Paper-2 - Career Point

Physics : Full SyllabusChemistry : Full SyllabusMathematics : Full SyllabusVIT-2011MOCK TEST # 2PHYSICS, CHEMISTRY & MATHEMATICSDuration : 2 : 30 Hrs. Max. Marks : 120Name :________________________________________________________ Roll No. : ________________________Instructions to CandidatesGENERAL:1. This paper contains 120 Qs. in all. All questions are compulsory.2. There is No Negative Marking. Guessing of answer is harmful.3. Write your Name & Roll No. in the space provided on this cover page of question paper.4. Do not break the seals of the question paper booklet before being instructed to do so by theinvigilator.5. The answer sheet, machine readable Optical Mark Recognition (OMR) is provided separately.6. Blank papers, Clipboards, Log tables, Slide Rule, Calculators, Cellular Phones, Pagers andElectronic Gadgets in any form are not allowed to be carried inside the examination hall.SEALMARKING SCHEME:1. Each Question has four options, only one option is correct. There is No Negative Marking.2. In Physics : Q. 1 - 40 carry 1 mark each,In Chemistry : Q. 41 - 80 carry 1 mark each,In Mathematics : Q. 81 - 120 carry 1 mark each,Corporate Office, CP Tower, Road No.1, IPIA, Kota (Rajasthan ) - 324 005Ph: 0744-3040000 (6 lines), Fax (0744) 3040050email : info@careerpointgroup.com ; Website : www.careerpointgroup.comNow, Schedule practice questions are available on internet also, Visit www.examtayari.com

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Q.1 A metallic ball has spherical cavity at its centre. Ifthe ball is heated, what happens to the cavity ?(A) Its volume increases(B) Its volume decreases(C) Its volume remains unchanged(D) Its volume may decrease or increase dependingupon the nature of materialQ.2 Which of the following produces more severeburns ?(A) Boiling water (B) Steam(C) Hot air(D) Sun raysQ.3 A polished metal plate has a rough and black spot.It is heated to 1400 K and brought immediately in adark room. Which of the following is true ?(A) The spot will appear brighter than the plate(B) The spot will appear darker than the plate(C) The spot and plate will appear equally bright(D) None of the aboveQ.4 If in an isothermal process, the volume of an idealgas is halved then we can say that -(A) internal energy of the system decreases(B) internal energy of the system increases(C) work done by the gas is negative(D) work done by the gas is positiveQ.5 Two simple harmonic motions are represented bythe equations :⎛ π ⎞Y 1 = 10 sin ⎜3πt+ ⎟⎝ 4 ⎠and Y 2 = 5 (sin 3πt + 3 cos 3πt).Their amplitudes are in the ratio of -(A) 2 : 1 (B) 3 : 1 (C) 1 : 3 (D) 1 : 4Q.6 Two sound waves having a phase difference of 60ºhave path difference of -(A) 2λ (B) λ/2 (C) λ/3 (D) λ/6Q.7 The gravitational potential at height h above theearth's surface is –5.12×10 7 J/kg and accelerationdue to gravity at this point is 6.4m/s 2 . If radius ofthe earth is 6400 km, the value of h is -(A) 1200 km (B) 1600 km(C) 1800 km (D) 2400 kmPHYSICSρ − ρ1 ρ2− ρ(A)(B)ρ − ρρ − ρ(C)2ρ + ρρ + ρ12(D)1ρ + ρρ + ρQ.9 An oil drop of radius 1 cm. is sprayed into 1000small equal drops of same radius. If surface tensionof oil drop is 0.05 N/m the work done is -(A) 18π × 10 –7 J (B) 180π × 10 –7 J(C) 1800π × 10 –7 J (D) 18000π × 10 –7 JQ.10 The earth’s radius is R and acceleration due togravity at its surface is g. If a body of mass m issent to a height of R/4 from the earth’s surface, thenpotential energy increased by -RR(A) mg (B) mg34RR(C) mg (D) 3mg516Q.11 Charge Q on a capacitor varies with voltage V asshown in the figure, where Q is taken along theX-axis and V along the Y-axis. The area of ∆OABrepresents:YVO B QX(A) capacitance(B) capacitive resistance(C) magnetic field between the plates(D) energy stored in the capacitorAQ.12 For ensuring dissipation of same energy in all threeresistors (R 1 , R 2 , R 3 ) connected as shown in figure,their values must be related as:R 1VR 2 R 321Q.8 A solid sphere of volume V and density ρ floats atthe interface of two immiscible liquids of densitiesρ 1 and ρ 2 respectively. If ρ 1 < ρ < ρ 2 , then the ratioof volume of parts of the sphere in upper and lowerliquid is -(A) R 1 = R 2 = R 3(B) R 2 = R 3 and R 1 = 4R 2(C) R 2 = R 3 and R 1 = (1/4) R 2(D) R 1 = R 2 + R 3Corporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 1

Q.13 A straight reaction PQ of a circuit lies along thea ax-axis from x = – to x = and carries a steady2 2current I. The magnetic field due to the section PQat a distance x = + a, will be :(A) proportional to a (B) proportional to a1(C) proportional to a 2(D) zeroQ.14 A magnetic dipole is placed in two perpendicularmagnetic field B r and B r0 and is in equilibriummaking angle θ with B r 0 . Then :(A) B = B 0(B) B cos θ = B 0 sin θ(C) B sin θ = B 0 cos θ (D) B = B 0 tan θQ.15 In the given figure, which voltmeter reads zerowhen ω is equal to resonant frequency of the RCLcombination ?V 1 V 210Ω10mH 10µFV 3~E=E 0 sin ωt(A) V 1 (B) V 2(C) V 3(D) None of theseQ.16 In photoelectric effect, the electrons are ejectedfrom metals if the incident light has a certainminimum:(A) wavelength (B) frequency(C) amplitude (D) angle of incidenceQ.17 The combination of the gates shown belowproduces:ABG 1(A) AND gate(C) NOR gateG 2G 3 G 4 Y(B) XOR gate(D) NAND gateQ.18 What is the electric field near the conductingsurface having a uniform charge density σ ?(A) σ/ε 0 and parallel to surface(B) 2σ/ε 0 and parallel to surface(C) σ/ε 0 and perpendicular to surface(D) 2σ/ε 0 and perpendicular to surfaceQ.19 Which of the following transitions in hydrogen atomproduces longest wavelength and radiation(or photon of minimum energy) ?(A) n = 2, p = 4 (B) n = 3, p = 4(C) n = 6, p = 8 (D) n = 5, p = 6Q.20 The discrete line spectrum of hydrogen specifiesthat:(A) light is quantized(B) energy levels of hydrogen are discrete(C) both (a) and (b)(D) neither (a) nor (b)Q.21 A coil of 50 turns has dimensions 10 cm × 10 cm. Itis rotated at the rate of 5 rad/s in a uniform magneticfield of flux density 0.7 T, the maximum emfinduced in it is:(A) 22 V(B) 5 V(C) 9 V(D) 110 VQ.22 The section of circuit AB as shown in figure absorbspower of 50 W and current i = 1.0 A passes throughit. The resistance of the device C is:i=1A2ΩC(A) 48 Ω (B) 25Ω (C) 50 Ω (D) 2ΩQ.23 A signal of 20 mV is applied to common-emittertransistor amplifier circuit. Due to this, the change inbase-current and the change in collector-current are20µA and 2mA. The load resistance is 10 kΩ. Thevoltage gain is:(A) 20 V(B) 10 V(C) 50 V(D) None of theseQ.24 A charged particle moves in an electric field fromA to B and then from B to A:(A) if W AB > W BA , then the field is conservative(B) if W AB + W BA = 0, then the field is conservative(C) if W AB + W BA > 0, then the field is conservative(D) if W AB = W BA , then the field is conservativeQ.25 A capacitor of capacitance C 0 is charged to apotential V 0 and then isolated. A small capacitor C isthen charged from C 0 , discharged and charged again,the process being repeated n times. Due to thispotential of the larger capacitor is decreased to V.Value of C is:⎛V0⎞(A) C0⎜⎟⎝ V ⎠1/ nn⎡⎛V0⎞(B) C 0 ⎢⎜⎟⎢⎣⎝ V ⎠1/ n⎤−1⎥⎥⎦⎡⎛V ⎞ ⎤⎡n0⎛V⎤0 ⎞(C) C0 ⎢⎜⎟ −1V⎥ (D) C 0 ⎢⎜⎟ + 1⎥⎣⎝⎠ ⎦ ⎢⎣⎝ V ⎠ ⎥⎦Corporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 2

Q.26 In an AC circuit, E = 220 sin 100 πt. If theimpedance is 110Ω and phase angle φ = 60º, thepower consumption is :(A) 440 W (B) 220 W (C) 110 W (D) 55 WQ.27 Hysteresis cycle for the material of permanentmagnet should be :(A) long & wide (B) long & thin(C) short & wide (D) short & thinQ.28 In the figure, the reading of an ideal voltmeter iszero. Then what is the relation b/w R 1 , r 1 & r 2 ?VE EQ.35 A long wire carries a current of 20 A along theaxis of solenoid, the field due to the solenoid is4mT. The resultant field at a pt. 3 mm from thesolenoid axis is -(A) 1.33 mT (B) 4.2 mT(C) 2.1 mT(D) 8.4 mTQ.36 Given below is a circuit diagram of an AMdemodulator. For good demodulation of AMsignal of carrier frequency f, the value of RCshould be -r 1r 2(AM signal)CR outputR(A) R = r 1 + r 2 (B) R = r 1 – r 2( r1– r2)(C) R = r 1 r 2 (D) R =2Q.29 If electric flux entering & leaving an enclosedsurface is φ 1 & φ 2 respectively, the electriccharge inside the surface will be -φ2 1(A)– φφ1+ φ2(B)εε(C)0φ1 – φε020(D) ε 0 (φ 1 + φ 2 )Q.30 The electric potential V as a function of distancex in meter is given by -V = (5x 2 + 10x – 9) voltThe value of electric field of x = 1m would be(A) 20 V/m(B) 6 V/m(C) 11 V/m(D) –23 V/mQ.31 Of the following an ideal voltmeter is -(A) moving coil galvanometer(B) voltameter(C) an electrometer(D) hot wire ammeterQ.32 A e – moves from point A to point C which arerespectively at potentials of +5V & –4V. The e –will acquire the velocity of -(e = 1.6 × 10 –19 C, m = 9 × 10 –31 kg)(A) 5 × 10 4 m/s (B) 1.1 × 10 6 m/s(C) 1.8 × 10 6 m/s (D) 5.7 × 10 5 m/sQ.33 If the elements with principal quantum numbern > 3 were not allowed in nature, the totalnumber of possible elements would have been -(A) 26 (B) 28 (C) 20 (D) 12Q.34 A current is made up of two components 3A DCand an AC components is given by i = 4 sinωt.The effective value of current will be -(A) 29 A (B) 17 A(C) 37 A (D) None of these(A) RC = f1(C) RC ≥ f1(B) RC < f1(D) RC >> f1Q.37 In producing chlorine through electrolysis100 W power at 125 V is being consumed. Howmuch chlorine per minute is liberated ? (ECE of- chlorine is 0.36 × 10 –6 kg/c) -(A) 17.6 mg (B) 21.3 mg(C) 24.3 mg (D) 13.6 mgQ.38 The voltage of clouds is 4 × 10 6 V with respect toground. In a lightening strike lasting 100 ms, acharge of 4C is delivered to the ground. Thepower of lightening strike is -(A) 160 MW (B) 80 MW(C) 20 MW(D) 500 MWQ.39 Hard X-rays for the study of fractures in bonesshould have a minimum wavelength of 10 –11 m.The accelerating voltage for electrons in X-raymachine should be - -(A) 124 V(C) between 60 KV and 70 KV(D) = 100 KVQ.40 To get an OR gate from a NAND gate we need -(A) only three NAND gates(B) two NOT gates obtained from NAND gateand one NAND gate(C) four NAND gates and two AND gatesobtained from NAND gate(D) three NAND gates and three NOT gatesobtained from NAND gateCorporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 3

Q41The first ionization potential of Na, Mg, Al and Siare in the order of :(A) Na < Mg > Al < Si(B) Na > Mg > Al > Si(C) Na < Mg < Al > Si(D) Na > Mg > Al < SiQ.42 The order in which the following oxides arearranged according to decreasing basic nature is:(A) CuO, Na 2 O, MgO, Al 2 O 3(B) Al 2 O 3 , MgO, CuO, Na 2 O(C) MgO, Al 2 O 3 , CuO, Na 2 O(D) Na 2 O, MgO, Al 2 O 3 , CuOQ.43 When K 4 [Fe(CN) 6 ] is added to FeCl 3 , thecomplex compound formed is -(A) Fe 3 [Fe(CN) 6 ] 4 (B) Fe 4 [Fe(CN) 6 ] 3(C) K 2 Fe [Fe(CN) 6 ] (D) K 2 Fe 3 [Fe(CN) 6 ] 2CHEMISTRYQ.49 Both geometrical and optical isomerisms areshown by(A) [Co(en) 2 Cl 2 ] + (B) [Co(NH 3 ) 5 Cl] 2+(C) [Co(NH 3 ) 4 Cl 2 ] + (D) [Cr(OX) 3 ] –3Q.50 A radioactive element which can decay to givetwo noble gases, is :(A) U 238 (B) Th 232(C) Ac 239 (D) Ra 226Q.51 There is no S – S bond in :(A) S (B) S 2−(C)2−2 O 42−S 2O 3(D)2 O 52−S 2O 7Q.52 The ratio of σ - and π – bonds in benzene is :(A) 2 : 1 (B) 6 : 1(C) 4 : 1 (D) 8 : 1Q.44 Which of the following is an acidic oxide ?(A) Mn 2 O 7 (B) Mn 3 O 4(C) MnO (D) Mn 2 O 3Q.45 Silver sulphide dissolves in sodium cyanidesolution to form the complex :(A) Na 2 [Ag(CN) 4 ] (B) Na[Ag(CN) 2 ](C) Na 3 [Ag(CN) 4 ] (D) AllQ.46 Amongst Ni(CO) 4 , [Ni(CN) 4 ] 2– and [NiCl 4 ] 2–(A) Ni(CO) 4 and [NiCl 4 ] 2– are diamagnetic and[Ni(CN) 4 ] 2– is paramagnetic(B) [NiCl 4 ] 2– and [Ni(CN) 4 ] 2– are diamagnetic and[Ni(CO) 4 ] is paramagnetic(C) Ni(CO) 4 and [Ni(CN) 4 ] 2– are diamagnetic and[NiCl 4 ] 2– is paramagnetic(D) Ni(CO) 4 is diamagnetic and [NiCl 4 ] 2– and[Ni(CN) 4 ] 2– are paramagneticQ.47 According to IUPAC nomenclature, sodiumnitroprusside is named as:(A) sodium nitro ferrocyanide(B)sodium penta pentacyanonitrosyl ferrate(II)(C) sodium nitroferricyanide(D) sodium pentacyanonitrosyl ferrate(III)Q.48 The complex used as an anticancer agent is :(A) mer-[Co(NH 3 ) 3 Cl 3 ](B) Cis-[PtCl 2 (NH 3 ) 2 ](C) Cis-K 2 [PtCl 2 Br 2 ](D) Na 2 [CoCl 4 ]Q.53 What is the weight of oxygen required for thecomplete combustion of 2.8 kg of ethylene ?(A) 2.8 kg(B) 6.4 kg(C) 9.6 kg(D) 96 kgQ.54 The kinetic energy of 2.8 g of nitrogen gas at127ºC is nearly(A) 249.3 J(B) 200.4 J(C) 2.5 J(D) 20.5 JQ.55 Aluminium metal crystallises in a face centredcubic lattice. If crystal radius of aluminium is 144pm, the edge length of a cube is(A) 407.3 pm (B) 207.3 pm(C) 309 pm(D) 507.3 pmQ.56 The orbital diagram in which the Aufbau principleis violated is(A)(B)(C)(D)2s 2 p↑↓↑↓2s 2 p↑↑↓↑↑2s 2 p↑↓↑↑2s 2 p↑↓↑↓↑↑↑↓↑Corporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 4

Q.57 If the half-life of an isotope X is 10 years. Itsdecay constant is(A) 6.932 Yr –1 (B) 0.6923 Yr –1(C) 0.06932 Yr –1 (D) 0.006932 Yr –1Q.58 If bond enthalpies of H–H, Br–Br and H–Brbonds are 433, 192 and 364 kJ mol –1 respectively.The ∆Hº for the reactionH 2 (g) + Br 2 (g) → 2HBr (g) is(A) –261 kJ(B) + 103 kJ(C) + 261 kJ (D) – 103 kJQ.59 (∆H – ∆U) for formation of carbon monoxide(CO)from its elements at 298 K is (R = 8.314 JK –1mol –1 )(A) –1238.78 J mol –1 (B) 1238.78 J mol –1(C) –2477.58 J mol –1 (D) 2477.58 J mol –1Q.60 For the equilibriumNH 4 HS(s) NH 3 (g) + H 2 S(g)K C = 1.8 × 10 –4 at 298 K. The value of K P at 298 Kwould be(A) 0.108 (B) 4.4 × 10 –3(C) 1.8 × 10 –4 (D) 4.4 × 10 –4Q.61 A mixture with [N 2 O 4 ] = 0.090 mol L –1 and [NO 2 ]= 0.135 mol L –1 is at equilibrium. The value of K Cfor the equilibrium :N 2 O 4 (g) 2NO 2 (g) is(A) 0.4 (B) 1.5(C) 0.15 (D) 0.2Q.62 For the equilibrium,CH 3 CH 2 CH 2 CH 3 (g)CH 3 –CH–CH 3 (g)CH 3n-Butaneiso-Butaneif the value of K C is 3.0, the percentage by massof iso-butane in the equilibrium mixture would be(A) 75 % (B) 90 %(C) 30 % (D) 60 %Q.63 The pH of an aqueous solution of a 0.1 Msolution of a weak monoprotic acid which is 1%ionised is(A) 1 (B) 2(C) 3 (D) 11Q.64 The precipitate of CaF 2 (K sp = 1.7 × 10 –10 ) isobtained when equal volumes of the following aremixed(A) 10 –4 M Ca 2+ + 10 –4 M F –(B) 10 –2 M Ca 2+ + 10 –3 M F –(C) 10 –5 M Ca 2+ + 10 –3 M F –(D) 10 –3 M Ca 2+ + 10 –5 M F –Q.65 The t 1/2 for the decomposition of CH 3 CHO atconstant temperature and at initial pressures of364 mm and 170 mm of Hg were 410 s and 880 srespectively. The order of the reaction is(A) 1 (B) 0.5(C) 1.5 (D) 2Q.66 The half-life of a first order reaction A → B + C, is10 minutes. The concentration of A would bereduced to 10% of the original concentration in(A) 10 minutes (B) 90 minutes(C) 33 minutes (D) 70 minutesQ.67 C 2 H 5 IAlcoholicKOHThe product ‘A’ is(A) succinic acid(C) oxalic acidXBr 2CCl 4YAKCNH 3 O +(B) melonic acid(D) maleic acidQ.68 The formula of ethyl carbinol is(A) CH 3 OH(B) CH 3 CH 2 OH(C) CH 3 CH 2 CH 2 OH (D) (CH 3 ) 3 COHQ.69 Which of the following is a Gattermann aldehydesynthesis(A) COCl H 2/PdBaSO 4CHO(B) H+CO+HCl(C)AlCl 3+HCl+HCN(i)Anhy. AlCl 3(ii)H 3 O +(D) COCl CrO 2Cl 2CHOCHOCHOQ.70 Glycerol on treatment with oxalic acid at 110ºC forms(A) formic acid (B) allyl alcohol(C) CO 2 and CO (D) acroleinQ.71 One mole of alkene X on ozonolysis gave onemole of acetaldehyde and one mole of acetone.The IUPAC name of X is(A) 2-methyl-2butene (B) 2-methyl -1- butene(C) 2-butene (D) 1-buteneZCorporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 5

Q.72 What are A , B, C in the following reactions?(I)(CH 3 CO 2 ) 2 Ca ∆ Α(II) CH 3 CO 2 HHIΒRed P(III) 2CH 3 CO 2 HP 4 Ο 10CABC(A) C 2 H 6 CH 3 COCH 3 (CH 3 CO) 2 O(B) (CH 3 CO) 2 O C 2 H 6 CH 3 COCH 3(C) CH 3 COCH 3 C 2 H 6 (CH 3 CO) 2 O(D) CH 3 COCH 3 (CH 3 CO) 2 O C 2 H 6Q.73 Proteins are composed of :(A) α-amino acids(C) vitamins(B) carbohydrates(D) minerals saltsQ.74 Phenol can be converted into salicylic acid by:(A) Cannizzaro’s reaction(B) Perkin’s reaction(C) Atrial’s reaction(D) Reimer Tiemann reactionQ.75 Which of the following polymer has esterlinkage?(A) nylon-66 (B) PVC(C) terylene(D) SBRQ.76 X + Br 2 + KOH ⎯⎯→C 2 H 5 NH 2 , X isQ.77 Which enzyme breaks sucrose into glucose andfructose ?(A) Zymase (B) Maltase(C) Diastase (D) InvertaseQ.78 Optical isomerism is shown by :(A) butanol – 1 (B) butanol –2(C) butene – 1 (D) butene – 2Q.79 Denatured alcohol is -(A) rectified spirit(B) undistilled ethanol(C) rectified spirit + 10–15% methanol +naptha + pyridine(D) 50% ethanol + 50% methanolQ.80 Identify the correct order of reactivity inelectrophilic substitution reactions of thefollowing compounds :CH 3 Cl NO 21 2 3 4(A) 1 > 2 > 3 > 4 (B) 4 > 3 > 2 > 1(C) 2 > 1 > 3 > 4 (D) 2 > 3 > 1 > 4(A) CH 3 CONH 2 (B) HCONH 2(C) CH 3 CH 2 CONH 2 (D) CH 3 CNCorporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 6

MATHEMATICSQ.81 The area (in sq. unit) of the quadrilateral formedby two pairs of lines2 2 2 2l x − m y − n(lx + my)= 0 and2222l x − m y + n(lx − my)= 0 is -(A)(C)2n2 | lm |n2 | lm |n(B)lm |(D)|22n4 | lm |Q.82 The equation of bisector of the angles between thelines | x | = | y | are -(A) y = 1 and x = 0 (B) x = 1/2 and y = 1/2(C) y = 0 and x = 0 (D) None of theseQ.89 If f(x) =then the value ofsin x + sin 2x+ sin 3x3 + 4sin x1+sin xπ/2∫0(A) 3 (B) 32f ( x)dx is -(C) 31sin 2x3sin xQ.90 The range of the functionsin (sin –1 x + cos –1 x), | x | ≤ 1 is -(A) [–1, 1] (B) [1, –1](C) {0} (D) {1}(D) 0sin 3x4sin x1Q.83 If e and e' are eccentricities of the ellipse5x 2 + 9y 2 = 45 and the hyperbola 5x 2 – 4y 2 = 45respectively, then ee' is equal to -(A) 9 (B) 4 (C) 5 (D) 1Q.84 The tangent at (1, 7) to the curve x 2 = y – 6touches the circle x 2 + y 2 + 16x + 12y + c = 0 at -(A) (6, 7) (B) (–6, 7)(C) (6, –7) (D) (–6, –7)Q.85 The line x – 1 = 0 is the directrix of the parabolay 2 – kx + 8 = 0, then one of the values of k is -11(A) (B) 8 (C) 4 (D) 8 4Q.86 The equation of pair of lines joining origin to thepoint of intersection of x 2 + y 2 = 9 and x + y = 3 is -(A) x 2 + (3 – x) 2 = 9 (B) xy = 0(C) (3 + y) 2 + y 2 = 9 (D) (x – y) 2 = 9Q.87 The combined equation of asymptotes of thehyperbola 2x 2 + 5xy + 2y 2 + 4x + 5y = 0 is -(A) 2x 2 + 5xy + 2y 2 = 0(B) 2x 2 + 5xy + 2y 2 – 4x + 5y + 2 = 0(C) 2x 2 + 5xy + 2y 2 + 4x + 5y – 2 = 0(D) 2x 2 + 5xy + 2y 2 + 4x + 5y + 2 = 021−t2tdyQ.88 If x = and y = , then22 is equal to1+t 1+t dxy y x x(A) − (B) (C) − (D)x x y yQ.91 If the tangent to the curve y = 6x− x is parallelto the line 4 x − 2y −1= 0 , then the point of tangencyon the curve is -(A) (2, 8) (B) (8, 2)(C) (6, 1) (D) (4, 2)Q.92 If F is function such that F(0) = 2, F(1) = 3,F(x + 2)) = 2F (x) – F (x + 1) for x ≥ 0, then F(5)is equal to -(A) – 7 (B) –3 (C) 17 (D) 13Q.93 The area bounded by the curve y = | sin x | , x-axisand the lines | x | = π, is -(A) 2 sq unit (B) 1 sq unit(C) 4 sq unit (D) None of these⎛2Q.94 Range of the function y = sin –1 ⎟ ⎞⎜x, is -⎝1+ x2⎠(A)⎛ π ⎞ ⎡ π ⎞ ⎛ π⎤⎡ π⎤⎜0 , ⎟ (B) ⎟⎝ 2⎢0 , (C) ⎜0 ,⎠ ⎣ 2⎥ (D)⎠ ⎝ 2⎢0, ⎥ ⎦ ⎣ 2 ⎦Q.95 The solution of the differential equationdy = sin (x + y) tan (x + y) – 1 is -dx(A) cosec (x + y) + tan (x + y) = x + c(B) x + cosec (x + y) = c(C) x + tan (x + y) = c(D) x + sec (x + y) = c2Corporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 7

Q.96nIf In =∫sin xdx,then nI n − ( n −1)In−2equals -n(A) sin 1 xcosx (B) ncos xsinxn(C) – sin 1 xcosx (D) – ncos xsinxQ.97 If g(x) is a polynomial satisfyingg(x) g(y) = g(x) + g(y) + g(xy) – 2 for all real xand y and g(2) = 5, then lim g(x) is -x→3(A) 9 (B) 10 (C) 25 (D) 20⎛ 1−x ⎞Q.98 The value of the integral∫e x ⎜2⎟ dx is -⎝1+x ⎠(A)(C)xe x ⎛ 1−⎞x⎜ ⎟ + c (B) e x ⎛ 1+⎞c2⎜ +2⎟⎝1+x ⎠⎝1+x ⎠e x + c (D) e x ( 1− x)+ c1+ x22Q.103 The volume of the parallelopiped whoseco-terminus edge are iˆ − ˆj+ kˆ, 2 iˆ− 4 ˆj+ 5kˆand3 iˆ− 5 ˆj+ 2kˆis -(A) 4 cu unit(C) 2 cu unit(B) 3 cu unit(D) 8 cu unitQ.104 If the co-ordinates of the vertices of triangle ABCbe A(–1, 3, 2), B(2, 3, 5) and C(3, 5, –2), then ∠Ais equal to -(A) 45º (B) 60º (C) 90º (D) 30ºQ.105 The sum of values of x satisfying the equation2x –3(31+ 8 15) + 1 = (32 + 8 15)2x −3is -(A) 3 (B) 0(C) 2(D) None of these⎛ y ⎞ ⎡ ⎛ y ⎞ ⎤πQ.99 If xsin ⎜ ⎟dy= y x dxx⎢ sin⎜⎟ −x⎥ and y(1) = ,⎝ ⎠ ⎣ ⎝ ⎠ ⎦ 2then the value of cos(A) x (B) x1⎛ y ⎞⎜ ⎟ is equal to -⎝ x ⎠(C) log x(D) e xQ.100x y zThe angle between the line = = and the2 3 4plane 3x + 2y – 3z = 4 is -(A) 45º (B) 0º− ⎛ 24(C)⎟ ⎞cos 1 ⎜⎝ 29 22 ⎠(D) 90ºr rQ.101 If a iˆˆjk b iˆˆr= + − ˆ, = − j + kˆ,c = iˆ− ˆj− kˆ,r r rthen a × ( b × c)is -(A)(C)iˆ − ˆj+ kˆ(B) 2iˆ− 2 ˆj3 iˆ− ˆj+ kˆ(D) 2iˆ+ 2 ˆj− kˆQ.102 Let ABCD be the parallelogram whose sides ABand AD are represented by the vectors2iˆ+ 4 ˆj− 5kˆand iˆ + 2 ˆj+ 3kˆrespectively. Then ifa r is a unit vector parallel to AC , then a r is equalto -1(A) (3ˆ 6 ˆ 2 ˆ 1i − j − k)(B) (3ˆ i + 6 ˆj− 2kˆ)331(C) (3ˆ 6 ˆ 3 ˆ 1i − j − k)(D) (3ˆ i + 6 ˆj− 2kˆ)77Q.106 If the roots of the equation (a – 1) (x 2 + x + 1) 2 =(a + 1) (x 4 + x 2 + 1) are real and distinct then thevalue of a ∈(A) (–∞, 3] (B) (–∞, –2) ∪ (2, ∞)(C) [–2, 2] (D) [–3, ∞)Q.107 If a, b ∈ R, a ≠ 0, and the quadratic equationax 2 – bx + 1 = 0 has imaginary roots then (a + b + 1)is -(A) positive(B) negative(C) 0(D) dependent on sign of bQ.1082 F(n)+ 1Suppose that F(n + 1) = for n = 1, 2, 3,2…… and F(1) = 2. Then, F(101) equals -(A) 50 (B) 52(C) 54(D) None of theseQ.109 If the ratio 2n C 3 : n C 3 is equal to 11 : 1, then nequals -(A) 6 (B) 7(C) 4 (D) 8Q.110 The no. of non negative integral solutions ofx + y + z + w ≤ 20 are -(A) 24 C 3 (B) 25 C 4(C) 24 C 4(D) None of theseCorporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 8

Q.111 The term in⎛⎞⎜a b3 + ⎟3⎝ b a ⎠which has thesame power of a and b is -(A) 9 th(B) 8 th(C) 7 th(D) 10 thQ.112 Maximum sum of coefficient in the expansion of(1– x sin θ + x 2 ) n is -(A) 1(B) 2 n(C) 3 n (D) 0Q.113 ∆ 1 =522and ∆ 2 =3(A) ∆ 24(C) ∆ 26333y z ( z6y z ( y3y z ( zxxx47– y– z– yyyy363258)))43366xz ( z3xz ( x3x z ( xzzz36921– z– x– z633)))4533x y ( y – x )2 6 6xy ( x – y )2 3 3xy ( y – x ). Then ∆ 1 ∆ 2 is equal to -(B) ∆ 22(D) None of theseQ.114 If A and B are symmetric matrices of the sameorder and X =AB + BA and Y = AB – BA, then(XY) T is equal to -(A) XY(B) YX(C) –YX(D) None of theseQ.117 If z = 3/(2 + cos θ + i sin θ), then locus of z is -(A) a straight line(B) a circle having centre on y-axis(C) a parabola(D) a circle having centre on x-axisQ.118 A natural number is chosen at random from thefirst 100 natural numbers. The probability that100x + > 50 is -x(A) 1/10 (B) 11/50(C) 11/20(D) None of theseQ.119 In a ∆ABC( a + b + c)(b + c − a)(c + a − b)(a + b − c)equals -(A) cos 2 A(C) sin 2 A24bc2(B) cos 2 B(D) sin 2 BQ.120 If cosx + cos 2 x = 1, then the value ofsin 12 x + 3 sin 10 x + 3 sin 8 x + sin 6 x – 1 is equal to -(A) 2 (B) 1 (C) –1 (D) 0⎡x3 2⎤Q.115 Given that matrix A =⎢ ⎥⎢1 y 4⎥. If xyz = 60 and⎢⎣2 2 z⎥⎦8x + 4y + 3z = 20, then A(adj A) is equal to -⎡640 0 ⎤ ⎡88(A)⎢ ⎥⎢0 64 0⎥(B)⎢⎢0⎢⎣0 0 64⎥⎦⎢⎣00 0 ⎤88 0⎥⎥0 88⎥⎦⎡680 0 ⎤ ⎡340 0 ⎤(C)⎢ ⎥⎢0 68 0⎥(D)⎢ ⎥⎢0 34 0⎥⎢⎣0 0 68⎥⎦⎢⎣0 0 34⎥⎦Q.116 The number of complex numbers z satisfying|z – 3 – i| = |z – 9 – i| and |z – 3 + 3i| = 3 are -(A) one(B) two(C) four(D) none of theseCorporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 line) || Mock Test-VIT || Page # 9