Practice Questions

Q64.A thin glass (refractive index 1.5) lens has optical power of −5D in air. Its optical power in a liquid medium with refractive index 1.6 will be (1) 1D (2) −1D (3) 25D (4) None of these

Q66.Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm . Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light = 500 nm ] (1) 5 m (2) 1 m (3) 6 m (4) 3 m

Q68.If I0 is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled? (1) 2I0 (2) 4I0 (3) I0 (4) I0/2

Q69.A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 1 m away, the number of electrons emitted by photo cathode would 2 (1) decrease by a factor of 4 (2) increase by a factor of 4 (3) decrease by a factor of 2 (4) increase by a factor of 2

Q70.If the kinetic energy of a free electron doubles. Its deBroglie wavelength changes by the factor (1) 1 (2) 2 2 (3) 1 (4) √2 √2

Q72.The intensity of gamma radiation from a given source is I. On passing through 36 mm of lead, it is reduced to I . The thickness of lead which will reduce the intensity to I will be 8 2 (1) 6 mm (2) 9 mm (3) 18 mm (4) 12 mm

Q73.Starting with a sample of pure 66Cu, 7/8 of it decays into Zn in 15 minutes. The corresponding half-life is (1) 10 minutes (2) 15 minutes (3) 5 minutes (4) 7 12 minutes

Q76.The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The band gap in (eV) for the semiconductor is (1) 1.1eV (2) 2.5eV (3) 0.5eV (4) 0.7eV

Q80.If we consider that 1 , in place of 1 ; mass of carbon atom is taken to be the relative atomic mass unit, the 6 12 mass of one mole of a substance will (1) Decrease twice (2) Increase two fold (3) Remain unchanged (4) Be a function of the molecular mass of the substance

Q82.In a multi – electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic acid and electric fields? (a) n = 1, l = 0, m = 0 (b) n = 2, l = 0, m = 0 (c) n = 2, l = 1, m = 1 (d) n = 3, l = 2, m = 1 (e) n = 3, l = 2, m = 0 (1) (a) and (b) (2) (b) and (c) (3) (c) and (d) (4) (d) and (e)

Q83.Of the following sets which one does NOT contain isoelectronic species? JEE Main 2005 JEE Main Previous Year Paper (1) (2) CN, N2, C22 PO−34 , SO−24 , ClO−4 (3) SO−23 , CO−23 , NO−3 (4) BO−33 , CO−23 , NO3

Q85.In which of the following arrangements the order is NOT according to the property indicated against it? (1) (2) Al3+ < Mg2+ < Na+ < F− B < C < N < O Increasing first ionization enthalpy Increasing ionic size (3) (4) Li < Na < K < Rb Increasing metallic radius l < Br < F < Cl Increasing electron gain enthalpy (with negative sign)

Q86.The photon of hard gamma radiation knocks a proton out of 2412Mg nucleus to form (1) the isotope of parent nucleus (2) the isobar of parent nucleus (3) the nuclide 2311Na (4) the isobar of 2311Na

Q88.Which one of the following species is diamagnetic in nature? (1) He+2 (2) H2 (3) H+2 (4) H−2

Q90.The molecular shapes of SF4, CF4 and XeF4 are (1) the same with 2,0 and 1 lone pairs of electrons on (2) the same with 1, 1 and 1 lone pair of electrons on the central atom, respectively the central atoms, respectively (3) different with 0, 1 and 2 lone pair of electrons on (4) different with 1, 0 and 2 lone pairs of electron on the central atoms, respectively the central atoms respectively

Q91.Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas? JEE Main 2005 JEE Main Previous Year Paper (1) The most probable speed increases (2) The fraction of the molecules with the most probable speed increases (3) The distribution becomes broader (4) The area under the distribution curve remains the same as under the lower temperature

Q95.The exothermic formation of ClF3 is represented by the equation: Cl2(g) + 3 F2(g) ⇌2ClF3(g); ΔrH = −329 kJ Which of the following will increase the quantity of ClF3 in an equilibrium mixture of Cl2, F2 and ClF3 ? (1) Increasing the temperature (2) Removing Cl2 (3) Increasing the volume of the container (4) Adding F2

Q96.If the bond dissociation energies of XY , X2 and Y2 (all diatomic molecules) are in the ratio of 1:1:0.5 and ΔtH for the formation of XY is −200 kJ mole−1 . The bond dissociation energy of X2 will be (1) 100 kJ mol−1 (2) 200 kJ mol−1 (3) 300 kJ mol−1 (4) None of these

Q98.A schematic plot of ln Keq versus inverse of temperature for a reaction is shown below The reaction must be (1) exothermic (2) endothermic (3) one with negligible enthalpy change (4) highly spontaneous at ordinary temperature

Q99.An amount of solid NH4HS is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm. Pressure. Ammonium hydrogen sulphide decomposes to yield NH3 and H2 S gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to 0.84 atm. The equilibrium constant for NH4HS decomposition at this temperature is (1) 0.30 (2) 0.18 (3) 0.17 (4) 0.11 Q100.The solubility product of a salt having general formula MX2 , in water is: 4 × 10−12 . The concentration of M2+ ions in the aqueous solution of the salt is (1) 2.0 × 10−6M (2) 1.0 × 10−4M (3) 1.6 × 10−4M (4) 4.0 × 10−10M Q101.Hydrogen ion concentration in mol / L in a solution of pH = 5.4 will be (1) 3.98 × 108 (2) 3.88 × 106 (3) 3.68 × 10−6 (4) 3.98 × 10−6 Q102.What is the conjugate base of OH−? (1) O2 (2) H2O (3) O− (4) O−2 Q103.Calomel (Hg2Cl2) on reaction with ammonium hydroxide gives (1) HgNH2Cl (2) NH2 −Hg −Hg −Cl (3) Hg2O (4) HgO Q104.Hydrogen bomb is based on the principle of (1) Nuclear fission (2) Natural radioactivity (3) Nuclear fusion (4) Artificial radioactivity Q105.Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point. (1) LiCl (2) NaCl (3) KCl (4) RbCl Q106.The number and type of bonds between two carbon atoms in calcium carbide are JEE Main 2005 JEE Main Previous Year Paper (1) One sigma, one pi (2) One sigma, two pi (3) Two sigma, one pi (4) Two sigma, two pi Q107.Heating an aqueous solution of aluminium chloride to dryness will give (1) AlCl3 (2) Al2Cl6 (3) Al2O3 (4) Al(OH)Cl2 Q108.In silicon dioxide (1) Each silicon atom is surrounded by four oxygen (2) Each silicon atom is surrounded by two oxygen atoms and each oxygen atom is bonded to two atoms and each oxygen atom is bonded to two silicon atoms silicon atoms (3) Silicon atoms is bonded to two oxygen atoms (4) There are double bonds between silicon and oxygen atoms Q109.The structure of diborane (B2H6) contains (1) four 2c-2e bonds and two 3c-2e bonds (2) two 2c-2e bonds and four 3c-2e bonds (3) two 2c-2e bonds and two 3c-3e bonds (4) four 2c-2e bonds and four 3c-2e bonds Q110.Due to the presence of an unpaired electron, free radicals are: (1) Chemically reactive (2) Chemically inactive (3) Anions (4) Cations Q111.The best reagent to convert pent -3- en-2-ol into pent -3-en-2-one is (1) Acidic permanganate (2) Acidic dichromate (3) Chromic anhydride in glacial acetic acid (4) Pyridinium chloro – chromate Q112. The decreasing order of nucleophilicity among the nucleophiles (1) (a), (b), (c), (d) (2) (d), (c), (b), (a) (3) (b), (c), (a), (d) (4) (c), (b), (a), (d) Q113.Of the five isomeric hexanes, the isomer which can give two monochlorinated compounds is (1) n-hexane (2) 2, 3-dimethylbutane (3) 2,2-dimethylbutane (4) 2-methylpentane Q114.Which types of isomerism is shown by 2,3-dichlorobutane? (1) Diastereo (2) Optical (3) Geometric (4) Structural JEE Main 2005 JEE Main Previous Year Paper Q115. The reaction is fastest when X is (1) Cl (2) NH2 (3) OC2H5 (4) OCOR Q116.An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be (1) A B (2) A2 B (3) A B3 (4) A3 B Q117.If α is the degree of dissociation of Na2SO4 , the vant Hoff's factor (i) used for calculating the molecular mass is (1) 1 + α (2) 1 −α (3) 1 + 2α (4) 1 −2α Q118.Equimolar solutions in the same solvent have (1) Same boiling point but different freezing point (2) Same freezing point but different boiling point (3) Same boiling and same freezing points (4) Different boiling and different freezing points Q119.For a spontaneous reaction the ΔG, equilibrium constant (K) and E∘cell will be respectively (1) -ve, >1, +ve (2) +ve, >1, -ve (3) -ve, < 1, -ve (4) -ve, >1, -ve Q120.The highest electrical conductivity of the following aqueous solutions is of (1) 0.1 M acetic acid (2) 0.1 M chloroacetic acid (3) 0.1 M fluoroacetic acid (4) 0.1 M difluoroacetic acid Q121.Aluminium oxide may be electrolysed at 1000∘C to furnish aluminium metal (Atomic mass = 27 amu; 1 Faraday = 96, 500 Coulombs). The cathode reaction is Al3+ + 3e−⟶Al∘ To prepare 5.12 kg of aluminium metal by this method would require (1) 5.49 × 107C of electricity (2) 1.83 × 107 C of electricity (3) 5.49 × 104C of electricity (4) 5.49 × 101C of electricity Q122. Calculate ∧∞HOAc Using appropriate molar conductances of the electrolytes listed above at infinite dilution in H2O at 25∘C (1) 517.2 (2) 552.7 (3) 390.7 (4) 217.5 Q123.A reaction involving two different reactants can never be JEE Main 2005 JEE Main Previous Year Paper (1) Unimolecular reaction (2) First order reaction (3) second order reaction (4) Bimolecular reaction Q124. t1/4 can be taken as the time taken for the concentration of a reactant to drop to 43 of its initial value. If the rate constant for a first order reaction is K, the t1/4 can be written as (1) 0.10/K (2) 0.29/K (3) 0.69/K (4) 0.75/K Q125.The volume of a colloidal particle, VC as compared to the volume of a solute particle in a true solution Vs , could be (1) VC ≃1 (2) Vc ≃1023 VS Vs (3) Vc ≃10−3 (4) Vc ≃103 VS Vs Q126.The disperse phase in colloidal iron (III) hydroxide and colloidal gold is positively and negatively charged, respectively, which of the following statements is NOT correct? (1) magnesium chloride solution coagulates, the (2) sodium sulphate solution causes coagulation in gold sol more readily than the iron (III) both sols hydroxide sol. (3) mixing the sols has no effect (4) coagulation in both sols can be brought about by electrophoresis Q127.During the process of electrolytic refining of copper, some metals present as impurity settle as ‘anode mud’ These are (1) Sn and Ag (2) Pb and Zn (3) Ag and Au (4) Fe and Ni Q128.The number of hydrogen atom(s) attached to phosphorus atom in hypophosphorous acid is (1) zero (2) two (3) one (4) three Q129.The correct order of the thermal stability of hydrogen halides (H – X) is (1) HI > HBr > HCl > HF (2) HF > HCl > HBr > HI (3) HCl < HF > HBr < HI (4) HI > HCl < HF < HBr Q130.Heating mixture of Cu2O and Cu2 S will give (1) Cu + SO2 (2) Cu + SO3 (3) CuO + CuS (4) Cu2SO3 Q131.The oxidation state of chromium in the final product formed by the reaction between KI and acidified potassium dichromate solution is (1) +4 (2) +6 (3) +2 (4) +3 Q132.The lanthanide contraction is responsible for the fact that JEE Main 2005 JEE Main Previous Year Paper (1) Zr and Y have about the same radius (2) Zr and Nb have similar oxidation state (3) Zr and Hf have about the same radius (4) Zr and Zn have the same oxidation Q133.Which of the following factors may be regarded as the main cause of lanthanide contraction? (1) Poor shielding of one of 4f electron by another (2) Poor shielding of one of 4f electron by another in the subshell in the subshell (3) Poorer shielding of 5d electrons by 4f electrons (4) Greater shielding of 5d electrons by 4f electrons Q134.The oxidation state of Cr in [Cr(NH3)4Cl2]+ is (1) +3 (2) +2 (3) +1 (4) 0 Q135.The IUPAC name of the coordination compound K3 [Fe(CN)6] is (1) Potassium hexacyanoferrate (II) (2) Potassium hexacyanoferrate (III) (3) Potassium hexacyanoiron (II) (4) tripotassium hexcyanoiron (II) Q136.Which of the following compounds shows optical isomerism? (1) [Cu(NH3)4]+2 (2) [ZnCl4]−2 (3) [Cr(C2O4)3]−3 (4) [Co(CN)6]−3 Q137.Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (At. No. Cr = 24, Mn = 25, Fe = 26, Co = 27 ) (1) [Cr(CN)6]−3 (2) [Mn(CN)6]−3 (3) [Fe(CN)6]−3 (4) [Co(CN)6]−3 Q138.The value of the ‘spin only’ magnetic moment for one of the following configurations is 2.84 BM. The correct one is (1) d4 (in strong ligand filed) (2) d4 (in weak ligand filed) (3) d3 (in weak as well as in strong fields) (4) d5 (in strong ligand filed) Q139.2 methylbutane on reacting with bromine in the presence of sunlight gives mainly (1) 1 – bromo -2 - methylbutane (2) 2 – bromo -2 - methylbutane (3) 2 – bromo -3 - methylbutane (4) 1 – bromo -3 – methylbutane Q140.Tertiary alkyl halides are practically inert to substitution by SN2 mechanism because of (1) insolubility (2) instability (3) inductive effect (4) steric hindrance Q141.Reaction of one molecule of HBr with one molecule of 1,3 -butadiene at 40∘C gives predominantly (1) 3-bromobutene under kinetically controlled (2) 1-bromo-2-butene under thermodymically conditions controlled conditions (3) 3-bromobutene under thermodynamically (4) 1-bromo-2-butene under kinetically controlled controlled conditions conditions Q142.Alkyl halides react with dialkyl copper reagents to give JEE Main 2005 JEE Main Previous Year Paper (1) alkenes (2) alkyl copper halides (3) alkanes (4) alkenyl halides Q143.Elimination of bromine from 2-bromobutane results in the formation of- (1) equimolar mixture of 1 and 2-butene (2) predominantly 2-butene (3) predominantly 1-butene (4) predominantly 2-butyne Q144.Acid catalyzed hydration of alkenes except ethene leads to the formation of (1) primary alcohol (2) secondary or tertiary alcohol (3) mixture of primary and secondary alcohols (4) mixture of secondary and tertiary alcohols Q145.p-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is (1) (2) (3) (4) Q146.Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of an acid forms a compound if water during the reaction is continuously removed. The compound formed is generally known as (1) a Schiff’s base (2) an enamine (3) an imine (4) an amine Q147.Among the following acids which has the lowest pKa value (1) CH3COOH (2) HCOOH (3) (CH3)2COOH (4) CH3CH2COOH Q148.Which one of the following methods is neither meant for the synthesis nor for separation of amines? (1) Hinsberg method (2) Hofmann method (3) Wurtz reaction (4) Curtius reaction Q149.Amongst the following the most basic compound is (1) benzylamine (2) aniline (3) acetanilide (4) p-nitroaniline JEE Main 2005 JEE Main Previous Year Paper Q150.Which of the following is a polyamide? (1) Teflon (2) Nylon – 66 (3) Terylene (4) Bakelite Q151.Which of the following is fully fluorinated polymer? (1) Neoprene (2) Teflon (3) Thiokol (4) PFC Q152.Which one of the following types of drugs reduces fever? (1) Analgesic (2) Antipyretic (3) Antibiotic (4) Tranquiliser Q153.In both DNA and RNA, heterocyclic base and phosphate ester linkages are at- (1) C′5 and C′2 respectively of the sugar molecule (2) C′2 and C′5 respectively of the sugar molecule (3) C′1 and C′5 respectively of the sugar molecule (4) C′5 and C′1 respectively of the sugar molecule Q154.The value of α for which the sum of the squares of the roots of the equation x2 −(a −2)x −a −1 = 0 assume the least value is (1) 1 (2) 0 (3) 3 (4) 2 Q155.If roots of the equation x2 −bx + c = 0 be two consectutive integers, then b2 −4c equals (1) −2 (2) 3 (3) 2 (4) 1 Q156.If both the roots of the quadratic equation x2 −2kx + k2 + k −5 = 0 are less than 5 , then k lies in the interval (1) (5, 6] (2) (6, ∞) (3) (−∞, 4) (4) [4, 5] Q157.If the cube roots of unity are 1, ω, ω2 then the roots of the equation (x −1)3 + 8 = 0 , are (1) −1, −1 + 2ω, −1 −2ω2 (2) −1, −1, −1 (3) −1, 1 −2ω, 1 −2ω2 (4) −1, 1 + 2ω, 1 + 2ω2 Q158.If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2| then arg z1 −arg z2 is equal to (1) π (2) −π 2 (3) 0 (4) −π2 Q159.If ω = z and |ω| = 1, then z lies on z−13 i (1) an ellipse (2) a circle (3) a straight line (4) a parabola. Q160.If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number JEE Main 2005 JEE Main Previous Year Paper (1) 601 (2) 600 (3) 603 (4) 602 Q161.If x = ∑∞n=0 an, y = ∑∞n=0 bn, z = ∑∞n=0 cn where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, then x, y, z are in (1) G.P. (2) A.P. (3) Arithmetic - Geometric Progression (4) H.P. Q162.If in a triangle ABC , the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in (1) G.P. (2) A.P. (3) Arithmetic - Geometric Progression (4) H.P. Q163.If non-zero numbers a, b, c are in H.P., then the straight line xa + yb + 1c = 0 always passes through a fixed point. That point is (1) (−1, 2) (2) (−1, −2) (3) (1, −2) (4) (1, −12 ) Q164.The sum of the series 1 + 4.2!1 + 16.4!1 + 64.6!1 + … … … ad inf. is (1) e−1 (2) e+1 √e √e (3) e−1 (4) e+1 2√e 2√e Q165.If A = [ 11 01 ] and I = [ 10 01 ] , then which one of the following holds for all n ≥1, by the principle of mathematical indunction (1) An = nA −(n −1)I (2) An = 2n−1A −(n −1)I (3) An = nA + (n −1)I (4) An = 2n−1A + (n −1)I Q166.If the coefficients of r th, (r + 1) th and (r + 2) th terms in the binomial expansion of (1+ y)m are in A.P., then m and r satisfy the equation (1) m2 −m(4r −1) + 4r2 −2 = 0 (2) m2 −m(4r + 1) + 4r2 + 2 = 0 (3) m2 −m(4r + 1) + 4r2 −2 = 0 (4) m2 −m(4r −1) + 4r2 + 2 = 0 Q167.The value of 50C4 + ∑6r=1 56−rC3 is (1) 55C4 (2) 55C3 (3) 56C3 (4) 56C4 Q168.If the coefficient of x7 in [ax2 + ( bx1 )]11 equals the coefficient of x−7 in [ax2 −( bx1 )]11 , then a and b satisfy the relation (1) a −b = 1 (2) a + b = 1 (3) a b = 1 (4) ab = 1 Q169.If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (−1, 2) and (3, 2), then the centroid of the triangle is JEE Main 2005 JEE Main Previous Year Paper (1) (−1, 37 ) (2) ( −13 , 73 ) (3) (1, 37 ) (4) ( 31 , 73 ) Q170.If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 −3ax + dy −1 = 0 intersect in two distinct points P and Q then the line 5x+ by −a = 0 passes through P and Q for (1) exactly one value of a (2) no value of a (3) infinitely many values of a (4) exactly two values of a Q171.A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is (1) an ellipse (2) a circle (3) a hyperbola (4) a parabola Q172.If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is (1) x2 + y2 −3ax −4by + (a2 + b2 −p2) = 0 (2) 2ax + 2by −(a2 −b2 + p2) = 0 (3) x2 + y2 −2ax −3by + (a2 −b2 −p2) = 0 (4) 2ax + 2by −(a2 + b2 + p2) = 0 Q173.If the pair of lines ax2 + 2(a + b)xy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then (1) 3a2 −10ab + 3b2 = 0 (2) 3a2 −2ab + 3b2 = 0 (3) 3a2 + 10ab + 3b2 = 0 (4) 3a2 + 2ab + 3b2 = 0 Q174.Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid point of PQ is (1) y2 −4x + 2 = 0 (2) y2 + 4x + 2 = 0 (3) x2 + 4y + 2 = 0 (4) x2 −4y + 2 = 0 Q175.An ellipse has OB as semi minor axis, F and F′ its focii and the angle FBF' is a right angle. Then the eccentricity of the ellipse is (1) 1 (2) 1 √2 2 (3) 1 (4) 1 4 √3 Q176.The locus of a point P(α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola x2 −y2 = 1 is a2 b2 (1) an ellipse (2) a circle (3) a parabola (4) a hyperbola Q177. limn→∞[ n21 sec2 n21 + n22 sec2 n24 + … . + n21 sec2 1] equals (1) 1 2 sec 1 (2) 12 cosec 1 (3) tan 1 (4) 21 tan 1 is equal toQ178.Let α and β be the distinct roots of ax2 + bx + c = 0, then limx→α 1−cos(ax2+bx+c)(x−α)2 (1) a2 2 (α −β)2 (2) 0 (3) −a22 (α −β)2 (4) 21 (α −β)2 JEE Main 2005 JEE Main Previous Year Paper Q179.If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately (1) 22.0 (2) 20.5 (3) 25.5 (4) 24.0 Q180.Let x1, x2, … , xn be n observations such that ∑x2i = 400 and ∑xi = 80. Then a possible value of n among the following is (1) 15 (2) 18 (3) 9 (4) 12 Q181.A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect after (1) 20 s (2) 1 s (3) 21 s (4) 24 s Q182.ABC is a triangle. Forces →P, →Q, →R acting along IA, IB and IC respectively are in equilibrium, where I is the incentre of △ABC . Then P : Q : R is (1) sin A : sin B : sin C (2) sin A2 : sin B2 : sin C2 (3) cos A2 : cos B2 : cos C2 (4) cos A : cos B : cos C are the roots of ax2 + bx + c = 0, a ≠0 thenQ183.In a triangle PQR, ∠R = π2 . If tan ( P2 ) and tan ( Q2 ) (1) a = b + c (2) c = a + b (3) b = c (4) b = a + c Q184.In a triangle ABC , let ∠C = π2 . If r is the inradius and R is the circumradius of the the triangle ABC , then 2(r + R) equals (1) b + c (2) a + b (3) a + b + c (4) c + a Q185.Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} . The relation is (1) reflexive and transitive only (2) reflexive only (3) an equivalence relation (4) reflexive and symmetric only Q186.If A2 −A + I = 0, then the inverse of A is (1) A + I (2) A (3) A −I (4) I −A Q187.The system of equations αx + y + z = α −1 x + αy + z = α −1 x + y + αz = α −1 has no solution, if α is JEE Main 2005 JEE Main Previous Year Paper (1) −2 (2) either −2 or 1 (3) not -2 (4) 1 Q188. 1 + a2x (1 + b2)x (1 + c2)x If a2 + b2 + c2 = −2 and f(x) = (1 + a2)x 1 + b2x (1 + c2)x then f(x) is a polynomial of degree (1 + a2)x (1 + b2)x 1 + c2x (1) 1 (2) 0 (3) 3 (4) 2 Q189. log an log an+1 log an+2 If a1, a2, a3, … , an, … are in G.P., then the determinant Δ = log an+3 log an+4 log an+5 is equal to log an+6 log an+7 log an+8 (1) 1 (2) 0 (3) 4 (4) 2 α, then 4x2 −4xy cos α + y2 is equal toQ190.If cos−1 x −cos−1 2y = (1) 2 sin 2α (2) 4 (3) 4 sin2 α (4) −4 sin2 α Q191.Let f : (−1, 1) →B, be a function defined by f(x) = tan−1 2x , then f is both one-one and onto when B 1−x2 is the interval (1) (0, π2 ) (2) [0, π2 ) (3) [−π2 , π2 ] (4) ( π2 , π2 ) Q192.A real valued function f(x) satisfies the functional equation f(x −y) = f(x)f(y) −f(a −x) f(a + y) where a is a given constant and f(0) = 1, f(2a −x) is equal to (1) −f(x) (2) f(x) (3) f(a) + f(a −x) (4) f(−x) Q193.Suppose f(x) is differentiable x = 1 and limh→0 h1 f(1 + h) = 5, then f ′(1) equals (1) 3 (2) 4 (3) 5 (4) 6 Q194.Area of the greatest rectangle that can be inscribed in the ellipse x2 + y2 = 1 is a2 b2 (1) 2ab (2) ab (3) 3ab (4) ab Q195.The normal to the curve x = a(cos θ + θ sin θ), y = a(sin θ −θ cos θ) at any point ' θ ' is such that (1) it passes through the origin (2) it makes angle π 2 + θ with the x-axis (3) it passes through (a π2 , −a) (4) it is at a constant distance from the origin Q196.A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Interval →Function (1) (−∞, ∞) →x3 −3x2 + 3x + 3 (2) [2, ∞) →2x3 −3x2 −12x + 6 (3) (−∞, 13 ] → 3x2 −2x + 1 (4) (−∞, −4] →x3 + 6x2 + 6 JEE Main 2005 JEE Main Previous Year Paper Q197.Let f be differentiable for all x. If f(1) = −2 and f ′(x) ≥2 for x ∈[1, 6], then (1) f(6) ≥8 (2) f(6) < 8 (3) f(6) < 5 (4) f(6) = 5 Q198.If f is a real-valued differentiable function satisfying |f(x) −f(y)| ≤(x −y)2, x, y ∈R and f(0) = 0, then f(1) equals (1) -1 (2) 0 (3) 2 (4) 1 1 x) 3 2Q199.If x is so small that x3 and higher powers of x may be neglected, then (1+x)3/2−(1+ (1−x)1/2 (1) 1 −38 x2 (2) 3x + 83 x2 (3) −38 x2 (4) x2 −38 x2 Q200.A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness than melts at a rate of 50 cm3/min. When the thickness of ice is 5 cm , then the rate at which the thickness of ice decreases, is (1) 36π 1 cm/min (2) 18π1 cm/min (3) 54π 1 cm/min (4) 6π5 cm/ min Q201.If the equation anxn + an−1xn−1 + … … + a1x = 0, a1 ≠0, n ≥2, has a positive root x = α, then the equation nanxn−1 + (n −1)an−1xn−2 + … . . +a1 = 0 has a positive root, which is (1) greater than α (2) smaller than α (3) greater than or equal to α (4) equal to α Q202. (log x−1) 2 dx is equal to ∫{ (1+(log x)2 } (1) log x + C (2) x + C (log x)2+1 x2+1 (3) xex + C (4) x + C 1+x2 (log x)2+1 Q203.If I1 = ∫10 2x2dx, I2 = ∫10 2x3dx, I3 = ∫21 2x2dx and I4 = ∫21 2x3dx then (1) I2 > I1 (2) I1 > I2 (3) I3 = I4 (4) I3 > I4 dt equalsQ204.Let f : R →R be a differentiable function having f(2) = 6, f ′(2) = ( 481 ). Then limx→2 ∫f(x)6 x−24t3 (1) 24 (2) 36 (3) 12 (4) 18 Q205.The value of ∫π−π cos21+axx dx, a > 0, is (1) aπ (2) π 2 (3) π (4) 2π a Q206.The area enclosed between the curve y = loge(x + e) and the coordinate axes is (1) 1 (2) 2 (3) 3 (4) 4 Q207.The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to bottom; then JEE Main 2005 JEE Main Previous Year Paper S1 : S2 : S3 is (1) 1 : 2 : 1 (2) 1 : 2 : 3 (3) 2 : 1 : 2 (4) 1 : 1 : 1 Q208.Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x), x-axis and . Then f ( π2 ) is the ordinates x = π4 and x = β > π4 is (β sin β + π4 cos β + √2β) + (1) ( π4 + √2 −1) (2) ( π4 −√2 1) + (3) (1 −π4 −√2) (4) (1 −π4 √2) Q209.The differential equation representing the family of curves y2 = 2c(x + √c), where c > 0, is a parameter, is of order and degree as follows: (1) order 1 , degree 2 (2) order 1, degree 1 (3) order 1, degree 3 (4) order 2, degree 2 Q210.If x dxdy = y(log y −log x + 1), then the solution of the equation is = cx (2) x log ( xy ) = cy (1) y log ( xy ) = cy (3) log ( xy ) = cx (4) log ( xy ) Q211.If C is the mid point of AB and P is any point outside AB, then −−−−−−(1) → → → (2) → → → PA + PB = 2PC PA + PB + 2PC = 0 −−−(3) → → → (4) None of these PA + PB + PC = 0 Q212.For any vectora a the value of (→a ×^i)2 + (→a × ^j)2 + (→a × ^k)2 is equal to (1) 3→a2 (2) →a2 (3) 2→a2 (4) 4→a2 + = [→a→b + →c→b] for Q213.If →a,→b, →c are non-coplanar vectors and λ is a real number then [λ(→a →b)λ2→bλ→c] (1) exactly one value of λ (2) no value of λ (3) exactly three values of λ (4) exactly two values of λ Q214.Let →a = ^i −^k,→b = x^i + ^j + (1 −x)^k and →c = y^i + x^j + (1 + x −y)^k . Then [→a,→b, →c] depends on (1) only y (2) only x (3) both x and y (4) neither x nor y Q215.The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is (1) 2 : 1 (2) 3 : √2 (3) 3 : 2 (4) 3 : 2√2 Q216.The line parallel to the x-axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx −2ay −3a = 0, where (a, b) ≠(0, 0) is (1) below the x-axis at a distance of 3 from it (2) below the x-axis at a distance of 2 from it 2 3 (3) above the x-axis at a distance of 3 from it (4) above the x-axis at a distance of 2 from it − 3 JEE Main 2005 JEE Main Previous Year Paper Q217.If the angle θ between the line x+1 1 = y−12 = z−22 and the plane 2x −y + √λz + 4 = 0 is such that sin θ = 13 the value of λ is (1) 5 (2) −3 3 5 (3) 3 (4) −4 4 3 Q218.The angle between the lines 2x = 3y = −z and 6x = −y = −4z is (1) 00 (2) 900 (3) 450 (4) 300 Q219.If the plane 2ax −3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres x2 + y2 + z2 + 6x −8y −2z = 13 and x2 + y2 + z2 −10x + 4y −2z = 8, then a equals (1) -1 (2) 1 (3) -2 (4) 2 Q220.The distance between the line →r = 2^i −2^j + 3^k + λ(^i −^j + 4^k) and the plane →r ⋅(^i + 5^j + ^k) = 5 is (1) 10 (2) 10 9 3√3 (3) 3 (4) 10 10 3 Q221.Let a, b and c be distinct non-negative numbers. If the vectors a^i + a^j + c^k,^i + ^k and c^i + c^j + b^k lie in a plane, then c is (1) the Geometric Mean of a and b (2) the Arithmetic Mean of a and b (3) equal to zero (4) the Harmonic Mean of a and b Q222.The plane x + 2y −z = 4 cuts the sphere x2 + y2 + z2 −x + z −2 = 0 in a circle of radius (1) 3 (2) 1 (3) 2 (4) √2 Q223.Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is (1) 2 (2) 1 9 9 (3) 8 (4) 7 9 9 Q224.A random variable X has Poisson distribution with mean 2. Then P(X > 1.5) equals (1) 2 (2) 0 e2 (3) 1 − 3 (4) 3 e2 e2 –1 1 1 Q225.Let A and B be two events such that P(A ∪B) = 6 , P(A ∩B) = 4 and P(¯A) = 4 , where ¯A stands for complement of event A . Then events A and B are (1) equally likely and mutually exclusive (2) equally likely but not independent (3) independent but not equally likely (4) mutually exclusive and independent JEE Main 2005 JEE Main Previous Year Paper

Q3. A ball is released from the top of a tower of height h metres. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds? (1) h/9 metres from the ground (2) 7 h/9 metres from the ground (3) 8 h/9 metres from the ground (4) 17 h/18 metres from the ground.

Q4. An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 cm. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be (1) 20 m (2) 40 m (3) 60 m (4) 80 m

Q5. A ball is thrown from a point with a speed v0 at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed v0/2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection? (1) yes, 60∘ (2) yes, 30∘ (3) no (4) yes, 45∘

Q6. A projectile can have the same range R for two angles of projection. If T1 and T2 be the time of flights in the two cases, then the product of the two time of flights is directly proportional to (1) 1/R2 (2) 1/R (3) R (4) R2

Q7. If t1 and t2 are the times of flight of two particles having the same initial velocity u and range R on the horizontal, then t21 + t22 is equal to (1) u2 (2) 4u2 g g2 (3) u2 (4) 1 2g