VishwaNath English+Hindi EEEE.pmd

This booklet contains 0 printed pages. ß ÈÁSÃ Ê apple ÈÁŒ Ã Îc 0 Ò PAPER - 1 : PHYSICS, CHEMISTRY & MATHEMATICS Ÿ ÈÁSÃ Ê - 1 : ÊÒÁÃ ÁflôÊÊŸ, U ÊÿŸ ÁflôÊÊŸ ÃÕÊ ªÁáÊÃ 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 1. 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.. The test is of hours duration.. 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, Chemistry and Mathematics having 0 questions in each part of equal weightage. Each question is allotted (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-1 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. 10. 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 9) at the end of the booklet. 11. 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. 1. The CODE for this Booklet is E. 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. 1. Do not fold or make any stray mark on the Answer Sheet. Name of the Candidate (in Capital letters ) : ËˇÊÊÕË Ê ŸÊ ( «apple ˇÊ Êapple apple ) Roll Number : in figures S S O 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 : 1. Invigilator s Signature : ËˇÊÊÕË apple SÃÊˇÊ ÁŸ ËˇÊ apple SÃÊˇÊ. Invigilator s Signature : ÁŸ ËˇÊ apple SÃÊˇÊ No. : Test Booklet Code ËˇÊÊ ÈÁSÃ Ê apple Ã E 1. UËˇÊÊ 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 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. 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, U ÊÿŸ ÁflôÊÊŸ fl ªÁáÊÃ apple 0 Ÿ Ò ÊÒ U Ë ŸÊapple apple ÊŸ Ò àÿapple Ÿ apple Ë ûê U apple Á (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 ¼ flê Êª 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-1 fl Îc U- U flê Á UÃ Áflfl UáÊ fl ûê U Á Ã 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. UËˇÊÊÕË 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 10. 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 Îc U U ( Îc U 9) ŒË ªß Ò 11. UËˇÊÊ ÊåÃ ÊappleŸapple U, UËˇÊÊÕË ˇÊ/ ÊÚ UÊapple«Ÿapple apple Ífl ûê U òê ˇÊ ÁŸ UËˇÊ Êapple fl ÿ ÊÒ Œapple UËˇÊÊÕË Ÿapple ÊÕ ß UËˇÊÊ ÈÁSÃ Ê Êapple apple Ê Ãapple Ò 1. ß ÈÁSÃ Ê Ê apple Ã E 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 UËˇÊÊÕË ŒÍ UË UËˇÊÊ ÈÁSÃ Ê ÊÒ U ûê U òê appleÿapple apple Á ÁŸ UËˇÊ Êapple ÃÈ UãÃ flªã UÊ 1. 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. 1. A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 9 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be : 9± s 9±5.0 s 9±1.8 s 9± s. 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 : Which of the following statements is false for the angular momentum L about the origin? mv L= R k when the particle is moving from A to B. R L= mv a k when the particle is moving from C to D. R L= mv + a k when the particle is moving from B to C. mv L= R k when the particle is moving from D to A. Êª A ÊÒÁÃ ÁflôÊÊŸ ÁŒ ªÿapple Ë ª Ê» Ê appleuπëÿ Ò ÊÒ U S apple apple ŸÈ Ê U appleuπê Á Ã Ÿ Ë Ò 1. UÊòÊ U - ÊflÃ -ŒÊapple apple 100 ÊflÎÁûÊÿÊapple Ê ÿ Ê U Ê ÃÊ Ò ÊÒ U Ÿ Êapple 90 s, 91 s, 95 s ÊÒ U 9 s ÊÃÊ Ò ßSÃapple Ê Ë ªß ÉÊ«Ë Ê ãÿíÿã À Ê Ê 1 s Ò Ã Ê apple ªÿapple Êäÿ ÿ Êapple apple Á πÿê øêá ÿapple 9± s 9±5.0 s 9±1.8 s 9± s. ÁøòÊ apple È Ê a Ê flª x-y Ã 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 E/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª Ã ÁŸêŸ apple apple ÊÒŸ Ê ÕŸ, ß áê apple Í Á ŒÈ apple ÁªŒ ÊappleáÊËÿ ÊÉÊÍáÊ L apple Á ÿapple, ª Ã Ò? L mv R k =, áê A apple B Ë Êapple U ø U Ê Ò R L mv a k =, áê C apple D Ë Êapple U ø U Ê Ò R L mv a k = +, áê B apple C Ë Êapple U ø U Ê Ò L mv R k =, áê D apple A Ë Êapple U ø U Ê Ò

. 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. The values of the coefficient of friction µ and the distance x(=qr), are, respectively close to : 0. and 6.5 m 0. and.5 m 0.9 and.5 m. m Œ ÿ ÊŸ Ê Á ŒÈ áê πè UŒ appleu Õ PQR (ÁøòÊ ŒappleÁπÿapple) 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 Êª PQ ÊÒ U QR U ø Ÿapple apple áê mê UÊ πø Ë ªß Ê UÊ U Ò PQ apple QR U ÊappleŸapple flê apple ÁŒ ÊÊ Œ Êfl apple Êappleß Ê πø Ÿ Ë ÊappleÃË Ã µ ÊÒ U ŒÍ UË x(=qr) apple ÊŸ ª ª Ò Ê 0. ÊÒ U 6.5 m 0. ÊÒ U.5 m 0.9 ÊÒ U.5 m 0.9 and 6.5 m 0.9 ÊÒ U 6.5 m E/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

. A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 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.8 10 7 J of energy per kg which is converted to mechanical energy with a 0% efficiency rate. Take g=9.8 ms :.5 10 kg 6.5 10 kg 9.89 10 kg 1.89 10 kg 5. A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to : turn left. turn right. go straight. turn left and right alternately.. Ê UÊappleûÊÊapple Ê U Êapple apple U ÊÒ U Á» U ŸËøapple Ã 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.8 10 7 J ÁÃ kg Ê U Ò, ÃÕÊ ß Ê ÊòÊ 0% ÿê ÁòÊ Ëÿ Ê apple Œ ÃÊ Ò ÿáœ Ê UÊappleûÊÊapple 10 kg apple Ê U Êapple 1000 Ê U 1 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 ).5 10 kg 6.5 10 kg 9.89 10 kg 1.89 10 kg 5. ŒÊapple Ê È Êapple Ÿ apple ÊË O U Êapple«U UÊapple U ŸÊÿÊ ªÿÊ Ò ÊÒ U apple AB fl CD appleu U Á Ã UπÊ ªÿÊ Ò (ÁøòÊ ŒappleÁπÿapple) UÊapple U Ê ˇÊ CD apple ê flã Ò ÊÒ U O ŒÊappleŸÊapple appleu apple ËøÊapple Ëø Ò À apple apple œ apple Ÿapple U UÊapple U appleu U ß Ê U È ŸÊ Ê Uê UÃÊ Ò Á O Ê øê Ÿ CD apple Ê Ã U Ò (ÁøòÊ ŒappleÁπÿapple) øêá Ã Êapple ÊŸapple apple ÊŒ ÿ UÊapple U Ê ÿë Êapple U È«appleªÊ ŒÊÿË Êapple U È«appleªÊ ËœÊ ø ÃÊ U appleªê Êÿapple ÃÕÊ ŒÊÿapple Ê È«ÃÊ U appleªê E/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

6. A satellite is revolving in a circular orbit at a height h from the earth s surface (radius of earth R ; h<<r). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth s gravitational field, is close to : (Neglect the effect of atmosphere.) gr gr gr / gr ( 1) 7. A pendulum clock loses 1 s a day if the temperature is 0 C and gains s a day if the temperature is 0 C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively : 5 C; α=1.85 10 5 / C 60 C; α=1.85 10 / C 0 C; α=1.85 10 / C 6. ÎâflË Ë Ã apple h øêß U ª flîûêê Ê U Õ U øä U Ê U U Ê Ò ( ÎâflË Ë ÁòÊíÿÊ R ÃÕÊ h<<r) ÎâflË apple ªÈL àfl ˇÊappleòÊ apple ÊÿŸ UŸapple apple Á ÿapple ß Ë ˇÊËÿ ªÁÃ apple Êfl ÿ ãÿíÿã Œ Êfl Ò (flêÿè «U Ëÿ Êfl Êapple Ÿªáÿ ËÁ ) gr gr gr / gr ( 1) 7. appleãu«èu ÉÊ«Ë 0 C ÃÊ ÊŸ U 1 s ÁÃÁŒŸ œë Ë Êapple ÊÃË Ò ÃÕÊ 0 C ÃÊ ÊŸ U s ÁÃÁŒŸ Ãapple$ Êapple ÊÃË Ò ÃÊ ÊŸ Á U ÿ Ë ÿ Œ ÊÊ ÿappleªë ÃÕÊ appleãu«èu Ë œêãè Ê appleuπëÿ- Ê U ªÈáÊÊ (α) Ê Ò 5 C; α=1.85 10 5 / C 60 C; α=1.85 10 / C 0 C; α=1.85 10 / C 55 C; α=1.85 10 / C 55 C; α=1.85 10 / C E/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

8. An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PV n =constant, then n is given by (Here C P and C V are molar specific heat at constant pressure and constant volume, respectively) : C n= P C V C CP n= C C V C P C n= C C C C n= C C V V P 9. n moles of an ideal gas undergoes a process A B as shown in the figure. The maximum temperature of the gas during the process will be : 9 P V nr 0 0 P 0 V0 nr 9 P V nr 0 0 9 P0 V0 nr 8. ÊŒ Ê ªÒ à áêëÿ SÕÒÁÃ - À apple ªÈ$ UÃË Ò ÃÕÊ Ë Êapple U- c Ê-œÊÁ UÃÊ C ÁSÕ U U ÃË Ò ÿáœ ß apple apple ŒÊ P fl ÊÿÃŸ V apple Ëø œ PV n =constant Ò (C P ÃÕÊ C V Ê ÁSÕ U ŒÊ fl ÁSÕ U ÊÿÃŸ U c ÊœÊÁ UÃÊ Ò) Ã n apple Á ÿapple Ë UáÊ Ò C n= P C E/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª V C CP n= C C V C P C n= C C C C n= C C V V P 9. n Êapple ÊŒ Ê ªÒ A B apple ªÈ$ UÃË Ò (ÁøòÊ ŒappleÁπÿapple) ß apple ŒÊÒ UÊŸ Ê Áœ Ã ÃÊ ÊŸ ÊappleªÊ 9 P V nr 0 0 P 0 V0 nr 9 P V nr 0 0 9 P0 V0 nr

10. 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 amplitude of the motion is : 10. áê A ÊÿÊ apple U - ÊflÃ ŒÊapple Ÿ U U Ê Ò ÿ Ÿapple Í -SÕÊŸ apple A U È øãê Ò Ã øêÿ ß Ë ªÁÃ ÁÃªÈŸË U ŒË ÊÃË Ò Ã ß Ê ŸÿÊ ÊÿÊ Ò A 1 A A 7 A 11. A uniform string of length 0 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is : (take g = 10 ms ) π s s s A 1 A A 7 A 11. 0 m ê Êß Ë ÊŸ «UÊapple UË Êapple ŒÎ ÊœÊ U apple U ÊÿÊ ªÿÊ Ò ß apple ÁŸø apple Á appleu apple Íˇ Ã Uª-S Œ øêá Ã ÊappleÃÊ Ò U ÊœÊ U Ã È øÿapple apple ªŸapple flê Ê ÿ Ò (g = 10 ms apple ) π s s s E/Page 7 s s SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

1. 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 : Q π a π π Q ( b a ) ( a b ) Q π a Q 1. ÁòÊíÿÊ a ÃÕÊ b apple ŒÊapple - apple ãœ Ë ªÊapple Êapple apple (ÁøòÊ ŒappleÁπÿapple) Ëø apple SÕÊŸ apple ÊÿÃŸ Êflapple Ê-ÉÊŸàfl A = r E/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª ρ Ò, Ê A ÁSÕ UÊ Ò ÃÕÊ r apple ãœ apple ŒÍ UË Ò ªÊapple Êapple apple apple ãœ 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 π a π π Q ( b a ) Q ( a b ) Q π a

1. A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the µf and 9 µf capacitors), at a point distant 0 m from it, would equal : 1. œêá UòÊÊapple apple Ÿapple Á U Õ Êapple ÁøòÊ apple ÁŒπÊÿÊ ªÿÊ Ò Á ãœè- Êflapple Ê Q (Á Ê ÊŸ µf ÃÕÊ 9 µf flê apple œêá UòÊÊapple apple È Êflapple ÊÊapple apple UÊ U Ò) apple mê UÊ 0 m ŒÍ UË U flòlèã-ˇêappleòê Ê Á U ÊáÊ ÊappleªÊ 0 N/C 60 N/C 0 N/C 80 N/C 1. The temperature dependence of resistances of Cu and undoped Si in the temperature range 00-00 K, is best described by : Linear increase for Cu, linear increase for Si. Linear increase for Cu, exponential increase for Si. Linear increase for Cu, exponential decrease for Si. Linear decrease for Cu, linear 0 N/C 60 N/C 0 N/C 80 N/C 1. ÃÊ Ê ÃÕÊ ÊÁŒÃ (undoped) Á Á ÊŸ apple ÁÃ UÊappleœÊapple Ë Ÿ apple ÃÊ ÊŸ U ÁŸ UÃÊ, 00-00 K ÃÊ ÊŸ Ã UÊ apple, apple Á ÿapple Ë ÕŸ Ò ÃÊ Ê apple Á ÿapple appleuπëÿ Êfl ÃÕÊ Á Á ÊŸ apple Á ÿapple appleuπëÿ Êfl ÃÊ Ê apple Á ÿapple appleuπëÿ Êfl ÃÕÊ Á Á ÊŸ apple Á ÿapple ø UUÉÊÊÃÊ Ë Êfl ÃÊ Ê apple Á ÿapple appleuπëÿ Êfl ÃÕÊ Á Á ÊŸ apple Á ÿapple ø UUÉÊÊÃÊ Ë ÉÊ UÊfl ÃÊ Ê apple Á ÿapple appleuπëÿ ÉÊ UÊfl ÃÕÊ Á Á ÊŸ apple Á ÿapple appleuπëÿ ÉÊ UÊfl decrease for Si. E/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

15. 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 : BB π 8 π 16 π 16 π 8 16. Hysteresis loops for two magnetic materials A and B are given below : These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use : A for electric generators and transformers. A for electromagnets and B for electric generators. A for transformers and B for electric generators. 15. 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 ÿáœ B A ÃÕÊ B B Ê flîûê apple apple ãœ ÃÕÊ flª apple apple ãœ U øèê Ëÿ ˇÊappleòÊ Ò, Ã ŸÈ ÊÃ A E/Page 10 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª π 8 π 16 π 16 π 8 B BB ÊappleªÊ 16. ŒÊapple øèê Ëÿ ŒÊÕ A ÃÕÊ B apple Á ÿapple Á S apple appleuá - Í ŸËøapple ÁŒπÊÿapple ªÿapple Ò ßŸ ŒÊÕÊappleZ Ê øèê Ëÿ ÿêappleª ÁfllÈÃ- appleÿapple appleu U U apple øèê, UÊã» ÊÚ U Ë Êapple«U fl ÁfllÈÃ-øÈê Ë Êapple«U ÊÁŒ apple ŸÊŸapple apple Á ÿê ÊÃÊ Ò Ã ÿ ÁøÃ Ò Á A Ê ßSÃapple Ê ÁfllÈÃ- appleÿapple appleu U U ÃÕÊ UÊã» ÊÚ U ŒÊappleŸÊapple apple Á ÿê Ê A Ê ßSÃapple Ê ÁfllÈÃ-øÈê apple ÃÕÊ B Ê ÁfllÈÃ- appleÿapple appleu U U apple Á ÿê Ê A Ê ßSÃapple Ê UÊã» ÊÚ U apple ÃÕÊ B Ê ÁfllÈÃ- appleÿapple appleu U U apple Á ÿê Ê B Ê ßSÃapple Ê ÁfllÈÃ-øÈê ÃÕÊ UÊã» ÊÚ U ŒÊappleŸÊapple apple Á ÿê Ê transformers. B for electromagnets and

17. An arc lamp requires a direct current of 10 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 : 80 H 17. Ê Òê Êapple ÊÁ ÊÃ UŸapple apple Á ÿapple 80 V U 10 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 80 H E/Page 11 0.08 H 0.0 H 0.065 H 18. Arrange the following electromagnetic radiations per quantum in the order of increasing energy : A : Blue light C : X-ray D, B, A, C A, B, D, C C, A, B, D B, A, D, C B : Yellow light D : Radiowave. 19. An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 0. To the observer the tree appears : 10 times taller. 10 times nearer. 0 times taller. 0 times nearer. 0.08 H 0.0 H 0.065 H 18. ÁŸêŸ ÁÃ ÄflÊ U flòlèã-øèê Ëÿ ÁflÁ UáÊÊapple Êapple Ÿ Ë Ê apple Ãapple È apple ªÊÿapple A : ŸË Ê Ê Ê C : X - Á UáÊapple D, B, A, C A, B, D, C C, A, B, D B, A, D, C SPACE FOR ROUGH WORK / U» Êÿ apple Á ª B : Ë Ê Ê Ê D : appleuá«uÿêapple Ã Uª 19. ŒÍ U ÁSÕÃ 10 m øapple apple«êapple 0 Êflœ Ÿ ˇÊ ÃÊ flê apple appleuá S Êapple apple ŒappleπŸapple U ÄÿÊ Í ÊappleªÊ? apple«10 ªÈŸÊ øê Ò apple«10 ªÈŸÊ Ê Ò apple«0 ªÈŸÊ øê Ò apple«0 ªÈŸÊ Ê Ò

0. The box of a pin hole camera, of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength λ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say b min ) when : a = λ λ and b L min = L λ a= λl and b min = L a= λl and b min = λl a = λ and b min = λl L 1. Radiation of wavelength λ, is incident on a photocell. The fastest emitted electron has speed v. If the wavelength is changed to λ, the speed of the fastest emitted electron will be : 1 > v 1 < v 1 = v 1 = v 0. Á Ÿ- Êapple Ò UÊ Ë ÀÊê Êß L Ò ÃÕÊ Á UŒ Ë ÁòÊíÿÊ a Ò U λ Ã UªŒÒÉÿ Ê Ê Ã U Ê Ê Ê ÁÃÃ Ò Á UŒ apple Ê Ÿapple flê Ë Ã U Ÿapple S ÊÚ U Ê ÁflSÃÊ U Á UŒ apple íÿêá ÃËÿ Ê Ê U ÃÕÊ ÁflflÃ Ÿ apple Ê UáÊ È ÁflSÃÊ U Ê È ÿêappleª Ò ß S ÊÚ U Ê ãÿíÿã Ê Ê U b min Ã ÊappleªÊ E/Page 1 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª a = λ ÃÕÊ b min = L λ L λ a= λl ÃÕÊ b min = L a a = λl ÃÕÊ b min = λl = λ ÃÕÊ b min = λl L 1.» Êapple UÊapple- apple U λ Ã UªŒÒÉÿ Ê Ê Ê Ê ÁÃÃ Ò à Á Ã ß appleä UÊÚŸ Ë Áœ Ã ªÁÃ v Ò λ ÿáœ Ã UªŒÒÉÿ Êapple Ã à Á Ã ß appleä UÊÚŸ Ë Áœ Ã ªÁÃ ÊappleªË 1 > v 1 < v 1 = v 1 = v

. Half-lives of two radioactive elements A and B are 0 minutes and 0 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :. ŒÊapple appleuá«uÿêappleœ Ë Ãàfl A ÃÕÊ B Ë h ÊÿÈ Ê 0 min ÃÕÊ 0 min Ò Ê U apple ŒÊappleŸÊapple apple Ÿ ÍŸÊapple apple ŸÊÁ Êapple Ë ÅÿÊ UÊ U Ò 80 min apple UÊ Ã A ÃÕÊ B apple ˇÊÿ È ŸÊÁ Êapple Ë ÅÿÊ Ê ŸÈ ÊÃ ÊappleªÊ 1 : 16 : 1 1 : 5 :. 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 : NOT AND OR 1 : 16 : 1 1 : 5 :. ªapple U apple a, b, c, d ßŸ È U Ò ÊÒ U x Ê U È U Ò Ã ÁŒÿapple ªÿapple UÊß -ª Ê» apple ŸÈ Ê U ªapple U Ò NOT AND OR E/Page 1 NAND NAND SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

. Choose the correct statement : 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. 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. 5. A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 5 th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 5 th division coincides with the main scale line? 0.75 mm 0.80 mm 0.70 mm 0.50 mm. Ë ÕŸ øèáÿÿapple ÊÿÊ Ê«È Ÿ apple ìê ÊflÎÁûÊ Ë flê U Ã Uª apple ÊÿÊ apple Œ Êfl äfláÿ Á ÇŸ apple ÊÿÊ apple ŸÈ ÊÃË Ò E/Page 1 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª ÊÿÊ Ê«ÈU Ÿ apple ìê ÊflÎÁûÊ Ë flê Ã Uª Ë ÊflÎÁûÊ apple Œ Êfl äfláÿ Á ÇãÊ apple ÊÿÊ apple ŸÈ ÊÃË Ò ÊflÎÁûÊ Ê«ÈU Ÿ apple ìê ÊflÎÁûÊ Ë flê Ã Uª apple ÊÿÊ apple Œ Êfl äfláÿ Á ÇãÊ apple ÊÿÊ apple ŸÈ ÊÃË Ò ÊflÎÁûÊ Ê«ÈU Ÿ apple ìê- ÊflÎÁûÊ Ë flê Ã Uª Ë ÊÿÊ apple Œ Êfl äfláÿ Á ÇŸ Ë ÊflÎÁûÊ apple ŸÈ ÊÃË Ò 5. S Í -ªapple Ê Á ø 0.5 mm Ò ÊÒ U apple flîûêëÿ- S apple U 50 Êª Ò ß apple mê UÊ Ã Ë ÀÿÈ ËÁŸÿ ÊË U Ë Êapple UÊß Ê Ë ªß Ê appleÿapple apple Ífl ÿ ÊÿÊ ªÿÊ Á S Í -ªapple apple ŒÊapple ÊÚflÊapple Êapple SÊê U apple ÊÿÊ ÊÃÊ Ò Ã 5 flê Êª ÈÅÿ S apple Êß Ÿ apple ÊÃË ÊappleÃÊ Ò ÊÒ U ÈÅÿ S apple Ê ÊÍãÿ (0) ÈÁ apple ÁŒπÃÊ Ò ÈÅÿ S apple Ê Ê KÊ ÿáœ 0.5 mm ÃÕÊ 5 flê Êª ÈÅÿ S apple Êß Ÿ apple ÊÃË Êapple, ÃÊapple ÊË U Ë Êapple UÊß ÄÿÊ ÊappleªË? 0.75 mm 0.80 mm 0.70 mm 0.50 mm

6. 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 : f f f f 7. A galvanometer having a coil resistance of 100 Ω gives a full scale deflection, when a current of 1 ma is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A, is : 0.01 Ω Ω 0.1 Ω Ω 8. In an experiment for determination of refractive index of glass of a prism by i δ, plot, it was found that a ray incident at angle 5, suffers a deviation of 0 and that it emerges at angle 79 Ιn that case which of the following is closest to the maximum possible value of the refractive index? 1.5 1.6 1.7 1.8 6. ŒÊappleŸÊapple Á UÊapple U πè 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 7. ªÒÀflappleŸÊapple Ë U U apple Êß Ê ÁÃ UÊappleœ 100 Ω Ò 1 ma œê UÊ flêá Ã UŸapple U ß apple»è -S apple ÁflˇÊapple Á ÃÊ Ò ß ªÒÀflappleŸÊapple Ë U U Êapple 10 A apple Ë U U apple Œ Ÿapple apple Á ÿapple Êapple ÁÃ UÊappleœ ªÊŸÊ ÊappleªÊ fl Ò 0.01 Ω Ω 0.1 Ω Ω 8. ÿêappleª U apple ÃÕÊ i δ ª Ê» ŸÊ U Ê ø apple Ÿapple Á ï Ê flã ŸÊ ÁŸ Ê Ê ÊÃÊ Ò Á UáÊ Êapple 5 U Ê ÁÃÃ UŸapple U fl 0 apple ÁfløÁ Ã ÊappleÃË Ò ÃÕÊ ÿ 79 U ÁŸª ÊappleÃË Ò ß ÁSÕÁÃ apple ÁŸêŸ apple apple ÊÒŸ Ê ÊŸ flã ŸÊ apple Áœ Ã ÊŸ apple apple Ê Ò? 1.5 1.6 1.7 1.8 E/Page 15 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

9. Identify the semiconductor devices whose characteristics are given below, in the order (a), (b), (c), (d) : 9. ÁøòÊ (a), (b), (c), (d) Œappleπ U ÁŸœÊ Á UÃ apple U Á ÿapple ÁøòÊ Ê Á Ÿ apple Ë ã«uä U U Á«UflÊß apple Á ˇÊÁáÊ ª Ê» Ò? Simple diode, Zener diode, Solar cell, Light dependent resistance Zener diode, Simple diode, Light dependent resistance, Solar cell Solar cell, Light dependent resistance, Zener diode, Simple diode Zener diode, Solar cell, Simple diode, Light dependent resistance 0. For a common emitter configuration, if α and β have their usual meanings, the incorrect relationship between α and β is : 1 1 = + 1 α β β α = 1 β β α = 1 + β β α = 1 + E/Page 16 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª ÊœÊ UáÊ «UÊÿÊapple«U, ËŸ U «UÊÿÊapple«, Êapple U apple, LDR ( Êß U Á«U appleã«appleuã U appleuá S appleuã ) ËŸ U «UÊÿÊapple«U, ÊœÊ UáÊ «UÊÿÊapple«U, LDR ( Êß U Á«U appleã«appleuã U appleuá S appleuã ), Êapple U apple Êapple U apple, LDR ( Êß U Á«U appleã«appleuã U appleuá S appleuã ), ËŸ U «UÊÿÊapple«U, ÊœÊ UáÊ «UÊÿÊapple«U ËŸ U «UÊÿÊapple«U, Êapple U apple, ÊœÊ UáÊ «UÊÿÊapple«U, LDR ( Êß U Á«U appleã«appleuã U appleuá S appleuã ) 0. ÿáÿc U- à ÁflãÿÊ apple Á ÿapple α ÃÕÊ β apple Ëø ÁŸêŸ apple apple ÊÒŸ Ê œ ª Ã Ò? α ÃÕÊ β Áøq Ê Êãÿ Ã flê apple Ò 1 1 = + 1 α β β α = 1 β β α = 1 + β β α = 1 + β β

E/Page 17 PART B CHEMISTRY 1. At 00 K and 1 atm, 15 ml of a gaseous hydrocarbon requires 75 ml air containing 0% O by volume for complete combustion. After combustion the gases occupy 0 ml. Assuming that the water formed is in liquid form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is : C H 6 C H 8 C H 8 C H 10. Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure p i and temperature T 1 are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to T. The final pressure p f is : p i p i p i p i T1T T + T T T 1 T1 + T 1 T + T 1 T1T T T 1 Êª B U ÊÿŸ ÁflôÊÊŸ 1. 00 K ÃÕÊ 1 atm ŒÊ U, 15 ml ªÒ Ëÿ Êß«UÊapple Ê Ÿ apple ÍáÊ Œ Ÿ apple Á ÿapple 75 ml flêÿè Á apple ÊÿÃŸ apple ÊœÊ U U 0% ÊÚÄ Ë Ÿ Ò, Ë Êfl ÿ ÃÊ ÊappleÃË Ò Œ Ÿ apple ÊŒ ªÒ apple 0 ml ÉÊapple UÃË Ò ÿ ÊŸÃapple È Á ŸÊ È Ê Œ fl M apple Ò ÃÕÊ Ë ÃÊ ÊŸ fl ŒÊ U ÊÿÃŸÊapple Ë Ê Ë ªß Ò ÃÊapple Êß«UÊapple Ê Ÿ Ê» Ê Í Ê Ò C H 6 C H 8 C H 8 C H 10. ÊŸ ÊÿÃŸ (V) apple ŒÊapple Œ À, Á Ÿ apple ÊŒ Ê ªÒ Ê UÁê ŒÊ p i ÃÕÊ ÃÊ T 1 U UË ªß Ò, Ÿªáÿ ÊÿÃŸ Ë Ã Ë UÿÍ apple È«apple Ò Ò Ê Á ŸËøapple apple ÁøòÊ apple ÁŒπÊÿÊ ªÿÊ Ò Á» U ßŸ apple apple À Ê ÃÊ Ê U T U ÁŒÿÊ ÊÃÊ Ò ÁÃ ŒÊ p f Ò SPACE FOR ROUGH WORK / U» Êÿ apple Á ª p i p i p i p i T1T T + T T T 1 T1 + T 1 T + T 1 T1T T + T + 1

. A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h/λ (where λ is wavelength associated with electron wave) is given by : mev mev mev mev. The species in which the N atom is in a state of sp hybridization is : NO + NO NO NO 5. The heats of combustion of carbon and carbon monoxide are 9.5 and 8.5 kj mol 1, respectively. The heat of formation (in kj) of carbon monoxide per mole is : 110.5 676.5. ª Á» Ê apple U apple ÁŸ Ë ß appleä UÊÚŸ œê UÊ Êapple V esu apple Áfl flêãã U Uπapple ŒÊapple ÊflappleÁ ÊÃ åàêapple UÊapple apple Ëø apple apple Ê ÊÃÊ Ò ÿáœ ß appleä UÊÚŸ apple Êflapple Ê ÃÕÊ ÁÃ Ê e ÃÕÊ m Êapple ÃÊapple h/λ Ê ÊŸ ÁŸêŸ apple apple Á apple mê UÊ ÁŒÿÊ ÊÿappleªÊ? ( ß appleä UÊÚŸ Ã Uª apple ê ÁãœÃ Ã UªŒÒäÿ λ Ò) mev mev mev mev. fl S Ë ÊË$, Á apple N U ÊáÊÈ sp UáÊ Ë flsõê apple Ò, ÊappleªË NO + NO NO NO 5. Ê Ÿ ÃÕÊ Ê Ÿ ÊappleŸÊappleÄ ÊÚß«U Ë Œ Ÿ c Êÿapple Ê 9.5 ÃÕÊ 8.5 kj mol 1 Ò Ê Ÿ ÊappleŸÊappleÄ Êß«U Ë flÿ c Ê (kj apple ) ÁÃ Êapple ÊappleªË 110.5 676.5 676.5 110.5 676.5 110.5 E/Page 18 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

6. 18 g glucose (C 6 H 1 O 6 ) is added to 178. g water. The vapor pressure of water (in torr) for this aqueous solution is : 7.6 6. 18 g Ç È Êapple (C 6 H 1 O 6 ) Êapple 178. g ÊŸË apple Á ÊÿÊ ÊÃÊ Ò ß Ëÿ Áfl ÿÿ apple Á Ê flêc ŒÊ (torr apple ) ÊappleªÊ 7.6 76.0 75. 759.0 7. The equilibrium constant at 98 K for a reaction A+B C+D is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in mol L 1 ) will be : 0.18 0.818 1.818 1.18 8. Galvanization is applying a coating of : Pb Cr Cu 76.0 75. 759.0 7. ÃÊ ÊŸ 98 K U, Á Á ÿê A+B C+D apple Á Êêÿ ÁSÕ UÊ 100 Ò ÿáœ Ê UÁê ÊãŒ ÃÊ Ë øê UÊapple S Ë ÊË apple apple àÿapple Ë 1 M ÊappleÃË, ÃÊapple D Ë Êêÿ ÊãŒ ÃÊ (mol L 1 apple ) ÊappleªË 0.18 0.818 1.818 1.18 8. ªÒÀflŸÊß apple ÊŸ ÁŸêŸ apple apple Á apple Êapple U apple ÊappleÃÊ Ò? Pb Cr Cu Zn E/Page 19 Zn SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

9. Decomposition of H O follows a first order reaction. In fifty minutes the concentration of H O decreases from 0.5 to 0.15 M in one such decomposition. When the concentration of H O reaches 0.05 M, the rate of formation of O will be : 6.9 10 mol min 1 6.9 10 mol min 1.66 L min 1 at STP 1. 10 mol min 1 0. For a linear plot of log (x/m) versus log p in a Freundlich adsorption isotherm, which of the following statements is correct? (k and n are constants) Both k and 1/n appear in the slope term. 1/n appears as the intercept. Only 1/n appears as the slope. log (1/n) appears as the intercept. 1. Which of the following atoms has the highest first ionization energy? Rb Na K 9. H O Ê ÁflÉÊ UŸ Õ ÊappleÁ U Ë Á Á ÿê Ò øê Á Ÿ U apple ß Ê U apple ÁflÉÊ UŸ apple H O Ë ÊãŒ ÃÊ ÉÊ U U 0.5 apple 0.15 M Êapple ÊÃË Ò H O Ë ÊãŒ ÃÊ 0.05 M È øãë Ò, ÃÊapple O apple ŸŸapple Ë Œ U ÊappleªË 6.9 10 mol min 1 6.9 10 mol min 1.66 L min 1 (STP U) 1. 10 mol min 1 0.» ÊÚÿã«UÁ Áœ ÊÊapple áê ÃÊ Ë fl apple log (x/m) ÃÕÊ log p apple Ëø πë øapple ªÿapple appleuπëÿ å Ê U apple Á ÁãÊêŸ apple apple ÊÒŸ Ê ÕŸ Ë Ò? (k ÃÕÊ n ÁSÕ UÊ Ò ) k ÃÕÊ 1/n ŒÊappleŸÊapple Ë S Êapple Œ apple ÊÃapple Ò 1/n ßã U U appleå U apple M ÊÃÊ Ò ÊòÊ 1/n S Êapple apple M apple ÊÃÊ Ò log (1/n) ßã U U appleå U apple M apple ÊÃÊ Ò 1. ÁŸêŸ U ÊáÊÈ Êapple apple Á Ë Õ ÊÿŸŸ Ê ëøã Ò? Rb Na K Sc Sc E/Page 0 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

. Which one of the following ores is best concentrated by froth floatation method? Magnetite Siderite.» ÊÚÕ ç Êapple appleu ÊŸ ÁflÁœ mê UÊ ÁŸêŸ apple apple fl ÊÒŸ Ê ÿs flê Áœ M apple ÊÁãŒ Ã Á ÿê Ê ÃÊ Ò? ÒÇŸapple UÊß U Á «appleu UÊß U Galena Malachite. Which one of the following statements about water is FALSE? Water is oxidized to oxygen during photosynthesis. Water can act both as an acid and as a base. There is extensive intramolecular hydrogen bonding in the condensed phase. Ice formed by heavy water sinks in normal water.. The main oxides formed on combustion of Li, Na and K in excess of air are, respectively : Li O, Na O and KO LiO, Na O and K O ªÒ appleÿê Ò Ê Êß U. apple ê ãœ apple ÁŸêŸ ÕŸÊapple apple apple ÊÒŸ Ê ª Ã Ò? Ê Ê apple áê apple ÊÄ Ë Î Ã Êapple U ÊÄ Ë$ Ÿ ŒappleÃÊ Ò, ê ÃÕÊ ˇÊÊ U ŒÊappleŸÊapple Ë M apple Êÿ U ÃÊ Ò ß apple ÉÊÁŸÃ ÊflSÕÊ apple ÁflSÃËáÊ Ã áêè Êß«UÊapple Ÿ Ê ãœ ÊappleÃapple Ò Ê UË mê UÊ ŸÊ» Ê Êãÿ apple «ÍU ÃÊ Ò. flê apple ÊÁœÄÿ apple Li, Na ÊÒ U K apple Œ Ÿ U ŸŸappleflÊ Ë ÈÅÿ ÊÄ Êß«apple U Ê Ò Li O, Na O ÃÕÊ KO LiO, Na O ÃÕÊ K O Li O, Na O and KO Li O, Na O and KO Li O, Na O ÃÕÊ KO Li O, Na O ÃÕÊ KO E/Page 1 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

5. The reaction of zinc with dilute and concentrated nitric acid, respectively, produces : N O and NO NO and NO 5. ÃŸÈ ÃÕÊ ÊãŒ ŸÊßÁ U Á «U apple ÊÕ Á Ë Á Á ÿê mê UÊ Ê à ãÿ ÊappleÃapple Ò N O ÃÕÊ NO NO ÃÕÊ NO NO and N O NO and N O 6. The pair in which phosphorous atoms have a formal oxidation state of + is : Orthophosphorous and pyrophosphorous acids Pyrophosphorous and hypophosphoric acids Orthophosphorous and hypophosphoric acids Pyrophosphorous and pyrophosphoric acids 7. Which of the following compounds is metallic and ferromagnetic? TiO CrO NO ÃÕÊ N O NO ÃÕÊ N O 6. fl ÿèç Á Ÿ apple» ÊS» Êapple U U ÊáÊÈ Êapple Ë» Ê ÊÚÄ Ë UáÊ flsõê + Ò, Ò ÊÕÊapple» ÊS» Êapple U ÃÕÊ Êÿ UÊapple» ÊS» Êapple U Á «U Êÿ UÊapple» ÊS» Êapple U ÃÕÊ Êß Êapple» ÊS» ÊappleÁ U Á «U ÊÕÊapple» ÊS» Êapple U ÃÕÊ Êß Êapple» ÊS» ÊappleÁ U Á «U Êÿ UÊapple» ÊS» Êapple U ÃÕÊ Êÿ UÊapple» ÊS» ÊappleÁ U Á «U 7. ÁŸêŸ apple apple ÊÒŸ Ê ÿêòáª œêáàfl ÃÕÊ»apple UÊapple ÒªŸappleÁ U ( ÊÒ øèê Ëÿ) Ò? TiO CrO VO VO MnO MnO E/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

8. The pair having the same magnetic moment is : [At. No. : Cr=, Mn=5, Fe=6, Co=7] [Cr(H O) 6 ] + and [CoCl ] [Cr(H O) 6 ] + and [Fe(H O) 6 ] + 8. Ë øèê Ëÿ ÊÉÊÍáÊ Ê ÿèç Ò [At. No. : Cr=, Mn=5, Fe=6, Co=7] [Cr(H O) 6 ] + ÃÕÊ [CoCl ] [Cr(H O) 6 ] + ÃÕÊ [Fe(H O) 6 ] + [Mn(H O) 6 ] + and [Cr(H O) 6 ] + [CoCl ] and [Fe(H O) 6 ] + 9. Which one of the following complexes shows optical isomerism? [Co(NH ) Cl ] cis[co(en) Cl ]Cl trans[co(en) Cl ]Cl [Co(NH ) Cl ]Cl (en=ethylenediamine) 50. The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be 1000 ppb, 0 ppb, 100 ppm and 0. ppm, respectively. This water is unsuitable for drinking due to high concentration of : Fluoride Lead Nitrate [Mn(H O) 6 ] + ÃÕÊ [Cr(H O) 6 ] + [CoCl ] ÃÕÊ [Fe(H O) 6 ] + 9. ÁŸêŸ apple apple ÊÒŸ Ê ÊÚêå appleä ÊÁ Ê ÊflÿflÃÊ ŒÁ Ê Ã appleuªê? [Co(NH ) Cl ] cis[co(en) Cl ]Cl trans[co(en) Cl ]Cl [Co(NH ) Cl ]Cl (en=ethylenediamine) 50. ÍÁ ªÃ ÊË apple ÊåÃ ÁÃŒ Ê apple ç Êapple UÊß«U, apple«u, ŸÊß appleu U ÃÕÊ Êÿ UŸ Ë ÊãŒ ÃÊ Ê 1000 ppb, 0 ppb, 100 ppm ÃÕÊ 0. ppm Êß ªß ÿ ÁŸêŸ apple apple Á Ë ìê ÊãŒ ÃÊ apple ËŸapple ÿêappleçÿ Ÿ Ë Ò? ç Êapple UÊß«U apple«u ŸÊß appleu U E/Page Iron Êÿ UŸ SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

51. The distillation technique most suited for separating glycerol from spent-lye in the soap industry is : Simple distillation 51. Ê ÈŸ lêappleª apple ÈÄÃ Êapple Êß (S appleã U Êß ) apple ÁÇ UÊÚ ÎÕ UŸapple apple Á apple ÿèäã Ê flÿ ÁflÁœ Ò Ê Êãÿ Ê flÿ Fractional distillation Steam distillation Distillation under reduced pressure 5. The product of the reaction given below is : Ê Ë Ê flÿ Êc Ê flÿ ÊŸËÃ ŒÊ U Ê flÿ 5. ŸËøapple ŒË ªß Á Á ÿê apple Á à ÊŒ ÊappleªÊ E/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

5. The absolute configuration of 5. ÁŒ ªÿapple ÿêòáª Ê ÁŸ U appleˇê ÁflãÿÊ Ò CO H CO H H OH H OH H Cl H Cl CH CH is : (R, S) (S, R) (S, S) (R, R) 5. -chloro--methylpentane on reaction with sodium methoxide in methanol yields : (a) (b) (c) All of these (a) and (c) (R, S) (S, R) (S, S) (R, R) 5. appleõappleÿêú apple -Ä Êapple UÊapple-- appleáõ appleã appleuÿ, ÊappleÁ«Uÿ appleõêä Êß«U apple ÊÕ Á Á ÿê U apple ŒappleÃË Ò (a) (b) (c) ßŸ apple apple Ë (a) ÃÕÊ (c) (c) only (a) and (b) ÊòÊ (c) (a) ÃÕÊ (b) E/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

55. The reaction of propene with HOCl (Cl +H O) proceeds through the intermediate : CH CH + CH OH CH CH + CH Cl 55. Êapple ËŸ Ë HOCl (Cl +H O) apple ÊÕ Á Á ÿê Á äÿflãë apple Êapple U ê ãÿ ÊappleÃË Ò, fl Ò CH CH + CH OH CH CH + CH Cl CH CH(OH) CH + CH CHCl CH + 56. In the Hofmann bromamide degradation reaction, the number of moles of NaOH and Br used per mole of amine produced are : One mole of NaOH and one mole of Br. Four moles of NaOH and two moles of Br. Two moles of NaOH and two moles of Br. Four moles of NaOH and one mole of Br. 57. Which of the following statements about low density polythene is FALSE? Its synthesis requires high pressure. It is a poor conductor of electricity. Its synthesis requires dioxygen or a peroxide initiator as a catalyst. It is used in the manufacture of buckets, dust-bins etc. CH CH(OH) CH + CH CHCl CH + 56. Ê» ÊŸ Êapple Ê Êß«U ÁŸêŸË UáÊ Á Á ÿê apple, NaOH ÃÕÊ Br apple ÿèäã Êapple Êapple Ë ÅÿÊ ÁÃ Êapple ËŸ apple ŸŸapple apple ÊappleªË Êapple NaOH ÃÕÊ Êapple Br øê U Êapple NaOH ÃÕÊ ŒÊapple Êapple Br ŒÊapple Êapple NaOH ÃÕÊ ŒÊapple Êapple Br øê U Êapple NaOH ÃÕÊ Êapple Br 57. ÁŸêŸ ÉÊãÊàfl apple Ê ËÕËŸ apple ê ãœ apple ÁŸêŸ apple apple ÊÒŸ Ê ÕŸ ª Ã Ò? E/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª ß apple apple áê apple ìê ŒÊ Ë Êfl ÿ ÃÊ ÊappleÃË Ò ÿ ÁfllÈÃ Ê ËŸ øê Ò ß apple «UÊß ÊÄ Ë Ÿ ÕflÊ U ÊÄ Êß«U ßŸËÁ ÿapple U ( Ê Uê ) à apple U apple M apple øêá ÿ apple U ( ÊÀ UË), «US U-Á Ÿ, ÊÁŒ apple à ÊŒŸ apple ÿèäã ÊappleÃË Ò

58. Thiol group is present in : Cytosine Cystine Cysteine 58. ÕÊÿÊapple ª È Á apple ÁSÕÃ Ò, fl Ò Êß UÊapple ËŸ Á ÁS UŸ (Cystine) Á S UËŸ (Cysteine) Methionine 59. Which of the following is an anionic detergent? Sodium stearate Sodium lauryl sulphate Cetyltrimethyl ammonium bromide Glyceryl oleate 60. The hottest region of Bunsen flame shown in the figure below is : region 1 region region appleõêß ÊappleŸËŸ 59. ÁŸêŸ apple apple ÊÒŸ Ê ŸÊßÁŸ Á«U U U apple U Ò? ÊappleÁ«Uÿ S UË appleu U ÊappleÁ«Uÿ ÊÁ U À»apple U appleá U UÊß appleáõ ÊappleÁŸÿ Êapple Êß«U ÁÇ Á U ÊappleÁ U 60. ŸËøapple ŒË ªß Á» ª U apple Èã Ÿ ç apple Ê flê Áœ ª Êª Ò UË Ÿ 1 UË Ÿ UË Ÿ E/Page 7 region UË Ÿ SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

PART C MATHEMATICS Êª C ªÁáÊÃ 1 61. If f (x)+f x =x, x 0, and S = x R : f ( x ) = f ( x ) ; then S : { } is an empty set. contains exactly one element. contains exactly two elements. contains more than two elements. 6. A value of θ for which + i sin θ 1 i sinθ is purely imaginary, is : π π 6 1 sin sin 1 1 6. The sum of all real values of x satisfying the equation x ( ) + x 60 x x 5 + 5 = 1 is : 1 61. ÿáœ f (x)+f x =x, 0 S x R : f ( x ) f ( x ) x Ò, ÃÕÊ = { = } Ò ; ÃÊapple S : Á UÄÃ ÈìÊÿ Ò apple apple fl flÿfl Ò apple ÃâÿÃ ŒÊapple flÿfl Ò apple ŒÊapple apple Áœ flÿfl Ò 6. θ Ê fl ÊŸ Á apple Á + i sin θ ÍáÊ Ã 1 i sinθ ÊÀ ÁŸ Ò, Ò π π 6 1 sin sin 1 1 6. x apple Ÿ Ë flêsãáfl ÊŸÊapple Ê ÿêappleª Êapple Ë UáÊ x ( ) + x 60 x x+ Ò, Ò 5 5 1 = Êapple ÃÈc U UÃapple 6 5 6 5 E/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

5 a b 6. If A = and A adj A=A A T, then 5a+b is equal to : 1 5 6. ÿáœ A 5 a b = ÃÕÊ A adj A=A A T Ò, ÃÊapple 5a+b UÊ U Ò 1 5 1 65. The system of linear equations x+λy z=0 λx y z=0 x+y λz=0 has a non-trivial solution for : infinitely many values of λ. exactly one value of λ. exactly two values of λ. exactly three values of λ. 66. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is : 6 th 59 th 5 nd 1 65. ÒUÁπ Ë UáÊ ÁŸ Êÿ x+λy z=0 λx y z=0 x+y λz=0 Ê ÃÈë U ÊappleŸapple apple Á λ apple Ÿ Ã ÊŸ Ò λ Ê ÃâÿÃ ÊŸ Ò λ apple ÃâÿÃ ŒÊapple ÊŸ Ò λ apple ÃâÿÃ ÃËŸ ÊŸ Ò 66. ÊéŒ SMALL apple ˇÊ UÊapple Ê ÿêappleª U apple, Ê ø ˇÊ UÊapple flê apple Ë ÊéŒÊapple ( Õ ÍáÊ ÕflÊ Õ ËŸ) Êapple ÊéŒ Êapple Ê apple ÊŸÈ Ê U UπŸapple U, ÊéŒ SMALL Ê SÕÊŸ Ò 6 flê 59 flê 5 flê 58 th E/Page 9 58 flê SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

67. If the number of terms in the expansion of n 1, x 0, x + x is 8, then the sum of the coefficients of all the terms in this expansion, is : 6 n 67. ÿáœ 1, x 0 x x + apple Ê U apple ŒÊapple Ë ÅÿÊ 8 Ò, ÃÊapple ß Ê U apple ÊŸapple flê apple Ë ŒÊapple apple ªÈáÊÊ Êapple Ê ÿêappleª Ò 6 187 79 68. If the nd, 5 th and 9 th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is : 8 5 1 7 69. If the sum of the first ten terms of the series 1 1 + + + + +..., 5 5 5 5 is 16 5 10 101 m, then m is equal to : 187 79 68. ÿáœ ø appleuã U Ê Ã U üêapple Ë Ê ŒÍ UÊ, 5 flê ÃÕÊ 9 flê Œ ªÈáÊÊappleûÊ U üêapple Ë apple Ò, ÃÊapple ªÈáÊÊappleûÊ U üêapple Ë Ê Êfl ŸÈ ÊÃ Ò 8 5 1 7 69. ÿáœ üêappleáêë 1 1 + + + + +..., 5 5 5 5 apple Õ Œ ŒÊapple Ê ÿêappleª 16 5 Ò 10 101 m Ò, ÃÊapple m UÊ U 100 99 100 99 E/Page 0 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

70. Let ( ) 1 x p= lim 1 + tan x then log p x + 0 is equal to : 1 70. ÊŸÊ ( ) 1 x p= + x Ò, ÃÊapple log p UÊ U Ò 1 lim 1 x + 0 tan 1 1 71. For x R, f (x)= log sinx and g(x)=f (f (x)), then : g is not differentiable at x=0 g (0)=cos(log) g (0)= cos(log) g is differentiable at x=0 and 7. Consider g (0)= sin(log) 1 1 + sin x π f ( x ) = tan, x 0,. 1 sin x A normal to y=f (x) at through the point : (0, 0) π 0, π, 0 6 x= π also passes 6 1 1 71. x R apple Á f (x)= log sinx ÃÕÊ g(x)=f (f (x)) Ò, ÃÊapple 7. x=0 U g fl ŸËÿ Ÿ Ë Ò g (0)=cos(log) Ò g (0)= cos(log) Ò x=0 U g fl ŸËÿ Ò ÃÕÊ g (0)= sin(log) Ò 1 1 sin x f ( x ) tan +, x π = 0, 1 sin x U ÁfløÊ U ËÁ y=f (x) apple Á ŒÈ x= π U 6 πë øê ªÿÊ Á ÁŸêŸ Á ŒÈ apple Ë Êapple U ÊÃÊ Ò (0, 0) π 0, π, 0 6 π, 0 E/Page 1 π, 0 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

7. A wire of length units is cut into two parts which are bent respectively to form a square of side=x units and a circle of radius=r units. If the sum of the areas of the square and the circle so formed is minimum, then : 7. ß Êß Ë ÃÊ U Êapple ŒÊapple ÊªÊapple apple Ê U U ã apple Ê x ß Êß È Ê flê apple flª ÃÕÊ r ß Êß ÁòÊíÿÊ flê apple flîûê apple M apple Êapple«Ê ÊÃÊ Ò ÿáœ ŸÊÿapple ªÿapple flª ÃÕÊ flîûê apple ˇÊappleòÊ» Êapple Ê ÿêappleª ãÿíÿã Ò, ÃÊapple x=(π+)r x=(π+)r ( π)x=πr ( π)x=πr x=r x=r x=r x=r 7. The integral to : x 5 ( x++ x 1 ) x 5 10 1 9 x + 5x 5 ( x+ x+ 1) 5 ( x++ x ) 1 x 5 5 ( x++ x ) 1 x 10 5 ( x++ x ) 1 + C + C + C dx is equal 7. Ê 1 9 x + 5x 5 ( x+ x+ 1) x 5 5 ( x++ x 1 ) x 10 5 ( x++ x ) 1 x 5 5 ( x++ x ) 1 x 10 5 ( x++ x ) 1 + C + C + C + C + C dx UÊ U Ò where C is an arbitrary constant. Ê C Sflappleë U ø U Ò E/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

1 n 1 n... n n lim n n n to : 75. ( + ) ( + ) is equal 1 n 1 n... n n lim n n n 75. ( + ) ( + ) UÊ U Ò 18 e 7 e 9 e log 76. The area (in sq. units) of the region { ( x, y ): y x and x + y x, x 0, y 0 } is : π 8 π π 76. ˇÊappleòÊ 18 e 7 e 9 e log { ( x, y ): y x ÃÕÊ x + y x, x 0, y 0 } Ê ˇÊappleòÊ» (flª ß ÊßÿÊapple apple ) Ò π 8 π π E/Page π π SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

77. If a curve y=f (x) passes through the point (1, 1) and satisfies the differential equation, y(1+xy) dx=x dy, then is equal to : 5 5 5 5 1 f 78. Two sides of a rhombus are along the lines, x y+1=0 and 7x y 5=0. If its diagonals intersect at ( 1, ), then which one of the following is a vertex of this rhombus? (, 9) (, 8) 1 8, 10 7, 79. The centres of those circles which touch the circle, x +y 8x 8y =0, externally and also touch the x-axis, lie on : a circle. an ellipse which is not a circle. a hyperbola. a parabola. 77. ÿáœ fl y=f (x) Á ŒÈ (1, 1) apple Êapple U ÊÃÊ Ò ÃÕÊ fl Ë UáÊ y(1+xy) dx=x dy Êapple ÃÈc U UÃÊ Ò, ÃÊapple E/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª 5 5 5 5 f 1 UÊ U Ò 78. ÿáœ øãè È Ë ŒÊapple È Ê, appleuπê Êapple x y+1=0 ÃÕÊ 7x y 5=0 Ë ÁŒ ÊÊ apple Ò ÃÕÊ ß apple Áfl áê Á ŒÈ ( 1, ) U ÁÃë appleuœ UÃapple Ò, ÃÊapple ß øãè È Ê ÁŸêŸ apple apple ÊÒŸ- Ê ÊË Ò? (, 9) (, 8) 1 8, 10 7, 79. Ÿ flîûêêapple apple apple ãœ, Êapple flîûê x +y 8x 8y =0 Êapple Ês M apple S Ê UÃapple Ò ÃÕÊ x- ˇÊ Êapple Ë S Ê UÃapple Ò, ÁSÕÃ Ò flîûê U ŒËÉÊ flîûê U Êapple flîûê Ÿ Ë Ò ÁÃ Ufl ÿ U Ufl ÿ U

80. If one of the diameters of the circle, given by the equation, x +y x+6y 1=0, is a chord of a circle S, whose centre is at (, ), then the radius of S is : 5 80. ÿáœ Ë UáÊ x +y x+6y 1=0 mê UÊ ŒûÊ flîûê Ê ÿê ãÿ flîûê S, Á Ê apple ãœ (, ) Ò, Ë ËflÊ Ò, ÃÊapple flîûê S Ë ÁòÊíÿÊ Ò 5 5 5 10 81. Let P be the point on the parabola, y =8x which is at a minimum distance from the centre C of the circle, x +(y+6) =1. Then the equation of the circle, passing through C and having its centre at P is : x +y x+8y+1=0 x +y x+y 1=0 x +y x +y =0 x +y x+9y+18=0 8. The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is : 5 5 10 81. ÊŸÊ Ufl ÿ y =8x Ê P apple Ê Á ŒÈ Ò Êapple flîûê x +(y+6) =1, apple apple ãœ C apple ãÿíÿã ŒÍ UË U Ò, ÃÊapple flîûê Ê Ë UáÊ Êapple C apple Êapple U ÊÃÊ Ò ÃÕÊ Á Ê apple ãœ P U Ò, Ò x +y x+8y+1=0 x +y x+y 1=0 x +y x +y =0 x +y x+9y+18=0 8. ÁÃ Ufl ÿ, Á apple ŸÊÁ Ë Êß 8 Ò ÃÕÊ Á apple ÿèç Ë ˇÊ Ë Êß Ë ŸÊÁ ÿêapple apple Ëø Ë ŒÍ UË Ë ÊœË Ò, Ë à apple ãœ ÃÊ Ò E/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

8. The distance of the point (1, 5, 9) from the plane x y+z=5 measured along the line x=y=z is : 10 8. Á ŒÈ (1, 5, 9) Ë Ã x y+z=5 apple fl ŒÍ UË Êapple appleuπê x=y=z Ë ÁŒ ÊÊ apple Ê Ë ªß Ò, Ò 10 10 10 0 x y+ z+ 8. If the line, = = lies in 1 the plane, lx+my z=9, then l +m is equal to : 6 18 5 85. Let a, b and c be three unit vectors such that b a b c = b+ c. If is not parallel to c, then the angle between a and b is : π π π 5π 6 10 E/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª 10 0 8. ÿáœ appleuπê x y+ z+ = = 1, Ã lx+my z=9 apple ÁSÕÃ Ò, ÃÊapple l +m UÊ U Ò 6 18 5 85. ÊŸÊ a, b ÃÕÊ c ÃËŸ apple apple ÊòÊ ÁŒ Ê Ò Á a b c b c. = + Ò ÿáœ b, c apple Ê Ã U Ÿ Ë Ò, ÃÊapple a ÃÕÊ b apple Ëø Ê ÊappleáÊ Ò π π π 5π 6

86. If the standard deviation of the numbers,, a and 11 is.5, then which of the following is true? a 6a+55=0 a a+8=0 86. ÿáœ ÅÿÊ Êapple,, a ÃÕÊ 11 Ê ÊŸ Áflø Ÿ.5 Ò, ÃÊapple ÁŸêŸ apple apple ÊÒŸ- Ê àÿ Ò? a 6a+55=0 a a+8=0 a a+91=0 a a+=0 87. Let two fair six-faced dice A and B be thrown simultaneously. If E 1 is the event that die A shows up four, E is the event that die B shows up two and E is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true? E 1 and E are independent. E and E are independent. E 1 and E are independent. E 1, E and E are independent. 88. If 0 x<π, then the number of real values of x, which satisfy the equation cosx+cosx+cosx+cosx=0, is : 5 a a+91=0 a a+=0 87. ÊŸÊ ŒÊapple ŸÁ ŸÃ U» Ëÿ Ê apple A ÃÕÊ B ÊÕ UÊ apple ªÿapple ÊŸÊ ÉÊ UŸÊ E 1 Ê apple A U øê U ÊŸÊ Œ ÊÊ ÃË Ò, ÉÊ UŸÊ E Ê apple B U ÊŸÊ Œ ÊÊ ÃË Ò ÃÕÊ ÉÊ UŸÊ E ŒÊappleŸÊapple Ê Êapple U ÊŸapple flê Ë ÅÿÊ Êapple Ê ÿêappleª Áfl Œ ÊÊ ÃË Ò, ÃÊapple ÁŸêŸ apple apple ÊÒŸ- Ê ÕŸ àÿ Ÿ Ë Ò? E 1 ÃÕÊ E SflÃ òê Ò E ÃÕÊ E SflÃ òê Ò E 1 ÃÕÊ E SflÃ òê Ò E 1, E ÃÕÊ E SflÃ òê Ò 88. ÿáœ 0 x<π Ò, ÃÊapple x apple Ÿ flêsãáfl ÊŸÊapple Ë ÅÿÊ Êapple Ë UáÊ cosx+cosx+cosx+cosx=0 Êapple ÃÈc U UÃapple Ò, Ò 5 7 9 E/Page 7 7 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

89. A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 0. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60. Then the time taken (in minutes) by him, from B to reach the pillar, is : 6 10 0 5 90. The Boolean Expression (p ~q) q (~p q) is equivalent to : ~ p q p q p q p ~ q - o O o - 89. ÿáäã äflê œ U π apple Ë Êapple U Ëœapple Õ U ÊŸ øê apple Ê U Ê Ò UÊSÃapple U Á ŒÈ A apple fl π apple apple Á Êπ U Ê ÛÊÿŸ ÊappleáÊ 0 Ê ÃÊ Ò A apple Ë ÁŒ ÊÊ apple 10 Á Ÿ U ÊÒ U ø Ÿapple apple ÊŒ Á ŒÈ B apple fl π apple apple Á Êπ U Ê ÛÊÿŸ ÊappleáÊ 60 ÊÃÊ Ò, ÃÊapple B apple π apple Ã È øÿapple apple apple ªŸapple flê Ê ÿ (Á Ÿ UÊapple apple ) Ò 6 10 0 5 90. Í apple apple ÿ (Boolean Expression) (p ~q) q (~p q) Ê ÃÈÀÿ Ò ~ p q p q p q p ~ q - o O o - SPACE FOR ROUGH WORK / U» Êÿ apple Á ª E/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

SPACE FOR ROUGH WORK /» Êÿ apple Á ª E/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

Read the following instructions carefully : 1. The candidates should fill in the required particulars on the Test Booklet and Answer Sheet (Side 1) with Blue/Black Ball Point Pen.. For writing/marking particulars on Side of the Answer Sheet, use Blue/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.. Out of the four options given for each question, only one option is the correct answer. 5. For each incorrect response, one fourth (¼) of the total marks allotted to the question would 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 one page (i.e. Page 9) 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. 10. No candidate, without special permission of the Superintendent or Invigilator, should leave his/her seat. 11. 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. 1. Use of Electronic/Manual Calculator and any Electronic device like mobile phone, pager etc. is prohibited. 1. The candidates are governed by all Rules and Regulations of the JAB/Board 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 JAB/Board. 1. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 15. 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. E/Page 0 ÁŸêŸÁ ÁπÃ ÁŸŒapple Ê äÿêÿ apple apple 1. UËˇÊÊÁÕ ÿêapple Êapple UËˇÊÊ ÈÁSÃ Ê ÊÒ U ûê U òê ( ÎD -1) U flê Á UÃ Áflfl UáÊ ŸË apple/ Ê apple ÊÚ åflêß U appleÿ apple Ë UŸÊ Ò. ûê U òê apple ÎD- U Áflfl UáÊ Á πÿapple/ Á Ã UŸapple apple Á apple fl ŸË apple/ Ê apple ÊÚ åflêß U appleÿ Ê ÿêappleª apple U. UËˇÊÊ ÈÁSÃ Ê/ ûê U òê U ÁŸœÊ Á UÃ SÕÊŸ apple ÊflÊ UËˇÊÊÕË ŸÊ ŸÈ Ê ãÿ Ë Ÿ Ë Á πapple. àÿapple Ÿ apple Á ÿapple ÁŒÿapple ªÿapple øê U Áfl À Êapple apple apple apple fl Áfl À Ë Ò 5. àÿapple ª Ã ûê U apple Á Ÿ apple Á ÁŸœÊ Á UÃ È Êapple apple apple -øêòõêß (¼) È ÿêappleª apple apple Ê U Á Ê ªapple ÿáœ ûê U òê apple Á Ë Ÿ Ê Êappleß ûê U Ÿ Ë ÁŒÿÊ ªÿÊ Ò, ÃÊapple È ÿêappleª apple apple Êappleß Ÿ Ë Ê appleu Ê ªapple 6. UËˇÊÊ ÈÁSÃ Ê fl ûê U òê Ê äÿêÿ Ífl ÿêappleª apple U ÄÿÊapple Á Á Ë Ë Á UÁSÕÁÃ apple ( apple fl UËˇÊÊ ÈÁSÃ Ê fl ûê U òê apple apple Ã apple Á ÛÊÃÊ Ë ÁSÕÁÃ Êapple UÊapple«U), ŒÍ UË UËˇÊÊ ÈÁSÃ Ê éœ Ÿ Ë UÊÿË Ê ªË 7. ûê U òê U Êappleß Ë U» Êÿ ÿê Á πêß Ê Ê UŸapple Ë ŸÈ ÁÃ Ÿ Ë Ò Ë ªáÊŸÊ fl Á πêß Ê Ê, UËˇÊÊ ÈÁSÃ Ê apple ÁŸœÊ Á UÃ ª Êapple Á U» Êÿ apple Á ª mê UÊ ŸÊ Ê Á Ã Ò, U Ë Á ÿê Ê ªÊ ÿ ª àÿapple ÎD U ŸËøapple Ë Êapple U ÊÒ U ÈÁSÃ Ê apple Ã apple ÎD U ( ÎD 9) ŒË ªß Ò 8. ËˇÊÊ ê ÛÊ ÊappleŸapple U, UËˇÊÊÕË ˇÊ/ ÊÚ UÊapple«Ÿapple apple Ífl ûê U òê ˇÊ ÁŸ UËˇÊ Êapple fl ÿ ÊÒ Œapple UËˇÊÊÕË Ÿapple ÊÕ ß UËˇÊÊ ÈÁSÃ Ê Êapple apple Ê Ãapple Ò 9. Ê ªapple ÊŸapple U àÿapple UËˇÊÊÕË ÁŸ UËˇÊ Êapple ŸÊ flapple Ê Ê«fl ÿ ÁŒπÊ 10. œëˇê ÿê ÁŸ UËˇÊ Ë Áfl Êapple ŸÈ ÁÃ apple Á ŸÊ Êappleß UËˇÊÊÕË ŸÊ SÕÊŸ Ÿ UÊapple«apple 11. 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