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Published in: AIEEE
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Parteek S / Jaipur

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Teaches: Mental Maths, Chemistry, English, Logic, Mathematics, Economics, NSTSE, AIEEE, BITSAT, IIT JEE Mains, WBJEE

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  1. AIEEE•S 1. 2. MOCK TEST Physics When an impurity is doped into an intrinsic semiconductor, the conductivity of the semiconductor : (b) decreases (g) increases (C) remains the same (d) becomes zero A singly ionized helium ion in ground state absorbs a photon of wavelength 10 nm. Assuming that entire photon energy is taken up by the electron, find the KE of electron. (b) 54.4 ev (a) 1242 ev (d) 13.6 (c) 69.8 ev The material of the suspension wire and spring of moving coil galvanometer is : (a) steel (b) copper 8. (119. Ile Electromagnetic are broduced by : (a) a static charge (b) a moving chårge / / (g) an accelerating charge/ (dj chargeless paticle A of frequency 500 HL is travelling with a Nelo&ity of 360 m/s. How far apart are two points 600 out of phase (b) 0.18m (d) 0.12 m (c) 0.56 m Two thermally insulated chambers are as showri- in figure. Mark the con-ect option regarding this. ( (c) phosphor-bronze (d) •brass 4. A parallel plate capacitor is made up of 'two b plates having area 10 cm2 and are separated by 2 mm. There is a vacuum in benveen the plates. If we double the amount of initial charge on the capacitor, then what would be the final , capacitance ? (3) 8.85 xlo 12 F (by 43425 x10 'l? F (c) li.7 x 10 F (d) None of these C 5, Iny decay, the : (a) mass number changes by one (b) N changes one •vhile Z remains unchanged (9 N and%rerhainirnchanged while nucleus comes from excited state to ground state or Jess excited'tate (d) åndZ bothdiange by one 6. Conductivity of a metal depends on : / (a) natured material (b) ,iemperyture (b) both (if neither (a) nor (b) Insulating Conducting Conducting B A c Insulating Fig-2 (a) In Fig. I, thermal equilibrium of A) B andC can be achieved, and hence final temperatures of A? B and C are same (b) In Fig. thermal equilibrium of A, B andC would be achieved (c) Both (a) and (b) are right (d) (b) is right but (a) is wrong A panicle executes simple harmonic motion with a frequency 'v. The frequency with which the kineüc energy oscillates is : (d) zero A beam of certain monochromatic light is incident on a plane surface, which absorbs 80% of the light, and rest has been reflected. If the incident beam can-ies 20 'W of power, find the force exerted by it on the surface. (b) 2.66 N (f
  2. 12. Particles each of mass m are falling into weighing pan from height h at a rate of n particles per sec. Find 'the reading of weighing pan after tirne t, if collision of particle with weighing pan is inelastic. perfecdy Neglect oscillation of weighing pan (a) mgnt (c) nignt+ tnnan (d) None of the above h 13. 14. Electric flux crossing the surface S, which encloses a charge q, will be maximum if surface (b) cube (a) spherical (c) cylindrical (9 same in all three A spool of thread rests as shown in figure on a level tabletop. The thread is pulled gently so that there is no slippage at P} the point of contact beä&een the spool and tne tabletop. For each of the thread positions a through d, 16. Q 17. 18. c 19. (b) 11.3 kev (a) 69.5 kev (d) 13.6 kev At time t = O, number of nuclei of a radioactive s(ubstance are 100. At t —Is these nurnbets become 90. Find the number of nuclei att 2s. (b) 72(Q (9) 81 (d) 92 (C 100 Jn a region of free spacé theßléttric;field at i - 32j - 64ic) same instant of time is, is field mignetic the and = (0.2i + 0.053 ej.2Ü)pTFD'etemine the poynting vectort for these fields. (a) 11.52i- 28.8 j (b) (c) 10.21 11.52 j (d) 41.52i-10.2j An ideal •monoatomic gas is confined in a cylinder, fitted with piston, which is connected to spring as shown in figure. The gas is heated by a small electric heater until the piston 'moves out slowly by 0.1 m. Find the work done by the gas. Spring constant = 8000 N/rn, piston area = 8 x 10-3 rn2, atmospheric pressure = 105 Pa. mark the correct b about statement which way the spool will roll. Note that in position d the line deterrnined by the thread passes through point P ? a (a) 40 J (c) 120 J Atmosphere (b) 80 J (d) 60J (a) For a the torque about P is clockwise, so the spool rotates clockvfise and rolls to the right, winding the string oh the pool (b) For c the torque abeutæ counter clockwise, so the spoor-rotates counter clockwise and rolls tb the left (c) For b the* torqUe; about P is counterclockwise, •o the spool rotates counterclockwise and rolls to the right (Y) All Of the above C 15. Find the maximum pötential difference which may bé 'applié& across an X-ray tube with tungsten without emitting any aråcteristic K or L X-ray, The energy levels of umgstenatoms are as follows : (ICsfielP69.5 kev, L shell—11.3 Rev, M shell—2.3 keV) A circular coil of wire consisting of 500 turns having radius 4-cm is placed between the poles of a large electromagnet, where the magnetic field is uniform and at an angle of 600 with the plane of coil as shown. The field decreases at the rate of 0.2 T/s. What are the direction and the magnitude of induced emf ? (a) 0.435 V, anticlockwise as seen from left (b) 0.435 V, clockwise as seen from left (c) 0.9 V, clockwise as seen from left (d) 0.9 V, anticlockwise as seen from right
  3. 20. Assume that the two liquids in the U-shaped cube of figure are water and oil. Compute the density of the oil, if the water stands 19 cm above the interface and the oil stands 24 cm above the interface : Oil (a) '786 kg/m3 (c) 789 kg/m2 24 cm '19 cm Water (b) 640 kg/ tn3 W) 792 kg/m3 25. 26. 27. 28. 29. (a) with A at higher potential with D at higher potential (b) 2 with A at higher pptential 2 (d) with B at highct 2 and A conducting square loosp•or resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A uniform and constant; magnetic field B exists along the pexpendféularto the plane* of the loop as shown in figure, The 'cuvrent induced in the loop is Blv g) clockwise (b) anticlockwise É2Blv anticlockwise ( (d) zero O x C 21. Regarding ideal gas, mark the incorrect option. (a) Internal energy is comprising ofPEand KE (b) Monoatomic gas has zero PE, because it is having single atom (c) Vibrational energy rnay have non-zero value for monoatomic gas (d) At room temperature, the internal energy is comprising of translational and rotational KE only A mass m suspended from a spring of constant k has period T. If a mass M is added, the period becomes .31'. Find M in terms of m. xxxxx 22. 23, (9 8m (cf7m (b) 16m (d) 5m A carnot engine takes 20000 of heat from a . reservoir at 500 K, doeS/somenwork and discards some heat to a reservoir at 350 'K How much work does it ; do and what' is the efficiency ? @ 1400J, (b) 600 J, 200/06 (c) 1400 J, 20% (d) 600 J, The image formed by a concave mirror is : (a) always real (b) a!ways virtual (c) certainly real if the object is virtual (d) 0 certainly 'virtual if the object is real A charged particle is whirled in a honzontal circle on a frictionless table by attaching, it to a string at one point. If a magnetic field is switched on in a vertical direction, the tension in the string : (a) will increase (b) will decrease Cc) will remain the same (d) •may increase or A coin of mass m slides a distance D along a tabletop. If the coefficient of friction between the coin and table is y ; find the work done on the coin by frictiom (a) —i prngD (c) 2P mgD . (b) mgD (d) None of these C 24. Find the emfrindüced -bétween the ends of C semicircular arc. 7 During charging and discharging of a capacitor (a) (b) (c) (d) current flows in the circuiti which is constant during charging or discharging duration no current flows in the circuit current flows in the circuit and is varying with time during charging ctnrent is constant but while discharging current is variable
  4. (135. 30. A projected at an angle 0 with apccd v hotn the ground, Find the change in of projectile when it hits the ground. (a) Zero -X (b) 2vsin Oj 36. A sonorncter wire of length 1 vibrates in fundamental mode when excited by a tuning fork of frequency 416 Ha. 'If the length is doubled keeping other things same, the string (a) vibrate with a frequency of 416 Ht (b) vibrate with a frequency'f 208 Hi (c) vibrate with a frequency of 332 (d) stop vibrating A uniform magn&field of 2 x T has been applied along@9 axis Of dees of a cyclotron; the radius of dees i' ORS m. Find the velocity •with which( the charge particle will emerge (d) - 2v sin ej (g) 2v cos Oi C 31. The ideal gas equation PV = nRT, holds good for ideal gases at all temperatures and pressures. For pracdcally found gases this works well : (a) at all temperatures and pressures (b) at low temperature and high pressure (c) at high temperature and low pressure (d) at high temperature and high pressure 32. In a projectile motion if angles of projeetion are 450+ 0 and 450—0, then their horizontal ranges are same. This statements is true : (a) for all values of 0 (b) for all values of 0, less rhan 450 provided speeds of projections are same (c) for all values of 0 less than 450, no matter what is the speed of projection (d) none of the above 33. dQ nCdT represents the : (a) change in amount. of heat contained in a body, as a result of temperature change (b) amount of heat energy, •vhich transits from one body tsobthcr due tb temperature difference (c) both la) and(b) are correct (d) none of the above 34. In the figure shown- from• the cyclotron. kg and Mass charge of 'particle of particle xx@B x x x x x x x (a) 6 x 105 m/s x x x x x x x x x X x XX/Q X (b) 4 x IOS m/s the block is released fromctop or incline and it \ takes Is to reach •the bottom. Fihd) thes length of ingline. crake g = 10 m/s2) (a) 3775 m (b) 3.02 m (d) 2.5m 5mJs2 37. '38. 39. (c) 6.42x10S m/s (d) m/s Mark the correct option. (a) Dielectric constant of water is 81, so 'it can be used as a effective dielectric for capacitors (b) When we insert the dielectric in between the plates of capacitor, its capacity, breakdown voltage and energy storage capacity will increase (c) If we Connect two plates of charged capacitor with plastic wire then discharging of capacitor will take place (d) All of the above A fluorescent lamp of length '1.6 m is placed horizontally at a depth of 1.2 m below a ceiling. A plane mirror of length 0.6 m is placed below the lamp parallel to and symmetric to the lamp at a distance of 2.4 m from it. Find the length of reflected patch of light on the ceiling ? (a) 0.4m (c) 2.4 m (b) 0.6m Which of the following four graphs may best represent the current-deflection relation in a tangent galvanometer ?
  5. c a b 40. A thick-walled hollow sphere has outside 'radius 'Rot It rolls down an incline without slipping, and its spccd at the bottom is Now the incline is waxed, so that it is practically frictionless, and the sphere is observed to slide down (without rolling). Its speed at the bottom is obsered to be Svo/4. Determine the radius of gyration of the hollow sphere about an axis through its centre. (C) RO/3 (b) 3Ro/4 (d) 3R0/5 | 41. Mark the one, which is not representing a force 'V (acting on a body) where symbol represents the usual meaning. (a) Gmtm2/r2 (b) ma (d) 6110rv 42. •rhe system of three IT)ds are as shown in figure. Thellnal conductivities, cross-sectional area ancl length of the rods are as indicated in figure. Find thc temperature of the junction. looec rc 30•c 32 nec 44. 46. 43. (a) 400C (b) 660c (c) 490c (d) 770c An astronauCis% doing maintenance work outside a space Stålion. He is coasting along the station at Qspeed of 1.00 m/s. He wishes to change his di(ection of motion by 900 and to increase his speed to 2.00 n/s. His total mass is his spacesuit and rocket belt, which plovides a thrust of 50 N. Find. the magnitüde and direction of the impulse needed to accomplish the desired change in motion. (a) 200 NS, at an onglc of coo (l/di) with initial direction of motion (b) 200 NS at an angle of cos (—1/J8) with initial direction of motion (c) 224 NS at an angle of cos-l(2/4ß) with initial direction of motion (d) 224 NS at an angle of cosrl(- 1/4€) wivlip initial direction of motion A magnetic needle is brought near to the Circuit as shown in figure. The signal generator 'is applied a voltage whose waveform is varying with time as shown in figure. t, (a) The deflection in needle would be observed for all the. time (b) The deflection in needle would 'be observed only for time when voltage is zero (c) The deflection in needle would be observed only for time when voltage is non-zero (d) None of the above Two charge panicles A and 13 are kept in isolation, then the angular morncntum of one panicle with respect to other is. (Assume no magnetic field will be produced due to motion of charges) : (a) changing as r changes (b) constant as force is acting along linc joining two charges (c) for some initial duration it increases and then becomes constant (d) information is insufficient A proton moving with velocity vo strikes another proton at rest, assume impact parameter to be zero i.e., head on collision. How close will the incident proton go to other proton ? [Note that both the protons are flee to move and take mass of proton as m (4x5 x mvo) 2 (c) (Rto x rnvo) e2 (27% x mvo) (d) Can't be determined
  6. 6 47. A series of thermodynamic process is shown in the PV diagram. During the proce5SAD, 150J of heat is added to system. Jn process DC, 600 J of heat is added. Find the internal energy change for ADC and heat supplied/released during process ABC ? p (kPa) 80 30 A: 2 51. C 52. 53. (a) -IV (c) ov A projectile has been fired with speed 10 m/s making an angle of 300 with the horizontal. Find the angle made by ve!oéity Nector of projectile with ground of; its firing. [Take g = 10 m/s2) (a) 600 (b) -600 (c) Can't say anythirig (d) None of theaboye Find the value of friction forces beÜNeen the blocks A and B B and ground. [Take g = 10 m) / (a) - 510 J, 600 J (released) (b) 510 J, 600J (supplied) (c) 600 J, 690 J (supplied) (d) —L 600 J, 690 J (released) c) 48. A particle is moving along a straight line whose posiüon as a function of time is given by- (3t2 6t3 + 6)11L . Find the time at which velocity would be maximum, also find this maximum velocity and position of particle at this moment. (a) Zero, 6rn/s, 100 m 115 (b) s, 2m/s, m 21 11 (c) s, m/s, zero 109 18 c) 49. If an isolated charge particle is, moving h a magnetic field then : (a) its kinetic energy remainsonstant (b) work done by rpagnetic force $ zero (c) velocity of particleånust vary with time (d) all of the above. (050. For the circuit—shownü figure, find .the potential difference across terminals A and BE IQ IQ 20 A B , Ground (a) 90 N (b) 5 N, 90 N (q) 75 .N 80 N 5 kg 80 15 kg = 0.6 A charge Q is distributed uniformly on an insulating solid sphere of radius R, the plot for E versus r (distance from centre) is : (a) R R
  7. 54. A coin has been dropped from a cliff of height q 1960 m. 'Find the time taken by coin to reach ground and distance travelled by the coin in 2nd second of its motion. (a) 20 s, 14.7m (b) 20 19.6 m (c) 20 s, 9.8 m (d) 40 s, 19.6 m 55. Figure shows a source of emf 12 V and internal resistance 2r, which is connected to an ideal voltmeter and ammeter as shown. Determine the readings of voltmeter and ammeter ? Cheniistrfl 56. The correct name of complex --cn- C.HOCHA 20 12V. 2r (a) 12 V, 6A 12 V, IA 12 V, OA 12 (c) (d) is : (a) potassium ferric oxalate (b) potassium iron (Ill) trioxalate (c) potassium trioxalato iron (Ill) (N) potassium trioxalatoferrate (Ill) b 62. ammeter may get damage czHs 57. The tendency to form complexes is maximum for: (a) normal elements transition elements Cl 63. (cfinner-transition elements (d) metals containing fully filled d-orbitals 58. In which of the following ores, calcination process is not applicable ? (a) cac03 (c) CuC03 (3) ZnS 59.4 In the contact process, the impurities of arsenic b are removed by : (a) Fe203 C! 60. The reaction, Dry Ether is called : (bf Claisen reaqtiqn (c) Benzoin condehsotion (d) Péikinlsxeaction 61. Which ofthefollowing is a plasticizer ? etaY Cresyl phpsphate (b) Ethylacetate *Pliifiålic anhydride (dj Phthalic acid 64. 66. The IUPAC name is : (4) 2,6-diethyl octane (b) 3-ethyl-7-methyl nonene (C) 3,7-diethyl octene. (d) 2,6-diethyl octane The number of d-elcctrons in l?e2• (Z 26) is: not equal to that of the : (a) p-electrons in Ne (at. no. = 10): q (b) s-eleclrons in Mg (al. no. = 12) (c) d-electrons in Fe CA, (d) p-electrons in Cl- (at. •no. Cl 17) If the energy required to eject an electron from an atom is Ee and the energy required to eject a nucleon from a nucleus Eli then (d) nothing can be stated CuS04 51-120 'hydrated copper sulphate ,saR 'is (a) compound (b) homogenous mixture (c) colloidal solution (d) complex co-ordinate compound Which of the following complexes has the highest stability constant at 298 K ? (a) [Coc14J2
  8. is an examplc of which type of the hydriåe ? (b) Ionic (a) Metallic (d) Polymeric Cc) Covalent 68. • The order of decreasing polarity in rhe compounds CaO. CSF, KCI, MgO is . (a) cao, CSF, KCI, Mgo (b) Mgo, KCI, cao, CsF (c) ,KcJ, cao, CSF, Mgo (Y) CSF, KCI, cao, Mgo (2169. WKich of the following is a solid compound ? 75. 76. Mark out the incorrect match : 3-formyl propanoic acid (b) cH2 — Pent-I -en-4-yne / (c) N N Etha9é -1 „2-dinitrÅle (d) ICH2C112F I-fluoro•iäodoethanc Which of the following-äs incon€ct about vulcanisation of rubber? @ Vulcanised rubber has excellerht elasticity (bf Vulcanised rubber increasés resistance to oxidation a-n&organicsolvenu (a) N20 (A) N205 (c) NO 70. When a metal is to be extracted from iB ore and if the gangue associated vith the ore is silica, then : (g) an acidic flux is needed (c) Vulcanisation usually establishes cross links ava)lylicpositi01i type reactive sites (d) Vulcanisecr 'rubber has high-water absorption tendency 77. Mark'ouethe corrgct set oå decreasing pKa for (bf a basic flux is needed the following molecules : COOH 71. 72. (c) both acidic and basic fluxes are needed (d) neither of them is needed H20 R —C —L product. The rate of hydrolysis is maximum when L is : (b) —OCH2CH3 (c) (d) —NH2 Which of the following compounds on hydroboration-oxidation gives 2- pentanone as COOE+ COOH 1 COOH cHF/ COOH 111 CH2 COOH COOH (CH2)2 COOH rhe majorproduct ? q)) Pent-2-eneTONJkö!t (a) Pent-I-ene (c) Pent-2-yne All of these 73. Mark out the correct decreasingxelative rates 74. of alkaline hydrolysis of ethyl p.substituted benzoate, (p-GC6H4COOC2H5) . (a) —N02 > —cl > —-CH3 > Loc/3 (b) —0013 > —CH3'> —CIS (5 —OCH3 > —cl > —cH3 (d) —CH3 > —cl > Mark out the isomeric form of butene for which Markownikoffs *and ahii Markownikoff's products are same : (a) 78. 79. 80. (b) 1>111 > Il > IV (a) IV > Il > All > I (d) IV > 11>1 > Ill (c) IV > 111>11 > I Which of the following is most acidic ? COOH (b) F COOH cool 1 3 N02 Which one is the most stable carbocation ? (a) CH2FCH*2 (c) CCla--CHi2 (b) CF3CH+2 3 Correct order of bond energy is CH3 H (d) none of the above
  9. 81. 82. 83- q 84, 85. The correct order of dipole moment is : (a H 4 < NF3 < NH 3 < 1-120 ( NF3 < cm < NHS < H20 (c) NH, < NF3 < < (d) H20 < NH3 < NF3 The vapour density of a chloride of a metal is 81S (H l) and the chloride contains 34.46% metal. The specific heat of the metal is 0.115. The molecular formula of chloride is : (a) Mc12 (c) Mc13 (b) M2c13 (d) MC14 Predict the coordination number of cation in MgO where cation and anion radii are equal to 65 pm and 140 pm respectively : When Oil mole of water at 373K vaporizes against an amosphezic pressure of 1.0 aun. Assuming ideal gas behaviour, the work done is : (a) 3100 J (b) 3060J (d) 101.3 J Which of the following doesn't cause origin of charge on colloid ? (a) Preferential adsorption (b) Bredigts arc method (c) Micelle's formation ("Brownian movement 86. What is the freezing point of a 10% (by weight) solution of CH30H in water ? (a) -6.450C (c) -I.orc (b) -5.10C (d) -3.50 c b 90. 91. C 92. Q 93. €94. 95. The following compounds have to be arranged in their 'increasing thermal stabilities. K2C03 (1), MgC03 (11), CaC03 (111), BeC03 (IV) Identify the correct order: (a) 1
  10. 96. Oxidation product of I, 2-cyclopentane-diol with 11104 give (b) (c) 101. OOH COOH (d) Which of the followingy æxpreSs correct OH OH (d) none of the above C 97- Mark out the correct decreasing order of boiling points : (a) neo-pentane > n-hexane > iso-pentane > n-pentane (b) n-pentane > iso-pentane > n-hexane > neo-pentane (c) n-hexane > n-pentane > iso-pentane > neo-pentane (d) n-hexane > neo-pentane > iso-pentane > n-pentane C 98. Which of the following doesn't give out methane gas ? (a) A14C3 + Ni 3000c (b) CO + 31-120 Electrolysis (c) CH3COONa NHa (d) CH3MgBr— 99. A + }-1104 3HCOOH+ b 102. C 103. relationship amongstvarious-eafbon-nitrogen bond (Indicated as a, b; And&c) O + cH3+ CVI=OH > product ooc cH3 (b) cH3 CH CH3 (c) CH3 (d) none of these HBr, Alci3 product glt:cosc dehvativc) Ais . (a) gluconic acid (c) glucitol COOH 100. +CHO—COOH (b) glucarié acid (d) glucouronic acid Predominant product is t (a) (c) CH2CH2CH3 (d) none of these 104. Predominant product is : coon (b) COOH An electron travels with a velocity of v ms- . For a proton to have the same de-Broglie velocity will. be wavelength, the approximately : 1840 (c) 1840 v 1840
  11. IOS. The molecular mass of each and CO is 28. if 095 L of N2 at 270 C and 700 mm pressure contaios n molecules, the number of molecules in 1.0 L of CO under identical conditions will be : b (a) 520 K (c) 600 K (b) 750 K (d) 575 K 106. 107. 108. (d) none of these 7.84 g of a sample of ferrous ammonium sulphate reacts completely with 10 mL of (aV)KMn04 solution. The percentage purity of the sample is : (a) 800/0 (d) 35% A unit cell of sodium chloride has four formula units. The edge 'length of the unit cell is 0.564 nm. What is the density of sodium chloride ? (a) 1.2Vcm3 (c) 3.64 g/cm3 The emf(E0 ) of the following cells are : Ag IAg+ (1M)l lcu24 (1M) I Cu;O —SOA6 V zn Izn2+ (1M)l lcu2+ (1M)VCu: // emf of the following cell is : zn tzn2+ ( Ag (b) 1.10 (a) 0.64 V (d) —o64V During. the preparation; of (per disulphuric also releases al anode as by product. When 972 L of VIZ releases at cathode and 2.35L02;at anode) the weight of (b) 29165g/cm3 (d) 4.S6 g/cm3 An open vessel at 27 oc is heated until three-fifth of the air has been expelled. The temperature to which the vessel has to be heated : Mathematics C 1, If the sum of the coefficients in the expansion of (1 + 2r)R is 6561, then the greatest _ coefficient in the expansion is : (b) 3594 (a) 896 (d) none of these (c) 1792 CI 2. Iff(x), g(x) and h(x) are three polynomials of degree 2} then k 110. 5, H2S29g produced is (a) 87.12 (b) 43.65 (c) 89.42 (d) 40.74 The function 2 is defined — \ \ cos (sin x)+ sm for : (c) ,xeR 2x (b) el-I, 11 f' g' 19) > h' is a polynomial of deg?ee . (d) none of these C 3. If and—t3, a-re distinct, the points 6. 7. (tl, 2at1+ at}), (t2, 2nt2 + at2) (eg;Oat3 + at3) are collinear, if : t3 = t1t2t3 and The set of all x for which log (1 + x) x is : 0 (d) none of these If is a vector of magnitude 21 and has DRS 2, —3, 6, then F is equal to : (c) 6; -9j-18ü sin A sin (A B) Il in a triangle ABC, then sinc sin (B -C)' (a) b, c are in AP (b) b2, c2 are in AP (c) a, b, care in HP
  12. The area of the region enclosed benveen the two circles x2 + Y2 = I agd (x —1)2 + equal to : then is 16. q and 17, q (a) 2 log 3 (c) log 3 (b) -2 log 3 (d) none of these (b) (d) none of these If n is an even natural number, then E is: (a) 3 (b) 9. 10. eciuals : (-1)n/2 (c) 1 n (d) none of these sq unit 2 sq 2 o €sq unit The two curves x3 — 3ry + 0 2 3 kg) cut at right angles (bf touch each other (c) cut at an angle T/ 3 (d) cut at an angle it/ 4 The vector e, directed along the 'intemal bisectoöof the angle between the vectors a — 47— 41Q and j + 2k with 11. The sum of all five digit numbers that can be formed using the digits 1, 2, 39 4, 5 when 0000000) repetition of digits is not allowed, is : (foo 366000 (b) 660000 18. G 011 coo) ray 0999960 (c) 360000 irh3e6eåu{låöi of the circle which is touched by y = x, has its centre on the positive direction of the x-axis and cuts off a chord ofléngth 2 unitr along the line Viy x = 0) is : 5 (g) -7 j + 210 (b) (5i + 5j + 217) 5 ' • Y (e) (i + 7 j + 2k) (d) I- (-5i + 5j+ 217K) 3 If P(x, y, z) is a point on the line segment joining 4) and R (3, 6) such that the 13 19 26 projections of OP on the axes are respectively, then P divides QR in 'the ratio : (a) + Y2 -4x4 2 2 2 2 19. If four dice are thrown together, then the probability that the sum of the numbers appearing on them is 13, is : 13. If thew tangent point P(2, 4) to the parabola y 2 = 8x meets the parabol} y 2 = 8xd 5 at qariI'RÄ&en the mid point of 20. (d) none of these 14t The eqLiaCionö6f the tangent to the curve 35 324 11 216 11 432 If A, B and C are angles of a triangle, then the minimum value of tan2 L + tanz + tan2 is: 1 (d) none of these • 211 -x) at the point of its maxima (d) 21. If ci and ß are different values of x satisfying cn+ß a cos x + b sin x = c, then tan 15. The value of cosec x cosec to : a (b) a-b dxis :
  13. 613 ICS IS o 22. b 23. In a triangle the angles are in AP and the lengths of the ovo larger sides are 10 and 9 respectively, then the length of the third side If are unit vectors such that the vector , a + 3b is perpendicular to 7 a— 5b and a I— 4 bis perpendicular t07 a 2b, then angle (c) 15-46 (b) 0.7 (d) none of these A vertical tower stands on a declivity which is inclined at ISO to the horizon. From the foot off the tower a man ascends the declivity for 80 feet and then finds that the tower subtends an h angle of 300. The height of the tower is : (a) 20 (UK - feet (b) 40 feet (C) 40 + 05) feet (d) none of the above between a and b is : '6 (9 (d) 30. b 24. The resulranr of two forces P and Q is at right I _ 31. angles to P, the resultant of P and Q' acting at 'the same angle cis at right angles to Q', then : (a) P, Q, Q/ are in GP (b) Q, P, Q f are in GP (d) Q', P) Q are in GP cl 25. A particle is projected up a smooth inclined plane of inclination 600 along the line of greatest slope. Ifiaomes to instantaneous _rest after 2 s, then the velocityof the is If the tangents and nonnals at the of a focal chord wofra ßrabola,tntersect at (Xls h) and (x2,€Y2) respectively, then : A sunrey shows that 63% of the Americans like cheese whereaSt 76%/ like apples. If x% of Americans like both cheese and apples, then : < 633 (b) 39 s x s 63 (c) 39k'x
  14. 36. If x cosa.+ a cosß + — sin ß= a cos a cos ß and a (a) tan tan 2 2 (c) tan a tan ß a osin a sin ß then : b2 b2 (x 2 + a2) 2 a2 38. Cl 39. 40. The vector i + xj + 3k is rotated through an angle 0 and doubled in magnitude, then it becomes 4i + (4x 2) j + 2i. The value of x is : 2 2 1 (b) (d) none of these b2 (d) none of,the above C | 37. A smooth sphere is supported in contact with a smooth vertical wall by a string fastened to a point on its surface, the other end being attached to a point in the wall. If the length of the string be equal to the radius of the sphere, then the relation between the tension V) and the reaction R of the wall is : (d) none of the above The equation of a sphere which passes thiough the points (1, O, 0b (0, 1, 1) and having radius as small ås possible, is : (a) 3(x2 + y2+ + J g g) - 1 = o 2 (c) 3(x2 + z2)- y + (d) none of the above The difference of thev tangents of the angles which the lines x 2 (sec20 — sin2 0) —2xy tan 0 + y 2 sin2 0 = 0 make with the x-axis, is : (a) 2tan 0 (c) 2 cot 0 (d) sin2 0

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