Q95.Species acting as both Bronsted acid and base is (1) (HSO4)−1 (2) Na2CO3 (3) NH3 (4) OH−1

Q96.Let the solubility of an aqueous solution of Mg(OH)2 be x then its ksp is (1) 4x3 (2) 108x5 (3) 27x4 (4) 9x

Q97.The solubility of Mg(OH)2 is S moles/litre. The solubility product under the same condition is (1) 4 S3 (2) 3S 4 (3) 4 S2 (4) S 3

Q99.Which one of the following statements is not true? (1) pH + pOH = 14 for all aqueous solutions (2) The pH of 1 × 10−8M HCI is 8 (3) 96,500 coulombs of electricity when passed (4) The conjugate base of H2PO−4 is HPO2−4 through a CuSO4 solution deposits 1 gram equivalent of copper at the cathode JEE Main 2003 JEE Main Previous Year Paper Q100.The solubility in water of a sparingly soluble salt AB is 1.0 × 10−5 mol L−1 . Its solubility product number will be (1) 4 × 10−10 (2) 1 × 10−15 (3) 1 × 10−10 (4) 4 × 10−15 Q101.When rain is accompanied by a thunderstorm, the collected rain water will have a pH value (1) slightly higher than that when the thunderstorm (2) uninfluenced by occurence of thunderstorm is not there (3) which depends on the amount of dust in air (4) slightly lower than that of rain water without thunderstorm Q102.Which one of the following processes will produce hard water? (1) Saturation of water with MgCO3 (2) Saturation of water with CaSO4 (3) Addition of Na2SO4 to water (4) Saturation of water with CaCO3 Q103.The substance not likely to contain CaCO3 is (1) calcined gypsum (2) sea shells (3) dolomite (4) a marble statue Q104.The solubilities of carbonates decrease down the magnesium group due to a decrease in (1) hydration energies of cations (2) inter-ionic attraction (3) entropy of solution formation (4) lattice energies of solids Q105.Several blocks of magnesium are fixed to the bottom of a ship to (1) make the ship lighter (2) prevent action of water and salt (3) prevent puncturing by under-sea rocks (4) keep away the sharks Q106.In curing cement plasters water is sprinkled from time to time. This helps in (1) developing interlocking needle-like crystals of (2) hydrating sand and gravel mixed with cement hydrated silicates (3) converting sand into silicic acid (4) keeping it cool Q107.Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that graphite (1) is an allotropic form of diamond (2) has molecules of variable molecular masses like polymers (3) has carbon atoms arranged in large plates of (4) is a non-crystalline substance rings of strongly bound carbon atoms with weak interplate bonds Q108.For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify before glass. The metal used can be (1) tin (2) sodium (3) magnesium (4) mercury JEE Main 2003 JEE Main Previous Year Paper Q109.Bottles containing C6H5 l and C6H5CH2I lost their original labels. They were labelled A and B for testing A and B were separately taken in test tubes and boiled with NaOH solution. The end solution in each tube was made acidic with dilute HNO3 and then some AgNO3 solution was added. Substance B gave a yellow precipitate. Which one of the following statements is true for this experiment? (1) A and C6H5CH2I (2) B and C6H5I (3) Addition of HNO3 was unnecessary (4) A was C6H5I Q110.Which one of the following statements is correct? (1) From a mixed precipitate of AgCl and AgI, (2) Ferric ions give a deep green precipitate on ammonia solution dissolves only AgCl adding potassium ferrocyanide solution (3) On boiling a solution having K+, Ca2+ and (4) Manganese salts give a violet borax bead test in HCO−3 ions we get a precipitate of K2Ca(CO3)2 . the reducing flame Q111.In the anion HCOO− the two carbon-oxygen bonds are found to be of equal length. What is the reason for it? (1) The C = O bond is weaker than the C −O bond (2) The anion HCOO− has two resonating structures (3) The anion is obtained by removal of a proton (4) Electronic orbitals of carbon atom are hybridised from the acid molecule Q112.The IUPAC name of CH3COCH(CH3)2 is (1) 2-methyl-3-butanone (2) 4-methylisopropyl ketone (3) 3-methyl-2-butanone (4) Isopropylmethyl ketone Q113.The general formula CnH2nO2 could be for open chain (1) carboxylic acids (2) diols (3) dialdehydes (4) deketones Q114. Among the following four structures I to IV. It is true that JEE Main 2003 JEE Main Previous Year Paper (1) only I and II are chiral compounds (2) only III i a chiral compound (3) only II and IV are chiral compounds (4) all four are chiral compounds Q115.Glass is a (1) super-cooled liquid (2) gel (3) polymeric mixture (4) micro-crystalline solid Q116.How many unit cells are present in a cubeshaped ideal crystal of NaCl of mass 1.00 g ? [Atomic masses: Na = 23, Cl = 35.5 ] (1) 5.14 × 1021 unit cells (2) 1.28 × 1021 unit cells (3) 1.71 × 1021 unit cells (4) 2.57 × 1021 unit cells Q117.Which of the following could act as apropellant for rockets? (1) Liquid oxygen + liquid argon (2) Liquid hydrogen + liquid oxygen (3) Liquid nitrogen + liquid oxygen (4) Liquid hydrogen + liquid nitrogen Q118.If liquids A and B form an ideal solution (1) the entropy of mixing is zero (2) the free energy of mixing is zero (3) the free energy as well as the entropy of mixing (4) the enthalpy of mixing is zero are each zero Q119.In a 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.3. Taking kf for water as 1.85 , the freezing point of the solution will be nearest to (1) −0.360∘C (2) −0.260∘C (3) +0.480∘C (4) −0.480∘C Q120.A pressure cooker reduces cooking time for food because (1) boiling point of water involved in cooking is (2) the higher pressure inside the cooker crushes the increased food material (3) cooking involves chemical changes helped by a (4) heat is more evenly distributed in the cooking rise in temperature space Q121.For a cell reaction involving a two-electron change, the standard e.m.f. of the cell is found to be 0.295 V at 25∘C. The equilibrium constant of the reaction at 25∘C will be (1) 29.5 × 10−2 (2) 10 (3) 1 × 1010 (4) 1 × 10−10 Q122.Standard reduction electrode potentials of three metals A,B\&C are respectively +0.5 V, −3.0 V& −1.2 V. The reducing, powers of these metals are (1) A > B > C (2) C > B > A (3) A > C > B (4) B > C > A Q123.When during electrolysis of a solution of AgNO39650 coulombs of charge pass through the electroplating bath, the mass of silver deposited on the cathode will be (1) 10.8 g (2) 21.6 g (3) 108 g (4) 1.08 g JEE Main 2003 JEE Main Previous Year Paper Q124.For the redox reaction Zn(s) + Cu2+(0.1M) →Zn2+(1M) + Cu(s) taking place in a cell, E0cell is 1.10 volt. E∘ for the cell will be (2.303 RTF = 0.0591) (1) 1.80 volt (2) 1.07 volt (3) 0.82 volt (4) 2.14 volt Q125.The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g , the mass of it remaining undecayed after 18 hours would be (1) 8.0 g (2) 12.0 g (3) 16.0 g (4) 4.0 g Q126.In respect of the equation k = Ae−Eo/RT in chemical kinetics, which one of the following statements is correct? (1) A is adsorption factor (2) Ea is energy of activation (3) R is Rydberg's constant (4) k is equilibrium constant Q127.The rate law for a reaction between the substances A and B is given by Rate = k[A]n[B]m On doubling the concentration of A and halving the concentration of B, the ratio of the new rate to the earlier rate of the reaction will be as (1) (m + n) (2) (n −m) (3) 2(n−m) (4) 1 2(m+n) Q128.For the reaction system: 2NO(g) + O2( g) →2NO2( g) volume is suddenly reduce to half its value by increasing the pressure on it. If the reaction is of first order with respect to O2 and second order with respect to NO, the rate of reaction will (1) diminish to one-eighth of its initial value (2) increase to eight times of its initial value (3) increase to four times of its initial value (4) diminish to one-fourth of its initial value Q129.Which one of the following characteristics is not correct for physical adsorption? (1) Adsorption increases with incresae in (2) Adsorption is spontaneous temperature (3) Both enthalpy and entropy of adsorption are (4) Adsorption on solids is reversible negative Q130.What may be expected to happen when phosphine gas is mixed with chlorine gas? (1) PCI3 and HCI are formed and the mixture (2) PCI5 and HCI are formed and the mixture cools warms up down (3) PH3. Cl2 is formed with warming up (4) The mixture only cools down Q131.Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The explanation for it is that JEE Main 2003 JEE Main Previous Year Paper (1) oxygen in air reacts with the emitted HCI gas to (2) strong affinity of HCI gas for miosture in air form a cloud of chlorine gas results in forming of droplets of liquid solution which appears like a cloudy smoke. (3) due to strong affinity for water, concentrated (4) concentrated hydrochloric acid emits strongly hydrochloric acid pulls moisture of air towards it smelling HCI gas all the time. self. This moisture forms droplets of water and hence the cloud. Q132.Which one of the following nitrates will leave behind a metal on strong heating? (1) Copper nitrate (2) Manganese nitrate (3) Silver nitrate (4) Ferric nitrate Q133.The radius of La3+ (Atomic number of La = 57 ) is 1.06Å . Which one of the following given values will be closest to the radius of Lu3+ (Atomic number of Lu = 71 )? (1) 1.40Å (2) 1.06Å (3) 0.85Å (4) 1.60Å Q134.The number of d-electrons retained in Fe2+ (At.no.of Fe = 26 ) ion is (1) 4 (2) 5 (3) 6 (4) 3 Q135.Which one of the following is an amphoteric oxide? (1) Na2O (2) SO2 (3) B2O3 (4) ZnO Q136.A red solid is insoluble in water. However it becomes soluble if some KI is added to water. Heating the red solid in a test tube results in liberation of some violet coloured fumes and droplets of a metal appear on the cooler parts of the test tube. The red solid is (1) HgI2 (2) HgO (3) Pb3O4 (4) (NH4)2Cr2O7 Q137.A reduction in atomic size with increase in atomic number is a characteristic of element of (1) d-block (2) f-block (3) radioactive series (4) high atomic masses Q138.What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid? (1) Cr2O2−7 and H2O are formed (2) CrO2−4 is reduced to +3 state of Cr (3) CrO2−4 is oxidized to +7 state of Cr (4) Cr3+ and Cr2O2−7 are formed Q139.The atomic numbers of vanadium (V), Chromium (Cr), manganese (Mn) and iron (Fe) are respectively 23 , 24,25 and 26 . Which one of these may be expected to have the highest second ionization enthalpy? (1) Cr (2) Mn (3) Fe (4) V Q140.Ammonia forms the complex ion [Cu(NH3)4]2+ with copper ions in alkaline solutions but not in acidic solutions. What is the reason for it? JEE Main 2003 JEE Main Previous Year Paper (1) In acidic solutions protons coordinate with (2) In alkaline solutions insoluble Cu(OH)2 is ammonia molecules forming NH+4 ions and NH3 precipitated which is soluble in excess of any molecules are not available alkali (3) Copper hydroxide is an amphoteric substance (4) In acidic solutions hydration protects copper ions. Q141.One mole of the complex compound Co(NH3)5Cl3 , gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with two moles of AgNO3 solution to yield two moles of AgCl (s). The structure of the complex is (1) [Co(NH3)3Cl3] ⋅2NH3 (2) [Co(NH3)4Cl2]Cl. NH3 (3) [Co(NH3)4Cl]Cl2. NH3 (4) [Co(NH3)5Cl]Cl2 Q142.In the coordination compound, K4 [Ni(CN)4], the oxidation state of nickel is (1) 0 (2) +1 (3) +2 (4) −1 Q143.On mixing a certain alkane with chlorine and irradiating it with ultravioletlight, it forms only one monochloroalkane. This alkane could be (1) pentane (2) isopentane (3) neopentane (4) propane Q144.Butene- 1 may be converted to butane by reaction with (1) Sn −HCI (2) Zn −Hg (3) Pd/H2 (4) Zn −HCI Q145.An ether is more volatile than an alcohol having the same molecular formula. This is due to (1) alcohols having resonance structures (2) inter-molecular hydrogen bonding in ethers (3) inter-molecular hydrogen bonding in alcohols (4) dipolar character of ethers Q146.During dehydration of alcohols to alkenes by heating with conc. H2SO4 the initiation step is (1) formation of carbocation (2) elimination of water (3) formation of an ester (4) protonation of alcohol molecule Q147.The reaction of chloroform with alcoholic KOH and p-toluidine forms (1) < smiles>Cc1ccc(Cl)cc1 < /smiles> (2) < smiles>Cc1ccc(NC(Cl)Cl)cc1 < /smiles> (3) < smiles>Cc1ccc(C)cc1 < /smiles> (4) < smiles>Cc1ccc(C#N)cc1 < /smiles> Q148.When CH2 = CH −COOH is reduced with LiAlH4 , the compound obtained will be (1) CH2 = CH −CH2OH (2) CH3 −CH2 −CH2OH (3) CH3 −CH2 −CHO (4) CH3 −CH2 −COOH Q149.Ethyl isocyanide on hydrolysis in acidic medium generates (1) propanoic acid and ammonium salt (2) ethanoic acid and ammonium salt (3) methylamine salt and ethanoic acid (4) ethylamine salt and methanoic acid Q150.The correct order of increasing basic nature for the bases NH3, CH3NH2 and (CH3)2NH is JEE Main 2003 JEE Main Previous Year Paper (1) (CH3)2NH < NH3 < CH3NH2 (2) NH3 < CH3NH2 < (CH3)2NH (3) CH3NH2 < (CH3)2NH < NH3 (4) CH3NH2 < NH3 < (CH3)2NH Q151.Nylon threads are made of (1) polyester polymer (2) polyamide polymer (3) polyethylene polymer (4) polyvinyl polymer Q152.Complete hydrolysis of cellulose gives (1) D-ribose (2) D-glucose (3) L-glucose (4) D-fructose Q153.The reason for double helical structure of DNA is operation of (1) dipole-dipole interaction (2) hydrogen bonding (3) electrostatic attractions (4) van der Waals' forces Q154.If the sum of the roots of the quadratic equation ax2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a c , ba and bc are in (1) Arithmetic - Geometric Progression (2) Arithmetic Progression (3) Geometric Progression (4) Harmonic Progression Q155.The value of ' a ' for which one root of the quadratic equation (a2 −5a + 3)x3 + (3a −1)x + 2 = 0 is twice as large as the other is (1) −13 (2) 23 (3) −23 (4) 13 Q156.The number of real solutions of the equation x2 −3|x| + 2 = 0 is (1) 3 (2) 2 (3) 4 (4) 1 Q157.If z and ω are two non-zero complex numbers such that |zω| = 1 and Arg(z) −Arg(ω) = π2 , then ¯zω is equal to (1) −i (2) 1 (3) −1 (4) i. Q158.Let Z1 and Z2 be two roots of the equation x2 + aZ + b = 0 being complex. Further, assume that the origin, Z1 and Z2 form an equilateral triangle. Then (1) a2 = 4b (2) a2 = b (3) a2 = 2b (4) a2 = 3b Q159.If ( 1+i1−i ) x = 1 then (1) x = 2n + 1 , where n is any positive integer (2) x = 4n, where n is any positive integer (3) x = 2n, where n is any positive integer (4) x = 4n + 1 , where n is any positive integer Q160.If nCr denotes the number of combination of n things taken r at a time, then the expression nCr+1 + nCr−1 + 2xnCr equals JEE Main 2003 JEE Main Previous Year Paper (1) n+1Cr+1 (2) n+2Cr (3) n+2Cr+1 (4) n+1Cr Q161.A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is (1) 346 (2) 140 (3) 196 (4) 280 Q162.The number of ways in which 6 men and 5 women can dine at a found table if no two women are to sit together is given by (1) 7 × 5 (2) 6 × 5 (3) 30 (4) 5 × 4 ′(1) f ′′(1) ′′(1) (−1)nf ′′(1) Q163.If f(x) = xn , then the value of f(1) −f 1 + 2! −f 3! + … … … … . n! is (1) 1 (2) 2n (3) 2n −1 (4) 0 Q164.If x1, x2, x3 and y1, y2, y3 are both in G.P. with the same common ratio, then the points (x1, y1), (x2, y2) and (x3 , y3 ) (1) are vertices of a triangle (2) lie on a straight line (3) lie on an ellipse (4) lie on a circle Q165.Let R1 and R2 respectively be the maximum ranges up and down an inclined plane and R be the maximum range on the horizontal plane. Then R1, R, R2 are in (1) Н.P (2) A.G.P (3) A.P (4) G.P. Q166.Let f(x) be a polynomial function of second degree. If f(1) = f(−1) and a, b, c are in A.P, then f ′(a), f ′(c) are in (1) Arithmetic-Geometric Progression (2) A.P. (3) G.P. (4) H.P. Q167.The sum of the series 1.2 1 − 2.31 + 3.41 … … … … … … .. up to ∞ is equal to (1) loge ( 4e ) (2) 2 loge 2 (3) loge 2 −1 (4) loge 2 Q168.If x is positive, the first negative term in the expansion of (1 + x)27/5 is (1) 6th term (2) 7th term (3) 5th term (4) 8th term Q169.The number of integral terms in the expansion of (√3 + 8√5)256 is (1) 35 (2) 32 (3) 33 (4) 34 Q170.A square of side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle α (0 < α < π4 ) with the positive direction of x-axis. The equation of its diagonal not passing JEE Main 2003 JEE Main Previous Year Paper through the origin is (1) y(cos α + sin α) + x(cos α −sin α) = a (2) y(cos α −sin α) −x(sin α −cos α) = a (3) y(cos α + sin α) + x(sin α −cos α) = a (4) y(cos α + sin α) + x(sin α + cos α) = a Q171.If the pair of straight lines x2 −2pxy −y2 = 0 and x2 −2pxy −y2 = 0 be such that each pair bisects the angle between the other pair, then (1) pq = −1 (2) p = q (3) p = −q (4) pq = 1 Q172.Locus of a centriod of the triangle whose vertices are (a cos t, a sin t), (b sin t, −b cos t) and (1, 0), where t is a parameter, is (1) (3x + 1)2 + (3y)2 = a2 −b2 (2) (3x −1)2 + (3y)2 = a2 −b2 (3) (3x −1)2 + (3y)2 = a2 + b2 (4) (3x + 1)2 + (3y)2 = a2 + b2 −−Q173.The vectors AB→ = 3^i + 4^k&AC→ = 5^i −2^j + 4^k are the sides of a triangle ABC. The length of the median through A is (1) √288 (2) √18 (3) √72 (4) √33 Q174.If the equation of the locus of a point equidistant from the point (a1, b1) and (a2, b2) is (a1 −b2)x + (a1 −b2)y + c = 0, then the value of 'c' is (2) 1 a2 2 2 + b22 −a21 −b21 + b21 −a22 −b22 (1) √a21 (3) a21 −a22 + b21 −b22 (4) 21 (a21 + a22 + b21 + b22) Q175.If the two circles (x −1)2 + (y −3)2 = r2 and x2 + y2 −8x + 2y + 8 = 0 intersect in two distinct point, then (1) r > 2 (2) 2 < r < 8 (3) r < 2 (4) r = 2 Q176.The lines 2x −3y = 5 and 3x −4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is (1) x2 + y2 −2x + 2y = 62 (2) x2 + y2 + 2x −2y = 62 (3) x2 + y2 + 2x −2y = 47 (4) x2 + y2 −2x + 2y = 47 Q177.The normal at the point (bt12, 2bt1) on a parabola meets the parabola again in the point (bt22, 2bt2), then (1) t2 = t1 + t12 (2) t2 = −t1 −2t1 (3) t2 = −t1 + 2 (4) t2 = t1 −2 t1 t1 y2 Q178.The foci of the ellipse x2 coincide. Then the value of b2 is 16 + = 1 and the hyperbola 144x2 −y281 = 251 b2 (1) 9 (2) 1 (3) 5 (4) 7 Q179. limn→∞ 1+24+34+…n4n5 −limn→∞ 1+23+33+…n3n5 (1) 1 (2) 1 5 30 (3) Zero (4) 1 4 JEE Main 2003 JEE Main Previous Year Paper Q180.If limx→0 log(3+x)−log(3−x)x = k, the value of k is (1) −23 (2) 0 (3) −13 (4) 23 Q181.Let f(a) = g(a) = k and their nth derivatives f n(a), gn(a) exist and are not equal for some n. Further if f(a)g(x)−f(a)−g(a)f(x)+f(a) limx→a g(x)−f(x) = 4 then the value of k is (1) 0 (2) 4 (3) 2 (4) 1 Q182. [1 −tan ( x2 )][1 −sin x] lim x→π2 [1 + tan ( x2 )] [π −2x3] is (1) ∞ (2) 18 (3) 0 (4) 1 32 Q183.The median of a set of 9 distinct observations is 20.5 . If each of the largest 4 observations of the set is increased by 2 , then median of the new set (1) remains the same as that of the original set (2) is increased by 2 (3) is decreased by 2 (4) is two times the original median Q184.In an experiment with 15 observations on x, the following results were available: Σx2 = 2830, Σx = 170 One observation that was 20 was found to be wrong and was replaced by the correct value 30 . The corrected variance is (1) 8.33 (2) 78.00 (3) 188.66 (4) 177.33 Q185.The upper 34 th portion of a vertical pole subtends an angle tan−1 53 at a point in the horizontal plane through its foot and at a distance 40 m from the foot. (1) 80 m (2) 20 m (3) 40 m (4) 80 m Q186.The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is (1) a 4 cot ( 2nπ ) (2) a cot ( nπ ) (3) a 2 cot ( 2nπ ) (4) acot ( 2nπ ) Q187.In a triangle ABC, medians AD and BE are drawn. If AD = 4, ∠DAB = π6 and ∠ABE = π3 , then the area of the △ABC is (1) 64 (2) 8 3 3 (3) 16 (4) None of these 3 Q188.If in a triangle ABCa cos2 ( C2 ) + c2 cos2 ( A2 ) = 32b , then the sides a, b and c (1) satisfy a + b = c (2) are in A.P. (3) are in G.P. (4) are in H.P. JEE Main 2003 JEE Main Previous Year Paper , then and A2 =Q189.If A = [ab ba ] [αβ αβ ] (1) α = 2ab, β = a2 + b2 (2) α = a2 + b2, β = ab (3) α = a2 + b2, β = 2ab (4) α = a2 + b2, β = a2 −b2 Q190.If the system of linear equations x + 2ay + az = 0 x + 3by + bz = 0 x + 4cy + cz = 0 has a non-zero solution, then a, b, c (1) satisfy a + 2b + 3c = 0 (2) are in A.P. (3) are in G.P. (4) are in H.P. Q191. 1 ωn ω2n If 1, ω, ω2 are the cube roots of unity, then Δ = ωn ω2n 1 is equal to ω2n 1 ωn (1) ω2 (2) 0 (3) 1 (4) ω Q192.The trigonometric equation sin−1 x = 2 sin−1 a has a solution for 1 1 (2) (1) |a| ≥ 1 < |a| < 2 √2 √2 (3) all real values of a (4) |a| < 12 + √x2 +Q193.The function f(x) = log (x 1), is (1) neither an even nor an odd function (2) an even function (3) an odd function (4) a periodic function Q194.Domain of definition of the function f(x) = 3 + log10 (x3 −x), is 4−x2 (1) (−1, 0) ∪(1, 2) ∪(2, ∞) (2) (0, 2) (3) (−1, 0) ∪(0, 2) (4) (1, 2) ∪(2, ∞) Q195.If f : R →R satisfies f(x + y) = f(x) + f(y), for all x, y ∈R and f(1) = 7 , then ∑nr=1 f(r) is (1) 7n(n+1) (2) 7n 2 2 (3) 7(n+1) (4) 7n + (n + 1) 2 2 , when n isodd isQ196.A function f from the set of natural numbers to integers defined by f(n) = n−1n { 2 , when n is even (1) neither one-one nor onto (2) one-one but not onto (3) onto but not one-one (4) one-one and onto both. |x| x ≠0 then f(x) isQ197.If f(x) = 1 + x1 ), {xe−(0 , x = 0 (1) discontinuous every where (2) continuous as well as differentiable for all x (3) continuous for all x but not differentiable at (4) neither differentiable nor continuous at x = 0 x = 0 Q198.If the function f(x) = 2x2 −9ax2 + 12a2x + 1 , where a > 0 , attains its maximum and minimum at p and q respectively such that p2 = q, then a equals JEE Main 2003 JEE Main Previous Year Paper (1) 1 (2) 3 2 (3) 1 (4) 2 Q199.The real number x when added to its inverse gives the minimum value of the sum at x equal to (1) −2 (2) 2 (3) 1 (4) −1 Q200.Let k, is dx > 0 . If ∫41 x3 esin 3dx = F(k) −F(1) then one of the possible values of d F(x) = ( esinxx )x (1) 64 (2) 15 (3) 16 (4) 63 Q201.If f(y) = ey, g(y) = y; y > 0 and F(t) = ∫t0 f(t −y)g(y), then (1) F(t) = te−t (2) F(t) = 1 −te−t(1 + t) (3) F(t) = et −(1 + t) (4) F(t) = tet Q202.If f(a + b −x) = f(x) then ∫ba xf(x)dx is equal to (1) a+b 2 ∫ba f(a + b −x)dx (2) a+b2 ∫ba f(b −x)dx (3) a+b 2 ∫ba f(x)dx (4) b−a2 ∫ba f(x)dx Q203.Let f(x) be a function satisfying f ′(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2 . Then the value of the integral ∫10 f(x)g(x)dx, is (1) e + e22 + 25 (2) e −e22 −52 (3) e + e22 −32 (4) e −e22 −32 Q204.The value of the integral I = ∫10 x(1 −x)ndx is (1) n+1 1 + n+21 (2) n+11 (3) 1 (4) n+2 n+1 1 − n+21 sec2 0 tdt isQ205.The value of limx→0 ∫x2 x sin x (1) 0 (2) 3 (3) 2 (4) 1 Q206.The area of the region bounded by the curves y = |x −1| and y = 3 −|x| is (1) 6 sq. units (2) 2 sq. units (3) 3 sq. units (4) 4 sq. units Q207.The degree and order of the differential equation of the family of all parabolas whose axis is X-axis, are respectively. (1) 2,3 (2) 2,1 (3) 1,2 (4) 3,2 = 0 , isQ208.The solution of the differential equation (1 + y2) + (x −etan−1 y) dxdy (1) xe2 tan−1 y = etan−1 y + k (2) (x −2) = ke2 tan−1 y (3) 2xetan−1 y = e2 tan−1 y + k (4) xetan−1 y = tan−1 y + k JEE Main 2003 JEE Main Previous Year Paper → → → Q209.A couple is of moment G and the force forming the couple is P. If P is turned through a right angle the → → moment of the couple thus formed is H . If instead, the force P are turned through an angle α, then the moment of couple becomes → → → → (1) (2) H sin α − G cos α G sin α − H cos α → → → (3) (4) H sin α + G cos α G sin α +→H cos α → → → → → → Q210.The resultant of forces P and Q is R. If Q is doubled then R is doubled. If the direction of Q is reversed, then → R is again doubled. Then P2 : Q2 : R2 is (1) 2 : 3 : 1 (2) 3 : 1 : 1 (3) 2 : 3 : 2 (4) 1 : 2 : 3 →Q211.Let →u = ^i +^j,→v = ^i −^j and w = ^i + 2^j + 3^k. If ^n is a unit vector such that →u ⋅^n = 0 and →v⋅^n = 0 , then |→w ⋅^n| is equal to (1) 3 (2) 0 (3) 1 (4) 2 Q212.A particle acted on by constant forces 4^i + ^j −3^k and 3^i + ^j −^k to the point 5^i + 4^j −^k. The total work done by the forces is (1) 50 units (2) 20 units (3) 30 units (4) 40 units y−3Q213.The lines x−2 1 = 1 = z−4−k and x−1k = y−41 = z−51 are coplanar if (1) k = 3 or −2 (2) k = 0 or −1 (3) k = 1 or −1 (4) k = 0 or −3 Q214. →a,→b, →c are 3 vectors, such that →a + →b + →c = 0, |→a| = 1, |→b| = 2 ∣→a then →a ⋅→b + →b ⋅→c + →c ⋅→a is equal to (1) 1 (2) 0 (3) −7 (4) 7 Q215.A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 1)B(2, 1, 3) and C(−1, 1, 2). Then the angle between the faces OAB and ABC will be (1) 90∘ (2) cos−1 ( 3519 ) (3) cos−1 ( 1731 ) (4) 30∘ Q216. a a2 1 + a3 If b b2 1 + b3 = 0 and vectors (1, a, a2), (a, b, b2) and (a, c, c2) are non-coplanar, then the product abc c c2 1 + c3 equals (1) 0 (2) 2 (3) −1 (4) 1 Q217.Consider points A, B, C and D with position vectors 7^i −4^j + 7^k,^i −6^j + 10^k, −^i −3^j + 4^k and 5^i −^j + 5^k respectively. Then ABCD is a JEE Main 2003 JEE Main Previous Year Paper (1) parallelogram but not a rhombus (2) square (3) rhombus (4) rectangle Q218.If →u, →v and →w are three non-coplanar vectors, then (→u + →v −→w). (→u −→v) × (→v −→w) equals (1) 3→u. →v × →w (2) 0 (3) →u ⋅→v×→w (4) →u ⋅→w ×→v Q219.The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + z2 + 4x −2y −6z = 155 is (1) 39 (2) 26 (3) 11 134 (4) 13 Q220.The two lines x = ay + b, z = cy + d and x = a′y + b′z = c′y + d′ will be perpendicular, if and only if (1) aa′ + cc′ + 1 = 0 (2) aa′ + bb′ + cc′ + 1 = 0 (3) a′ + bb′ + cc′ = 0 (4) (a + a′) (b + b′) + (c + c′) = 0 Q221.The radius of the circle in which the sphere x2 + y2 + z2 + 2x −2y −4z −19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is (1) 4 (2) 1 (3) 2 (4) 3 Q222.Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a′, b′, c′ from the origin then (1) 1 + 1 + 1 − 1 − 1 − 1 = 0 (2) 1 + 1 + 1 + 1 + 1 + 1 = 0 a2 b2 c2 a′2 b′2 c′2 a2 b2 c2 a22 b22 c22 (3) 1 + 1 − 1 + 1 + 1 − 1 = 0 (4) 1 − 1 − 1 + 1 − 1 − 1 = 0 a2 b2 c2 a′2 b′2 c′2 a2 b2 c2 a′2 b′2 c′2 Q223.The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P (X = 1) is (1) 1 (2) 1 4 32 (3) 1 (4) 1 16 8 Q224.Events A, B, C are mutually exclusive events such that P(A) = 3x+13 , P(B) = x−14 and P(C) = 1−2x4 . The set of possible values of x are in the interval. (1) [0, 1] (2) [ 31 , 12 ] (3) [ 13 , 23 ] (4) [ 13 , 133 ] Q225.Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is (1) 2 (2) 4 5 5 (3) 3 (4) 1 5 5 JEE Main 2003 JEE Main Previous Year Paper