PAPER - 1INSTRUCTIONS A. General : 1. This Question Paper contains 72 questions. 2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet. 3. No additional sheets will be provided for rough work. 4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed. 5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately. 6. Do not Tamper / mutilate the ORS or this booklet. 7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators. 8. Write your Name, Roll No. and Sign in the space provide on the back page of this booklet. B. Filling the Top-half of the ORS : Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the ORS. 9. Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS in the space provided (if the ORS is both side printed). 10. Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball point pen. 11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be displayed and 5 marks will be deducted (paper wise) from the total. 12. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while darken the bubble corresponding to your answer. 13. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the ORS. 14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will be taken as final. C. Question paper format and Marking scheme : 15. The question paper consists of 3 parts (Physics, Chemistry & Mathematics). Each part consists of Three Sections. 16. For each question in Section–I, you will be awarded 3 marks if you darken the bubble(s) corresponding to the correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 17. For each question in Section–II, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 18. For each question in Section–III, you will be awarded 4 marks if you darken the bubble corresponding to the correct choice for the answer and zero mark if no bubbled is darkened. There is no negative marking for incorrect answer(s) in this section. D O N O T B R E A K T H E S E A L S W I T H O U T B E I N G I N S T R U C T E D T O D O S O B Y T H E I N V I G I L A T O R Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. Date : 14-04-2013 Duration : 3 Hours Max. Marks : 249 CODE 0 FULL SYLLABUS TEST (FST)-XI TARGET : JEE (ADVANCED)-2013 COURSE : REVISION CLASSES RESONANCE P1FST-XI-140413C0-1 PHYSICS Space for Rough Work Space for Rough Work PART- I - PHYSICS SECTION - I Straight Objective Type This section contains 13 multiple choice questions. Each question has choices (A), (B), (C), and (D) out of which ONLY ONE is correct. 1. When a gas is compressed adiabatically by moving a piston down, the temperature of the gas increases. At the microscopic level, the average kinetic energy of the molecule increase. This increase in kinetic energy occurs due to : (A) Collision of gas molecules with entire walls (B) Collision of gas molecules with moving piston (C) The decrease in contact area (D) Because of elastic nature of collisions 2. A rigid container has a hole in its wall. When the container is evacuated, its weight is 100 gm. When some air is filled in it at 27ºC, its weight becomes 200 gm. Now the temperature of air inside is increased by AT, the weight becomes 150 gm. AT should be : (A) 27º C (B) 4 º 27 C (C) 300ºC (D) 327ºC 3. A wire AB of length 1m, has a sliding support at one end A and fixed support at end B. This wire is vibrated by a tuning fork of frequency 100 Hz due to which the wire AB vibrates in its fundamental tone. The particle at point A is vibrating with an amplitude of 10 mm and at t = 0, the photo graph of the wire is as shown in the figure below. (all the particles are at mean position at t = 0) The transverse displacement of the particles as a function of x and t will be : (A) y (x, t) = (10 mm) sin | . | \ | t x 2 cos (200 tt) (B) y (x, t) = (10 mm) sin | . | \ | t x 2 sin (200 tt) (C) y (x, t) = (10 mm) cos | . | \ | t x 2 sin (200 tt) (D) y (x, t) = (10 mm) cos | . | \ | t x 2 cos (200 tt) RESONANCE P1FST-XI-140413C0-2 PHYSICS Space for Rough Work Space for Rough Work 4. Two particle A and B are initially at a distance x. Initial velocity of particles A and B are 10 m/s and 25 m/s respectively in the direction shown in figure and their constant accelerations are 1 m/s 2 and 2 m/s 2 respectively in the direction shown in figure. What should be the minimum value of x, so that these particle can just avoid collision: (A) 2 125 m (B) 2 75 m (C) 4 75 m (D) 4 125 m 5. Four Students perform resonance tube experiment. The first, second and the third resonant length observed are respectively 1 , 2 and 3 . Whose readings are most appropriate. (A) 1 = 20 cm, 2 = 58 cm, 3 = 98 cm (B) 1 = 20 cm, 2 = 58 cm, 3 = 96 cm (C) 1 = 20 cm, 2 = 62 cm, 3 = 104 cm (D) 1 = 20 cm, 2 = 60 cm, 3 = 100 cm 6. In a cylindrical container, open to the atmosphere from the top, a liquid is filled upto 10 m depth. Density of the liquid varies with depth from the surface as µ(h) = 100 + 6h 2 where h is in meter and µ is in kg/m 3 .The pressure at the bottom of the container will be : (atmospheric pressure = 10 5 Pa, g = 10 m/sec 2 ) (A) 1.7 × 10 5 Pa (B) 1.4 × 10 5 Pa (C) 1.6 × 10 5 Pa (D) 1.3 × 10 5 Pa RESONANCE P1FST-XI-140413C0-3 PHYSICS Space for Rough Work Space for Rough Work 7. For a cyclic process, pressure (P) V/s volume (V) graph is as shown in the figure. Here for process B to C, P · V 1 . The correct graph of root mean square speed (C rms ) V/s density (µ) is : (A) (B) (C) (D) 8. A canon of mass 1 kg (including the bullet) is connected with a spring of a spring constant k = 100 N/m, and is performing SHM with an amplitude of 1 m. When the cannon reaches x = 2 3 m from the equilibrium, moving along +x–direction, a bullet of 2 1 kg is suddenly fired from it with a velocity of 20 m/s relative to the ground. What will be the new amplitude of the cannon ? (A) 2 3 (B) 2 5 (C) 2 7 (D) 2 11 RESONANCE P1FST-XI-140413C0-4 PHYSICS Space for Rough Work 9. A uniform solid cylinder is given a linear velocity and angular velocity, so that it rolls without sliding up the incline. Out of the four points A,B,C and centre of mass, about which point its angular momentum will be conserved? (A and C are taken at appropriate distance) (A) Point A (B) Point B (C) Point C (D) Centre of mass 10. On a horizontal disc, a block of mass 1kg is placed at a distance 3cm from the centre of the disc. The contact surface between the disc and the block is rough having µ s = 1/2. . Now the disc is rotated with a constant angular velocity of 10 rad/sec about its own axis The contact force applied by the disc on the block is : (A) 109 N (B) 125 N (C) 3 N (D) 10 N 11. Two identical spheres, touching each other, are placed on a rough horizontal surface of static friction co-efficient µ s as shown in figure . An another identical sphere of same mass and same radius is also placed on the spheres symmetrically. The contact surface between sphere C, with other spheres is smooth. What should be the minimum value of µ s , so that the system can stay in equilibrium. (A) 3 2 1 (B) 3 3 1 (C) 3 1 (D) 2 2 1 RESONANCE P1FST-XI-140413C0-5 PHYSICS Space for Rough Work Space for Rough Work 12. A man squatting (sitting) on a weighing machine, gradually stands up and then becomes stationary. the reading of weighing machine during this process will be : (A) constant and equal to mg in magnitude (B) constant and greater than mg in magnitude (C) variable but always greater than mg (D) Initially greater than mg, then less than mg, and then becomes constant equal to mg. 13. In a container, 1 gm 0ºC ice is covered by a very light piston which is in the contact with atmosphere from above. Now it is slowly heated. How much heat is required to convert it into 190ºC superheated steam ? Assume the steam to be an ideal gas. L f for ice = 80 cal/gm, L v for water = 540 cal/gm, S water = 1 cal/gmºC and for the steam ¸ = 4/3, R = 2 cal/mol.K (A) 755 cal (B) 760 cal (C) 765 cal (D) 770 cal SECTION - II Multiple Correct Answers Type This section contains 5 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct. 14. Velocity of particle varies with time as v = t 2 – 5t + 6. The motion of the particle will be : (A) Accelerating for t e (2, 2.5) (B) Retarding for t e (2, 2.5) (C) Accelerating for t e (2.5, 3) (D) Retarding for t e (2.5, 3) 15. On a triangular wedge a block is placed. The contact surface between them is rough having friction co-efficient µ s = 3 1 . With how much acceleration should we accelerate the wedge, so that neither static nor kinetic friction acts on the block. (A) g tan u i ˆ (B) (2g cot u ) (– i ˆ ) (C) 2g cot u j ˆ (D) (g secu) (– j ˆ ) RESONANCE P1FST-XI-140413C0-6 PHYSICS Space for Rough Work Space for Rough Work 16. A wedge of mass m, having a smooth semi circular part of radius R is resting on smooth horizontal surface. Now a particle of mass m/2 is released from the top point of the semicircular part. Then : (A) The maximum displacement of the wedge will be R (B) The maximum displacement of the wedge will be 3 R 2 (C) The wedge will perform simple harmonic motion of amplitude R (D) The wedge will perform oscillatory motion of amplitude 3 R 17. A horizontal cylinder is fixed, its inner surface is smooth and its radius is R. A small block is initially at the lowest point. the minimum velocity that should by given to the block at the lowest point, so that it can just cross the point P is u then (A) If the block moves anti clockwise then u= gR 5 . 3 (B) If the block moves anti clockwise then u= gR 3 (C) If the block moves clockwise then u= gR 5 . 3 (D) If the block moves clockwise then u= gR 5 RESONANCE P1FST-XI-140413C0-7 PHYSICS Space for Rough Work 18. A Uniform verticle rod of mass m and length 2 is hinged at its highest point and is initially at rest. A small pendulum of mass m and string length , is also suspended from the same point. Initially it is at an angle 60º with vertical and then it is released. The pendulum strikes the rod, just after collision, the pendulum comes to rest, the angular speed of the rod becomes e and co-efficient of restitution of this collision is e then (A) e = g 4 3 (B) e = g 3 2 (C) e = 3 2 (D) e = 4 3 SECTION - III Comprehension Type This section contains 3 paragraphs. Based upon each paragraph, 2 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. RESONANCE P1FST-XI-140413C0-8 PHYSICS Space for Rough Work Space for Rough Work Paragraph for Question Nos. 19 to 20 Buckling of a column Suppose a rod fixed at both the ends, is subjected to a compressive force. When the compressive force is too much, the rod may fail due to lateral deflection which is called buckling. According to Euler’s formula, if the compressive force F exceed the critical load F Cr = 2 4 3 L Yr t , the rod starts buckling. Here Y = young’s modulus, r = cross section radius of the rod and L = length fo the rod. Thus short, fat and stiff column has a very low tendency to buckle. While long and thin column has a very high tendency to buckle. 19. An elastic rod is just fit between the walls. Now the temperature of the rod is increased by AT. What should be the minimum value of AT, so that the rod starts buckle ? (linear expansion coefficient of the rod is o) (A) AT = 2 2 2 L r o t (B) AT = 2 2 3 r L o t (C) AT = L 2 o t (D) AT = r L 2 o t RESONANCE P1FST-XI-140413C0-9 PHYSICS Space for Rough Work Space for Rough Work 20. An isolated part of a bridge of mass m is supported by two identical columns each of length , cross–sectional radius r and young's modulus Y. What should be the minimum cross–section radius r, so that the beam bearing more load, can escape from buckling ? (A) 4 / 1 3 2 Y mg | | . | \ | t (B) 4 / 1 3 2 Y 3 mg 2 | | . | \ | t L/2 L/4 cm (C) 4 / 1 3 2 Y 3 mg | | . | \ | t (D) 4 / 1 3 2 Y 2 mg 3 | | . | \ | t Paragraph for Question Nos. 21 to 22 In a ventury meter tube of cross section area A, water (µ w = 10 3 kg/m 3 ) is flowing steadily. In between the tube, a narrow section is made whose cross section area is 2 A . To measure the pressure difference at both the sections, two provisions are used. 1st provision: Two vertical tube are fitted above the sections. To measure the difference in water level, both the air column are vibrated by a tuning fork of frequency 160 Hz. The air column of first tube vibrates in fundamental tone and the air column of the second tube vibrates in first overtone. IInd provision: Now a U-tube is arranged between the two sections as shown in the figure, in which a heavy liquid (µ = 11 × 10 3 kg/m 3 ) is used and the difference in its level is Ah. (Speed of sound in air = 320 m/sec, neglect end correction) 21. Velocity of water flowing in the ventury tube of cross section A is : (A) 3 10 m/sec. (B) 3 20 m/sec (C) 3 40 m/sec. (D) 3 50 m/sec. 22. The difference in the liquid level in the U-tube is : (A) Ah = 10 cm (B) Ah = 20 cm (C) Ah = 30 cm (D) Ah = 40 cm RESONANCE P1FST-XI-140413C0-10 PHYSICS Space for Rough Work Paragraph for Question Nos. 23 to 24 An elastic ball is released from a height of 1m above the ground as shown in figure. It falls freely for a distance of y, and then strikes a smooth fixed incline plane of angle 45º. Due to an elastic collision, the ball bounces horizontally and then performs projectile motion, it reaches the ground at a horizontal distance 'R'. 23. The horizontal distance (R) at which the ball strikes the ground is : (A) ) y 1 ( y 2 ÷ (B) ) y 1 ( y 2 ÷ (C) ) y 2 ( y ÷ (D) 2 ) y 2 ( y ÷ 24. The value of y, so that the range R becomes maximum is : (A) y = 2 1 (B) y = 3 1 (C) y = 4 1 (D) y = 4 3 RESONANCE CHEMISTRY P1FST-XI-140413C0-11 PART- II - CHEMISTRY Atomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28, P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75, Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207] SECTION - I Straight Objective Type This section contains 13 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct. 25. Consider the balanced reaction 2Cl 2 O 7 ÷÷ 4ClO 2 + 3 O 2 (Cl = 35.5) What can be concluded from the coefficients of species in this balanced equation? (A) For this reaction, exactly 2 g of Cl 2 O 7 must be taken to start the reaction (B) For this reaction, exactly 2 mol of Cl 2 O 7 must be taken to start the reaction (C) Mole ratio of Cl 2 O 7 , ClO 2 and O 2 during a chemical reaction at any instant (excluding any negative sign) are 2, 4 and 3 respectively (D) The ratio of change in number of moles of Cl 2 O 7 , ClO 2 and O 2 is 2 : 4 : 3 (excluding any negative sign) 26. Given : LiCl . 3NH 3 (s) LiCl . NH 3 (s) + 2NH 3 (g) ; K P = 9 atm 2 1 mole of LiCl . NH 3 (s) is placed in an 82.1 L vessel that contains Ne at 3 atm pressure. As some NH 3 is added to the system maintained at 300 K : (A) LiCl . 3NH 3 (s) begins to form due to backward reaction as per given equation. (B) 2 mole NH 3 is required to be added for complete conversion of LiCl . NH 3 (s) to LiCl . 3 NH 3 (s) (C) Pressure in the vessel remains constant at 3 atm. (D) No LiCl . 3NH 3 (s) is formed till the pressure in vessel increases to 6 atm. 27. The work done in adiabatic compression of 2 mole of an ideal monoatomic gas by constant external pressure of 2 atm starting from intial pressure of 1 atm and initial temperature of 300 K (R = 2 cal/mol-degree) (A) 360 cal (B) 720 cal (C) 800 cal (D) 1000 cal Space for Rough Work RESONANCE CHEMISTRY P1FST-XI-140413C0-12 Space for Rough Work 28. Which of the following is the best reducing agent amongst the following ? (A) H 3 BO 3 (B) NaOH (C) NaHCO 3 (D) NaH 29. Which of the following molecule contains shortest N–O bond ? (A) NOF (B) NO 2 – (C) NO 3 – (D) NH 2 OH 30. A new flurocarbon of molar mass 102 g mol ÷1 was placed in an electrically heated vessel. When the pressure was 650 torr, the liquid boiled at 77 0 C. After the boiling point had been reached, it was found that a current of 0.25 A from a 12.0 volt supply passed for 600 sec vaporises 1.8g of the sample. The molar enthalpy & internal energy of vaporisation of new flourocarbon will be : (A) AH = 102 kJ/mol, AE = 99.1 kJ/mol (B) AH = 95 kJ/mol, AE = 100.3 kJ/mol (C) AH = 107 kJ/mol, AE = 105.1 kJ/mol (D) AH = 92.7 kJ/mol, AE = 97.4 kJ/mol 31. The correct order of increasing bond order : (A) CO < CO 2 < CO 3 2– (C–O bond) (B) CN – < NCN 2– < (C–N bond) (C) ClO – < ClO 2 < ClO 3 – < ClO 4 – (Cl-O bond) (D) SO 2 < SO 4 2– < SO 3 2– (S–O bond) 32. Two mole of an ideal gas is expanded irreversibly and isothermally at 37ºC until its volume is doubled and 3.41 kJ heat is absorbed from surrounding. AS total (system + surrounding) is : (A) –0.52 J/K (B) 0.52 J/K (C) 22.52 J/K (D) 0 RESONANCE CHEMISTRY P1FST-XI-140413C0-13 Space for Rough Work 33. has correct IUPAC name as : (A) 3-Carbamoylbenzene-1-carbonitrile (B) 3-Cyanobenzene-1-carboxamide (C) 3-Cyanobenzamide (D) 3-Aminocarbonylcyanobenzene 34. Which of the following pairs contain functional isomers? (A) , (B) , (C) , (D) , 35. Silane, SiH 4 , cannot be obtained by treating : (A) Mg 2 Si with H 2 O (B) SiCl 4 with NaH (C) SiCl 4 with PH 3 (D) all the above options would produce SiH 4 36. Which of the following pairs consists of only +M groups? (A) (B) (C) –Cl, –NO 2 (D) RESONANCE CHEMISTRY P1FST-XI-140413C0-14 Space for Rough Work 37. The enthalpy of neutralisation of a weak acid in 1 M solution with a strong base is – 56.1 kJ mol –1 . If the enthalpy of ionization of the acid is 1.5 kJ mol –1 and enthalpy of neutralization of the strong acid with a strong base is – 57.3 kJ equiv –1 , what is the % ionization of the weak acid in molar solution (assume the acid to be monobasic)? (A) 10 (B) 15 (C) 20 (D) 25 SECTION - II Multiple Correct Answer Type This section contains 5 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct. 38. Point out the correct statement(s) : (A) Condensation occurs at minima of Z vs P graph when Z < 1. (B) Each of these lines represents isotherms (C) T 1 > critical temperature (D) T 4 > critical temperature RESONANCE CHEMISTRY P1FST-XI-140413C0-15 Space for Rough Work 39. Among B 2 H 6 , CH 4 , C 2 H 6 and SiH 4 , which gases burn to produce a glassy solid? (A) B 2 H 6 (B) CH 4 (C) C 2 H 6 (D) SiH 4 40. Consider an isothermal previously evacuated vessel containing two separate vessels with H 2 O() and Na 2 SO 4 (s) as shown in the figure. Given that H 2 O () H 2 O (g) ; K p 1 = P 1 atm Na 2 SO 4 . 10H 2 O(s) Na 2 SO 4 (s) + 10H 2 O(g) ; K P 2 = (P 2 ) 10 atm 10 Then, (A) P 1 must be equal to P 2 (B) If P 1 < P 2 no Na 2 SO 4 would be converted to Na 2 SO 4 .10 H 2 O at all (C) If P 1 > P 2 , all the H 2 O () must dry up eventually. (D) Partial pressure of water vapour in the vessel finally (P) must lie in the range P 2 s P s P 1 if P 1 > P 2 . RESONANCE CHEMISTRY P1FST-XI-140413C0-16 Space for Rough Work 41. 1mole each of H 2 (g) and I 2 (g) are introduced in a 1L evacuated vessel at 523K and equilibrium H 2 (g) + I 2 (g) 2HI (g) is established. The concentration of HI(g) at equilibrium (A) Changes on changing pressure (B) Changes on changing temperature (C) Is same even if only 2 mol of HI (g) were introduced in the vessel in the begining. (D) Is same even when a platinum gauze is introduced to catalyse the reaction. 42. Which of the following statement (s) is/are true for the solutions of alkali metals and alkaline earth metals in ammonia () ? (A) Concentrated solutions of alkali metals in ammonia are copper - bronzed coloured and have a metallic lusture. (B) Dilute solutions of alkaline earth metals are bright blue/deep bule black in colour due to the spectrum from the solvated electron. (C) Concentrated solutions of the alkaline earth metals in ammonia are bronze coloured. (D) Evaporation of the ammonia from solutions of alkali metals yields the metal, but with alkaline earth metals evaporation of ammonia gives hexammoniates of the metals. SECTION - III Comprehension Type This section contains 3 paragraphs. Based upon each paragraph, there are 2 questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. RESONANCE CHEMISTRY P1FST-XI-140413C0-17 Paragraph for Question Nos. 43 to 44 The structure of the boron atom clusters in boron hydrides and related species are usefully summarised by Wade's rules, which have a foundation in molecular orbital theory but are presented here as an empirical basis for remembering and predicting structures in the following steps: (A) Any borane or borane anion can be represented by the formula ÷ + p m n n H B ; e.g. for B 5 H 111 , n = 5, m = 6, p = 0 for – 2 14 10 H B , n = 10, m = 4, p = 2. (B) Count the number of valence electrons in the species [3n+(n + m) + p] (C) Assign 2n to n ordinary two-electron B–H bonds, the remaining 2R = 2n + m + p electrons (or half that number of electron pairs, R) are used for bonding the cluster. (D) if R= n + 1, this is called a closo (closed) cluster, a complete polyhedron. (E) if R = n+2, this is called a nido (nest) cluster, a polyhedron with one vertex missing. (6) if R = n+3, this is called an arachno (web) cluster, a polyhedron with two vertices missing. For example, consider B 12 H 12 2— , B 5 H 9 and B 5 H 11 . An electron count shows that there are n + 1, n + 2 and n + 3 electron pairs available for boron cluster bondings in B 12 H 12 2— , B 5 H 9 and B 5 H 11 respectively; hence the description of their boron clusters is given as a dodecahedron (a closo structure), an octahedron with one position vacant, a square pyramid (a nido structure), and a pentagonal bipyramid with two positions vacant (an arachno structure), respectively. Space for Rough Work RESONANCE CHEMISTRY P1FST-XI-140413C0-18 Space for Rough Work It should be noted that in cases where there is choice we have not predicited which positions are vacant, nor what the polyhedron will be (though symmetric structures would be expected to be favoured). In practice the polyhedron is found to be a trigonal bipyramid, an octahedron, a pentagonal bipyramid, a dodecahedron, an octadecahedron and an icosahedron for 5, 6, 7, 8, 11 and 12 vertices respectively. 43. ÷ 2 6 6 H B has - (A) closo-structure (B) nido-structure (C) arachno-structure (D) unpredictable structure 44. B 4 H 10 has - (A) closo-structure (B) nido-structure (C) arachno-structure (D) unpredictable structure Paragraph for Question Nos. 45 to 46 If given the right amount of energy, electrons can be promoted from a low-energy atomic orbital to a higher- energy one. This gives rise to an atomic absorption spectrum. Exactly the same process can occur with molecular orbitals. HOMO-LUMO gap Electrons can be promoted from any filled orbital to any empty orbital. The smallest energy difference between a full and empty molecular orbital is between the HOMO and the LUMO. The smaller this difference, the less energy will be needed to promote an electron from the HOMO to the LUMO : the smaller the amount of energy needed, the longer the wavelength of light needed since AE = hv. Therefore, an important measurement is the wavelength at which a compound shows maximum absorbance, ì max . The energy difference between the HOMO and LUMO for conjugated butadiene is less than that for ethene. Therefore we would expect butadiene to absorb light of longer wavelength than ethene (the longer the wavelength the lower the energy, AE = hc/ì). This is found to be the case : butadiene absorbs at 215 nm compared to 185 nm for ethene. The conjugation in butadiene means it absorbs light of a longer wavelength than ethene. In fact, this is true generally. The more conjugated a compound is, the smaller the energy transition between its HOMO and LUMO and hence the longer the wavelength of light it can absorb. Hence UV-visible spectroscopy can tell us about the conjugation present in a molecule. RESONANCE CHEMISTRY P1FST-XI-140413C0-19 Space for Rough Work Both ethene and butadiene absorb in the far-UV region of the electromagnetic spectrum (215 nm is just creeping in to the UV region) but, if we extend the conjugation further, the gap between HOMO and LUMO will eventually be sufficiently decreased to allow the compound to absorb visible light and hence be coloured. A good example is the red pigment in tomatoes. It has eleven conjugated double bond (plus two unconjugated) and absorbs light. Approximate wavelengths for different colours Absorbed frequency, nm Colour absorbed Colour transmitted R(CH=CH) n R, n = 200-400 ultraviolet — < 8 400 violet yellow-green 8 425 indigo-blue yellow 9 450 blue orange 10 490 blue-green red 11 510 green purple 530 yellow-green violet 550 yellow indigo-blue 590 orange blue 640 red blue-green 730 purple green Look at the table above and answer the following questions : RESONANCE CHEMISTRY P1FST-XI-140413C0-20 Space for Rough Work 45. Lycopene is expected to absorb which of the following wavelength to a maximum extent ? (A) 640 nm (B) 380 nm (C) 420 nm (D) 470 nm 46. Look at the structure of |-carotene. Its colour is expected to be (A) red (B) green (C) orange (D) yellow Paragraph for Question Nos. 47 to 48 ‘THE DRINKING BIRD’ Let us consider the scheme of a Chinese toy known as the “drinking bird” (Fig. a and b). Once triggered to action, which is done by bringing it to position b, the “bird” continues to swing up and down: in one position it “drinks” water from the glass . and then returns to the upper position, in a seemingly perpetual motion. A detailed analysis of the action of the toy show, however, that it corresponds to the laws of thermodynamics. Construction of Toy: As seen from Fig. the “bird” consists of two flasks joined by a tube, these flasks containing a volatile liquid and thermetically sealed. The entire system is capable of rotating about its axis fixed in the stationary support, the position of equilibrium shown on the left of the figure. The head of the “bird” is covered by a layer of a moisture—absorbing material, cotton. RESONANCE CHEMISTRY P1FST-XI-140413C0-21 Working of Toy: The system is brought into action by moistening the head, say, when the beak is dipped in water, as in position b. Then, the system acts on its own i.e. water vaporizing from the coating of the head lowers its temperature by a few degrees as compared with the temperature of the body (and of the surroundings). This lowers the vapour pressure in the head chamber. The pressure difference that arises runs the liquid in the direction of the head. The centre of gravity is shifted, the head becomes heavier and bends forward. At the turning point of motion the “bird” assumes a nearly horizontal position, as shown on the right. The beak dips in water, maintaining the moisture content of the head coating. The end of the connecting tube emerges from the liquid residue in the left flask. In this position of the system, when the liquid being acted on by the force of gravity flows back into the left flask, the initial position of equilibrium is restored and the cycle then repeats itself. The “drinking bird” acts better at a higher temperature and a lower moisture content. With a relative moisture content close to 100 per cent the action discontinues. The working substance must have a high vapour pressure, a higher density and a low heat of vaporization; Freon—(CCI 3 F) is a suitable substance. The efficiency of the system can be increased by replacing water in the beaker with a more volatile liquid. 47. When the ‘bird’ is vertical, the liquid flows up because of : (A) low pressure zone created in bird’s head due to cooling (B) low pressure zone created in bird’s head due to vaporisation of liquids within bird’s head (C) High pressure zone created in bird’s tail due to latent heat (D) none of these 48. A person purchases the toy and keeps it in a small closed glass cabinet. After a few days, the bird will stop drinking liquid. Just for fun, the person replaces the water beaker by alcohol. Then, when the beak of bird is dipped in alcohol and released, the bird : (A) seems to like alcohol, and begins drinking again ! (B) shows no change in its behaviour and refuses to take up alcohol (a Gandhian Bird!) (C) does not take up alcohol but rebegins to drink water now (for washing away alcohol : Saintly bird!) (D) shows erratic behaviour and flies away Space for Rough Work RESONANCE P1FST-XI-140413C0-22 MATHEMATICS PART- III - MATHEMATICS SECTION - I Straight Objective Type This section contains 13 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct. 49. If equation sin 4 x + asin 2 x + 1 = 0 has a solution then a e (A) (–·, –2] (B) [–2, 2] (C) (–·, –2] [2, ·) (D) [2, ·) 50. Given S n = ¿ = n 0 r r 2 1 , S = ¿ · =0 r r 2 1 . If S – S n < 1000 1 , then least value of n is (A) 8 (B) 9 (C) 10 (D) 11 51. The remainder obtained when 1! + 2! + 3! +.....+ 95! divided by 15, is (A) 3 (B) 14 (C) 1 (D) none of these 52. Total number of polynomials of the form x 3 + ax 2 + bx + c that are divisible by x 2 + 1, where a,b,c e {1,2,3,.....9,10} is equal to (A) 10 (B) 15 (C) 5 (D) 8 53. If ( ( ( ¸ ( ¸ 1 1 – 3 0 1 0 1 2 1 – ( ( ( ¸ ( ¸ z y x = ( ( ( ¸ ( ¸ 1 2 0 , then ordered triplet (x,y,z) is equal to (A) | . | \ | 4 7 , 2 , 4 9 – (B) | . | \ | 4 9 – , 2 , 4 7 (C) | . | \ | 4 7 , 2 – , 4 9 (D) | . | \ | 4 9 , 2 – , 4 7 Space for Rough Work RESONANCE P1FST-XI-140413C0-23 MATHEMATICS Space for Rough Work 54. 0 x lim ÷ [sinx], where [.] denotes the greatest integer function (A) is equal to 1 (B) is equal to zero (C) doesn't exist (D) none of these 55. A variable line L is drawn through O(0,0) to meet the lines L 1 : y – x – 10 = 0 and L 2 : y – x – 20 = 0 at the points A and B respectively. A point P is taken on L such that OP 2 = OA 1 + OB 1 and P, A, B lies on same side of origin O. Locus of P is (A) 3x + 3y = 40 (B) 3x + 3y + 40 = 0 (C) 3x – 3y = 40 (D) 3y – 3x = 40 56. In triangle ABC equation of side BC is x – y = 0. Circumcentre and orthocentre of the triangle are (2, 3) and (5, 8) respectively. Equation of circumcircle of the triangle is (A) x 2 + y 2 – 4x + 6y – 27 = 0 (B) x 2 + y 2 – 4x – 6y – 27 = 0 (C) x 2 + y 2 + 4x + 6y – 27 = 0 (D) x 2 + y 2 + 4x – 6y – 27 = 0 57. If two different tangents of y 2 = 4x are normals to x 2 = 4by, then (A) |b| > 2 2 1 (B) |b| < 2 2 1 (C) |b| > 2 1 (D) |b| < 2 1 58. If normal drawn to the ellipse 9 y 16 x 2 2 + = 1 at a point (4cosu, 3sinu) passes through point | . | \ | u u 2 2 sin 3 , 2 cos 4 , value of cosu can be (A) – 23 16 (B) – 2 1 (C) – 23 19 (D) – 23 21 59. A circle cuts the rectangular hyperbola xy = c 2 at the points (x i , y i ) , i = 1,2,3,4. Values of x 1 .x 2 .x 3 .x 4 and y 1 .y 2 .y 3 .y 4 are respectively (A) c 4 , – c 4 (B) c 2 , – c 2 (C) c 4 , c 4 (D) c 2 , c 2 RESONANCE P1FST-XI-140413C0-24 MATHEMATICS Space for Rough Work 60. The value of ¿ = t 10 0 r 3 3 r cos is equal to (A) – 2 9 (B) – 2 7 (C) – 8 9 (D) – 8 1 61. If the length of medians AA 1 , BB 1 and CC 1 of triangle ABC are m a , m b and m c respectively, then (where s is semi-perimeter of triangle) (A) a a,b,c 3 m s 2 > ¿ (B) a a,b,c m 3s > ¿ (C) a a,b,c 5 m s 2 > ¿ (D) a a,b,c m 2s > ¿ SECTION - II Multiple Correct Answer Type This section contains 5 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct. 62. In an arithmetic progression, consisting of 10 terms, if the sum of the terms occupying the even places is equal to 15 and the sum of those occupying the odd places is equal to 2 1 12 , then (A) first term of the sequence is 3 1 (B) common difference of sequence is 2 1 (C) first term of the sequence is 2 1 (D) common difference of sequence is 3 1 63. If a, b, c are in H.P., then (A) a – c b a + , b – a c b + , c – b a c + are in H.P.. (B) b 2 = a – b 1 + c – b 1 (C) a – 2 b , 2 b , c – 2 b are in G.P. .P. (D) c b a + , a c b + , b a c + are in H.P.. RESONANCE P1FST-XI-140413C0-25 MATHEMATICS Space for Rough Work 64. Total number of ways of giving at least one coin out of three 25 paise and two 50 paise coins to a beggar is equal to (A) 32 (B) 12 (C) 11 (D) coefficient of x 10 in (1 + x + x 2 + x 3 +....upto ·) 2 , where |x| < 1 65. A(1, 2) and B(7, 10) are two points. If P(x,y) is a point such that the angle APB is 60º and the area of the AAPB is maximum, then which of given are TRUE ? (A) P lies on any line perpendicular to AB. (B) P lies on the right bisector of AB. (C) P lies on the straight line 3x + 4y = 36. (D) P lies on the circle passing through the points A(1, 2) and B(7, 10) and having a radius of 10 units. 66. If (acosu i , asinu i ) ; i = 1,2,3 represent the vertices of an equilateral triangle inscribed in a circle, then (A) cosu 1 + cosu 2 + cosu 3 = 0 (B) sinu 1 + sinu 2 + sinu 3 = 0 (C) tanu 1 + tanu 2 + tanu 3 = 0 (D) cotu 1 + cotu 2 + cotu 3 = 0 SECTION - III Comprehension Type This section contains 3 paragraphs. Based upon each paragraph, there are 2 questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 67 to 68 Let PQ be a variable focal chord of the parabola y 2 = 8ax and A be vertex. Locus of, centroid of triangle APQ is a parabola ‘P 1 ’ 67. Latus rectum of parabola P 1 is (A) 3 a 2 (B) 3 a 4 (C) 3 a 8 (D) 3 a 16 68. Vertex of parabola P 1 is (A) | . | \ | 0 , 3 a 2 (B) | . | \ | 0 , 3 a 4 (C) | . | \ | 0 , 3 a 8 (D) | . | \ | 0 , 3 a RESONANCE P1FST-XI-140413C0-26 MATHEMATICS Space for Rough Work Paragraph for Question Nos. 69 to 70 If a, b e prime numbers and n, p,q e N, then rational terms (or terms free from radicals) in the expansion of (a 1/p + b 1/q ) n are the terms in which indices of a and b are integers. 69. In the expansion of (7 1/3 + 11 1/9 ) 6561 , the number of terms free from radicals is (A) 729 (B) 725 (C) 730 (D) 745 70. The number of integral terms in the expansion of ( ) 256 1/ 8 3 5 + is (A) 32 (B) 33 (C) 34 (D) 35 Paragraph for Question Nos. 71 to 72 If p 1 , p 2 , p 3 are altitudes of a AABC from the vertices A,B,C respectively and A is the area of triangle and s is semi-perimeter of the triangle. 71. If 1 p 1 + 2 p 1 + 3 p 1 = 2 1 then the least value of p 1 p 2 p 3 is (A) 8 (B) 27 (C) 125 (D) 216 72. 1 p A cos + 2 p B cos + 3 p C cos = (A) r 1 (B) R 1 (C) R 2 c b a 2 2 2 + + (D) A 1 Name of the Candidate Roll Number I have read all the instructions and shall abide by them. -------------------------------- Signature of the Invigilator I have verified all the information filled in by the Candidate. -------------------------------- Signature of the Candidate (Space for rough work)
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