IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 1 www.vidyadrishti.com An education portal for future IITians Name Reg. No. PAPER 2 INSTRUCTIONS A. General: 1. This Question Paper contains 28 pages having 66 questions. 2. The question paper CODE is printed on the right hand top corner of this sheet and also on the back page (page no. 28) of this booklet. 3. No additional sheets will be provided for rough work. 4. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed. 5. Log and Antilog tables are given in page numbers 30 and 31 respectively. 6. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately. 7. Do not Tamper /Mutilate the ORS or this booklet. 8. Do not break the seals of the question – paper booklet before instructed to do so by the invigilators. B. Filling the bottom-half of the ORS: 9. The ORS has CODE printed on its lower and upper Parts. 10. Make sure the CODE on the ORS is the same as that on this booklet. If the Codes do not match, ask for a change of the Booklet. 11. Write your Registration No., Name and Name of centre and sign with pen in appropriate boxes. Do not write these anywhere else. 12. Darken the appropriate bubbles under each digit of your Registration No. with HB Pencil. C. Question paper format and Marking scheme: 13. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of four Sections. 14. For each question in Section I: you will be awarded 5 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 two (−2) mark will be awarded. 15. For each question in Section II, 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. Partial marks will be awarded for partially correct answers. No negative marks will be awarded in this Section. 16. For each question in Section III: you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this Section. 17. For each question in Section IV: you will be awarded 2 marks for each row in which your darkened the bubbles(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) in this Section. IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 2 www.vidyadrishti.com An education portal for future IITians PHYSICS SECTION – I (Single Correct Choice Type) This Section contains 6 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct. 1. A circular loop of radius R = 20 cm is placed in a uniform magnetic field 2BT= in x-y plane as shown in figure. The loop carries a current i = 1.0 A in the direction shown in figure. Find the magnitude of torque acting on the loop is (a) 0.50 N-m (b) 0.125 N-m (c) 0.25 N-m (d) 0 2. An angular metallic disc of inner and outer radii a and b respectively is rotating with angular velocity ω in the uniform magnetic field of induction B normal to the plane. The induced emf between inner and outer edge of the disc is (a) ()222Babω+ (b) ()222Bbaω− (c) B ω(a – b) (d) B ω(a + b) SPACE FOR ROUGH WORK x B 45o i y IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 3 www.vidyadrishti.com An education portal for future IITians 3. If starting from the position drawn in figure, the loop is pulled rightward with constant velocity, all the way through the magnetic field of width d (d > L) then. Which graph best shows the magnetic flux through the rectangle as a function of time? (a) (b) (c) (d) SPACE FOR ROUGH WORK Magnetic field d L w flux time 0 flux time 0 flux time 0 flux time 0 IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 4 www.vidyadrishti.com An education portal for future IITians 4. A current carrying rod AB is placed perpendicular to an infinitely long current carrying wire as shown in the figure. The point at which the conductor should be hinged so that it will not rotate. (a) A (b) B (c) C (d) somewhere between A and C 5. A rectangular loop of side a and b has resistance R and lies at a distance c from an infinite straight wire carrying l0. The current decreases to zero in time t0. ()0000,0.ttItIttt−=<< The charge flown through the rectangular loop is (a) μ0I0t0 (b) 0002abItcµ (c) 00ln2bIacRcµπ+ (d) 0002ItabRcµ 6. Three infinitely long conductors A, B and C carrying currents as shown in the figure. The position of the point lying on the straight line AC where magnetic field is zero is between (a) I1 and I2 at a distance of 3.2 cm from B (b) I2 and I3 at a distance of 3.2 cm from A (c) I1 and I2 at a distance of 1.3 cm from B (d) I2 and I3 at a distance of 1.3 cm from B SPACE FOR ROUGH WORK C l B A l l c b a C A B 2l l l 5 cm 5 cm IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 5 www.vidyadrishti.com An education portal for future IITians SECTION – II (Multiple Correct Choice Type) This section contains 4 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONE OR MORE may be correct. 7. Three voltmeters all having different resistances, are joined as shown in the figure. When some potential difference is applied across A and B, their readings are V1, V2, V3. Then (a) V1 = V2 (b) V1 ≠ V2 (c) V1 + V2 = V3 (d) V1 + V2 > V3 8. Two cells of emf E1 = 6 V and E2 = 5 V are joined in parallel, without any external load. If their internal resistance are r1 = 2 Ω and r2 = 3 Ω respectively, then (a) terminal p.d. across any cell is less than 5 V (b) terminal p.d. across any cell is 5.6 V (c) current through the cell is 0.2 A (d) current through the cells is zero if E1 = E2 9. In the circuit shown in the figure, switch S is closed at time t = 0. Select the correct statements. (a) Rate of increase of charge is same in both the capacitors. (b) Ration of charge stored in capacitors C and 2C at any time t would be 1:2. (c) Time constants of the capacitors are equal. (d) Steady state charge in capacitors C and 2C are in the ratio of 1:2 SPACE FOR ROUGH WORK C R 2C E 2R S B A V3 V2 V1 IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 6 www.vidyadrishti.com An education portal for future IITians 10. An electrical circuit is shown in the given figure. The resistance of each voltmeter is infinite and each ammeter is 100 Ω. The charge on the capacitor of 100 μF in steady state is 4 mC. Choose correct statement(s) regarding the given circuit. (a) Reading of voltmeter V2 is 16 V. (b) Reading of Ammeter A1 is zero and A2 is 1.25A (c) Reading of voltmeter V1 is 40 V. (d) EMF of the ideal cell is 66 V. SPACE FOR ROUGH WORK 100Ω A1 Ideal cell C V2 200Ω A2 V1 IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 7 www.vidyadrishti.com An education portal for future IITians SECTION-III (Integer Type) This section contains TEN questions. The answer to each question is a single digit integer ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled. 11. A steady current is set up in a cubic network composed of wires of equal resistance and length d as shown in figure. What is the magnetic field at the centre P due to the cubic network? 12. A rectangular loop of sides of length l and b is placed in x-y plane. A uniform but time varying magnetic field of strength 2201050Btitjk=++ where t is time elapsed. The magnitude of induced e.m.f. (in volts) at time t is 13. In the circuit shown, the voltage drop across the 15 Ω resistor is 30 V having the polarity as indicated. The ratio of potential difference across 5 Ω resistor and R resistance R is SPACE FOR ROUGH WORK A G H F P C B E D R 3A F G 15Ω 2A C 5Ω B 5A A 100V + -H IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 8 www.vidyadrishti.com An education portal for future IITians 14. For the circuit shown in the figure, potential difference VA – VB (in volts) is 15. Find the current (in amperes) supplied by the battery in the circuit shown in figure. 16. A proton beam passes force, without deviation through a region of space where there are uniform transverse mutually perpendicular electric and magnetic fields with 120kVEm= and B = 50 mT. Then, the beam strikes a grounded target. Find the force in 10–5 N imparted by the beam on the target if the beam current is equal to I = 0.80 mA. SPACE FOR ROUGH WORK 2/11Ω 6V D 5/11Ω 11/2Ω C 4V B 2V A 11/5Ω 8Ω 12Ω 24V IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 9 www.vidyadrishti.com An education portal for future IITians 17. A coil has 600 turns which produces 5 x 10-3 Wb/turn of flux when 3 A current flows in the wire. This produced 6 x 10-3 Wb/turn in 1000 turns secondary coil. When the switch is opened the current drops to zero in 0.2 s in primary. Find the mutual inductance in henry. 18. An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance 5.0 μF, and resulting L-C circuit is set oscillating at its natural frequency. Let Q denote the instantaneous charge on the capacitor, and I the current in the current. It is found that the maximum value of Q is 200 μC. What is the maximum value of I in A? 19. In the circuit shown in figure power factor of box is given 0.5 and power factor of circuit is given 3.2Current leading the voltage. Find the effective resistance of the box in Ω. 20. In an L-C-R series circuit, R = 150 Ω, L = 0.750 H, and C = 0.0180 μF. The source has voltage amplitude V = 150 V and a frequency equal to the resonance frequency of the circuit. What is the power factor SPACE FOR ROUGH WORK 10 Ω box IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 10 www.vidyadrishti.com An education portal for future IITians SECTION-IV (Matrix Match Type) This Section 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. 21. In the circuit L1 = L2. The switch is moved very quickly from 1 to at time t = 0, then (neglect losses in switching). Match the quantities in Column I with positive value in Column II. Column I Column II (A) ()1Current through /LVR (P) 0 (B) ()2Current through /LVR (Q) 12 (C) Energy in Total energyC (R) 1 (D) 21Energy in Energy in LL (S) ∞ SPACE FOR ROUGH WORK R V C L1 L2 1 2 IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 11 www.vidyadrishti.com An education portal for future IITians 22. Match the following Column I Column II a) Dielectric ring uniformly charged p) Time independent electrostatic field out of system b) Dielectric ring uniformly charged rotating with angular velocity ω q) Magnetic field c) Constant current in a ring 0i r) Induced electric field d) A variable current in a ring, 0siniitω= s) Magnetic moment SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 12 www.vidyadrishti.com An education portal for future IITians CHEMISTRY SECTION – I (Single Correct Choice Type) This Section contains 6 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct. 1. The correct reactivity order of following C = C /C ≡ C bonds towards BR⊕ is (a) 4 > 3 > 2 > 1 (b) 3 > 2 > 1 > 4 (c) 1 > 3 > 4 > 2 (d) 1 > 3 > 2 > 4 2. Both H2C = CH – CH2Cl (I) and CH3CH2CH2Cl (II) are primary halides. While (I) undergoes substitution by SN1 mechanism, (II) undergoes substitution by SN2 mechanism. This is due to (a) the easy leaving nature of Clө in II (b) Cl is attached to an sp2 carbon in I (c) The resonance stabilization of the incipient carbonium ion (d) steric factor caused by the propyl group 3. 2, 4-cyclohexadienone (a) exists as a ketone exclusively (b) has structural features which affect the tautomerization significantly (c) exists as an enol because of the extra stability associated with the aromatic system (d) has an enol/keto constant which is too small to measure SPACE FOR ROUGH WORK (2) (3) (1) O (4) IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 13 www.vidyadrishti.com An education portal for future IITians 4. Which of the following methods can be used to prepare allyl fluoride? (a) NaF, acetone22ClCHCHCH=→ (b) 322CHCHCHFhυ=+→ (c) 22HOCHCHCHHF∆=+→ (d) 22ClCHCHCHAgF=+→ 5. Consider the two structures (I) and (II) given above. Choose the correct statement from among the ones given. (a) I and II are canonical structures (b) Nitrogen has 10 valence electrons in one of the structures (c) I and II are tautomeric structures. (d) None of these. 6. Identify the correct statement relating to (a) It is aromatic and hence does not decolourize cold dil. KMnO4 and Br2/CCl4. (b) It is a planar cyclic structure with a conjugated system of (1, 3, 5, 7) – double bonds. (c) A stable compound C8H2-8 2K+ is obtained on treatment with potassium metal and its stabilization due to aromaticity overweights the negative charge. (d) The C – C – C bond angle corresponds to 120o for sp2 hybridised orbital and favourable for π overlap in the di-anion which has the Huckel number of 10 electrons. SPACE FOR ROUGH WORK 3NH⊕ (I) 3NH⊕ (II) IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 14 www.vidyadrishti.com An education portal for future IITians SECTION – II (Multiple Correct Choice Type) This section contains 4 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONE OR MORE may be correct. 7. A hydrocarbon ‘A’ (C7H10) on catalytic hydrogenation takes up only one equivalent of H2 forming ‘B’ (C7H12). ‘A’ with hot KMnO4 gives meso form of 1, 3-cyclopentane dicarboxylic acid. Choose the correct statement(s). (a) ‘A’ with Baeyer’s reagent gives C7H12O2 (b) ‘A’ is optically inactive (c) ‘B’ is optically active (d) ‘A’ gives same alkylhalide with HBr in the presence and absence of peroxide. 8. The regents used to convert (E) -2, 3-dibromo-2-butene to 2-butyne C = C → CH3 – C ≡ C – CH3 (a) Zn dust/Δ (b) Mg, Δ (c) NaI/acetone/Δ (d) alc.KOH 9. An alkene having molecular formula (C16H16) (shows geometrical isomerism) ()()ReductiveNaOCl3ozonolusisCHClAB→→+ Which of the following statements are correct for the above reaction? (a) ‘B’ is a salt of carboxylic acid (b) ‘B’ on decarboxylation gives an aromatic compound (c) ‘A’ is a carbonyl compound (d) ‘A’ on reduction gives 2o alcohol SPACE FOR ROUGH WORK Br Br CH3 H3C IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 15 www.vidyadrishti.com An education portal for future IITians 10. Which order is are correct regarding boiling point (a) C = C > C = C (b) C = C > C = C (c) > (d) > SPACE FOR ROUGH WORK H CH3 H H3C H H CH3 H3C H Cl H H3C H H Cl H3C Cl Cl Cl Cl CH3 Cl CH3 Cl IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 16 www.vidyadrishti.com An education portal for future IITians SECTION-III (Integer Type) This section contains TEN questions. The answer to each question is a single digit integer ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled. 11. The number of structural (including stereoisomers) isomer that could be obtained by replacing one hydrogen of propene with chlorine are 12. The number of sp2 – s sigma bonds in benzene are 13. Total number of organic products obtained from ozonolysis of cyclopentene is 14. The volume of methane (at NTP) formed from 18.3 g of sodium acetate by fusion with sodalime is 15. 11.14 g of 1, 1, 2, 2-tetrachloropropane was heated with zinc dust and the product was bubbled through ammoniacal AgNO3 [Atomic wt. of Ag = 108]. The mass of precipitate obtained is 16. The degrees of unsaturation are there in the following compound is n. Find [n], where [.] denotes greatest integer function. 17. Total number of stereoisomers formed by the given compound is SPACE FOR ROUGH WORK OH OH O IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 17 www.vidyadrishti.com An education portal for future IITians 18. CX HY (organic compound, A) 2Br, (monochlorination)hv→ Product (enantiomeric) 24Br, CClA→ No relation 2Br, FeA→ mono bromoderivative product What can be minimum number of carbon atom (x) for the organic compound A? 19. CH3 – CH2 – CH – CH2 – CH3 2Cl, (monochlorination)hvP→ Find the total number of isomeric products (P). 20. Find the number of chiral carbon atoms in sucrose? SPACE FOR ROUGH WORK CH3 IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 18 www.vidyadrishti.com An education portal for future IITians SECTION-IV (Matrix Match Type) This Section 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. 21. Match the following Column I Column II (A) CH3CH2 – CH = CH2 24(i) Hg(OAc)/HOH(ii) NaBH→ (P) CH3CH2 – CH – CH3 (B) CH3 -CH2 – CH = CH2 234(i) Hg(OAc)/CHOH(ii) NaBH→ (Q) CH3CH2 – CH – CH3 (C) CH3 -CH2 – CH = CH2 234(i) Hg(OAc)/CHCOOH(ii) NaBH→ (R) CH3CH2 – CH – CH3 (D) CH3 -CH2 – CH = CH2 224(i) Hg(OAc)/HO(ii) NaBD→ (S) CH3CH2 – CH – CH2 -D SPACE FOR ROUGH WORK CH3 C O O OH OH OH IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 19 www.vidyadrishti.com An education portal for future IITians 22. Match the following conversions in Column – I with types of reactions involved in the conversion in Column – II Column I Column II (A) (P) EAS (B) (Q) ArSN (C) (R) Radical substitution (D) (S) Aliphatic SN SPACE FOR ROUGH WORK CH3 O O2N ONa Dil. H2SO4 SO3H (via ethyl benzene) CH2 (via halo benzene) OH IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 20 www.vidyadrishti.com An education portal for future IITians SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 21 www.vidyadrishti.com An education portal for future IITians MATHEMATICS SECTION – I (Single Correct Choice Type) This Section contains 6 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct. 1. The value of ()2201dxx−∫ is (a) -2 (b) 0 (c) 15 (d) Indeterminate 2. Let f(x) be a function defined by ()()2132,14.xfxxxxdxx=−+≤≤∫ Then, the (a) maximum value of f(x) is 534 (b) maximum value of f(x) is 634 (c) minimum value of f(x) is 12− (d) minimum value of f(x) is 14− SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 22 www.vidyadrishti.com An education portal for future IITians 3. Let ()()()22sincos1100sincos,xxfxtdttdt−−=+∫∫ then (a) f(x) is a constant function (b) 04fπ= (c) 34fππ= (d) 44fππ= 4. If a line y = mx + 2 cuts the parabola x2 = 2y at points (x1, y1) and (x2, y2) such that x1 < x2, then value of m for which 21222xxxmxdx+−∫ is minimum, is (a) 3 (b) 2 (c) 13 (d) None of these SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 23 www.vidyadrishti.com An education portal for future IITians 5. The tangent to the graph of the function y = f(x) at point x = 1 form an angle 30o and at point (2, f(2)) and (3, f (3)) make angles 60o & 45o respectively with the positive direction of x-axis, then the value of ()()()3321'""fxfxdxfxdx+∫∫ (such that f” (x) is continuous) is (a) 43133− (b) 2313− (c) 433− (d) None of these 6. In [0, 1] lagrange’s mean value theorem is not applicable to (a) ()211221122xxfxxx−∀<=−∀≥ (b) ()sin,01,0xxfxxx≠== (c) f(x) = x|x| (d) f(x) = |x| SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 24 www.vidyadrishti.com An education portal for future IITians SECTION – II (Multiple Correct Choice Type) This section contains 4 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONE OR MORE may be correct. 7. For ()03,xFxtdt=∫ the tangent lines which are parallel to the bisector of first coordinate angle is (a) 13yx=− (b) 13yx=+ (c) 16yx=− (d) 16yx=+ 8. If P(x) = f(x) + f(2a – x) & f”(x) > 0, a > 0, 0 ≤ x ≤ 2a then (a) P(x) increases in (a, 2a) (b) P(x) decreases (a, 2a) (c) P(x) increases in (0, a) (d) P(x) decreases in (0, a) SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 25 www.vidyadrishti.com An education portal for future IITians 9. If ()()(),,'022fxfyxyfxyRfa++=∀∈= and f(0) = b then (a) ()102afxdxb=+∫ (b) f’(4) = f’(0) (c) Max f(x) = a + b (d) Min f(x) = a – b 10. The angle between the two curves y = [|sin x| + |cos x|] and x2 + y2 = 5, where [x] denotes the greatest integer function is (a) 2π (b) The curves are orthogonal (c) tan-1 2 (d) 12cos5− SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 26 www.vidyadrishti.com An education portal for future IITians SECTION-III (Integer Type) This section contains TEN questions. The answer to each question is a single digit integer ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled. 11. If A > 0, c, d, u, v are non – zero constants, and the graphs of f(x) = |Ax + c| + d and g(x) = -|Ax + u| + v intersect exactly at 2 points (1, 4) and (3, 1), then the value of ucA+ equals 12. If cos6cos9sin4sin,12cos5xxxdxxCxk+=−−+−∫ then the value of k is 13. The value of 12tan12tan1tan,1tantanxxdxxCxxAA−+=−+++∫ then the value of A is 14. Evaluate ()111sin1;[.]xxdxπ−++∫ is the greatest integer function. 15. Find the value of ()()512242sin3sin1233.xdxxxdx−−−++++∫∫ SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 27 www.vidyadrishti.com An education portal for future IITians 16. Let f be a twice differentiable function such that f”(x) = -f(x) and f’(x) = g(x) if h(x) = (f(x))2 + (g(x))2 and h(5) = 2, then h(10) = 17. If the tangent to the curve xy + ax + by = 0 at (1, 1) makes an angle tan-1 2 with x-axis, then abab=+ 18. {}[]2limsgnxxx→ =, where {.} and [.] represents fractional part & integer part function respectively 19. If f(x) is a non-negative continuous function ∀ x ∈ R such that ()()21,2fxfx−=+ then ()limxfx→∞= 20. 22,1xdxx∞−∞=+∫ (where [.] and |x| represents integer part function & modulus function respectively SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 28 www.vidyadrishti.com An education portal for future IITians SECTION-IV (Matrix Match Type) This Section 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. 21. Match the following Column I Column II (A) If {}()00xxtdttdt=∫∫ where 0,xxI>∉ and {x} denotes fractional part of x, then set of x (P) (9, 12) (B) All possible set of x > 0 in which solution of belongs (Q) 1110,53 (C) The constant a > 0 such that 1100cotaaanxdxxdx−−=∫∫ (R) (0, 1) (D) If a is an arbitrary constant and satisfying (a – [|sin x|])! = 3!. 5!. 7! Where [.] denotes G.I.F. then set in which a belongs. (S) (0, 3) SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 29 www.vidyadrishti.com An education portal for future IITians 22. Match the following Column I Column II (A) Let 3123530xxxx++= where [x] denotes the greatest integer function of x and x is a natural number chosen from 1 to 100. Then the probability that x satisfies the given equation is (P) 2940 (B) In a group of equal number of men and women 10% of men and 45% of women are employed. The probability that a candidate is chosen from the group is employed is (Q) 1621 (C) The probability that a randomly chosen number n from 1 to 50 satisfies the equation n2 – 50n + 100 > 0 is (R) 3100 (D) The odds against A solving a problem are8 to 6 and the odds in favour of B solving the problem is 14 to 10. Then the probability that if both of them try then the problem is solved is (S) 1120 SPACE FOR ROUGH WORK IIT-JEE 2011 4th Test Series, Paper2 www.vidyadrishti.com 30 www.vidyadrishti.com An education portal for future IITians SPACE FOR ROUGH WORK Please send your feedback to www.vidyadrishti.com/feedback.php