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NARAYANA I I T A C A D E M Y ALL INDIA TEST SERIES NFT – 9_PAPER – II (20.03.2011) Tim e: 3 hou r s Ma x im um ma r ks: 24 3 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS Bubble (A) if both the statements are TRUE and A. General: STATEMENT-2 is the correct explanation 1. This booklet is your Question Paper containing 66 of STATEMENT-1. questions. The booklet has 24 pages. Bubble (B) if both the statements are TRUE but 2. The question paper CODE is printed on the right hand STATEMENT-2 is NOT the correct top corner of this booklet. explanation of STATEMENT-1. 3. Black papers, clipboards, log tables, slide rules, Bubble (C) if STATEMENT-1 is TRUE and calculators, cellular phones, pagers, and electronic STATEMENT-2 is FALSE. gadgets in any form are not allowed to be carried inside Bubble (D) if STATEMENT-1 is FALSE and the examination hall. STATEMENT-2 is TRUE. 4. The answer sheet, a machine-readable Objective 14. Section III contains 2 paragraphs. Based upon each Response Sheet (ORS), is provided separately. paragraph, 3 multiple choice questions have to be 5. DO NOT TAMPER WITH / MUTILATE THE ORS OR answered. Each question has 4 choices (A), (B), (C) THE BOOKLET. and (D), out of which only one is correct. 6. Do not break the seals of the question-paper booklet 15. Section IV contains 3 questions. Each question before being instructed to do so by the invigilators. contains statements given in 2 columns. Statements in the first column have to be matched with statements in B. Filling the ORS the second column. The answers to these questions 7. On the lower part of the ORS, write in ink, your name in have to be appropriately bubbled in the ORS as per the box L1, your Registration No. in box L2 and Name of instructions given at the beginning of the section. the Centre in box L3. Do not write these anywhere else. D. Marking Scheme: 8. Write your Registration No. in ink, in the box L4 16. For each questions in Section I, you will be awarded 3 provided in the lower part of the ORS and darken the marks if you have darkened only the bubble appropriate bubble UNDER each digit of your corresponding to the correct answer and zero mark if no Registration No. with a good quality HB pencil. bubble is darkened. In all other cases, minus one (–1) 9. The ORS has a CODE printed on its lower and upper mark will be awarded. parts. 17. For each question in Section II, you will be awarded 3 10. Make sure the CODE on the ORS is the same as that marks if you have darken only the bubble on this booklet and put your signature in ink in box L5 corresponding to the correct answer and zero mark if on the ORS affirming that you have verified this. no bubble is darkened. In all other cases, minus one (– 1) mark will be awarded. C. Question paper format: 18. For each question in Section III, you will be awarded 4 11. The question paper consists of 3 parts (Part I: marks if you darken only the bubble corresponding to Mathematics, Part II: Physics, Part III: Chemistry). Each the correct answer and zero mark if no bubble is part has 4 sections. darkened. In all other cases, minus one (–1) mark will 12. Section I contains 9 multiple choice questions. Each be awarded. question has 4 choices (A), (B), (C) and (D), out of 19. For each question in Section IV, you will be awarded 6 which only one is correct. marks if you ALL the bubble corresponding ONLY to 13. Section II contains 4 questions. Each question contains the correct answer or awarded 1 mark each for correct TATEMENT-1 AND STATEMENT-2. bubbling of answer in any row. No negative mark will be awarded for an incorrectly bubbled answer. USEFUL DATA Gas Constant R = 8.314 J K–1 mol–1 1 Faraday = 96500 Coulomb = 0.0821 Lit atm K–1 mol–1 1 calorie = 4.2 Joule = 1.987 2 Cal K–1 mol–1 1 amu = 1.66 10–27 kg Avogadro’s Number Na = 6.023 1023 1 Ev = 1.6 10–1 J Planck’s constant h = 6.625 10–34 J . s = 6.625 10–27 erg . s Atomic No: H = 1, D = 1, Li = 3, Na = 11, K = 19, Rb = 37, Cs = 55, F = 9, Ca = 20, He = 2, O = 8, Au = 79, Ni = 28, Zn = 30, Cu = 29, Cl = 17, Br = 35, Cr = 24, Mn = 25, Fe = 26, S = 16, P = 15, C = 6, N = 7, Ag = 47. Atomic Masses: He = 4, Mg = 24, C = 12, O = 16, N = 14, P = 31, Br = 80, Cu = 63.5, Fe = 56, Mn = 55, Pb = 207, Au = 197, Ag = 108, F = 19, H = 1, Cl = 35.5, Sn = 118.6, Na = 23, D = 2, Cr = 52, K = 39, Ca = 40, Li = 7, Be = 4, Al = 27, S = 32. NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II MATHEMATICS PAPER - II SECTION – I Straight Objective Type This section contains 9 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. If a, b, c are non zero real numbers and the equation az2 + bz + c + i = 0 has purely imaginary roots, then (A) a2 = bc (B) a = b2c 2 2 (C) a = b c (D) abc = 1 2. Number of ordered triplets of natural number (a, b, c) for which abc 11 is (A) 52 (B) 53 (C) 55 (D) 56 3. If a, b, c are positive real numbers such that a + b + c = 9, then minimum value of 1 1 1 1 1 1 is a b c 64 (A) (B) 3 27 (C) 9 (D) 27 4. The centroid of triangle ABC, where A, B, C are points on the parabola 4y2 - 3y + 6x + 1 = 0, whose normals are concurrent always lie on the line. (A) 8y - 3 = 0 (B) x = 0 (C) y = 0 (D) 4y - 3 = 0 5. If the straight line 3x + 4y + 1 = 0 is a normal to the parabola y2 + x = 0, then distance between focus and directrix of the parabola is (A) 64/123 (B) 32/123 (C) 16/123 (D) 80/123 Space for rough work 2 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS 6. If a curve has the property that normal at point P on it, lines OP (O origin) and x–axis form an isosceles triangle, then curve must be (taking x-axis as base of isosceles triangle) (A) ellipse (B) parabola (C) circle (D) hyperbola 7. Let f(x) = 2x3 + ax2 + bx, (a, bN), if graph of f(x) cuts the x–axis at 3 distinct points, then minimum value of a2 + b2 is (A) 10 (B) 2 (C) 9 (D) 8 1 4 4 lim ecos t dt ecos t dt is equal to 2 2 8. x 0 x y xy 2 2 (A) ecos y ( - sin2y) (B) ecos y 2 (C) 0 (D) e4 - ecos y 9. If , , , , are 4 solutions of the equation tan = 3 tan3, such that tan tan 4 tan tan, then tan tan is equal to (A) 1 (B) -3 (C) -2 (D) 4 Space for rough work 3 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II SECTION – II Assertion – Reason Type This section contains 4 reasoning type questions. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Code (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. (B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1. (C) Statement – 1 is True, Statement – 2 is False. (D) Statement – 1 is False, Statement – 2 is True. 10. i j ˆ STATEMENT–1: The vector which is orthogonal to ˆ ˆ k and coplanar with j ˆ j ˆ ˆ j ˆ 2ˆ k and ˆ 2ˆ k is 4i ˆ 2k i and STATEMENT–2: ( ) is perpendicular to and lie in the plane of and 11. STATEMENT–1: If in ABC a, b, c are in A.P., then 2r < ac < R (where a, b, c are the side lengths, r, R are in radius & circum radius) and STATEMENT-2: In any triangle R 2r 12. STATEMENT–1: The differential equation of all the rectangular hyperbola in xy–plane must be of order 4. and STATEMENT–2: The general equation of any rectangular hyperbola will be ax2 + by2 + 2hyx + 2gx + 2fy + c = 0 with abc + 2fgh - af2 - bg2 - ch2 0. 13. STATEMENT–1: Let f : R R, defined by f(x) = [x] + {x}3 ([.] denotes the G.I.F. and {.} denotes the fractional part) then f(x) is strictly increasing function. STATEMENT–2: f(x) is continuous every where in R Space for rough work 4 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS SECTION – III Linked Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. C14-16 : Paragraph for Questions Nos. 14 to 16 x 2 y2 Many properties of an ellipse in the standard form 2 2 = 1 can be used easily in the a b general form also. Consider an ellipse with the equation. (15x - 3)2 + (15y + 5)2 = (12x + 5y - 2)2 14. Eccentricity of the ellipse will be 1 1 (A) (B) 13 19 13 13 (C) (D) 15 19 15. Locus of foot of perpendicular from foci to tangents to ellipse will be a circle of radius 19 13 (A) (B) 56 225 19 38 (C) (D) 169 195 16. Equation of major axis of ellipse is (A) 3x + 4y - 7 = 0 (B) 12x + 5y = 0 (C) 5x - 12y = 0 (D) 5x - 12y - 5 = 0 Space for rough work 5 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II C17-19 : Paragraph for Questions Nos. 17 to 19 Let Ar (rN) be the area of region bounded by curves 63 ry2 = x and 6e2y = x. Then 17. A1 , A2 , A3 , . . . . are in (A) A.P. (B) G.P. (C) H.P. (D) none of these 18. Lim A1A 2 A3 A 2 A3A 4 A3A 4 A5 ...... n terms is n 9 9 e 1 e (A) (B) 2 9 9 1 e 1 e (C) (D) 3 4 1 1 1 lim e e e .....n terms , is A1 A2 A3 19. n 1 3 3 3 (B) e e 1 3 e (A) e 2 2 3 3 3 (D) e e 1 3 e (C) e Space for rough work 6 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS SECTION – IV Matrix Match Type Matrix-Match Type p q r s This section contains 3 questions. Each question contains statements given in two column which have to be matched. Statements (A, B, C, D) in Column I have to be A p q r s matched with statements (p, q, r, s) in Column II. The answers to these questions B p q r s have to be appropriately bubbles as illustrated in the following example. C p q r s If the correct matches are A–p, A–s, B–q, B–r, C–p, C–q and D–s, then the correctly bubbled 4 × 4 matrix should be as follows : D p q r s 20. Column I Column II (A) Number of terms in (x + y - z + w)6 is (p) 67 (B) Last two digits in 72011 is (q) 84 (C) Number of rational terms in (r) 4 1001 3 7 5 11 is (D) Remainder when 22011 is divided by (s) 43 127 is 21. Column I (Function) Column II (A) f(x) = 2x2 - ln |x| (p) strictly increasing in 0, 4 (B) f(x) = 2x + e-x (q) 3 strictly, decreasing in 2, 2 (C) f(x) = cosx + ex (r) strictly increasing in (e, ) (D) f(x) = ecosx - e-cosx (s) strictly decreasing in (-, e) Space for rough work 7 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II 22. Column I Column II (A) The distance of the point of intersection of the (p) 256 ˆ j) ˆ ˆ planes r . (2i ˆ 0, r . (4j 3k) 24, and ˆ ˆ r . (12i 7k) 24 from the origin is (B) The value of such that the planes x – 2y – z = 10, (q) 36 3x + 3y + z 8 and 2x – y + 2z = k are not able to make faces of a tetrahedron is (C) The product of distances of any vertex from the (r) 81 remaining vertices of a nine-sided regular polygon inscribed in a circle of radius 2 units is (D) If on the complex plane the numbers 72 56i 3 , (s) 144 a + b i 3 (a, b R, b 0) and 0 represent vertices of an equilateral triangle then the value of (a + b)2 is Space for rough work 8 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS PHYSICS PAPER - II SECTION – I Straight Objective Type This section contains 9 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 23. Three sources of emf, V0sint, V0cost and V0 are connected in R series as shown. RMS value of current in the circuit is V0 V 0s V in t V0 (A) (B) 0 ~ ~ R 2 R V o cs t 0 V0 2 2V0 (C) (D) . R R y 24. A refracting surface separates two medium of refractive index 1 and 2 as shown. Surface is = n1 = n2 symmetrical about x–axis. Parallel mono–chromatic x rays are incident on the surface and refracted rays are O F focused at f = 1 m from O (origin of co–ordinate system). Equation of surface is (A) x 2 y 2 2xy 0 (B) 2x 2 3y 2 4x 0 (C) 3x 2 4y 2 4x 0 (D) 3x 2 2y 2 2y 0 25. An equilateral prism produces a deviation of 60º. If prism is rotated in the plane of incident and refracted ray by an angle 30º, deviation remains same. Possible values of angle of incidence are (A) 45º and 75º (B) 15º and 45º (C) 30º and 60º (D) 35º and 80º Space for rough work 9 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II 26. A 3.6 m long vertical pipe is filled completely with a liquid. A small hole is drilled at the base of the pipe due to which liquids starts leaking out. This pipe resonates with a tuning fork. The first two resonances occur when height of water column is 3.22 m and 2.34 m respectively. The area of corss–section of pipe is (A) 25 cm2 (B) 100 cm2 (C) 200 cm2 (D) 400 cm2. 27. The following equations represent transverse waves z1 = A cos (3Kx – t) …(i) z2 = A cos (4Ky – t) …(ii) A wave is formed by the superposition of waves (i) and (ii). This wave is 3 (A) traveling in the direction making an angle tan 1 with +ve x–axis 4 4 (B) traveling in the direction making an angle tan 1 with +ve x–axis 3 3 (C) traveling in the direction making an angle tan 1 with +ve y–axis 4 4 (D) traveling in the direction making an angle tan 1 with +ve y–axis. 3 28. Peak emission from a black body at a certain temperature occurs at a wavelength . On increasing its temperature, total radiation emitted is increased 16 times. At the initial temperature, when peak radiation from the black body is incident on a metal surface, it does not cause photoemission from surface. After the increase of temperature the peak radiation from black body caused photoemission. To bring these photoelectrons to rest, a potential equivalent to the excitation energy between n = 2 to n = 3 Bohr levels of hydrogen atom is required. If work function of metal is 2.24 eV, then value of is [hc = 12400 ev – Å] (A) 3000 Å (B) 6000Å (C) 9000Å (D) 12000Å. Space for rough work 10 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS 29. An ice cube is floating in water above which a layer of a Oil lighter oil is poured. As the ice melts, interface and the c Ie nef c I t ra e uppermost level of oil will respectively ar t We (A) rise and fall (B) fall and rise (C) not change and not change (D) no change and fall 30. A hollow sphere of inner radius R and outer radius 2R is made from a material of thermal conductivity K. It is surrounded by another hollow sphere of inner radius 2R and outer radius 3R made by material of thermal conductivity 2K. The inside of smaller sphere and outside of bigger sphere are maintained at 0ºC and 70ºC respectively. Temperature of interface in steady state, will be (A) 20º C (B) 40º C (C) 50º C (D) 60º C 31. Two large fixed plates are 3 cm apart. Space between the y 1 plates is filled with a liquid having coefficient of viscosity 0.1 F 2 2 y 2 N s/m . A very thin plate of area 2 m is placed between the plates as shown. If force require to drag the plate with a y1 constant speed 1 m/s is 30 N then is y2 (A) 1/2 or 2 (B) 3 or 1/3 (C) 1 (D) 4 or ¼ Space for rough work 11 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II SECTION – II Assertion – Reason Type This section contains 4 reasoning type questions. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Code (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. (B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1. (C) Statement – 1 is True, Statement – 2 is False. (D) Statement – 1 is False, Statement – 2 is True. 32. STATEMENT – 1 If a body is thrown upwards distance covered by it, in the last second of upward motion is always equal to 5 m if g = 10 m/s2. because STATEMENT – 2 Distance covered in last second of upward motion is always equal to that covered in last second of downward motion. 33. STATEMENT – 1 In LC oscillation there is no loss of energy in the form of heat even as charge keeps changing on capacitor. because STATEMENT – 2 In LC oscillation, potential difference across capacitor differs in phase with current in the capacitor by . 2 34. STATEMENT – 1 It is necessary to have same amplitudes of interfering waves in YDSE. because STATEMENT – 2 For sustainable interference pattern in YDSE phase difference between participating waves must remains a constant with respect to time. Space for rough work 12 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS 35. STATEMENT – 1 A thick steel wire of a given length has a lower value Young's modulus as compared to a thin steel wire of same length. because STATEMENT – 2 Area of a thick wire is greater as compared to area of a thin wire. SECTION – III Linked Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. C36-68 : Paragraph for Questions Nos. 36 to 38 I. Two capacitors P and Q having capacitances C each are charged to C C potential differenceV0 and 2V0 respectively, and then connected to +P– – + Q an inductor of inductance L as shown. Switch is closed at t = 0 and at t = t0 current is found to be maximum. L S 36. Maximum current in the inductor C C (A) V0 (B) V0 2L L C C (C) V0 (D) V0 . 3L 6L 37. Charge on capacitor P at t = t0 CV0 3CV0 (A) (B) 2 2 (C) CV0 (D) 3CV0. 38. Potential difference across capacitor Q at t = t0 V0 (A) V0 (B) 2 3V0 (C) (D) 3V0. 2 Space for rough work 13 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II C39-41 : Paragraph for Questions Nos. 39 to 41 II A lift of mass M has to be raised through height h from a state of rest to state of rest, with the help of cables which can have variable tension starting from zero to maximum value 3 Mg. If process is done in shortest possible time. 39. the graph showing variation of velocity with time is (A) (B) v v t t ta 2 , ta g n =g n = a g a 2 t n =, t n =g (C) (D) v v t t ta ta g n = n= a 2 , a g t n =g t n = Space for rough work 14 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS 40. graph showing variation of power produced by tension in the cable with time is (A) (B) P P t t tan=6Mg 2 ta 6 g 2 tan=6Mg 2 n =M (C) (D) P P t t tan=6Mg 2 tan 6 g2 =M tan=Mg 2 tan M 2 = g . 41. graph showing variation of power produced by net force acting on lift, with time is (A) (B) p P t t ta 4 g n = M2 ta 4 g ta M 2 n = M2 n= g (C) (D) p p t t tan=4M 2 g ta M n= g 2 tan=M 2 g Space for rough work 15 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II SECTION – IV Matrix Match Type Matrix-Match Type p q r s This section contains 3 questions. Each question contains statements given in two A p q r s column which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II. The answers to these questions B p q r s have to be appropriately bubbles as illustrated in the following example. p q r s C If the correct matches are A–p, A–s, B–q, B–r, C–p, C–q and D–s, then the correctly p q r s D bubbled 4 × 4 matrix should be as follows : 42. Two moles of an ideal monoatomic gas is taken through a cycle P ABCA as shown in the P–T diagram. During process AB gas 8P B C follows the process PT2 = constant. Match the quantity in Column A with those in Column B. 2P A O T T 2T Column A Column B (A) During process AB (p) U > 0 (B) During process BC (q) W>0 (C) During process CA (r) Q < 0 (D) During cyclic process ABCA (s) Q > 0 43. Two capillary tubes A and B are immersed in water, one is A B straight and the other is in the form of a rectangular U–tube. h The tube A is sufficiently long and water rises in it upto height h. The lower end of the bent tube is at a depth H as shown. In H Column A, values of H is given and in Column B shape of meniscus is given. Column A Column B (A) H>h (p) Water will flow out (B) 0<Hh (q) Water will not flow out (C) H=0 (r) Convex or flat (D) H<0 (s) Concave Space for rough work 16 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS 44 Two particles A and B are situated at the origin of co-ordinate at time t = 0. Particle A is moving on a circle x2 + y2 + 120y = 0 (x and y are in m) with constant speed 2 m/s. Particle B starts moving with zero initial velocity but with constant acceleration. At time t r uu uu r = 10 s, velocity of A is found to be equal to velocity of B VA VB . Match the quantities in column – I with quantities in column – II Column – I Column – II (A) Average velocity (in m/s) of A for t = 0 to t = 10 s (p) (B) Average velocity (in m/s) of B for t = 0 to t = 10 s (q) 5 (C) Average acceleration of A (in m/s) for t = 0 to t = 10 s (r) 6 (D) Average acceleration of B (in m/s) for t = 0 to t = 10 s (s) is constant. CHEMISTRY PAPER - II SECTION – I Straight Objective Type This section contains 9 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 45. In the following sequence of reactions, end product is O OH CH3 I II III I2 / NaOH H CH3CH 2 OH, i) RO ii) CH3 Br O O O C (A) (B) CH3 CH3 O O O C C (C) OC2H5 (D) CH3 CH3 Space for rough work 17 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II 46. Phenol [C6H5OH] and water are taken in the weight ratio x : y in a stoppered flask and shaken thoroughly. After system settles down, it is observed that two layers are formed, one of which contains 70% phenol and the other 10% phenol. If the layers are equal in weight what is x : y ? (A) 2 : 3 (B) 1 : 2 (C) 3: 5 (D) 3 : 4 47. Two elements X and Y combine to form two compounds XY2 and X3Y2. When 0.1 mole of former weighs 10 grams while 0.05 moles of the latter weighs 9grams. Then the weight of 0.2 moles of X2Y is (A) 11 grams (B) 22 grams (C) 2.2 grams (D) 1.1 grams 48. Amongst the following statements I : The structure of [BrF4]+ is regular tetrahedral II : Bond order of O2 decreases by the removal of an electron III : Br3 and Br3 are having same shape and same structure IV : The hybrid orbital of phosphorous in PCl5 is sp3dxy The incorrect statements is/are (A) only II (B) I, III, IV (C) I, II, III (D) I, II, III, IV 49. Which of the following is not true? (A) Ordinary water is electrolysed more rapidly than D2O (B) Reaction between H2 and Cl2 is much faster than D2 and Cl2 (C) D2O freezes at lower temperature than H2O (D) Bond dissociation energy for D2 is greater than H2 Space for rough work 18 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS 50. Which of the following carbanions is the most stable? CH 2 CH 2 (A) NO 2 (B) CN CH2 CH2 (C) Cl (D) F 51. The incorrect statement is/are (A) Higher will be floccculation value lower will be coagulating power (B) Zeta potential is also called electrokinetic potential x (C) Freundlich adsorption isotherm is kp1/n ;n 1 m (D) Smoke is an aerosol 52. Which is NOT TRUE about polymers? (A) Polymers do not carry any net charge (B) Polymers have high viscosity (C) Polymers scatter light (D) Polymers have low molecular weight 53. Which of the following is a copolymer? (A) Buna-S (B) PAN (C) Polythene (D) PTFE Space for rough work 19 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II SECTION – II Assertion – Reason Type This section contains 4 reasoning type questions. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Code (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. (B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1. (C) Statement – 1 is True, Statement – 2 is False. (D) Statement – 1 is False, Statement – 2 is True. 54. STATEMENT 1: Magnetite Fe3O4 has the inverse spinel structure. because STATEMENT 2: This is because high spin Fe3+ has no crystal field stabilization energy and high spin Fe2+ has higher crystal field stabilization energy in an octahedral environment than in tetrahedral one. 55. STATEMENT – I: Electrophilic substitution reaction on cumene is slower than toluene. STATEMENT – II: Positive inductive effect of isopropyl group is lesser than methyl group. 56. STATEMENT – I: When solid chloride is heated with Conc. H2SO4 in presence of K2Cr2O7 deep red vapour are formed. STATEMENT – II: Deep red vapours are due to formation of CrO2Cl2 and hence the acidic radical is chloride. Space for rough work 20 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS 57. STATEMENT – I: H HO O O HOH 2C HO OH does not give effervescence with aqueous NaHCO3 solution STATEMENT – II: H HO O O HOH 2C O OH is stabilized by resonance in much the same way as a carboxylate ion. SECTION – III Linked Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. C58–60 : Paragraph for Questions Nos. 58 to 60 Compound (A) on strong heating produces a gas mixture and leaves behind the metal. The compound (A) on treatment with HCl forms a ppt(B) which is soluble in excess KCN. A on treatment with K2CrO4 forms a ppt(C), whereas (A) on treatment with KI forms a precipitate (D). Compound (A) does not give any effervescence on treatment with dil H2SO4 but give brown coloured gas on treatment with hot conc. H2SO4. 58. Compound (A) is (A) NH4NO3 (B) AgNO3 (C) Cu(NO2)2 (D) Pb(NO3)2. 59. Precipitate (B) and precipitate (D) both are soluble in (A) Dil HNO3 (B) Sodium thiosulphate solution (C) Dil NH3 (D) Both (B) and (C) 60. Which of the following is correct about precipitate (C) ? (A) It is a yellow coloured compound. (B) It is soluble in NH3. (C) It is insoluble in dil HNO3 (D) It has the same colour as that of Ag2CO3. Space for rough work 21 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II C61–63 : Paragraph for Questions Nos. 61 to 63 Order of reaction is an experimentally determined quantity. It may be zero, positive, negative and fractional. The kinetic equations of nth order reaction is 1 1 1 kt= (a x)n1 a n1 (n 1) Half-life of nth order reaction depends on initial concentration according to the following relation. 1 t1/2 n1 a Unit of the rate constant varies with the order but general relation for unit of nth order reaction is n1 1 1 Unit of k = time conc. The differential rate law for nth order reaction may be given as dx k[ A]n dt where A denotes the reactant 61. The unit of rate and rate constant are same for a: (A) zero order reaction (B) first order reaction (C) second order reaction (D) half order reaction 62. For a reaction: I + OCl IO + Cl in an aqueous medium, the rate of the reaction is given by k I OCl d IO - dt [OH ] The overall order of the reaction is (A) –1 (B) 1 (C) zero (D) 2 63. In a chemical reaction A B, it is found that the rate of the reaction doubles when the concentration of A is increased four times. The order of the reaction with respect to A is (A) 0 (B) 1/2 (C) 1 (D) 2 Space for rough work 22 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NFT (AITS) Paper - II NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS SECTION – IV Matrix Match Type Matrix-Match Type p q r s This section contains 3 questions. Each question contains statements given in two column which have to be matched. Statements (A, B, C, D) in Column I have to be A p q r s matched with statements (p, q, r, s) in Column II. The answers to these questions B p q r s have to be appropriately bubbles as illustrated in the following example. C p q r s If the correct matches are A–p, A–s, B–q, B–r, C–p, C–q and D–s, then the correctly bubbled 4 × 4 matrix should be as follows : D p q r s 64. Column – I Column – II (A) CH3 (p) Reacts faster in EAS reactions than C6H5–Cl (B) CH3 (q) On oxidation with KMnO4 produces a compound which is a raw material for producing terylene CH3 (C) CH3 (r) On nitration with conc. HNO3 and H2SO4 can produce only one mononitro product. CH3 (D) CH3 (s) On oxidation with KMnO4 produces a compound CH3 which on heating with soda lime produces C6H6. Space for rough work 23 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319 NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS NFT-9 Paper - II 65. Column I have mixture of solutions and column – II shows pH of the resulting solution. Now, match the column. Column – I Column – II (A) A saturated solution of (p) pH = 7 Mg(OH)2[KspMg(OH)2 = 4 10-12] (B) 300 ml of 0.1 M BOH + (q) Ka , Ka 2 & Ka 3 are the 100 ml. of 0.1 M HCl pKa pKa 1 pH 2 3 successive dissociation (Kb (BOH) = 104) 2 constants of H PO 3 4 (C) 300 ml. of 0.1 M BOH + (r) pH = 10 + log 2 300 ml. of 0.1 M HA [Ka = Kb = 104] (D) 0.01 M aqueous solution (s) 1 1 1 Na2HPO4 [Given that : pH = pK w pK a pKb 2 2 2 pKa ( H3 PO4 ) 4.3 ; 1 pKa ( H3 PO4 ) 8.102 ; 2 pKa ( H 3 PO4 ) 12.5 ] 3 66. Column – I Column – II (A) H3BO3 (p) Weak Bronsted acid (B) HCN (q) Weak Lewis acid (C) H3AsO4 (r) Monobasic acid (D) H3PO3 (s) Tribasic acid Space for rough work 24 Narayana IIT Academy, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 • Ph.: (011) 42707070, Fax : (011) 41828319