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NARAYANA I I T A C A D E M Y ALL INDIA TEST SERIES NA RA YA NA FULL TEST – 4 PAPER – II Ti m e : 3 ho ur s M a xi mu m m ar k s: 2 4 3 INSTRUCTIONS : 1) This booklet is your Questions Paper containing 57 questions. Maximum marks: 237. 2) The question paper consists of 3 parts (Chemistry, Mathematics and Physics). Each part consists of 4 sections. 3) Section-I contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. For each question in Section I, you will be awarded 5 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus two (-2) mark will be awarded. 4) Section-II contains a group of 5 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled. For each question in Section II, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. No negative marks will be awarded for incorrect answers in this Section. 5) Section-III contains 2 paragraphs. Based upon each of the paragraphs 3 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. For each question in Section III, you will be awarded 3 marks if you darken only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (-1) mark will be awarded. 6) Section-IV contains 2 questions. Each question has four statements (A, B, C and D) given in Column I, and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS. For each question in Section IV, you will be awarded 2 marks for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marks awarded for incorrect answer(s) for this section. NFT-4_ PAPER-2 CHEMISTRY SECTION-1 Section-I (Single Correct Choice Type) contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. For each question in Section I, you will be awarded 5 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus two (-2) mark will be awarded. 1) During the Hinsbergs Test, which of the following primary amines is most likely to be detected as a secondary amine? A) MeNH 2 B) NH2 C) NH2 D) NH2 2) Which of the following will not show fermentation? CHO CHO CHO H OH H OH CHO H OH H OH A) HO H B) C) H OH D) H OH H OH CH2OH H OH CH2OH H OH CH 2OH CH 2OH 3) In qualitative analysis, ammonia is used to separate A) NaCl from KCl B) AgCl from Hg 2 Cl2 C) PbCl2 from Mg ( OH )2 D) FeCl3 from AlCl3 4) Which oxide of Mn is acidic in nature ? A) B) C) D) Space for rough work Page 2 of 20 NFT-4_ PAPER-2 5) In which of the following does the overlap of two orbitals give a non bonding interaction ? A) + - + B) - + + + C) - + + - D) + - 6) The correct order of ionic mobilities of the following ions in aqueous solution is: A) Li+ > Na + > K+ > Rb + B) Na + > K+ > Rb + > Li+ C) Rb + > K+ > Na + > Li+ D) Rb + > Na + > Li+ > K+ SECTION-2 Section-II (Integer Type) contains a group of 5 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled. For each question in Section II, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. No negative marks will be awarded for incorrect answers in this Section. 7) Some % of sample of N2 must be allowed to escape off. Its temperature, pressure and volume are to be changed from 2200 C , 3 atm, 2L to1100 C , 0.6 atm and 1L respectively. If answer for % is mn % , what is the value of (m - n)? 8) An electron beam can undergo diffraction by crystals. Through what potential should a beam of electrons be accelerated so that its wavelength becomes equal to 0 1.54 A ? Take answer as " xy " volts , what is value of x + y ? (For example if volts = 81 then x + y = 9) 9) A metal M of molar mass 96 gm/mole reacts with fluorine to form a salt that can be represented as MFx . In order to determine X, a 41.20gm of the sample of the salt is dissolved in 100gm of water and its elevation in boiling point was determined to be 1.38K. What is value of x? Given K b (water) = 0.512K kg / mole . Space for rough work Page 3 of 20 NFT-4_ PAPER-2 ® 10) Z(s) + Cu 2+ (aq) ¾ ¾ Cu(s) + z 2+ (aq) At 300K; E cell = 1.10volt and at 310K, E cell = 1.12Volt then if entropy change (D S)for the above cell reaction is "xyz"J / K . Find (x + z - y).(for example if D S = 449 J / K then X + Z - Y = 9 ) 11) The binding energy of electrons in a metal is 250 KJ/mol, then if threshold frequency of metal is given by x ´ 10y sec- 1 . Value of x to nearest integer is ? SECTION-3 Section-III (Paragraph Type) contains 2 paragraphs. Based upon each of the paragraphs 3 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. For each question in Section III, you will be awarded 3 marks if you darken only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (-1) mark will be awarded. P) Although chlorobenzene is inert to nucleophilic substitutions, it gives quantitative yield of phenol when heated with aq. NaOH at high temperature and under high pressure. Phenol, so formed, is a weaker acid than the carboxylic acid, hence it dissolves only in strong base like NaOH, but not weak like NaHCO3 . It reacts with acid chlorides and acid anhydrides in the absence of AlCl3 to form esters. As far as nucleophilic substitution in phenol is concerned, the - OH is an activating group, hence its presence enhances the electrophilic substitution in the ortho and para position. Condensation with formaldehyde is one of the important properties of phenol. The condensation may take place in presence of acids or alkali and leads to the formation of Bakelite, an important industrial polymer. 12) Conversion of chlorobenzene into phenol involves: A) Modified SN1 mechanism B) Modified SN2 mechanism C) Both (a) and (b) D) Elimination addition 13) The o acylation of phenols with acid anhydrides can be catalysed by A) Sulphuric acid B) NaOH C) Both D) None Space for rough work Page 4 of 20 NFT-4_ PAPER-2 14) Condensation of phenol with formaldehyde is an electrophilic substitution, in which A) H2C = 0 as such is the electrophile in both acidic as well as basic medium. B) H2C = 0 is the real electrophile in acidic medium while in basic medium + - C H2 - O is the real electrophile. C) + H2C = O H and CH2 = 0 are the electrophiles in acidic and basic medium respectively. D) + - H2C = 0 and C H2 - O are the electrophiles is acidic and basic medium respectively. P) The carboxyl group consists of C = O and - OH , it is The - OH group undergoes change, either loss of H+ or replacement by another group. However, the carbonyl group markedly influences the reactions of carboxylic acids. The presence of the C = O part is also responsible for nucleophilic substitution reactions in acid derivative. Presence of an electron withdrawing group increases the acidity of aliphatic as well as aromatic acids. On the other hand, electron releasing groups impart opposite effect. 15) The marked acidity of RCOOH over ROH is due to the presence of A) B) C = O C) Both D) None 16) Which statement is correct when an acid weakening group is present in benzoic acid? A) Acid weakening groups activate the ring towards electrophilic substitution. B) Acid weakening groups deactivate the ring towards electrophilic substitution. C) Acid weakening groups activate the ring towards nucleophilic substitution. D) None of the above. 17) The C = O part in carboxylic acids and their derivatives make acyl compounds more reactive than alkyl compounds towards nucleophilic attack because: A) The carbonyl group is electron donating. B) The alkyl group(R) in the acid is electron donating. C) The attack of a nucleophile on a flat acyl compound is less sterically hindered. D) Tetrahedral carbon atoms cannot have pentavalent transition states. Space for rough work Page 5 of 20 NFT-4_ PAPER-2 SECTION-4 Section-IV (Matrix Type) contains 2 questions. Each question has four statements (A, B, C and D) given in Column I, and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS. For each question in Section IV, you will be awarded 2 marks for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marks awarded for incorrect answer(s) for this section. 18) Match the Following: Column I Column II (a) Ilmenite (p) Iron (b) Dolomite (q) Magnesium (c) Carnallite (r) Potassium (d) Chromite (s) Titanium (t) Calcium 19) Match the Following: Column I Column II (a) Gas evolved by the action of (p) Colour of acidified KMnO4 is dilute H2SO4 on a sulphite discharged (b) Gas evolved by the action of (q) Acidified dichromate solution is dilute H2SO4 on a carbonate turned green (c) Gas evolved by heating an (r) Nesslers reagent gives a brown ammonium salt with NaOH precipitate (d) Gas evolved by the action of (s) Baryta water turns milky dilute H2SO4 on a sulphide (t) Alkaline nitro prusside turns violet Space for rough work Page 6 of 20 NFT-4_ PAPER-2 MATHEMATICS SECTION-1 Section-I (Single Correct Choice Type) contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. For each question in Section I, you will be awarded 5 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus two (- 2) mark will be awarded. 20) If f x y f x g y f y g x x, y R ,(where f x is not identically (zero)), then A) If f ' 0 exists, then f ' 0 also exists but not equal B) If f ' 0 exists, then f ' 0 does not exists C) If f ' 0 exists, then it is equal to f ' 0 D) None of these 21) Suppose i is a solution of the polynomial equation a4 z 4 ia3 z3 a2 z 2 ia1z a0 0 , where , , a j R j 0,1, 2,3, 4 which one of the following must also be a solution? A) i B) i C) i D) i 22) The set of values of ' a ' for which in-equation a 1 x2 a 1 x a 1 0 is true for all x 2 is 7 7 A) , B) 1, C) ,1 D) 3, 2 3 3 23) Let AB be any chord of the circle x 2 y 2 4 x 4 y 4 0 which subtends an angle of 90 at the point 2,3 then the locus of the mid point of AB is a circle whose centre is 3 5 5 A) 1,5 B) 1, C) 1, D) 2, 2 2 2 Space for rough work Page 7 of 20 NFT-4_ PAPER-2 24) A B A B In ABC, if BC 1,sin x1, sin x2 , cos x3 &cos x4 with 2 2 2 2 2010 2009 x1 x 3 0 ,then length of AC is equal to x2 x4 1 A) 1 B) 1 C) D) 1 2 x 25) Let f x t 2 2t 2 dt ,where ' x ' is the set of real numbers satisfying the 0 in-equation log2 1 6 x x2 8 0 . If f x , , then maximum value of is 103 104 105 106 A) B) C) D) 3 3 3 3 SECTION-2 Section-II (Integer Type) contains a group of 5 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled. For each question in Section II, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. No negative marks will be awarded for incorrect answers in this Section. 26) If the number of ordered pairs of positive integers m, n satisfying m 2n 60 & n 2m 60 is 2 K 3 K 2 2 K , then K 27) x 1 , x0 If f x , then the number of solutions of the equation x 1 2 , x 1 f x f 1 x 0 is/are 28) 2 If the system of equations sin x cos 2 y a 2 1 1 and cos x sin 2 y a 1 has a solution, then the value of a 2 is 29) If the number of ordered triplets x, y, z such that L.C.M x, y 3375, L.C.M y, z 1125, L.C.M z, x 3375 is equal to ' k ' then k 47 is equal to Space for rough work Page 8 of 20 NFT-4_ PAPER-2 30) x 2 y 1 z If the length of the shortest distance between the lines ; 2 3 4 2 x 3 y 5z 6 0 3x 2 y z 3 is K , then 3 K is equal to (where [.] denotes greatest integer function) SECTION-3 Section-III (Paragraph Type) contains 2 paragraphs. Based upon each of the paragraphs 3 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. For each question in Section III, you will be awarded 3 marks if you darken only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (-1) mark will be awarded. n P) If 1 px x 2 1 a1x a2 x 2 ...... a2n x 2 n , where n N , p R . 31) If n 40, p 3, r 5 ,then which of the following is true. A) 135a5 6a6 4a4 B) 105a5 6a6 76a4 C) 105a5 6a6 36a4 D) 135a5 6a6 36a4 32) The remainder obtained when a1 5a2 9a3 13a4 ..... 8n 3 a2n is divided by p 2 is A) 1 B) 2 C) 3 D) 0 33) If p 3 & n is even number, then the value of a1 3a2 5a3 7a4 ...... 4n 1 a2n is A) n B) 2n 1 C) 2n 2 D) 2n P) To find the point of contact P x , y of a tangent to the graph of y f x passing 1 1 through origin O, we equate the slope of tangent to y f x at ' P ' to the slope of OP . f x1 Hence, we solve the equation f ' x1 to get x1 and y1 . x1 34) The equation ln mx p x, where ' m ' is a positive constant has a single root for m e e m A) 0 p B) p C) 0 p D) p e m m e Space for rough work Page 9 of 20 NFT-4_ PAPER-2 35) The equation ln mx p x, where ' m ' is a positive constant has exactly two roots for m e e m A) p B) p C) 0 p D) 0 p e m m e 36) The equation ln mx p x, where ' m ' is a positive constant has exactly three roots for m m e e A) p B) 0 p C) 0 p D) p e e m m SECTION-4 Section-IV (Matrix Type) contains 2 questions. Each question has four statements (A, B, C and D) given in Column I, and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS. For each question in Section IV, you will be awarded 2 marks for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marks awarded for incorrect answer(s) for this section. 37) Match the following: Column -I Column -II (A) If x i 8 1for i 1, 2,3 where 0,1, 2,3,..... , then 2 (p) 9 the number of positive integral solutions of equations x1 x2 x3 21 is (B) n (q) 55 If Dn is the digit in the units place of the number r!, r 1 then D1 D3 D5 .... D21 is equal to (C) Let S a N , a 100 . If the equation (r) 2 tan 2 x tan x a 0 has real roots, then number of elements in ' S ' is (where [.] represents greatest integer function) (D) The number of solutions for (s) 37 3sin 2 x cos2 x 2 3 sin x cos x 4 is/are where x , Space for rough work Page 10 of 20 NFT-4_ PAPER-2 38) Match the following: Column -I Column -II (A) Area bounded by the curves y cos A cos B cos C , (p) 23 A B C y 7 sin sin sin , where A, B, C are angles of a 2 2 2 triangle & [.] denotes greatest integer function and the curve x y 2 is (B) (q) 3 25I 7 If I n e x sin x dx ,then n is equal to 0 I5 (C) If the total number of positive unequal integral solutions (r) 2 of the equation x y z w 20 is 24k , then k (D) If y 2 5 y 3 x 2 x 1 2 x x R , then the (s) 21 number of integers lying in the range of ' y ' are Space for rough work Page 11 of 20 NFT-4_ PAPER-2 PHYSICS SECTION-1 Section-I (Single Correct Choice Type) contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. For each question in Section I, you will be awarded 5 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus two (- 2) mark will be awarded. 39) An opaque sphere of radius ‘a’ is just immersed in a transparent liquid as shown in figure. A point source is placed on the vertical diameter of the sphere at a distance a/2 from the top of the sphere. One ray originating from the point source after refraction from the air liquid interface forms tangent to the sphere. The angle of refraction for that particular ray is 300 . The refractive index of the liquid is Point source a/2 air liquid a A) 2 3 B) 3 5 C) 4 5 D) 4 7 Space for rough work Page 12 of 20 NFT-4_ PAPER-2 40) A particle having charge q enters a region of uniform magnetic field B (directed inwards) and is deflected as shown. The magnitude of the momentum of the momentum of the particle is B x y x+2 qBy 2 qB y2 qBy x 2 A) qB B) C) +x D) +x 2 x 2 x 2 y 41) The mutual inductance between the rectangular loop and the long straight wire as shown in figure is M. b B c a i μ 0a c A) M = zero B) M= ln 1+ 2π b μ 0a a + c μ 0a b C) M= ln D) M= ln 1 2π b 2π c Space for rough work Page 13 of 20 NFT-4_ PAPER-2 42) In the shown AC circuit phase different between currents I1 and I 2 is XL X XC A) tan 1 B) tan 1 L 2 R R XL X XC C) tan 1 D) tan 1 L 2 2 R R 43) The K X-rays emission line of tungsten occurs at 0.021nm . The energy difference between K and L levels in this atom is about A) 0.51 MeV B) 1.2 MeV C) 59 keV D) 13.6 eV 44) Activity of a radioactive substance is R1 and time t1 and R 2 at time t 2 t 2 t1 . Then the R2 ratio is : R1 t2 t t A) B) e t1 t2 C) e 1 2 D) e t1 t2 t1 λ Space for rough work Page 14 of 20 NFT-4_ PAPER-2 SECTION-2 Section-II (Integer Type) contains a group of 5 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled. For each question in Section II, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. No negative marks will be awarded for incorrect answers in this Section. 45) A observer can see through a pin-hole the top end of a thin rod of height h , placed as shown in the figure. The beaker height is 3h and its radius h . When the beaker is filled with a liquid up to a height 2h , he can see the lower end of the rod. Then the refractive index of the liquid is . Find the value of 2 2 . 46) In the Youngs double slit experiment apparatus shown in figure, the ratio of maximum to minimum intensity on the screen is 9. The wavelength of light used is , then the value of y D is . Find the value of d 47) A large metal sheet carries an electric current along its surface. Current per unit length is . Magnetic field near the metal sheet is 0 . Find the value of 2x x Space for rough work Page 15 of 20 NFT-4_ PAPER-2 48) A charged particle is projected with velocity v0 along positive x-axis. The magnetic field B is directed along negative z-axis between x 0 and x L . The particle emerges out at x L at an angle of 60 with the direction of projection. The velocity with which the same particle is projected at x 0 along positive x-axis so that when it emerges out at x L , the angle made by it is 30 with the direction of projection is pv0 . Find the value of 2 p 2 49) The activity of a sample reduces from A to A / 3 in one hour. If the activity after 3 hours 0 0 A0 more will be , then find the value of k k SECTION-3 Section-III (Paragraph Type) contains 2 paragraphs. Based upon each of the paragraphs 3 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. For each question in Section III, you will be awarded 3 marks if you darken only the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (-1) mark will be awarded. P) A network of resistance is constructed with R1 and R 2 as shown in figure. The potential at the points 1, 2, 3,……, N are V1, V2 , V3 ,....Vn respectively, each having a potential k times smaller than the previous one. (Example V0 = kV1, V1 = kV2 , V2 = kV3 ,....... ) V1 V2 V3 VN 1 N V0 R1 R1 R1 R1 R2 R2 R2 R2 R3 R1 50) The ratio is: R2 k 1 2 1 k 1 A) k 2 B) C) k D) k k 1 k2 k Space for rough work Page 16 of 20 NFT-4_ PAPER-2 R2 51) The ratio is : R3 k 1 2 1 k 1 A) B) k 2 C) D) k k k k 1 k2 52) The current that passes through the resistance R 2 nearest to the V0 is : k 1 k 1 2 2 V0 V0 A) B) k R3 k R3 1 V2 k 1 V0 C) k + 2 D) k R3 k2 R3 P) In an organ pipe (may be closed or open) of 99 cm length standing wave is setup, whose equation is given by longitudinal displacement 2π ξ = 0.1mm cos y + 0.01m cos2π 400 t where y is measured from the top of the tube 0.8 in meters and t in second. Here 0.01m is the end correction. 53) The upper end and the lower end of the tube are respectively: A) open-closed B) closed-open C) open-open D) closed-closed Space for rough work Page 17 of 20 NFT-4_ PAPER-2 54) The air column is vibrating in A) First overtone B) Second overtone C) Third harmonic D) Fundamental mode 55) Equation of the standing wave in terms of excess pressure is (Bulk modulus of air B = 5×105 N / m 2 ) A) 2π B) 2π Pex = 125π N/m2 sin Pex = 125π N/m2 cos 0.8 0.8 y + 0.01m cos 2π 400 t y + 0.01m sin 2π 400 t C) 2π D) 2π Pex = 225π N/m2 sin Pex = 225π N/m2 cos 0.8 0.8 y + 0.01m cos 2π 200 t y + 0.01m sin 2π 200 t Space for rough work Page 18 of 20 NFT-4_ PAPER-2 SECTION-4 Section-IV (Matrix Type) contains 2 questions. Each question has four statements (A, B, C and D) given in Column I, and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS. For each question in Section IV, you will be awarded 2 marks for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marks awarded for incorrect answer(s) for this section. 56) The circuit involves two ideal cells connected to a 1 F capacitor via a key K. Initially the key K is in position 1 and the capacitor is charged fully by 2V cell. The key is then pushed to position 2. Column I gives physical quantities involving the circuit after the key is pushed from position 1. Column II gives corresponding results. Match the following : - C 1 F 2V 4V K 1 2 Column I Column II (a) The net charge crossing the 4 volt cell in C is (p) 2 (b) The magnitude of work done by 4 Volt cell in (q) 6 J is (c) The gain in potential energy of capacitor in J is (r) 8 (d) The net heat produced in circuit in J is (s) 16 (t) None of these Space for rough work Page 19 of 20 NFT-4_ PAPER-2 57) Magnetic flux (f) in a circular coil of resistance 10 changes with time as shown in figure. direction indicates a direction perpendicular to paper inwards. Match the following table Column I Column II (a) At 1 s induced current is (p) Clock wise (b) At 5 s induced current is (q) anticlockwise (c) At 9 s induced current is (r) zero (d) At 15 s induced current is (s) 2A (t) None Space for rough work Page 20 of 20