cos x x π ( π x) equals : 50. lim cot x cos x x π ( π x) UÊ U Ò 4 4 4 4 6 6 8 5. If 5(tan x cos x)=cos x+9, then the value of cos 4x is : 7 9 5 9 5. If the image of the point P(,, ) in the plane, x+y 4z+=0 measured x y z parallel to the line, = = is Q, then 4 5 PQ is equal to : 6 5 5 4 4 8 5. ÿáœ 5(tan x cos x)=cos x+9, ÃÊapple cos 4x Ê ÊŸ Ò 7 9 5 9 5. ÿáœ Á ŒÈ P(,, ) Ê Ã x+y 4z+=0 apple fl ÁÃÁ Êapple appleuπê x y z 4 5 Ò = = apple Ê Ã U Ò, Q Ò, ÃÊapple PQ UÊ U 6 5 5 4 4 B/Page 4 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

5. The distance of the point (,, 7) from the plane passing through the point (,, ), having normal perpendicular x y+ z 4 to both the lines = = x y+ z+ 7 and = =, is : 5. Ã Êapple Á ŒÈ (,, ) apple Êapple U ÊÃÊ Ò ÃÕÊ Á Ê Á ŒÊappleŸÊapple appleuπê Êapple x y+ z 4 = = x y+ z+ 7 = = (,, 7) apple ŒÍ UË Ò ÃÕÊ U Ò, Ë Á ŒÈ 0 74 0 74 0 74 0 8 5 8 54. If for x 0,, the derivative of 4 6x x tan 9x equals : + 9x 9 + 9x x x 9x is x g( x), then g(x) x 9x 54. ÿáœ x 0 74 0 8 5 8 0, 4 apple Á tan 6x x 9x fl Ÿ x g( x) Ò, ÃÊapple g(x) UÊ U Ò + 9x 9 + 9x x x 9x x 9x Ê B/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

55. The radius of a circle, having minimum area, which touches the curve y=4 x and the lines, y= x is : 55. ãÿíÿã ˇÊappleòÊ» flê apple apple apple flîûê, Êapple fl y=4 x ÃÕÊ appleuπê Êapple y= x Êapple S Ê UÃÊ Ò, Ë ÁòÊíÿÊ Ò 4( + ) 4( + ) ( + ) ( + ) ( ) ( ) 4 56. A box contains 5 green and 0 yellow balls. If 0 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is : 6 ( ) ( ) 4 56. Ä apple apple 5 UË ÃÕÊ 0 Ë Ë ªapple Œapple Ò ÿáœ - U apple ÿêœîë UÿÊ, ÁÃSÕÊ ŸÊ Á Ã, 0 ªapple Œapple ÁŸ Ê Ë Ê, ÃÊapple UË ªapple ŒÊapple Ë ÅÿÊ Ê UáÊ Ò 4 6 5 5 6 4 6 5 5 B/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

57. The eccentricity of an ellipse whose centre is at the origin is. If one of its directrices 57. ŒËÉÊ flîûê, Á Ê apple ãœ Í Á ãœè U Ò, Ë à apple ãœ ÃÊ Ò ÿáœ Ë ÁŸÿÃÊ x= 4 Ò, is x= 4, then the equation of the normal ÃÊapple apple Á ŒÈ, U apple Á Ê to it at, is : Ë UáÊ Ò x+y=4 x+y=4 y x= 4x y= 4x+y=7 58. If two different numbers are taken from the set {0,,,,..., 0}; then the probability that their sum as well as absolute difference are both multiple of 4, is : 7 55 6 55 55 y x= 4x y= 4x+y=7 58. ÿáœ ÈìÊÿ {0,,,,..., 0} apple apple ŒÊapple ÁflÁ ÛÊ ÅÿÊ ÁŸ Ê Ë ªßZ, ÃÊapple Ÿ apple ÿêappleª» ÃÕÊ Ÿ apple Ã U apple ÁŸ U appleˇê ÊŸ, ŒÊappleŸÊapple apple øê U apple ªÈáÊ ÊappleŸapple Ë ÊÁÿ ÃÊ Ò 4 45 7 55 6 55 55 4 45 B/Page 7 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

59. For three events A, B and C, P(Exactly one of A or B occurs) =P(Exactly one of B or C occurs) =P(Exactly one of C or A occurs)= 4 and 59. ÃËŸ ÉÊ UŸÊ Êapple A, B ÃÕÊ C apple Á P(A ÕflÊ B apple apple apple fl ÉÊÁ UÃ ÊappleÃË Ò) =P(B ÕflÊ C apple apple apple fl ÉÊÁ UÃ ÊappleÃË Ò) =P(C ÕflÊ A apple apple apple fl ÉÊÁ UÃ ÊappleÃË Ò)= 4 ÃÕÊ P(All the three events occur simultaneously)= 6. Then the probability that at least one of the events occurs, is : 60. If 6 7 7 6 7 64 A = 4, then adj (A +A) is equal to : 7 6 84 5 7 84 6 5 5 6 84 7 5 84 6 7 P( Ë ÃËŸ ÉÊ UŸÊ ÊÕ ÉÊÁ UÃ ÊappleÃË Ò )= 6 Ò, ÃÊapple ÊÁÿ ÃÊ Á apple ÉÊ UŸÊ ÉÊÁ UÃ Êapple, Ò 60. ÿáœ A 6 7 7 6 7 64 UÊ U Ò 4 = Ò, ÃÊapple adj (A +A) 7 6 84 5 7 84 6 5 5 6 84 7 5 84 6 7 B/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

PART C CHEMISTRY 6. Which of the following compounds will form significant amount of meta product during mono-nitration reaction? Êª C U ÊÿŸ ÁflôÊÊŸ 6. ÊappleŸÊappleŸÊß appleu ÊŸ Á Á ÿê apple ÁŸêŸ apple apple ÊÒŸ Ê ÿêòáª apple UÊ à ÊŒ Ë àfl ÍáÊ ÊòÊÊ à ãÿ appleuªê? 6. U is equal to : Isochoric work Isobaric work Adiabatic work Isothermal work 6. The increasing order of the reactivity of the following halides for the S N reaction is : CH CH CH Cl (I) (II) p H CO C 6 H 4 CH Cl (III) (III) < (II) < (I) (II) < (I) < (III) (I) < (III) < (II) (II) < (III) < (I) 6. U Á apple UÊ U Ò, fl Ò - ÊÿÃÁŸ Êÿ ŒÊ Ë Êÿ L hêapplec Êÿ ÃÊ Ë Êÿ 6. S N Á Á ÿê apple Á ÁŸêŸ Ò Êß«UÊapple Ë Á Á ÿêà ÃÊ Ê ÃÊ Ò CH CH CH Cl (I) (II) p H CO C 6 H 4 CH Cl (III) (III) < (II) < (I) (II) < (I) < (III) (I) < (III) < (II) (II) < (III) < (I) B/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

64. The radius of the second Bohr orbit for hydrogen atom is : (Planck s Const. h=6.66 0 4 Js; mass of electron=9.09 0 kg; charge of electron e=.600 0 9 C; permittivity of vacuum 0 =8.85485 0 kg m A ).65 Å 4.76 Å 0.59 Å. Å 65. pk a of a weak acid (HA) and pk b of a weak base (BOH) are. and.4, respectively. The ph of their salt (AB) solution is : 7. 6.9 7.0.0 66. The formation of which of the following polymers involves hydrolysis reaction? Nylon 6 Bakelite Nylon 6, 6 Terylene 67. The most abundant elements by mass in the body of a healthy human adult are : Oxygen (6.4%); Carbon (.9%), Hydrogen (0.0%); and Nitrogen (.6%). The weight which a 75 kg person would gain if all H atoms are replaced by H atoms is : 5 kg 7.5 kg 7.5 kg 0 kg 64. Êß«UÊapple Ÿ U ÊáÊÈ apple ÁmÃËÿ Êapple U ˇÊÊ Ê h ÿê ÊappleªÊ (å Ò ÁSÕ UÊ h=6.66 0 4 Js; ß appleä UÊÚŸ Ê Œ ÿ ÊŸ=9.09 0 kg; ß appleä UÊÚŸ U Êflapple Ê e=.600 0 9 C; ÁŸflÊ Ã Ê UÊflÒlÈÃÊ 0 =8.85485 0 kg m A ).65 Å 4.76 Å 0.59 Å. Å 65. ŒÈ ê (HA) Ê pk a ÃÕÊ ŒÈ ˇÊÊ U (BOH) Ê pk b Ê. ÃÕÊ.4 Ò Ÿ apple fláê (AB) apple Áfl ÿÿ Ê ph ÊappleªÊ 7. 6.9 7.0.0 66. ÁŸêŸ È Êapple apple apple ÊÒŸ apple È apple ÉÊ UŸ Á Á ÿê ÁãŸÁ Ã Ò? ŸÊß ÊÚŸ 6 apple apple Êß U ŸÊß ÊÚŸ 6, 6 appleu UË ËŸ 67. SflSÕ ŸÈcÿ apple Ê UË U apple ÊòÊÊ Ë ŒÎÁc U apple ÈÃÊÿÃ apple Á Ÿapple flê apple Ãàfl Ò ÊÚÄ Ë Ÿ (6.4%); Ê Ÿ (.9%), Êß«UÊapple Ÿ (0.0%); ÃÕÊ ŸÊß UÊapple Ÿ (.6%) 75 kg fl Ÿ flê apple ÿáäã apple Ê UË U apple Ë H U ÊáÊÈ Êapple Êapple H U ÊáÊÈ Êapple apple Œ ÁŒÿÊ Êÿ ÃÊapple apple Ê U apple Êapple flîáh ÊappleªË, fl Ò 5 kg 7.5 kg 7.5 kg 0 kg B/Page 0 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

68. Which of the following, upon treatment with tert-buona followed by addition of bromine water, fails to decolourize the colour of bromine? 68. ÁŸêŸ apple apple ÊÒŸ, tert-buona apple ÊÕ Á Î Ã UŸapple ÃÕÊ Êapple ËŸ apple Á ÊŸapple U, Êapple ËŸ apple Uª Êapple Uª ËŸ UŸapple apple Õ ÊappleÃÊ Ò? 69. In the following reactions, ZnO is respectively acting as a/an : (a) ZnO+Na O Na ZnO (b) ZnO+CO ZnCO base and acid base and base acid and acid acid and base 70. Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is : both form basic carbonates both form soluble bicarbonates both form nitrides nitrates of both Li and Mg yield NO and O on heating 69. ÁŸêŸ Á Á ÿê Êapple apple, ZnO Ê Êÿ appleuªê (a) ZnO+Na O Na ZnO (b) ZnO+CO ZnCO ˇÊÊ U ÃÕÊ ê ˇÊÊ U ÃÕÊ ˇÊÊ U ê ÃÕÊ ê ê ÃÕÊ ˇÊÊ U 70. Áfl áê ê ãœ apple Ê UáÊ, ËÁÕÿ ÃÕÊ ÒÇŸËÁ Êÿ ŒÊappleŸÊapple ß Ò apple ªÈáÊ ŒÁ Ê Ã UÃapple Ò Á» U Ë, fl Êapple ª Ã Ò, Ò ŒÊappleŸÊapple ˇÊÊ UËÿ Ê Êapple Ÿapple U ŸÊÃapple Ò ŒÊappleŸÊapple ÉÊÈ Ÿ ÊË Êß Ê Êapple Ÿapple U ŸÊÃapple Ò ŒÊappleŸÊapple ŸÊß UÊß«U ŸÊÃapple Ò ËÁÕÿ ÃÕÊ ÒÇŸËÁ Êÿ, ŒÊappleŸÊapple apple Ë ŸÊß appleu U ª U UŸapple U NO ÃÕÊ O ŒappleÃapple Ò B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

7. -Methyl-pent--ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is : Six Zero Two Four 7. UÊÄ Êß«U Ë ÁSÕÁÃ apple, - appleáõ - appleã U--ß Ÿ, HBr apple ÊÕ Á Á ÿê UŸapple U Ÿ à ÊŒ ŸÊÃÊ Ò à ÊŒ apple Á ê fl ÁòÊÁfl Ê ÊÿÁflÿÊapple Ë ÅÿÊ ÊappleªË U ÊÍãÿ ŒÊapple øê U 7. A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is a, the closest approach between two atoms in metallic crystal will be : a a a a 7. Two reactions R and R have identical pre-exponential factors. Activation energy of R exceeds that of R by 0 kj mol. If k and k are rate constants for reactions R and R respectively at 00 K, then ln(k /k ) is equal to : (R=8.4 J mol K ) 8 6 4 7. œêãè» apple ÁãŒ Ã ÉÊŸ UøŸÊ apple Á S UÁ Ã ÊappleÃË Ò ÿáœ ß apple apple Ë Êapple U ê Êß a Ò, ÃÊapple œêáàfl Á S U apple ŒÊapple U ÊáÊÈ Êapple apple Ëø ÁÛÊ UÃ ŒÍ UË ÊappleªË a a a a 7. ŒÊapple Á Á ÿê Êapple, R ÃÕÊ R apple Ífl ø UÉÊÊÃÊ Ë ªÈáÊ Ò apple Ò R Ë Á ÿáê Ê R apple Á ÿáê Ê apple 0 kj mol íÿêœê Ò ÿáœ Á Á ÿê R ÃÕÊ R apple Á 00 K U Œ U ÁŸÿÃÊ Ê k ÃÕÊ k Êapple ÃÊapple ln(k /k ) ÁŸêŸ apple apple Á apple UÊ U ÊappleªÊ? (R=8.4 J mol K ) 8 6 4 B/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

74. The correct sequence of reagents for the following conversion will be : 74. ÁŸêŸ M ÊãÃ UáÊ apple Á Á Êapple Ê Ë ÊappleªÊ + + [Ag(NH ) ] OH, H /CHOH, CHMgBr + + [Ag(NH ) ] OH, H /CHOH, CHMgBr + CHMgBr, H /CHOH, + [Ag(NH ) ] OH + CHMgBr, [Ag(NH ) ] OH, + H /CHOH + [Ag(NH ) ] OH, CHMgBr, + H /CHOH 75. The Tyndall effect is observed only when B/Page following conditions are satisfied : (a) (b) (c) (d) The diameter of the dispersed particles is much smaller than the wavelength of the light used. The diameter of the dispersed particle is not much smaller than the wavelength of the light used. The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude. The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude. (a) and (d) (b) and (d) (a) and (c) (b) and (c) + CHMgBr, H /CHOH, + [Ag(NH ) ] OH SPACE FOR ROUGH WORK / U» Êÿ apple Á ª + CHMgBr, [Ag(NH ) ] OH, + H /CHOH + [Ag(NH ) ] OH, CHMgBr, + H /CHOH 75. Á Uã«U Êfl Ã Ë ÁŒπÊÿË «appleªê ÁŸêŸ ÊÃapple ÃÈc U ÊappleÃË Ò (a) Á UˇÊappleÁ Ã áêêapple Ê ÿê, ÿèäã Ê Ê apple Ã UªŒÒÉÿ Ë ÃÈ ŸÊ apple ÈÃ UÊapple UÊ Êapple (b) (c) (d) Á UˇÊappleÁ Ã áêêapple Ê ÿê, ÿèäã Ê Ê apple Ã UªŒÒÉÿ Ë ÃÈ ŸÊ apple ÈÃ UÊapple UÊ Ÿ Ë Êapple Á UˇÊappleÁ Ã ÊflSÕÊ ÃÕÊ Á UˇÊapple áê Êäÿ apple flã ŸÊ Á U ÊáÊ ª ª Ò apple Ê apple Á UˇÊappleÁ Ã ÊflSÕÊ ÃÕÊ Á UˇÊapple áê Êäÿ apple flã ŸÊ Á U ÊáÊ ÈÃ Á ãÿ Êapple (a) ÃÕÊ (d) (b) ÃÕÊ (d) (a) ÃÕÊ (c) (b) ÃÕÊ (c)

76. Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution? 76. Ëÿ KOH Áfl ÿÿ apple ÁŸêŸ apple apple ÊÒŸ Ê ÿêòáª øêÿ Ê UÊ apple M apple ÿfl Ê U appleuªê? 77. Given C (graphite) +O (g) CO (g) ; r H = 9.5 kj mol H (g)+ O (g) H O(l) ; r H = 85.8 kj mol CO (g)+h O(l) CH 4 (g)+o (g) ; r H =+890. kj mol Based on the above thermochemical equations, the value of r H at 98 K for the reaction C (graphite) +H (g) CH 4 (g) will be : +74.8 kj mol +44.0 kj mol 74.8 kj mol 44.0 kj mol B/Page 4 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª 77. ÁŒÿÊ ªÿÊ Ò, C (graphite) +O (g) CO (g) ; r H = 9.5 kj mol H (g)+ O (g) H O(l) ; r H = 85.8 kj mol CO (g)+h O(l) CH 4 (g)+o (g) ; r H =+890. kj mol U ÁŒÿapple ªÿapple c UÊ ÊÿÁŸ Ë UáÊÊapple apple ÊœÊ U U 98 K U Á Á ÿê C (graphite) +H (g) CH 4 (g) apple r H Ê ÊŸ ÊappleªÊ +74.8 kj mol +44.0 kj mol 74.8 kj mol 44.0 kj mol

78. Which of the following reactions is an example of a redox reaction? XeF 4 + O F XeF 6 + O XeF + PF 5 [XeF] + PF 6 XeF 6 + H O XeOF 4 + HF XeF 6 + H O XeO F + 4HF 78. ÁŸêŸ apple apple ÊÒŸ Ë Á Á ÿê øÿêapple øÿ (Á U«UÊÚÄ ) Á Á ÿê Ê ŒÊ UáÊ Ò? XeF 4 + O F XeF 6 + O XeF + PF 5 [XeF] + PF 6 XeF 6 + H O XeOF 4 + HF XeF 6 + H O XeO F + 4HF 79. The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are : ClO and ClO ClO and ClO Cl and ClO Cl and ClO 80. The major product obtained in the following reaction is : (±)C 6 H 5 CH(O t Bu)CH C 6 H 5 C 6 H 5 CH=CHC 6 H 5 (+)C 6 H 5 CH(O t Bu)CH C 6 H 5 ( )C 6 H 5 CH(O t Bu)CH C 6 H 5 8. Sodium salt of an organic acid X produces effervescence with conc. H SO 4. X reacts with the acidified aqueous CaCl solution to give a white precipitate which decolourises acidic solution of KMnO 4. X is : C 6 H 5 COONa HCOONa CH COONa Na C O 4 79. Ä Êapple UËŸ ªÒ U«appleU fl ÃŸÈ Ëÿ NaOH apple ÊÕ Á Á ÿê UÃË Ò ÃÊapple ÊåÃ ÊappleŸapple flê apple à ÊŒ Êapple ªapple ClO ÃÕÊ ClO ClO ÃÕÊ ClO Cl ÃÕÊ ClO ClO Cl ÃÕÊ 80. ÁŸêŸ Á Á ÿê apple ÊåÃ ÊappleŸapple flê Ê ÈÅÿ à ÊŒ Ò (±)C 6 H 5 CH(O t Bu)CH C 6 H 5 C 6 H 5 CH=CHC 6 H 5 (+)C 6 H 5 CH(O t Bu)CH C 6 H 5 ( )C 6 H 5 CH(O t Bu)CH C 6 H 5 8. Ê ÁŸ ê Ê ÊappleÁ«Uÿ ÀÊfláÊ X ÊãŒ H SO 4 apple ÊÕ ÈŒ ÈŒÊ U ŒappleÃÊ Ò X ê Ëÿ Ëÿ CaCl apple ÊÕ Á Á ÿê UÃÊ Ò ÊÒ U»apple Œ flˇêapple ŒappleÃÊ Ò Êapple KMnO 4 apple ê Ëÿ Áfl ÿÿ Êapple Uª ËŸ ŸÊ ŒappleÃÊ Ò X Ò C 6 H 5 COONa HCOONa CH COONa Na C O 4 B/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

8. Which of the following species is not paramagnetic? NO CO O B 8. ÁŸêŸ apple apple ÊÒŸ Ë S Ë ÊË$ ŸÈøÈê Ëÿ Ÿ Ë Ò? NO CO O B 8. The freezing point of benzene decreases by 0.45 C when 0. g of acetic acid is added to 0 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be : (K f for benzene=5. K kg mol ) 64.6% 80.4% 74.6% 94.6% 84. Which of the following molecules is least resonance stabilized? 8. Á Á U Á «U Ê 0. g apple ËŸ apple 0 g apple Á ÊÿÊ ÊÃÊ Ò ÃÊapple apple ËŸ Ê Á Ê 0.45 C apple Êapple ÊÃÊ Ò ÿáœ Á Á U Á «U apple ËŸ apple ªÈÁáÊÃ Êapple U «UÊß U (ÁmÃÿ) ŸÊÃÊ Ò ÃÊapple Á Á U Á «U Ê ÁÃ ÊÃÃÊ ªÈáÊŸ ÊappleªÊ ( apple ËŸ apple Á K f =5. K kg mol ) 64.6% 80.4% 74.6% 94.6% 84. ÁŸêŸ apple apple ÊÒŸ Ê áêè ŸÈŸÊÁŒ M apple ãÿíÿã ÁSÕ U Ò? B/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

85. On treatment of 00 ml of 0. M solution of CoCl.6H O with excess AgNO ;. 0 ions are precipitated. The complex is : [Co(H O) 4 Cl ]Cl.H O [Co(H O) Cl ].H O [Co(H O) 6 ]Cl [Co(H O) 5 Cl]Cl.H O 85. CoCl.6H O apple 0. M Áfl ÿÿ apple 00 ml Êapple AgNO apple ÊÁœÄÿ apple Á Î Ã UŸapple U. 0 ÊÿŸ flˇêappleá Ã ÊappleÃapple Ò È Ò [Co(H O) 4 Cl ]Cl.H O [Co(H O) Cl ].H O [Co(H O) 6 ]Cl [Co(H O) 5 Cl]Cl.H O 86. The major product obtained in the following reaction is : 86. ÁŸêŸ Á Á ÿê apple ÊåÃ ÈÅÿ à ÊŒ Ò B/Page 7 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

87. A water sample has ppm level concentration of following anions 87. ÁÃŒ Ê apple Ë. Ë.. (ppm) SÃ U Ë ÁŸêŸ áêêÿÿêapple Ë ÊãŒ ÃÊ Ò F 0 ; SO = 4 = 00 ; NO = 50 F 0 ; SO = 4 = 00 ; NO = 50 The anion/anions that make/makes the water sample unsuitable for drinking is/ are : fl /flapple áêêÿÿ Êapple ÁÃŒ Ê Êapple ËŸapple apple Á ŸÈ ÿèäã ŸÊÃÊ Ò/ ŸÊÃapple Ò, Ò/ Ò only NO both SO 4 and NO only F only SO 4 88. gram of a carbonate (M CO ) on treatment with excess HCl produces 0.086 mole of CO. The molar mass of M CO in g mol is : 86 84. 8.6.86 ÊòÊ NO 4 SO ÃÕÊ NO ŒÊappleŸÊapple ÊòÊ F ÊòÊ SO 4 88. Ê Êapple Ÿapple U (M CO ) apple ª Ê Êapple HCl apple ÊÁœÄÿ apple Á Á Ã Á ÿê ÊÃÊ Ò ÊÒ U apple 0.086 Êapple CO ÒŒÊ ÊappleÃË Ò M CO Ê Êapple U Œ ÿ ÊŸ g mol apple Ò 86 84. 8.6.86 B/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

89. Given 89. ÁŒÿÊ ªÿÊ Ò, + Cl /Cl Cr /Cr E =.6 V, E = 0.74 V + Cl /Cl Cr /Cr E =.6 V, E = 0.74 V + + CrO 7 /Cr MnO 4/Mn E =. V, E =.5 V. Among the following, the strongest reducing agent is : Cr + + CrO 7 /Cr MnO 4/Mn E =. V, E =.5 V. ÁŸêŸ apple apple Ã øêÿ Ò Cr Mn + Cr + Cl 90. The group having isoelectronic species is : O, F, Na +, Mg + O, F, Na, Mg + O, F, Na, Mg + O, F, Na +, Mg + - o 0 o - Mn + Cr + Cl 90. fl ª È Á apple ß appleä UÊÚŸË S Ë ÊË Ò, Ò O, F, Na +, Mg + O, F, Na, Mg + O, F, Na, Mg + O, F, Na +, Mg + - o 0 o - SPACE FOR ROUGH WORK / U» Êÿ apple Á ª B/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

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Read the following instructions carefully :. The candidates should fill in the required particulars on the Test Booklet and Answer Sheet (Side ) with Black Ball Point Pen.. For writing/marking particulars on Side of the Answer Sheet, use Black Ball Point Pen only.. The candidates should not write their Roll Numbers anywhere else (except in the specified space) on the Test Booklet/Answer Sheet. 4. Out of the four options given for each question, only one option is the correct answer. 5. For each incorrect response, ¼ (one fourth) marks of the total marks allotted to the question (i.e. mark) will be deducted from the total score. No deduction from the total score, however, will be made if no response is indicated for an item in the Answer Sheet. 6. Handle the Test Booklet and Answer Sheet with care, as under no circumstances (except for discrepancy in Test Booklet Code and Answer Sheet Code), another set will be provided. 7. The candidates are not allowed to do any rough work or writing work on the Answer Sheet. All calculations/ writing work are to be done in the space provided for this purpose in the Test Booklet itself, marked Space for Rough Work. This space is given at the bottom of each page and in four pages (Page 40-4) at the end of the booklet. 8. On completion of the test, the candidates must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. 9. Each candidate must show on demand his/her Admit Card to the Invigilator. 0. No candidate, without special permission of the Superintendent or Invigilator, should leave his/her seat.. The candidates should not leave the Examination Hall without handing over their Answer Sheet to the Invigilator on duty and sign the Attendance Sheet again. Cases where a candidate has not signed the Attendance Sheet second time will be deemed not to have handed over the Answer Sheet and dealt with as an unfair means case. The candidates are also required to put their left hand THUMB impression in the space provided in the Attendance Sheet.. Use of Electronic/Manual Calculator and any Electronic device like mobile phone, pager etc. is prohibited.. The candidates are governed by all Rules and Regulations of the Examination body with regard to their conduct in the Examination Hall. All cases of unfair means will be dealt with as per Rules and Regulations of the Examination body. 4. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 5. Candidates are not allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, electronic device or any other material except the Admit Card inside the examination room/hall. 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