PHYSICS (MAIN) PART – A PHYSICS SECTION I: (SINGLE CHOICE QUESTIONS) This section contains 30 Multiple Choice Questions. Each question has four choices (1), (2), (3) and (4) out of which ONLY ONE is correct. 1. A square plate ABCD of mass 10 kg and side 1 m is placed on a frictionless surface. Two men having masses 85 kg & 35 kg are initially at the corners A & B respectively. What is magnitude of displacement of plate when they move along the diagonals and reach to corners C & D respectively? (1) 1 m (2) 5 m (3) 12 m (4) 13 m 2. Consider a uniform thin hemispherical shell. A, B and C are three points on the circular base of hemisphere, such that A is the centre. Let the gravitational potential at points A, B and C be VA, VB, VC respectively. Then (1) V A > V B >V C (2) V C > V B >V A (3) V B >V A and V B > V C (4) V A = V B =V C 3. A nucleus of mass M m is at rest and decays into two daughter nuclei of mass 4. When the gap is closed without placing any object in the screw gauge whose least count is 0.005 mm, the 5th division on its circular scale with the reference line on main scale. When a small sphere is placed, reading on main scale advances by 4 divisions, whereas circular scale reading advances by five times to the corresponding reading when no object was placed. There are 200 divisions on the circular scale. The radius of the sphere is (1) 4.100 mm (2) 4.050 mm (3) 2.100 mm (4) 2.050 mm 5. Figure shows a cubical block of side 10 cm and relative density 1.5 suspended by a wire of cross sectional area 10–6 m2. The breaking stress of the wire is 7 × 106 N/m2. The block is placed in a beaker of base area 2 200 cm and initially i.e. at t = 0, the top surface of water & the block coincide. There is a pump at the bottom corner which ejects 2 cm3 of water per sec. The time at which the wire will break is (g =10 m/s2) (1) 40 s (2) 80 s (3) 100 s (4) 120 s 6. M 3M & each 4 4 M and m is mass defect. Speed of light is c. The speed of daughter nucleus of mass is : 4 m 2m 6m (1) c (2) c (3) c (4) c M m M m M M If the magnitude of tangential and normal accelerations of a particle moving on a curve in a plane be constant throughout, then which of the following represent the variation of radius of curvature with time? CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 1 PHYSICS (MAIN) (1) r (2) r t 7. r t (4) r t t A sphere of radius R, mass M0 is filled with a liquid of density 0.This sphere is under pure rolling on a horizontal surface as shown in figure. The kinetic energy of sphere is (liquid is non-viscous) 5 14 M 0V 2 R 3 0 V 2 6 23 5 4 3 2 (3) M 0 R 0 V 6 3 (1) 8. (3) 1 14 M 0V 2 R 3 0 V 2 2 23 2 1 4 M 0V 2 R 3 0 V 2 (4) 3 23 (2) A current carrying uniform square frame is suspended from hinged supports as shown in the figure such that it can freely rotate about its upper side. The length and mass of each side of the frame is 2m and 4kg respectively. A uniform magnetic field B 3iˆ 4jˆ T is applied. When the wire frame is rotated to 45° from vertical and released it remains in equilibrium. What is current in the wire? (1) 4.5 A (2) 10 A (3) 7 A (4) 2 A 9. A block & wedge system is released from rest from the position as shown. After some time the block is moving with speed v on horizontal surface. What is work done by gravity on the block? (neglect friction) 1 m 1 (1) 1 mv 2 (2) mv 2 2 M 2 1 1 (3) Mv 2 (4) m M v 2 2 2 m M 10. The deflection of a moving coil galvanometer falls from 60 divisions to 12 divisions for the same value of current in the circuit, when a shunt of 12 is connected. The resistance of the galvanometer is (1) 2 ohm (2) 20 ohm (3) 48 ohm (4) 96 ohm 11. A charged capacitor discharges through a resistance R with time constant . The two are now placed 1 in series across in AC source of angular frequency . The impedance of the circuit will be R (1) (2) R (3) 2R (4) 2R 2 CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 2 PHYSICS (MAIN) 12. A condenser of capacity 6 μF is fully charged using a 6-volt battery. The battery is removed and a resistance less 0.2 mH inductor is connected across the condenser. The current which is flowing through the inductor, when one-third of the total energy is in the magnetic field of the inductor is:(1) 0.1 A (2) 0.2 A (3) 0.4 A (4) 0.6 A 13. The momentum of an electron in an orbit is h / where h is a constant and is wavelength associated with it. The nuclear magneton of electron of charge e and mass me is given as eh n . The dimensions of n is 3672me (1) ML2 I (2) ML3 I (3) L2 I (4) ML2 14. Davisson Germer experiment is experimental proof of :(1) Wave nature of light (3) Wave nature of electron (2) Particle nature of light (4) Particle nature of electron 15. Figure shows the adiabatic curve for 2 moles of an ideal gas. dP The Bulk modulus i.e. B at the point P will be : dV / V T T (1) R 1 0 (2) 2R 1 0 V0 V0 V (T0, V0) P 45 T 2RT0 (4) None of these V0 The upper one third of an inclined plane with inclination is perfectly smooth, while the rest part is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the rest part is given by3 3 3 3 (1) sin (2) cos (3) tan (4) cot 2 2 2 2 (3) 16. 17. In a YDSE experiment = 540 nm, D = 1m, d = 1 mm. A thin film is pasted on upper slit and the central maxima shifts to the point just in front of the upper slit. What is the path difference at the centre of the screen? (1) 540 nm (2) 270 nm (3) 500 nm (4) 810 nm 18. In figure, a solid cylinder of 5 cm radius is positioned on a frictionless plane inclined at 30º above horizontal. A force F is exerted by a string wrapped around the cylinder. When F has a certain critical value the centre of mass of the spool does not move. When this is the case, what is the angular acceleration of the spool? (1) 200 rad/s2 (2) 340 rad/s2 (3) 150 rad/s2 (4) 100 rad/s2 19. F 30 An ideal monatomic gas obeys the law PV X = constant. For what value of x, it has negative molar specific heat– (1) x > 1.67 (2) x < 1.67 (3) 1 < x < 1.4 (4) 1 < x < 1.67 CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 3 PHYSICS (MAIN) 20. A bead of mass 'm' is released from rest at A to move along the fixed smooth circular track as shown in figure. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point P0 described by the angle '' ( 0) would (g = 10 m/s2) (1) increase with (2) decrease with (3) remains constant (4) first increase with then decrease A R P0 21. A stone is hung in air from a wire which is stretched over a sonometer. The bridges of the sonometer are l1 distance apart when the wire is in unison with a tuning fork of frequency f. When the stone is completely immersed in water, the length between the bridges is l2 for re-establishing unison. The specific gravity of the material of the stone is: l l l2 l2 (1) 2 1 2 (2) 2 1 2 (3) f 2 (4) f 1 l1 l2 l1 l2 l1 l2 22. In a circuit, voltmeter reads 3V and the ammeter reads 2A. Then which of the following is incorrect ? (1) the resistance R is 1 ohm (2) the emf E is 12 V (3) the current in 3 resistor is 1 A (4) the emf E is 9 V 23. 6V 3 2 IR R V A 2.5 E A uniform rod of length l is in equilibrium with help of two strings as shown. Just after string on the right is cut, angular acceleration of rod is , horizontal component (to the right) of acceleration of center of mass is ax & vertical component (downward) is ay . Then, l l (2) ax cos , a y sin 2 2 l l (3) a y ax cot (4) a y a x sin 2 2 A diatomic gas goes through a process U W 0 . Now if (1) = 2, then process is adiabatic (2) = 0, then process is isochoric 5 (3) = , then the process is isobaric 2 5 (4) = , then the process is isothermal 2 (1) ax 0, a y 24. 25. l 2 A uniform wire of mass m, length l, cross sectional area A & Young’s modulus Y is rotating with constant angular velocity about an axis through its one end & perpendicular to it. What is elastic potential energy stored in the wire ? (Neglect gravity) m 24l3 m 24l3 m 24l3 m 24l3 (1) (2) (3) (4) 15 A Y 8AY 9AY 5AY CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 4 PHYSICS (MAIN) 26. A rod of length is in motion such that its ends A and B are moving d along x-axis and y-axis respectively. It is given that = 2 rad/s dt always. P is a fixed point on the rod. Let M be the projection of P on x-axis. In the time interval in which changes from 0 to . Pick the 2 correct statement. (1) The acceleration of M is always directed towards right (2) M executes SHM (3) M moves with constant speed (4) M moves with constant acceleration 27. The acceleration of a particle moving along x-axis is a = – 100x + 50. It is released from x = 2. Here ‘a’ and ‘x’ are in S.I units. The speed of the particle at origin will be (1) 10 2 m/s (2) 1.5 m/s (3) 10 m/s (4) None of these 28. An infinitely long metal cylinder of radius R and surface charge density is placed symmetrically with an imaginary surface of the shape of a prism. The length of prism is L and its 3 sides are all equal to 3R. The flux through the prism is RL RL RL 2RL (1) (2) (3) (4) 3 0 2 0 0 0 29. A conductor of sufficient length and negligible resistance is moved with constant velocity v in a crossed magnetic field over conducting rails of resistance per unit length as shown in figure. Which of the following statements is correct? (1) force required to move the conductor with constant velocity is constant (2) heat generated in the circuit per unit time is constant (3) current in the circuit is constant (4) current in the circuit is variable 30. A soap film of surface tension S forms a sub-hemisphere on a horizontal ring of radius R as shown. If mass of film is m then its radius of curvature is 2R 2 S 3R 2 S 4R 2 S R 2 S (1) (2) (3) (4) mg 2mg mg mg v R CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 5 (CHEMISTRY) PART B CHEMISTRY Straight Objective Type This section contains 30 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE OPTION is correct. 31. The product of the following reaction, CH3 H / H 2O ? O O H would be (1) CH2 CH3 CH3 (2) O OH O OH (3) (4) O Cl (i ) CH CHO Product Mg 3 32. Br Et 2O ( ii ) aq. NH 4Cl The product of above reaction is O = C CH3 (1) Cl (2) Br CH(OH)CH3 Br (3) COCH3 (4) CH(OH)CH3 Cl 33. When 150 ml of ozonized oxygen was passed through red hot tube, the volume increased by 10 ml then the volume percentage of ozone in the sample is (1) 25% (2) 51% (3) 13.33% (4) 17.84% 34. The volume of water needed to dissolve 1 mg of PbSO4 (Ksp = 1.44 108 M2) at 25°C is approximately (molar mass of Pb = 207) (1) 10 ml (2) 27 ml (3) 43 ml (4) 80 ml 35. Which of the following is a salt of sulphurous acid ? (1) NaHSO4 (2) Na2S2O 3 (3) Na2S4O 6 (4) Na2S2O 5 The solution of weak acid H2N2O2 decomposes spontaneously at room temperature. The gaseous product obtained is (1) NO (2) N2O (2) N2 (4) NO2 The correct statement for different solvents at constant temperature is (1) The higher is the molar mass of solvent larger is Kb. (2) The higher is the molar mass of solvent smaller is Kb. (3) The higher is the molar mass of solvent larger is Kf. (4) The higher is the molar mass of solvent smaller is Kf. Which of the following are true for 3Methyl butanone (S1) This compound is an isomer of 4penten1ol (S2) It may be prepared by acidic Hg2+ catalyzed hydration of 3methyl1butyne (S3) It may prepared by CrO3 oxidation of 2methyl2butanol (S4) It can not give positive iodoform test. (1) S1, S2 (2) S1, S3 (3) S3, S4 (4) S2, S4 36. 37. 38. PACE CENTRE : MUMBAI | DELHI | NASIK | LUCKNOW | KANPUR | PUNE | GOA | PATNA 6 (CHEMISTRY) 39. 40. 41. Boric acid is polymeric due to : (1) its acidic nature (2) the presence of hydrogen bonds (3) its monobasic nature (4) its geometry The correct facts regarding shape and hybridization of complexes [CuCl5]3 and [Ni(CN)5]3 will be (S1) both have similarly hybridized states on central metal ion (S2) both have different shapes (S3) both have different hybridized states on central metal ion (S4) both have similar shapes (1) S1, S2 (2) S2, S3 (3) S3, S4 (4) S1, S4 On the basis of following graphs between volume of gas adsorbed and pressure of gas V(cc/g) V(cc/g) I II P(torr) P(torr) which of the following is/are correct ? (S1) graph I is of chemisorption (S3) graph II is of chemisorption (1) S1, S2 (2) S2, S4 (S2) graph II is of physiosorption (S4) graph I is of physiosorption (3) S3, S4 (4) S1, S3 42. One litre sample of hard water contains 136 mg of CaSO4 and 190 mg of MgCl2. What is the total hardness of water in terms of CaCO3 ? (1) 100 ppm (2) 200 ppm (3) 300 ppm (4) 150 ppm 43. NaCl 1. H Blue solution. A B NaOH yellow solution 2. H 2 O 2 H 2SO4 (orange red) The blue colour obtained at the end of reaction is due to salt formation. The oxidation number of the metal in the salt is (1) 3 (2) 6 (3) 2 (4) 7 Electron is now a days considered as probability wave function with quantized angular momentum and energy. The angular momentum of e in 1s orbital is. 44. h h h (3) 6 (4) 12 2 2 2 The number of atomic orbitals involved in the hybridization at central metal ion of [K3Fe(CN)6] are (1) 0 45. (2) 2 (1) s p x p y p z d z d xy (2) s px p y pz d z d x (3) s px p y pz d x y d xy (4) s p x p y p z d xy d yz 2 2 2 46. 2 Which is not correct route that can prepare HO 2 y2 OH ? CH3 CH–CH3 O / (1) dil. H SO 4 2 2 Conc. H2SO4 NaOH ( fuse ) H H3C CH–CH3 (2) O2 / dil. H2 SO 4 KMnO 4 PACE CENTRE : MUMBAI | DELHI | NASIK | LUCKNOW | KANPUR | PUNE | GOA | PATNA 7 (CHEMISTRY) O NO2 (3) O–C–CH3 Sn / HCl NaNO / HCl steam 2 (4) NO2 47. LiAlH 4 HI (1 mol ) O–CH3 In the given reaction sequence X Br2 / H2O Y Z the reactant X is (1) 48. (2) (3) (4) Diazocoupling reaction in aromatic compounds is an electrophilic substitution reaction. In which of the following reaction the ring subsitution is most suitable for diazocoupling reaction. (1) (3) + (2) + + (4) + 49. Mention true (T) and false (F) out of the following S1 : Sucrose gives negative tests with benedict's and Tollen's solutions. S2 : Sucrose does not form an osazone S3 : Sucrose does not undergo mutarotation S4 : Octamethyl derivative of sucrose, on hydrolysis, gives 2, 3, 4, 6-tetra-O- methyl-D-glucose and 1, 3, 4, 6tetra-O- methyl D-fructose S5 : One mole of sucrose on acid hydrolysis yields one mole of D-glucose and one mole of D-fructose Codes : (1) T T T T T (2) F T F T F (3) F F F T T (4) T F F F T 50. Salicin (structure given below) is a glycoside, found in the bark of willow tree, used in relieving pain. Observe the following reaction of salicin dil. HCl +Q Salicin (1) P is D- glucose (2) Q is 2-hydroxybenzylalcohol (3) Q can be converted to a modern analgesic (pain killer), aspirin (4) The above reaction occurs through a carbocation Mention true (T) and false (F) out of the following (1) T T T T (2) F T T F (3) F F T T (3) T F F T PACE CENTRE : MUMBAI | DELHI | NASIK | LUCKNOW | KANPUR | PUNE | GOA | PATNA 8 (CHEMISTRY) 51. The correct option for products P and Q in the following sequence of reqction is / are O 15 O || C C – NH2 Br2 / KOH NH2 + CH3 P O || CH3 – C – Cl Br2 / Fe H3O+ / NO2 NO2 Q CH3 15 NH2 NH2 CH3 NH2 NO2 15 (1) P is + NO2 (2) P is NH2 NO2 CH3 + NO2 CH3 CH3 15 NH2 Br 15 NH2 (3) Q is NH2 CH3 Br + NO2 CH3 (1) 1, 3 52. NO2 (4) Q is (2) 1, 4 NH2 Br Br NO2 + NO2 CH3 (3) 2, 3 CH3 (4) 2, 4 Which of the following is a nonreducing sugar ? (1) OHCH2 C (CHOH)3 CH2OH (2) || O (3) (4) Q 53. R S T (U) The product U is (1) (2) (3) (4) PACE CENTRE : MUMBAI | DELHI | NASIK | LUCKNOW | KANPUR | PUNE | GOA | PATNA 9 (CHEMISTRY) 54. Under the same reaction conditions, initial concentration of 1.386 mol dm–3 of a substance becomes half in k 1 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio k of the rate 0 constant for first order (k1) and zero order (k0) of the reaction is. (1) 0.5 mol–1 dm3 (2) 1.0 mol dm–3 (3) 1.5 mol dm–3 (4) 2.0 mol–1 dm3 55. For a certain reaction the variation of the rate constant with temperature is given by the equation ln kt = ln k0 + 0.0693 t (t 0°C) The value of the temperature coefficient of the reaction rate is therefore (1) 0.1 (2) 1.0 (3) 10 (4) 2 56. 60 ml, 11.2 V H2O2 sample is oxidised by 0.1 M KMnO4 and 0.1 M K2Cr2O7 solution in acidic medium separately then. (1) volume of KMnO4 used is more than K2Cr2O7 (2) volume of KMnO4 used is less than K2Cr2O7 (3) volume of KMnO4 used is equal to K2Cr2O7 (4) Can not be calculated. 57. The standard reduction potential of Cu2+/Cu and Cu2+/Cu+ are 0.337 and 0.153 respectively. The standard electrode potential of Cu+/Cu half-cell is (1) 0.184 V (2) 0.827 V (3) 0.521 V (4) 0.490 V 58. The standard reduction potentials at 25°C for the following half reactions are given against each Zn2+(aq) + 2e¯ Zn(s), –0.762 V 3+ Cr (aq) + 3e¯ Cr(s), –0.740 V 2H+ + 2e¯ H2(g), 0.00 V 3+ 2+ Fe + e¯ Fe , 0.77 V Which is the strongest reducing agent (1) Zn (2) Cr (3) H2(g) (4) Fe3+(aq) 59. The Van der Waals equation of state for a non-ideal gas can be rearranged to give PV V a = – for 1 mole of gas. The constants a & b are RT V b VRT positivenumbers . When applied to H2 at 80K, the equation gives the curve as shown in the figure. Which one of the following statements is(are) correct ? (S1) at 40 atm the two terms V/(V - b) & a/VRT are equal (S2) at 80 atm the two terms V/(V - b) & a/VRT are equal (S3) at a pressure greater than 80 atm, the term V/(V - b) is greater than a/VRT. (S4) at 60 atm the term V/(V - b) is smaller than 1 (1) S1, S2 60. (2) S2, S3 a VRT (3) S3, S4 Match list I with list II and select the correct answer List I A. van Arkel method 1. B. Solvay process 2. C. Cupellation 3. D. Poling 4. 5. A B C D (1) 2 1 3 4 (2) (3) 2 3 5 4 (4) (4) S1, S4 using the codes given below the lists . List II Manufacture of caustic sods Purification of titanium Manufacture of Na 2CO 3 Purification of copper Refining of silver A B C D 4 3 2 5 5 1 3 4 PACE CENTRE : MUMBAI | DELHI | NASIK | LUCKNOW | KANPUR | PUNE | GOA | PATNA 10 MATHEMATICS (MAIN) PART – C MATHEMATICS SECTION I: (SINGLE CHOICE QUESTIONS) This section contains 30 Multiple Choice Questions. Each question has four choices (1), (2), (3) and (4) out of which ONLY ONE is correct. 61. 1/ x If lim 1 x ln 1 b2 (1) 4 x 0 2b sin 2 , b 0 and ( , ] , then the value of is (2) 3 (3) (4) 2 n 62. 63. r n C r . r C m is equal to r 1 m 0 n (1) 2 1 (2) 3n 1 6 Value of 68. 6 (3) 384 (4) 54 (2) (1, 8) (3) [1, 9] (4) [2, 5] A circle with its centre on the line y x 1 is drawn to pass through the origin and touch the line y x 2 . The centre of the circle is 1 2 67. 10 If | z 1| | z 3 | 8, then the range of values of | z 4 |, (where i 1) is 1 2 (1) , 66. 4 (2) 55 (1) (0, 7) 65. (4) none of these Total number of divisors of n 2 . 3 . 5 . 7 that are of the form 4 + 2, (where I+ ) is equal to 5 (1) 385 64. (3) 3n 2 n (2) (–1, 0) (3) 1 1 , 2 2 (4) (–1, 2) If a circle passes through the point (1, 2) and cuts the circle x 2 y 2 4 orthogonally, then the equation of the locus of the centre is (1) x 2 y 2 3x 8y 1 0 (2) x 2 y 2 2x 6y 7 0 (3) 2x 4y 9 0 (4) 2x 4y 1 0 x 2 y2 1, and having its centre (0, 3) is 16 9 7 (1) 4 (2) 3 (3) (4) 12 2 1 3 1 1 Four persons independently solve a certain problem correctly with probabilities , , , . Then the 2 4 4 8 The radius of the circle passing through the foci of the ellipse probability that the problem is solved correctly by at least one of them is (1) 69. 235 256 (2) 21 256 (3) 3 256 (4) 253 256 . Let the slope of the curve at each point ( x, y ) be 6 A curve passes through the point 1, y y sec , x 0 . Then the equation of the curve is x x 1 1 y y 2y 2y (1) sin log e x (2) cos ec log e x 2 (3) sec log e x 2 (4) cos log e x 2 2 x x x x CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 14 MATHEMATICS (MAIN) 70. If x 2 a b x 1 a b 0 , where a, b R , then the values of a for which equation has unequal real roots for all values of b is (1) , 71. The line 1, (2) (3) , 1 (4) none of these x y 1 meets the axis of y and axis of x at A and B respectively. A square ABCD is constructed on 3 4 the line segment AB away from the origin, the coordinates of the vertex of the square farthest from the origin are (1) (7, 3) (2) (4, 7) (3) (6, 4) (4) (3, 8) 72. The function f : 0, 3 1, 29, defined by f(x) = 2x3 – 15x2 + 36x + 1, is (1) one – one and onto (2) onto but not one – one (3) one – one but not onto (4) neither one – one nor onto 73. The equation of a plane passing through the line of intersection of the planes x 2 y 3 z 2 and 2 from the point (3,1, 1) is 3 x y z 3 and at a distance (1) 5 x 11 y z 17 (2) 2 x y 3 2 1 (3) x y z 3 (4) x 2 y 1 2 If xy m 2 9 be a rectangular hyperbola whose branches lie only in 2nd and 4th quadrant, then 74. (1) | m | 3 (2) | m | 3 (3) | m | 3 (4) | m | 3 ln 3 75. The value (1) 76. 1 3 ln 4 2 (2) 1 3 ln 2 2 (3) ln 3 2 (4) 1 3 ln 6 2 The set of values of p for which the equation ln x px 0 possess three distinct roots is (1) 0, 77. x sin x 2 sin x2 sin(ln 6 x 2 )dx is ln 2 1 e (2) 0, 1 (3) 1, e (4) 0, e sin 2x dx a cot 1 b tan 2 x c , then 4 sin x cos x (1) a 1, b 1 (2) a 1, b 1 If (3) 4 a 1, b 1 (4) none of these x 78. ln t 1 dt , x 1 . Then F e equals , where f x 2 1 t t x 1 Let F x f x f (1) 79. 1 2 (2) 0 (3) 1 (4) e If three points z1 , z 2 , z 3 are selected on z 1 , then area of ABC with 1 1 1 A z1 , B z 2 , C z3 is z1 z2 z3 (1) 80. z1z2 z 3 Range of f x ln (2) cos x cos x z1z2 z 2 z3 z3 z1 (3) 1 (4) 0 1 , x 0, is 2 CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 15 MATHEMATICS (MAIN) ln e 1 , ln 2 e (1) 81. (2) 1 1 e (3) ln 1 , ln 2 (4) e ln 1 e , ln 2 1e 2 x cos , x 0 Let f x where x R, then f is x 0 , x0 (1) differentiable at x = 0 and at x = 2 (2) differentiable at x = 0 but not differentiable at x = 2 (3) not differentiable at x = 0 but differentiable at x = 2 2 82. Sn 2 1 n 1 n 1 ! (2) 1 36 The value of the expression Let log 1 (3) n 1 n 1 ! 1 n 1 n 1 ! (4) none of these C1 4 36 C4 7 36 C7 ...... 34 36C34 is (1) 36 236 1 84. (4) None of these 2 111 1 2 2 1 n n 2 ........ 2 , then 2 1 1 2 ! 2 2 3 ! n n n 1 ! (1) 1 83. none of these (2) 36 235 1 (3) 12 235 1 (4) 3.237 12 | z |2 | z | 1 2 , where z is a complex number, then z 3 2 | z | (1) lies outside a circle of radius 5 with centre at the origin (2) lies inside a circle of radius 5 with centre at the origin (3) lies inside a circle of radius 5 3 with centre at the origin 85. If | z i Re(z) || z Im(z) |, (where i (1) Re(z) 2 86. 17 21 Re(z) Im(z) 2 n cos , then 2n 2n 2 (2) n (1, 4] (3) n [1, 4) (4) none of these (4) n (4,8) (2) (4) 13 21 (2) Non integral rational roots (4) Complex roots 2 2 2 ( ) If x, y, z are real and 4x 9y 16z 6xy 12yz 8zx 0 , then x, y, z are in : xyz ¹ 0 (1) A.P. 90. (3) 19 20 (3) 21 21 2 The equation x k 1x k 2 0, k 1 , k 2 l , cannot have (1) Integral roots (3) Irrational roots 89. Im(z) 2 7 girls G1, G2, G3,...G7 are such that their ages are in order G1<G2<G3<.....<G7. Five girls are selected at random and arranged in increasing order of their ages, then the probability that G5 & G7 are not consecutive, is (1) 88. 1), then z lies on Let n be a positive real such that sin (1) n [3,5] 87. (2) (4) none of these (2) H.P. (3) G.P. (4) None of these The number of ways in which nine boys and five girls can be arranged in two vans each having numbered seats, three in the front and five at the back such that at least four girls should always sit together is 11 P9 5! k, then k is (where [.] represent greatest integer function) (1) 2 (2) 3 (3) 5 (4) 6 CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 16 IIT-JEE 2015 MOCK TEST PAPER JEE (MAIN) ANSWER KEY Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans. 1 [1] 11 [3] 21 [2] 31 [C] 41 [A] 51 [C] 61 [4] 71 [2] 81 [2] Note : 2 [4] 12 [4] 22 [4] 32 [D] 42 [C] 52 [C] 62 [2] 72 [2] 82 [1] 3 [4] 13 [3] 23 [ 3] 33 [C] 43 [B] 53 [C] 63 [3] 73 [1] 83 [4] 4 [4] 14 [3] 24 [3] 34 [B] 44 [A] 54 [A] 64 [3] 74 [1] 84 [2] 5 [3] 15 [2] 25 [1] 35 [D] 45 [B] 55 [D] 65 [3] 75 [1] 85 [4] 6 [2] 16 [3] 26 [2] 36 [B] 46 [B] 56 [A] 66 [3] 76 [1] 86 [4] 7 [1] 17 [3] 27 [1] 37 [A] 47 [D] 57 [C] 67 [1] 77 [2] 87 [1] 8 [2] 18 [1] 28 [3] 38 [A] 48 [C] 58 [A] 68 [1] 78 [2] 88 [2] 9 [1] 19 [4] 29 [3] 39 [B] 49 [A] 59 [C] 69 [1] 79 [4] 89 [2] 10 [3] 20 [3] 30 [3] 40 [B] 50 [A] 60 [C] 70 [2] 80 [3] 90 [4] Result available on our website after 7 days of the test. www.reports.iitianspace.com Detailed solution to this test is available on Monday (13- 01-2014) after 10.00 pm on our website.: www.iitianspace.com CENTERS : MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA

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