This booklet contains 40 printed pages. ß ÈÁSÃ Ê apple ÈÁŒ à Îc 40 Ò PAPER - : PHYSICS, MATHEMATICS & CHEMISTRY Ÿ ÈÁSÃ Ê - : ÊÒÁà ÁflôÊÊŸ, ªÁáÊà ÃÕÊ U ÊÿŸ ÁflôÊÊŸ Do not open this Test Booklet until you are asked to do so. ß ËˇÊÊ ÈÁSÃ Ê Êapple à à Ÿ Êapple 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 Blue / Black Ball Point Pen provided by the Board.. 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. 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 5. There are three parts in the question paper A, B, C consisting of Physics, Mathematics and Chemistry having 30 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 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 Blue/Black Ball Point Pen provided by the Board. 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 one page (i.e. Page 39) 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 H. 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. 3. Do not fold or make any stray mark on the Answer Sheet. Name of the Candidate (in Capital letters ) : ˡÊÊÕË Ê ŸÊ ( «apple ˇÊ Êapple apple ) Roll Number : in figures S S O ŸÈ Ê Êapple apple : in words ÊéŒÊapple apple Examination Centre Number : ˡÊÊ apple 㜠Ÿê U Name of Examination Centre (in Capital letters) : UˡÊÊ apple ãœ Ê ŸÊ ( «apple ˇÊ UÊapple apple ) Candidate s Signature :. Invigilator s Signature : ˡÊÊÕË apple SÃÊˇÊ ÁŸ ËˇÊ apple SÃÊˇÊ. Invigilator s Signature : ÁŸ ËˇÊ apple SÃÊˇÊ No. : Test Booklet Code ˡÊÊ ÈÁSÃ Ê apple à H. UˡÊÊ ÈÁSÃ Ê apple ß Îc U U Êfl ÿ Áflfl UáÊ apple fl Êapple«U mê UÊ éœ UÊÿapple ªÿapple ŸË apple / Ê apple ÊÚ åflêß U appleÿ apple Ãà Ê apple. ûê U òê ß UˡÊÊ ÈÁSÃ Ê apple 㜠U UÊ Ò Ê Êapple UˡÊÊ ÈÁSÃ Ê Êapple Ÿapple Êapple Ê Ê, ÃÊapple ûê U òê ÁŸ Ê U ÊflœÊŸË Ífl Áflfl UáÊ apple U 3. UˡÊÊ Ë flᜠ3 ÉÊ appleu Ò 4. ß UˡÊÊ ÈÁSÃ Ê apple 90 Ÿ Ò Áœ à 360 Ò 5. ß UˡÊÊ ÈÁSÃ Ê apple ÃËŸ ʪ A, B, C Ò, Á apple àÿapple ʪ apple ÊÒÁà ÁflôÊÊŸ, ªÁáÊà fl U ÊÿŸ ÁflôÊÊŸ apple 30 Ÿ Ò ÊÒ U Ë ŸÊapple apple ÊŸ Ò àÿapple Ÿ apple Ë ûê U apple Á 4 (øê U) ÁŸœÊ Á Uà Á ÿapple ªÿapple Ò 6. èÿáõ ÿêapple Êapple àÿapple Ë ûê U apple Á UÊappleÄà ÁŸŒapple ÊŸ ÅÿÊ 5 apple ÁŸŒapple ÊÊŸÈ Ê U ÁŒÿapple Êÿapple ªapple àÿapple Ÿ apple ª à ûê U apple Á ÿapple ¼ flê ʪ Ê U Á ÿê ÊÿappleªÊ ÿᜠûê 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 à ûê U ÊŸÊ ÊÿappleªÊ ÊÒ U UÊappleÄà 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 Uà Áflfl UáÊ fl ûê U Á à UŸapple appleãè Êapple«U mê UÊ éœ UÊÿapple ªÿapple apple fl ŸË apple/ Ê apple ÊÚ åflêß UU appleÿ Ê Ë ÿêappleª apple U 9. UˡÊÊÕË mê UÊ UˡÊÊ ˇÊ/ ÊÚ apple flapple Ê Ê«U apple ÊflÊ Á Ë Ë Ê U Ë Ê Ũÿ Ê ª Ë, ÈÁŒ à ÿê SÃÁ ÁÃ, ʪ 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 Áà Ÿ Ë Ò 0. U» Êÿ UˡÊÊ ÈÁSÃ Ê apple apple fl ÁŸœÊ Á Uà ª U Ë ËÁ ÿ ª àÿapple Îc U U ŸËøapple Ë Êapple U ÊÒ U ÈÁSÃ Ê apple à apple Îc U U ( Îc U 39) ŒË ªß Ò. UˡÊÊ Êåà ÊappleŸapple U, UˡÊÊÕË ˇÊ/ ÊÚ UÊapple«Ÿapple apple Ífl ûê U òê ˇÊ ÁŸ UËˇÊ Êapple fl ÿ ÊÒ Œapple UˡÊÊÕË Ÿapple ÊÕ ß UˡÊÊ ÈÁSÃ Ê Êapple apple Ê Ãapple Ò. ß ÈÁSÃ Ê Ê apple à H Ò ÿ ÈÁŸÁ øã U apple Á ß ÈÁSÃ Ê Ê apple Ã, ûê U òê apple Îc U- U U apple apple à apple Á ÃÊ Ò ÊÒ U ÿ Ë ÈÁŸÁ øã U apple Á UˡÊÊ ÈÁSÃ Ê ÊÒ U ûê U òê Ë ÅÿÊ Á ÃË Ò ª U ÿ Á ÛÊ Êapple ÃÊapple UˡÊÊÕË ŒÍ UË UˡÊÊ ÈÁSÃ Ê ÊÒ U ûê U òê appleÿapple apple Á ÁŸ UËˇÊ Êapple ÃÈ Uãà flªã UÊ 3. ûê U òê Êapple Ÿ Êapple«apple fl Ÿ Ë U ãÿ ÁŸ ÊÊŸ ªÊ
PART A PHYSICS ALL THE GRAPHS GIVEN ARE SCHEMATIC AND NOT DRAWN TO SCALE. ʪ A ÊÒÁà ÁflôÊÊŸ ÁŒ ªÿapple Ë ª Ê» Ê appleuëÿ Ò ÊÒ U S apple apple ŸÈ Ê U appleuê Á à Ÿ Ë Ò. A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance A from equilibrium position. The new 3 amplitude of the motion is : A 3. áê A ÊÿÊ apple U - Êflà ŒÊapple Ÿ U U Ê Ò ÿ Ÿapple Í -SÕÊŸ apple 3A U È øãê Ò Ã øêÿ ß Ë ªÁà ÁÃªÈŸË U ŒË ÊÃË Ò Ã ß Ê ŸÿÊ ÊÿÊ Ò A 3 7 A 3 7 A 3 A 4 3 3A A 4 3 3A. For a common emitter configuration, if α and have their usual meanings, the incorrect relationship between α and is :. ÿáÿc U- à ÁflãÿÊ apple Á ÿapple α ÃÕÊ apple Ëø ÁŸêŸ apple apple ÊÒŸ Ê œ ª à Ò? α ÃÕÊ Áøq Ê Êãÿ à flê apple Ò + + + + = + α = + α H/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª
3. A student measures the time period of 00 oscillations of a simple pendulum four times. The data set is 90 s, 9 s, 95 s and 9 s. If the minimum division in the measuring clock is s, then the reported mean time should be : 3. UÊòÊ U - Êflà -ŒÊapple apple 00 ÊflÎÁûÊÿÊapple Ê ÿ 4 Ê U Ê ÃÊ Ò ÊÒ U Ÿ Êapple 90 s, 9 s, 95 s ÊÒ U 9 s ÊÃÊ Ò ßSÃapple Ê Ë ªß ÉÊ«Ë Ê ãÿíÿã À Ê Ê s Ò Ã Ê apple ªÿapple Êäÿ ÿ Êapple apple Á ŸÊ øêá ÿapple 9±.8 s 9±.8 s 9±3 s 9±3 s 9± s 9± s 9±5.0 s 9±5.0 s 4. If a, b, c, d are inputs to a gate and x is its output, then, as per the following time graph, the gate is : 4. ªapple U apple a, b, c, d ߟ È U Ò ÊÒ U x Ê U È U Ò Ã ÁŒÿapple ªÿapple UÊß -ª Ê» apple ŸÈ Ê U ªapple U Ò OR OR NAND NAND NOT NOT AND AND H/Page 3 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª
5. A particle of mass m is moving along the side of a square of side a, with a uniform speed v in the x-y plane as shown in the figure : 5. ÁøòÊ apple È Ê a Ê flª x-y à apple Ò m Œ ÿ ÊŸ Ê áê ÊŸ ªÁÃ, v apple ß flª Ë È Ê U ø U Ê Ò Ò Ê Á ÁøòÊ apple Œ ÊÊ ÿê ªÿÊ Ò Which of the following statements is false for the angular momentum L about the origin? à ÁŸêŸ apple apple ÊÒŸ Ê ÕŸ, ß áê apple Í Á ŒÈ apple ÁªŒ ÊappleáÊËÿ ÊÉÊÍáÊ L apple Á ÿapple, ª à Ò? R L= mv + a k when the particle is moving from B to C. R L mv a k = +, áê B apple C Ë Êapple U ø U Ê Ò mv L= R k when the particle is moving from D to A. L mv R k =, áê D apple A Ë Êapple U ø U Ê Ò mv L= R k when the particle is moving from A to B. L mv R k =, áê A apple B Ë Êapple U ø U Ê Ò R L= mv a k when the particle is moving from C to D. H/Page 4 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª R L mv a k =, áê C apple D Ë Êapple U ø U Ê Ò
6. Choose the correct statement : H/Page 5 In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal. In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the frequency of the audio signal. In amplitude modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal. In amplitude modulation the frequency of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal. 7. Radiation of wavelength λ, is incident on a photocell. The fastest emitted electron has speed v. If the wavelength is changed to 3 λ, the speed of the fastest emitted 4 electron will be : 4 = v 3 = v 4 4 > v 4 < v 6. Ë ÕŸ øèáÿÿapple ÊflÎÁûÊ Ê«ÈU Ÿ apple ìê ÊflÎÁûÊ Ë flê à Uª apple ÊÿÊ apple Œ Êfl äfláÿ Á ÇãÊ apple ÊÿÊ apple ŸÈ ÊÃË Ò SPACE FOR ROUGH WORK / U» Êÿ apple Á ª ÊflÎÁûÊ Ê«ÈU Ÿ apple ìê- ÊflÎÁûÊ Ë flê à Uª Ë ÊÿÊ apple Œ Êfl äfláÿ Á ÇŸ Ë ÊflÎÁûÊ apple ŸÈ ÊÃË Ò ÊÿÊ Ê«È Ÿ apple ìê ÊflÎÁûÊ Ë flê U à Uª apple ÊÿÊ apple Œ Êfl äfláÿ Á ÇŸ apple ÊÿÊ apple ŸÈ ÊÃË Ò ÊÿÊ Ê«ÈU Ÿ apple ìê ÊflÎÁûÊ Ë flê à Uª Ë ÊflÎÁûÊ apple Œ Êfl äfláÿ Á ÇãÊ apple ÊÿÊ apple ŸÈ ÊÃË Ò 7.» Êapple UÊapple- apple U λ à UªŒÒÉÿ Ê Ê Ê Ê ÁÃÃ Ò à Á Ã ß appleä UÊÚŸ Ë Áœ à ªÁà v Ò λ ÿᜠà UªŒÒÉÿ 3 4 Êapple à à Á Ã ß appleä UÊÚŸ Ë Áœ à ªÁà ÊappleªË 4 = v 3 = v 4 4 > v 4 < v
8. Two identical wires A and B, each of length l, carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side a. If B A and B B are the values of magnetic field at the centres of the circle and square respectively, then the ratio BA is : B B 8. ŒÊapple ÊŸ ÃÊ U A fl B àÿapple Ë ê Êß l, apple ÊŸ œê UÊ I flêá Ã Ò A Êapple Êapple«U R ÁòÊíÿÊ Ê flîûê ÊÒ U B Êapple Êapple«U È Ê a Ê flª ŸÊÿÊ ÊÃÊ Ò ÿᜠB A ÃÕÊ B B Ê flîûê apple apple 㜠ÃÕÊ flª apple apple 㜠U øèê Ëÿ ˇÊappleòÊ Ò, B BB à ŸÈ Êà A ÊappleªÊ 6 6 8 8 8 8 6 6 9. A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now : 9. ŒÊappleŸÊapple Á UÊapple U È apple Êß Ë flêÿè apple Í - ÊflÎÁûÊ f Ò Êß Êapple äflê œ U Ë ÊœË- ê Êß Ã ÊŸË apple «ÈU ÊÿÊ ÊÃÊ Ò Ã ß apple øapple flêÿè- Ê Ë Í ÊflÎÁûÊ ÊappleªË f f f f f f 3f 3f 4 4 H/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª
0. The region between two concentric spheres of radii a and b, respectively (see figure), A has volume charge density ρ =, where r A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is : 0. ÁòÊíÿÊ a ÃÕÊ b apple ŒÊapple - apple ãœ Ë ªÊapple Êapple apple (ÁøòÊ ŒappleÁÿapple) Ëø apple SÕÊŸ apple Êÿß Êflapple Ê-ÉÊŸàfl A = r ρ Ò, Ê A ÁSÕ UÊ Ò ÃÕÊ r apple 㜠apple ŒÍ UË Ò ªÊapple Êapple apple apple 㜠U Á ãœè- Êflapple Ê Q Ò A Ê fl ÊŸ ÃÊÿapple Á apple ªÊapple Êapple apple Ëø apple SÕÊŸ apple ÊŸ flòlèã-ˇêappleòê Êapple Q ( a b ) Q ( a b ) Q a Q a Q a Q a Q ( b a ) Q ( b a ). An arc lamp requires a direct current of 0 A at 80 V to function. If it is connected to a 0 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to : 0.044 H 0.065 H 80 H 0.08 H. Ê Òê Êapple ÊÁ Êà UŸapple apple Á ÿapple 80 V U 0 A Ë ÁŒc U œê UÊ (DC) Ë Êfl ÿ ÃÊ ÊappleÃË Ò Ë Ê Êapple 0 V (rms) 50 Hz àÿêflãë œê UÊ (AC) apple ø ÊŸapple apple Á ÿapple üêappleáêë apple ªŸapple flê apple apple U àfl Ê ÊŸ Ò 0.044 H 0.065 H 80 H 0.08 H H/Page 7 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª
. n moles of an ideal gas undergoes a process AB as shown in the figure. The maximum temperature of the gas during the process will be :. n Êapple ÊŒ Ê ªÒ AB apple ªÈ$ UÃË Ò (ÁøòÊ ŒappleÁÿapple) ß apple ŒÊÒ UÊŸ Ê Áœ à ÃÊ ÊŸ ÊappleªÊ 9 P V nr 0 0 9 P V nr 0 0 9 P0 V0 nr 9 P0 V0 nr 9 P V 4nR 0 0 9 P V 4nR 0 0 3 P 0 V0 nr 3 P 0 V0 nr 3. A person trying to lose weight by burning fat lifts a mass of 0 kg upto a height of m 000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8 0 7 J of energy per kg which is converted to mechanical energy with a 0% efficiency rate. Take g=9.8 ms : 9.89 0 3 kg.89 0 3 kg.45 0 3 kg 6.45 0 3 kg 3. Ê UÊappleûÊÊapple Ê U Êapple apple U ÊÒ U Á» U ŸËøapple à ÊÃÊ Ò ÿ ÊŸÊ ÊÃÊ Ò Á Á» Ê U Êapple U apple ÊŸapple apple Êÿ ÊappleÃÊ Ò ÊÒ U ŸËøapple ÊŸapple apple ÁSÕÁÃ Ê Ê OÊ ÊappleÃÊ Ò Ê UË U Ë fl Ê Ê ŒappleÃË Ò Êapple ÿê ÁòÊ Ëÿ Ê apple Œ ÃË Ò ÊŸ apple Á fl Ê mê UÊ ŒË ªß Ê 3.8 0 7 J Áà kg Ê U Ò, ÃÕÊ ß Ê ÊòÊ 0% ÿê ÁòÊ Ëÿ Ê apple Œ ÃÊ Ò ÿáœ Ê UÊappleûÊÊapple 0 kg apple Ê U Êapple 000 Ê U m Ë øêß Ã U ÊÒ U ŸËøapple UÃÊ Ò Ã apple Ê UË U apple fl Ê Ê ˇÊÿ Ò (g=9.8 ms apple ) 9.89 0 3 kg.89 0 3 kg.45 0 3 kg 6.45 0 3 kg H/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª
4. A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals µ. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. 4. m Œ ÿ ÊŸ Ê Á ŒÈ áê È UŒ appleu Õ PQR (ÁøòÊ ŒappleÁÿapple) U ø U Ê Ò áê ÊÒ U Õ apple Ëø ÉÊ áê ªÈáÊÊ µ Ò áê P apple UÊapple«apple ÊŸapple apple ÊŒ R U È ø U L ÊÃÊ Ò Õ apple ʪ PQ ÊÒ U QR U ø Ÿapple apple áê mê UÊ ø Ë ªß Ê UÊ U Ò PQ apple QR U ÊappleŸapple flê apple ÁŒ ÊÊ Œ Êfl apple Êappleß Ê ø Ÿ Ë ÊappleÃË Ã µ ÊÒ U ŒÍ UË x(=qr) apple ÊŸ ª ª Ò Ê The values of the coefficient of friction µ and the distance x(=qr), are, respectively close to : 0.9 and 3.5 m 0.9 ÊÒ U 3.5 m 0.9 and 6.5 m 0.9 ÊÒ U 6.5 m 0. and 6.5 m 0. ÊÒ U 6.5 m 0. and 3.5 m 0. ÊÒ U 3.5 m H/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª
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