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FIITJEE MOCK TEST JEE (Advanced) (03.05.2024) PAPER – 2 Tim...
FIITJEE MOCK TEST JEE (Advanced) (03.05.2024) PAPER – 2 Time Allotted: 3 Hours Maximum Marks: 183 General Instructions: The test consists of total 54 questions. Each subject (PCM) has 18 questions. This question paper contains Three Sections. Section-I is Physics, Section-II is Chemistry and Section-III is Mathematics. Each Section is further divided into One Part: Part-A. 1. Part–A (01 – 07) contains 7 multiple choice questions which have only one correct answer. Each question carries +3 marks for correct answer and –1 mark for wrong answer. Part-A (08 – 14) contains 7 multiple choice questions which have one or more than one correct answer. Each question carries +4 marks for correct answer and –2 marks for wrong answer. Partial Marks +1 for each correct option provided no incorrect option is selected. Part–A (15 – 18) contains 2 paragraphs. Each paragraph is having 2 multiple choice questions having 4 options with only one correct answer. Each question carries +3 marks for correct answer. There is no negative marking. FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 2 Physics SECTION – I PART – A (One Options Correct Type) This part contains 07 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct. 1. In the Young’s double slit experiment using a monochromatic light of wavelength , the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is (A) (2n 1) (B) (2n 1) 2 4 (C) (2n 1) (D) (2n 1) 8 16 2. The speed of a wave on a string is 150 m/s when the tension is 120 N. The percentage increase in the tension in order to raise the wave speed by 20% is: (A) 44% (B) 40% (C) 20% (D) 10% R 3. A frictionless tunnel is dug along a chord of the earth at a perpendicular distance 2 from the centre of earth (where R is radius of earth). An object is released from one end of the tunnel. The correct graph, showing the variation of acceleration of particle with its distance r from centre of earth is a a (A) (B) r r R R R R 2 2 a a (C) (D) r r R R R R 2 2 Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 3 4. A closed organ pipe of length L is vibrating in its first overtone. There is a point Q inside the pipe at a distance 7L/9 from the open end. The ratio of pressure amplitude at Q to the maximum pressure amplitude in the pipe is (A) 1 : 2 (B) 2 : 1 (C) 1 : 1 (D) 2 : 3 5. A charge particle q of mass m is placed at a v0 v0 -2q distance d from another charge particle – 2q of q mass 2m in a uniform magnetic field B as shown. XB If particles are projected towards each other with equal speed v0, so that the two particles touches each other without collision during its motion. (Assume only force due to magnetic field acts on the particle) qBd qBd (A) (B) m 2m 2qBd 3qBd (C) (D) m 2m 6. When the electron in a hydrogen atom jumps from the second orbit to the first orbit, the wavelength of the radiation emitted is . When the electron jumps from the third to the first orbit, the wavelength of the radiation emitted as 9 4 (A) (B) 4 9 27 32 (C) (D) 32 27 7. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens 2 is times the wavelength in free space. The radius of the curved surface of the lens is 3 (A) 1 m (B) 2 m (C) 3 m (D) 6 m Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 4 (One or More than one correct type) This part contains 07 questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct. 8. A bimetallic strip is formed by two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are C and B. On heating, the temperature of the strip goes up by T and the strip bends to from an arc of radius of curvature R. Then R is (A) proportional to T (B) inversely proportional to T (C) proportional to B C (D) inversely proportional to B C 9. Two parallel long straight conductors lie on a smooth horizontal surface. Two other parallel conductors rest on them at right angles so as to form a square of side a initially. A uniform magnetic field B exists in vertical direction. Now all the four conductors start moving outwards with a constant velocity v. The induced e.m.f. e and induced current i will vary with time t as e e (A) (B) t t i i (C) (D) t t Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 5 10. Consider the decay 238 Pu 234 U 4 He The atomic masses are given as 238 234 4 238.04955 u Pu 234.04095 u U 4.002633 u He Neglecting the recoil of the residual nucleus (A) the kinetic energy of the particle emitted is 5.58 MeV (B) the kinetic energy of the particle emitted is 5.58 eV (C) conservation of electric charge is valid for the given reaction (D) conservation of electric charge is not valid for the given reaction 11. In a thermodynamic process Helium gas obeys the law TP2/5 constant. If temperature of 2 moles of the gas is raised from T to 3T, then (A) Heat given to the gas is 9 RT (B) Heat given t the gas zero (C) Work done by the gas is 6RT (D) VdP for the process in the given temperature range is 10RT 12. Sounds from two identical sources S1 and S2 reach a point P. when the sounds reach directly and in the same phase the intensity at P is l0. The power of S1 is now reduced by 64% and the phase difference between S1 and S2 is varied continuously the maximum and minimum intensities recorded at P are now lmax and lmin (A) lmax 0.64 l0 (B) lmin 0.36 l0 (C) lmax / lmin 16 (D) lmax / lmin 1.64 / 0.36 13. A wave disturbance in a medium is described by y(x, t) = 0.02 cos (50 t + /2) cos (10 x), where ‘x’ and ‘y’ are in metre and ‘t’ in seconds. (A) A node occurs at x = 0.15 m (B) An antinode occurs at x = 0.3 m (C) The speed of the component wave is 5.0 m/s (D) The wavelength is 0.2 m. Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 6 14. A cannon shell is fired to hit a target at a horizontal distance R, however it breaks into two equal parts at its highest point, one part returns to the cannon. The other part (A) will fall at a distance R beyond target (B) will fall at a distance 3R beyond target (C) will hit the target (D) have nine times kinetic energy of first Paragraph Type (One Option Correct) This part contains 02 paragraph each describing theory, experiment, data etc. Four questions relate to the paragraph. Each question of a paragraph has Only One correct answer among the four choices (A), (B), (C) and (D). Paragraph for Question Nos. 15 and 16 In a photoelectric effect, a point source of green light of power 40 W emits mono-energetic photons that can just emit photoelectrons from an isolated metallic sphere of radius r = 1 cm, placed at a distance of 1m from the light source. Now, four other separate sources of violet, blue, red and yellow light emitting same number of photons as that of green light are brought near the source of green light. Assume one photoelectron is emitted out of every 106 incident photons on sphere. (Take violet = 4136 Å, blue = 5000 Å, red = 7200 Å, green = 4963 Å, hc = 12408 eV Å) 15. No. of photoelectrons emitted from the sphere per second is (A) 2.5 × 109 (B) 2.5 × 108 7 (C) 2.5 × 10 (D) 2.5 × 106 16. The potential of the sphere when emission of photoelectrons will stop is (A) 0.7 V (B) 0.5 V (C) 0.6 V (D) 0.8 V Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 7 Paragraph for Question Nos. 17 and 18 One mole of a monatomic gas undergoes the cycle shown in the diagram: The pressure, volume and temperature at A are P0, V0 2P0 B and T0 respectively; the pressure at B is 2P0 and the volume at D is 2V0. The processes AB and CD are isochoric. During BC DA, C the gas undergoes the processes such that during an infinitesimal A contraction or expansion, the heat absorbed dQ, the change in P0 internal energy dU and dW, the work done satisfy the relation: D 1 2 dQ dU dW 2 3 For the process BC, DA, we can write V0 2V0 1 2 dQ = dU dW dU dW 2 3 1 1 1 3 1 or, dU dW ; or, RdT dW 2 3 2 2 3 13 pdV + Vdp RdT ; or, pdV + Vdp = 0 9 13 or, pV 9 = constant 17. Find the temperature at C (A) 2T0 (B) 3T0 (C) 25/9 T0 (D) 3 5/9 T0 18. What is the efficiency of the cycle? Assume 25 / 9 1.5,24 / 9 4 / 3 approximately (A) 24% (B) 30% (C) 36% (D) 42% Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 8 Chemistry SECTION – II PART – A (One Options Correct Type) This part contains 07 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct. 1. O i SOCl 2 Product Major is OH 2 2 ii CH N Ph Me iii Ag2O iv EtOH O OEt (A) (B) OEt Ph Me Ph Me OEt OH (C) Ph Me (D) Ph Me O O 2. Which one of the following reagent can be used for differentiating the Cu2+ and Bi3+? (A) H2S gas in presence of dil HCl (B) NH4OH(excess) (C) K4[Fe(CN)6] (D) (B) and (C) both O HCl Cat. 3. X The compound[X] is O O (A) (B) O O (C) (D) Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 9 4. The compound formed by dissolving gold and platinum in aqua-regia is (A) [AuCl4]3– and [PtCl6]2– (B) [AuCl4]– and [PtCl6]4– – 2– (C) [AuCl4] and [PtCl6] (D) [AuCl4]– and [PtCl6]2– 5. The pair of compounds having the same hybridization for the central atom is (A) [Cu(NH3)4]2+ and [Ni(NH3)4]2+ (B) [NiCl4]2– and [PtCl4]2– 2+ 2+ (C) [Cu(NH3)4] and [Zn(NH3)4] (D) [Co(NH3)6]3+ and [Co(H2O)6]3+ 6. The major products M and N formed in the following reactions are:– M OH H 3 I/Na C N OH CH 2N N 2 (A) H3C M= N= N OH N OCH3 (B) M= N= N OCH 3 N O CH3 (C) M= N= N O N OCH3 CH3 (D) H3C M= N= N O N OH CH3 Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 10 7. The highest occupied MO in N2 and O 2 respectively are (take x-axis as inter nuclear axis) (A) 2px, 2py (B) 2py, 2pz (C) 2px, 2px (D) 2py, 2pz (One or More than one correct type) This part contains 07 questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct. 8. Which of the following statement(s) are correct? (A) CH3 – Cl > CH3 – F > CH3 – Br > CH3 – I (Order of dipole moment) (B) Cl2 > F2 > Br2 > I2 (Order of bond energy) (C) S 2O32 ,S 2O24 ,S 2O52 (All have S – S linkage) (D) PCl5 > SiCl4 > AlCl3 > MgCl2 (Order of hydrolysis) 9. Which of the following statements is/are true about the transition metal alkene complexes? K [Pt Cl3C2H4] (A) Back bonding weakens the double bond of the alkene (B) bonding and back-bonding synergistically strengthen metal alkene interaction (C) Electron withdrawing substituents on alkene reduce back bonding (D) –acidic co-ligands on metal strengthen back bonding 10. On electrolysis, in which of the following, O2 would be liberated at the anode? (A) dil H2SO4 with Pt electrode (B) aq. AgNO3 with Pt electrode (C) dil H2SO4 with Cu electrode (D) aq. NaOH with Pt electrode 11. Which of them can act as oxidizing agent in acidic as well as in alkaline medium? (A) KMnO4 (B) K2Cr2O7 (C) H2O2 (D) Cl2 Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 11 12. In which of the following reactions benzaldehyde will form in final product. CN CH3 (A) (B) SnCl HCl CrO Cl /CS 2 2 2 H O 2 H O 3 3 OH CO HCl (C) Anhyd.AlCl /CuCl (D) 3 KOH/ CCl4 H 13. A dilute solution contains ‘t’ moles of solute X in 1 kg of solvent with molal elevation constant Kb. The solute dimerises in the solution according to the following equation. The degree of association is . 2X X2 2 K b t Tb (A) The degree of association KbT (B) The molecular mass observed will be lesser than actual molecular mass (C) The colligative properties observed will be Tb obs < Tb theoretical ; Tf obs < Tf theoretical; P obs < Ptheoretical K K t Tb (D) The equilibrium constant for the process can be expressed as: K b b 2 2Tb K b t 14. The correct statements about the following reaction are CH3 2 6 1B H CH3 COCl/Pyridine H3 O 2 H O /OH X Y Z Acetic acid 2 2 (A) (X) is transisomer of 2-Methylcyclopentan-1-ol (B) (Y) is Cis isomer of ester (C) (Z) is geometrical isomers of (X) (D) (X) and (Z) have identical boiling point Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 12 Paragraph Type (One Option Correct) This part contains 02 paragraph each describing theory, experiment, data etc. Four questions relate to the paragraph. Each question of a paragraph has Only One correct answer among the four choices (A), (B), (C) and (D). Paragraph for Question Nos. 15 and 16 MnO2 is the most important oxide of manganese. MnO2 occurs naturally as the black coloured mineral pyrolusite. It is an oxidizing agent and decomposes to Mn3O4 on heating to 530oC. It is used in the preparation of potassium permanganate and in the production of Cl2 gas. Over half a million tons per year of MnO2 is used in dry batteries. 15. In the laboratory, MnO2 is made by (A) Heating Mn in O2 (B) Oxidizing Mn2+ in air (C) Electrolytic oxidation of MnSO4 (D) Precipitating MnO2 from solution when performing titration of KMnO4 in alkaline medium 16. In which of the following species, the colour is due to charge transfer. (I) [Mn(OH)4]2– (ii) MnO24 (iii) MnO2 (iv) KMnO4 (A) I, II, III correct (B) II, IV are correct (C) I, III are correct (D) only IV is correct Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 13 Paragraph for Question Nos. 17 and 18 Acid-base indicators are either weak organic acids or weak organic bases. Indicators change colour in dilute solution when the hydronium ion concentration reaches a particular value. For example, phenolphthalein is a colourless substance in any aqueous solution with pH less than 8.3. In between the pH range 8.3 to 10, transition of colour(colourless to pink) takes place and if pH of solution is greater than 10 solution is dark pink. Considering an acid indicator HIn, the equilibrium involving it and it’s conjugate base(In–) can be represented as: HIn H In acidic form basic form In pH of solution can be computed as: pH pK In log HIn In general, transition of colour takes place in between the pH range, pKIn 1. 17. An indicator is a weak acid and pH range is 4.0 to 6.0. If indicator in 50% ionized in a given solution, then what is the ionization constant of the acid? (A) 10–4 (B) 10–5 –6 (C) 10 (D) None of these 18. Select the correct statement(s) (A) at midway in the transition of an acidic indicator pH = pKIn (B) Methyl orange(3.1 to 4.4) is suitable indicator for titration of weak acid and strong base (C) Bromothymol blue(6.0 to 7.6) is not a good indicator for titration of HCl and NaOH (D) Thymol blue(1.2 to 2.8) is a very good indicator for titration of 100 mL of 0.1 M NH4OH (pKb = 1.74) and 0.1 M HCl Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 14 Mathematics SECTION – III PART – A (One Options Correct Type) This part contains 07 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct. 1. If roots of quadratic equation x 2 a2 7 x 15a 0 lie on either side of 2, then complete set of values of a is: 9 (A) (–2, 4) (B) 2, 2 9 3 (C) , 2 (D) , 6 2 2 2. Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. If a 1,b 3 and C 60o , then sin2 B is equal to: 27 3 (A) (B) 28 28 81 1 (C) (D) 28 3 3. 18 points are indicated on the perimeter of a triangle A ABC (see figure). How many triangles are there with vertices at these points? (A) 331 (B) 408 (C) 710 (D) 711 B C Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 15 4. If the mapping f x mx c, m 0 maps [–1, 1] onto [0, 2] then 1 tan tan1 cot 1 8 cot 1 18 is equal to: 7 2 1 (A) f (B) f 3 3 1 2 (C) f (D) f 3 3 nxn1 n 1 xn 1 5. lim where n 100 is equal to: x 1 e x e sin x 5050 100 (A) (B) e e 5050 4950 (C) (D) e e x 3/5 if x 1 6. Let f x 3 then the number of critical points on the graph of the x 2 if x 1 function is: (A) 1 (B) 2 (C) 3 (D) 4 7. The equation to the orthogonal trajectories of the system of parabolas y ax2 is: x2 y2 (A) y2 c (B) x 2 c 2 2 x2 y2 (C) y2 c (D) x 2 c 2 2 Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 16 (One or More than one correct type) This part contains 07 questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct. 8. If 2cos sin 1 , then the value of 4 cos 3 sin is equal to: (A) 3 (B) –5 7 (C) (D) –4 5 x dx 9. x 4 equals: x2 1 2 2x 2 1 1 1 2x 1 1 2x 1 (A) tan1 C (B) tan tan C 3 3 3 3 3 1 2x 2 1 1 1 2x 1 1 2x 1 (C) tan1 C (D) tan tan C 3 3 3 3 3 Where C is an arbitrary constant. x 3 5x 2 10. The co – ordinates of the point (s) on the graph of the function, f x 7x 4 3 2 where the tangent drawn cut off intercepts from the co – ordinate axes which are equal in magnitude but opposite in sign, is: 8 7 (A) 2, (B) 3, 3 2 5 (C) 1, (D) none of these 6 x 1 11. Let f x then which of the following is correct? x2 (A) f x has minima but no maxima. (B) f x increases in the interval (0, 2) and decreases in the interval ,0 2, . (C) f x is concave down in ,0 0,3 (D) x = 3 is point of inflection Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 17 12. If 2xy dy x 2 y 2 1 dx, y 1 0 and y x 0 3, then x 0 can be: (A) 2 (B) –2 (C) 3 (D) –3 13. A line L passing through the point P (1, 4, 3), is perpendicular to both the lines x 1 y 3 z2 x 2 y 4 z 1 and . 2 1 4 3 2 2 2 If the position vector of point Q on L is a1,a2 ,a3 such that PQ 357, then a a 2 a3 can be: (A) 16 (B) 15 (C) 2 (D) 1 14. Solutions of the differential equation 1 x 2 dy dx xy ax where a R, is: (A) a conic which is an ellipse or a hyperbola with principal axes parallel to coordinates axes. (B) centre of the conic is (0, a). (C) length of one of the principal axes is 1 (D) length of one of the principal axes is equal to 2. Paragraph Type (One Option Correct) This part contains 02 paragraph each describing theory, experiment, data etc. Four questions relate to the paragraph. Each question of a paragraph has Only One correct answer among the four choices (A), (B), (C) and (D). Paragraph for Question Nos. 15 and 16 Let f x x 2 a 2 x a2 a 2. Given a, , be real numbers and , are the roots of the equation f x 0. 15. If 2 , then a lies in the interval: (A) (0, 1) (B) (1, 2) (C) (2, 3) (D) (3, 4) Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 18 16. If both roots of the equation f x 0 lies in interval 0, , then range of a, is : 2 (A) , 2 (B) , 2 3 (C) 0, (D) Paragraph for Question Nos. 17 and 18 6x 2 13 Let f be an even function satisfying f x 2 f x 2 x R and x 2 3x, 0 x 1 f x 4 x, 1 x 4 [Note: [y] denotes greatest integer function of y.] 17. The area bounded by the graph of f x and the x – axis from x = –1 to x = 9 is: 31 (A) (B) 15 2 15 (C) 12 (D) 2 18. The value of f 89 f 67 f 46 is equal to : (A) 4 (B) 5 (C) 6 (D) 7 Space for Rough work FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com FIITJEE MOCK TEST PHYSICS, CHEMISTRY & MATHEMATICS (03.05.2024) ANSWER KEY (Paper-2) MOCK TEST (JEE ADVANCED) Q. Q. Q. PHYSICS CHEMISTRY MATHEMATICS No. No. No. 1. B 1. C 1. D 2. A 2. D 2. A 3. D 3. C 3. D 4. A 4. C 4. D 5. B 5. A 5. C 6. C 6. C 6. C 7. C 7. A 7. A 8. BD 8. ACD 8. AC 9. AD 9. AB 9. BC 10. AC 10. ABD 10. AB 11. BCD 11. ACD 11. BCD 12. AC 12. ABC 12. AB 13. ABCD 13. ACD 13. BD 14. AD 14. AD 14. ABD 15. A 15. D 15. B 16. B 16. D 16. D 17. C 17. B 17. B 18. B 18. A 18. A FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com FIITJEE MOCK TEST JEE (Advanced) (03.05.2024) PAPER – 2 ANSWERS, HINTS & SOLUTIONS Physics SECTION – I PART – A 1. B 2 Sol. = x = (2n 1) 2 2. A T 6V Sol. v V' 5 T' 36 V' T' T 25 % T = 44 % 3. D Sol. Let mass of the earth is Me and mass of object is m. GMem A Force on object at A r towards centre. r 3 Re R 2 R2 r2 GMem 4 Force on object along the tunnel 3 r R r GM R2 Acceleration of object along the tunnel 3 e r 2 R 4 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 4. A Sol. Pm = 2P0 cos kx (assuming closed end as origin) 7L 2L At point Q, x = L 9 9 2 2L Pm = 2P0 cos P0 9 Required ratio = 1 : 2 5. B mv 0 2mv 0 Sol. d= qB 2qB 6. C hc 1 1 3 Sol. R 2 2 R …(i) 1 2 4 hc 1 1 8 R 2 2 R …(ii) ' 1 3 9 ' 3 9 27 , ' 4 8 32 7. C 3 1 Sol. = ; V=8 ; m= 2 3 V V 1+m= f 2R 8. BD l Sol. R B C t 9. AD d(emf ) d Sol. Bu = constant dt dt Bu i= = constant 10. AC Sol. All the mass defect will convert into KE of -particle. 11. BCD Sol. TP2/5 = constant PV 5/3 = constant or P3/5 V = k This an adiabatic process. H = 0 Work done = –U = 6RT FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com k dP nRT VdP P 3/5 = 10 RT (5 / 2) 12. AC Sol. Let I be the power of source S1 and S2. 2 Initially Io = 4I, finally Imax = I 0.36I 2.56I 2 and Imin = I 0.36I 0.16I 13. ABCD Sol. y = 2a cos (t + ) cos (Kx) comparison with given equation gives 2 1 K 10 m 5 = 2f = 50 f = 25 Hz v = 5 ms–1 at x = 0.15 m cos (10 × 0.15) = cos (1.5) = –1 for all t at x = 0.3 cos (10 × 0.3) = cos 3 = – 0 for all t 14. AD Sol. At highest point, linear momentum 2 mv = mv1 – mv v1 = 3v At highest point, velocity of other part after explosion = 3v Centre of mass of particles will be at a distance R from initial point on ground. 15. A hc 12408 Sol. Work function of the metal () = 2.5 eV green 4963 40 No. of photon emitted from the power source per unit time = 1020 2.5 1.6 10 19 photons 1020 (1 102 )2 No. of photons incident on the metallic surface per unit time = 2.5 1015 4 (1)2 photons No. of photoelectrons coming out from the metal surface per unit time 2.5 1015 = 6 = 2.5 × 109 photoelectrons 10 16. B FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com hc Sol. The emission of photoelectron will stop when eV , where V is the potential of violet sphere. 12408 2.5 eV ; V 0.5 V 4136 17. C PB Sol. TB TA 2T0 PA 13 13 1 1 (2T0 )V09 TC (2V0 )9 TC 25/9 T0 18. B Sol. Heat is absorbed during the process AB and BC 3 3 Q AB R(TB TA ) = RT0 2 2 3 9 3 QBC R R (TC TB ) R (2 25/9 )T0 2 4 4 3 15 Qabs (4 25/9 )RT0 RT0 [25/9 1.5] 4 8 3 21 Qrej (2 25/9 )RT0 RT0 8 16 3 QCD R(TD TC ) 2 3 9 QDA R R (TA TD ) 2 4 9 W W RT0 ; 30% 16 Qabs FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com Chemistry SECTION – II PART – A (One Options Correct Type) This part contains 07 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct. 1. C Sol. SOCl2 RCOOH CH2N2 RCOCl Ag2O RCOCHN2 RCH C O EtOH RCH2 C O OEt R= Ph Me 2. D Sol. Fact based. 3. C Sol. O H O O HO H 4. C Sol. Au 4H NO3 4 Cl AuCl4 NO 2H2O 3PtCl62 4NO 8H2O 3 Pt 16 H 4NO3 18 Cl 5. A Sol. Fact based. 6. C Sol. CH3I NaOH N OH N O CH3 CH2 N2 N OH N OCH3 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 7. A Sol. For N2 2PY2 KK 2s2 * 2s2 2PX2 2PX2 2PZ2 For O 2 * 2 1 KK 2s2 * 2s2 2PX2 * 2PY2 2PY * 2PZ 2PZ 2PZ 8. ACD Sol. (B) is incorrect, correct order is Cl2 > Br2 > F2 > I2. 9. AB Sol. Fact based. 10. ABD Sol. O2 4H 4e at anode (A) 2H2O (B) Aq. AgNO3 at anode 4 OH 2H2O O 2 4 e (D) Aq. NaOH at anode 4 OH 2H2O O 2 4 e 11. ACD Sol. K2Cr2O7/H+ acts as oxidant not in basic medium, rest all acts as oxidizing agent in acidic as well as alkaline medium. 12. ABC Sol. (A) Stephan’s reduction, (B) Etard’s reaction, (C) Gattermann Koch synthesis 13. ACD Sol. 2X X2 i 1 1 2 2 tb 0.65 i 1 Kbt 2 t K t t b 1 b b 2 Kbt Kbt 2 K b t tb A Kb t and as i < 1 MC 1 so MC < Mo Mo C.P obs 1...... C C.P cal 14. AD FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com Sol. CH3 2 6 1B H CH3 COCl H3O 2 H O /OH X Pyridine Y Z Acetic acid 2 2 CH3 O OH OC - CH3 OH X Y Z 15. D Sol. MnO 4 OH MnO 2 16. D Sol. KMnO4 is purple coloured due to charge transfer. 17. B Sol. For 50% ionization(In–) = [HIn] pH = PKIn Thus PKIn= 10–5 (as pH = 5) 18. A Sol. At midway pH = PKIn FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com Mathematics SECTION – III PART – A (One Options Correct Type) This part contains 07 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct. 1. D Sol. f 2 0 3 a 6 2a 3 0 a ,6 2 2. A 12 32 c 2 C Sol. By Cosine law, cos 60o 2.1.3 c 7 b c Now, (By sine law) sinB sinC b=3 a=1 3 3 b sin C 2 3 3 sinB c 7 2 7 27 A c C Hence, sin2 B 28 3. D 18 Sol. C3 3. 7C3 816 105 711 4. D Sol. Clearly, f x x 1 As m 1, c 1 1 1 1 Now, tan tan1 tan1 tan1 7 8 18 1 1 1 tan tan1 7 8 tan1 1 1 1 18 7 8 15 1 3 1 tan tan1 tan 1 tan tan 1 tan1 55 18 11 18 3 1 1 1 2 tan tan1 11 18 tan tan1 f 1 3 1 3 3 3 11 18 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 5. C Sol. l lim nx n x 1 x n 1 x 1 e x e sin x Put x 1 h so that as x 1,h 0 l lim n h.n 1 h 1 h 1 n h 0 h e e 1 sin h n.h 1 nC1h nC2h2 nC3h3 ... l lim 1 nC1h nC2h2 nC3h3 .... 1 h 0 eh 1 sin h e h2 h h n 2 nC 2 2n2 n n 1 n2 n n n 1 e 2e 2 e 2 e If n 100 5050 l e 6. C Sol. A, B, C are the 3 critical points of y f x y A B C x 0 1 2 7. A dy y Sol. 2ax 2x 2 dx x dy 2y dx x dy x dy x Now m 1 m dx 2y dx 2y x2 y2 c 2 8. AC Sol. 2 cos 2 1 sin 2 5 sin2 2sin 3 0 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 3 sin 1 or , now 5 3 If sin 1 cos 0 E 3; If sin 5 7 Hence E 5 9. BC 1 t 1 dt 1 dt 1 2 2 1 tan 1 2t 1 Sol. I . tan1 2 t t 1 2 1 2 2 3 2 3 3 3 3 t 2 2 4 1 2x 2 1 tan1 C 3 3 10. AB Sol. Since intercepts are equal in magnitude but opposite in sign. dy 1 dx P dy Now x 2 5x 7 1 dx x 2 5x 6 0 x 2 or 3 11. BCD 2x x3 y Sol. f ' x 3 and f " x 4. x x 1/4 x O 1 2 3 12. AB dy Sol. 2xy x2 y 2 1 dx dt Put y 2 t, x x2 t 1 dx dt t x 2 1 dx x x 1 I.F. x FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com t x2 1 1 Hence 2 dx x C x x x 2 2 y x 1, C 0 as y 1 0 Now, y x 0 3 3 x 20 1 x 20 4 x 0 2 13. BD x 1 y 4 z 3 Sol. Equation of the line passing through P(1, 4, 3) is: …….(i) a b c x 1 y 3 z 2 x 2 y 4 z 1 Since equation (i) is perpendicular to and 2 1 4 3 2 2 Hence 2a b 4c 0 and 3a 2b 2c 0 a b c a b c 2 8 12 4 4 3 10 16 1 x 1 y 4 z 3 Hence the equation of the lines is ………(ii) 10 16 1 Now any point Q on (2) can be taken as 1 10, 16 4, 3 2 2 Distance of Q from P (1, 4, 3) 10 16 2 357 100 256 1 2 357 1 or 1 Q is 9,20, 4 or 11, 12, 2 Hence a1 a2 a3 15 or 1 14. ABD dy x ax Sol. y dx 1 x 2 1 x2 x 1 1 x2 dx log 1 x 2 1 I.F. e e 2 1 x2 y x a 3/2 dx C 1 x2 1 x2 Let 1 x 2 2 2x dx 2 d x dx d y d a Hence a 3 C y a C y a C 1 x2 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 2 y a C2 1 x 2 C2 1 x 2 or C2 x 2 1 2 2 y a C2 x2 C2 or y a C2 x2 C2 2 2 y a x2 y a x2 1 or 1 Centre (0, a) C2 1 C2 1 15. B Sol. f x x 2 a 2 x a2 a 2 0 –2 f 2 0 2 4 2a 4 a a 2 0 a2 3a 2 0 1 a 2 a 1, 2 Not integral values of a. 16. D Sol. Given, x 2 a 2 x a2 a 2 0 2 Now, D 0 a2 ………(i) 3 Product of roots > 0 a2 a 2 0, which is true a R ……….(ii) and sum of roots 0 a 2 0 a 2 ……….(iii) Equation i ii iii a 17. B 1 1 Sol. Required area 2 4 3 2 1 3 15 2 2 18. A Sol. f 89 f 67 f 46 f 1 f 3 f 2 3 1 2 4 f x 2 f x 6 f x f x 8 y 3 x –4 –1 1 4 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com
