Practice Questions

Q48.In a metre bridge experiment null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y . If X < Y , then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y? (1) 50 cm (2) 80 cm (3) 40 cm (4) 70 cm

Q51.The length of a magnet is large compared to its width and breadth. The time period of its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be (1) 2 s (2) 2/3 s (3) 2√3 s (4) 2/√3 s

Q54.A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be (1) nB (2) n2 B (3) 2nB (4) 2n2B JEE Main 2004 JEE Main Previous Year Paper

Q55.The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54μT. What will be its value at the centre of the Loop? (1) 250μT (2) 150μT (3) 125μT (4) 75μT

Q56.Two long conductors, separated by a distance d carry current I1 and I2 in the same direction. They exert a force F on each other. Now the current in one of them increased to two times and its direction reversed. The distance is also increased to 3 d . The new value of the force between them is (1) −2 F (2) F/3 (3) −2F/3 (4) −F/3

Q63.An electromagnetic wave of frequency v = 3.0MHz passes from vacuum into a dielectric medium with permittivity ε = 4.0 . Then (1) wavelength is doubled and the frequency remains (2) wavelength is doubled and frequency becomes unchanged half (3) wavelength is halved and frequency remains (4) wavelength and frequency both remain unchanged unchanged.

Q64.A light ray is incident perpendicular to one face of a 90∘ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is 45∘ , we conclude that the refractive index n (1) n < 12 (2) n > √2 (3) n > 1 (4) n < √2 √2

Q67.The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment is (1) infinite (2) five (3) three (4) zero

Q68.A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (1) E/c (2) 2E/c (3) Ec (4) E/c2

Q70.The work function of a substance is 4.0eV . Then longest wavelength of light that can cause photoelectron emission from this substance approximately (1) 540 nm (2) 400 nm (3) 310 nm (4) 220 nm

Q72.A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1. The ratio of their nuclear sizes will be (1) 21/3 : 1 (2) 1 : 31/2 (3) 31/2 : 1 (4) 1 : 21/3

Q73.The binding energy per nucleon of deuteron (21H) and helium nucleus (42He) is 1.1MeV and 7MeV respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is (1) 13.9MeV (2) 26.9MeV (3) 23.6MeV (4) 19.2MeV

Q74.When npn transistor is used as amplifier (1) electrons move from base to collector (2) holes move from emitter to base (3) electrons move from collector to base (4) holes move from base to emitter.

Q78.To neutralize completely 20 mL of 0.1M aqueous solution of phosphorous acid (H3PO3), the volume of 0.1M aqueous KOH solution required is (1) 10 mL (2) 60 mL (3) 40 mL (4) 20 mL JEE Main 2004 JEE Main Previous Year Paper

Q80.Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers I = 1 and 2 are respectively (1) 12 and 4 (2) 16 and 5 (3) 16 and 4 (4) 12 and 5

Q81.The wavelength of the radiation emitted, when in hydrogen atom electron falls from infinity to stationary state 1 , would be (Rydberg constant = 1.097 × 107 m−1) (1) 91 nm (2) 9.1 × 10−8 nm (3) 406 nm (4) 192 nm

Q83.Which one the following ions has the highest value of ionic radius? (1) Li+ (2) F− (3) O2− (4) B3+

Q84.Consider the following nuclear reactions 238 92 M →xyN + 42He N y N →ABL + 2β+ The number of neutrons in the element L is (1) 142 (2) 146 (3) 140 (4) 144

Q85.The correct order of bond angles (smallest first) in H2 S, NH3, BF3 and SiH4 is (1) H2 S < SiH4 < NH3 < BF3 (2) H2 S < NH3 < BF3 < SiH4 (3) H2 S < NH3 < SiH4 < BF3 (4) NH3 < H2 S < SiH4 < BF3

Q87.The states of hybridization of boron and oxygen atoms in boric acid (H3BO3) are respectively (1) sp2 and sp2 (2) sp3 and sp3 (3) sp3 and sp2 (4) sp2 and sp3

Q88.Which one of the following has the regular tetrahedral structure? JEE Main 2004 JEE Main Previous Year Paper (1) XeF4 (2) [Ni(CN)4]2− (3) BF4−4 (4) SF4

Q90.Which one of the following aqueous solutions will exhibit highest boiling point? (1) 0.01MNa2SO4 (2) 0.015M glucose (3) 0.015M urea (4) 0.01MKNO3

Q94.The formation of the oxide ion O2−(g) requires first an exothermic and then an endothermic step as shown below O(g) + e−O−(g)ΔH∘= −142kJmol−1 O−(g) + e−O2−(g)ΔH∘= 844kJmol−1 (1) Oxygen is more electronegative (2) O− ion has comparatively larger size than oxygen atom (3) O− ion will tend to resist the addition of another (4) Oxygen has high electron affinity electron

Q96.The enthalpies of combustion of carbon and carbon monoxide are −393.5 and −283 kJ mol−1 respectively. The enthalpy of formation of carbon monoxide per mole is (1) 110.5 kJ (2) −110.5 kJ (3) −676.5 kJ (4) 676.5 kJ

Q99.The equilibrium constant for the reaction N2( g) + O2( g) ⇌2NO(g) at temperature T is 4 × 10−4 . The value of Kc for the reaction NO(g) ⇌12 N2( g) + 21 O2( g) at the same temperature is (1) 2.5 × 102 (2) 0.02 (3) 4 × 10−4 (4) 50 Q100.Among Al2O3, SiO2, P2O3 and SO2 the correct order of acid strength is (1) SO2 < P2O3 < SiO2 < Al2O3 (2) Al2O3 < SiO2 < P2O3 < SO2 (3) Al2O3 < SiO2 < SO2 < P2O3 (4) SiO2 < SO2 < Al2O3 < P2O3 Q101.The conjugate base of H2PO−4 is (1) PO3−4 (2) HPO2−4 (3) H3PO4 (4) P2O5 Q102.The molar solubility product is Ksp . ' s ' is given in terms of Ksp by the relation (1) Ksp 1/4 (2) Ksp 1/5 s = s = ( 128 ) ( 256 ) (3) S = (256 Ksp)1/5 (4) s = (128 Ksp)1/4 Q103.Excess of KI reacts with CuSO4 solution and then Na2 S2O3 solution is added to it. Which of the statements is incorrect for this reaction? (1) Cu2I2 is reduced (2) Evolved I2 is reduced (3) Na2 S2O3 is oxidized (4) Cul2 is formed Q104.Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN− ion towards metal species is (1) a, b, c (2) a, b, c (3) c, a (4) b, c Q105.Beryllium and aluminium exhibit many properties which are similar. But the two elements differ in (1) exhibiting maximum covalency in compound (2) exhibiting amphoteric nature in their oxides (3) forming covalent halides (4) forming polymeric hydrides Q106.Aluminium chloride exists as dimer, Al2Cl6 in solid state as well as in solution of non-polar solvents such as benzene. When dissolved in water, it gives (1) Al3+ + 3Cl− (2) Al2O3 + 6HCl (3) [Al(OH)6]3− (4) [Al(H2O)6]3+ + 3Cl− Q107.The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons got converted to grey powder. This transformation is related to JEE Main 2004 JEE Main Previous Year Paper (1) an interaction with nitrogen of the air at very (2) an interaction with water vapour contained in the low temperatures humid air (3) a change in the partial pressure of oxygen in the (4) a change in the crystalline structure of tin air Q108.For which of the following parameters the structural isomers C2H5OH and CH3OCH3 would be expected to have the same values? (Assume ideal behaviour) (1) Heat of vaporization (2) Gaseous densities at the same temperature and pressure (3) Boiling points (4) Vapour pressure at the same temperature Q109.The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is (1) Fe4[Fe(CN)6]3 (2) Na4 [Fe(CN)5NOS] (3) Fe(CN)3 (4) Na3 [Fe(CN)6] Q110.The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100 mL of 0.1M sulphuric acid. The excess of acid required 20 mL of 0.5M sodium hydroxide solution hydroxide solutio for complete neutralization. The organic compound is (1) acetamide (2) thiourea (3) urea (4) benzamide Q111. The IUPAC name of the compound (1) 3, 3- dimethyl -1- hydroxy cyclohexane (2) 1,1-dimethyl -3- cyclohexanol (3) 3,3- dimethyl -1- cyclohexanol (4) 1,1 - dimethyl -3- hydroxy cyclohexane Q112.Which of the following will have meso-isomer also? (1) 2- chlorobutane (2) 2- hydroxyopanoic acid (3) 2,3 - dichloropentane (4) 2-3- dichlorobutane Q113. Rate of the reaction (1) Cl (2) OCOCH3 (3) OC2H5 (4) NH2 Q114.Amongst the following compound, the optically active alkane having lowest molecular mass is JEE Main 2004 JEE Main Previous Year Paper (1) (2) (3) (4) Q115.Which of the following compound is not chiral? (1) 1- chloropentane (2) 3-chloro-2- methyl pentane (3) 1-chloro -2- methyl pentane (4) 2- chloropentane Q116.Which one of the following has the minimum boiling point? (1) n-butane (2) isobutane (3) 1- butene (4) 1- butyne Q117.The smog is essentially caused by the presence of (1) O2 and O3 (2) O3 and N2 (3) Oxides of sulphur and nitrogen (4) O2 and N2 Q118.What type of crystal defect is indicated in the diagram below? Na+Cl−Na+Cl−Na+Cl− Cl−□Cl−□Na+□Na+ Na+Cl−□Cl−Na+Cl−Cl−Na+Cl−Na+□Na+ (1) Frenkel defect (2) Frenkel and Schottky defects (3) Interstitial defect (4) Schottky defect Q119.Which of the following liquid pairs shows a positive deviation from Raoult's law? (1) Water - hydrochloric acid (2) Acetone - chloroform (3) Water - nitric acid (4) Benzene - methanol Q120.In hydrogen - oxygen fuel cell, combustion of hydrogen occurs to (1) generate heat (2) remove adsorbed oxygen from electrode surfaces (3) produce high purity water (4) create potential difference between the two electrodes Q121.Consider the following E∘ values E∘Fe3+/Fe2+ = 0.77 V E∘Sn2+/Sn = −0.14 V Under standard conditions the potential for the reaction Sn(s) + 2Fe3+(aq) ⟶2Fe2+(aq) + Sn2+(aq) is (1) 1.68 V (2) 0.63 V (3) 0.91 V (4) 1.40 V Q122.The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at 25∘C. The equilibrium constant of the reaction is (F = 96, 500Cmol−1 : R = 8.314JK−1 mol−1) JEE Main 2004 JEE Main Previous Year Paper (1) 1.0 × 101 (2) 1.0 × 1030 (3) 1.0 × 1010 (4) 1.0 × 105 Q123.The limiting molar conductivities Λ∘ for NaCl, KBr and KCl are 126,152 and 150 S cm2 mol−1 respectively. The Λ∘ for NaBr is (1) 128 S cm2 mol−1 (2) 302 S cm2 mol−1 (3) 278 S cm2 mol−1 (4) 176 S cm2 mol−1 Q124.In a cell that utilises the reaction Zn(s) + 2H+(aq) ⟶Zn2+(aq) + H2( g) addition of H2SO4 to cathode compartment, will (1) lower the E and shift equilibrium to the left (2) increases the E and shift equilibrium to the left (3) increase the E and shift equilibrium to the right (4) Lower the E and shift equilibrium to the right Q125.The E∘M+3/M2+ values for Cr, Mn, Fe and Co are −0.41, +1.57, +0.77 and +1.97 V respectively. For which one of these metals the change in oxidation state form +2 to +3 is easiest? (1) Cr (2) Co (3) Fe (4) Mn Q126.In first order reaction, the concentration of the reactant decreases from 0.8M to 0.4M in 15 minutes. The time taken for the concentration to change from 0.1M to 0.025M is (1) 30 minutes (2) 60 minutes (3) 7.5 minutes (4) 15 minutes Q127.The rate equation for the reaction 2 A + B ⟶C is found to be: rate k[A][B]. The correct statement in relation to this reaction is that the (1) unit of K must bes−1 (2) values of k is independent of the initial concentration of A and B (3) rate of formation of C is twice the rate of (4) t1/2 is a constant disappearance of A Q128.The half - life of a radioisotope is four hours. If the initial mass of the isotope was 200 g , the mass remaining after 24 hours undecayed is (1) 1.042 g (2) 4.167 g (3) 3.125 g (4) 2.084 g Q129.Which one of the following ores is best concentrated by froth - floatation method? (1) Magnetite (2) Malachite (3) Galena (4) Cassiterite Q130.Which among the following factors is the most important in making fluorine the strongest oxidizing halogen? (1) Electron affinity (2) Bond dissociation energy (3) Hydration enthalpy (4) Ionization enthalpy Q131.Which one the following statement regarding helium is incorrect? JEE Main 2004 JEE Main Previous Year Paper (1) It is used to fill gas balloons instead of hydrogen (2) It is used in gas - cooled nuclear reactors because it is lighter and non inflammable (3) It is used to produce and sustain powerful (4) It is used as cryogenic agent for carrying out superconducting reagents experiments at low temperatures Q132.One mole of magnesium nitride on the reaction with an excess of water gives (1) one mole of ammonia (2) two moles of nitric acid (3) two moles of ammonia (4) one mole of nitric acid Q133.Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them? (1) (n −1)d8ns2 (2) (n −1)d5ns2 (3) (n −1)d3ns2 (4) (n −1)d5 ns−1 Q134.Cerium (Z = 58) is an important member of the lanthanoids. Which of the following statements about cerium is incorrect? (1) The common oxidation states of cerium are +3 (2) Cerium (IV) acts as an oxidizing agent and +4 (3) The +4 oxidation state of cerium is not known (4) The +3 oxidation state of cerium is more stable in solutions than the +4 oxidation state Q135.The coordination number of central metal atom in a complex is determined by (1) the number of ligands around a metal ion bonded (2) the number of only anionic ligands bonded to the by sigma bonds metal ion (3) the number of ligands around a metal ion bonded (4) the number of ligands around a metal ion bonded by sigma and pi- bonds both by pi-bonds Q136.Which one of the following complexes in an outer orbital complex? (1) [Fe(CN)6]4− (2) [Ni(NH3)6]2+ (3) [Co(NH3)6]3+ (4) [Mn(CN)6]4− Q137.Coordination compound have great importance in biological systems. In this context which of the following statements is incorrect? (1) Chlorophylls are green pigments in plants and (2) Carboxypeptidase −A is an enzyme and contains calcium contains zinc (3) Cyanocobalamin is B12 and contains cobalt (4) Haemoglobin is the red pigment of blood and contains iron Q138.Which one the following has largest number of isomers? (1) [Ru(NH3)4Cl+2 ] (2) [Co(en)2Cl2]+ (3) [lr (PR3)2H(CO)]2+ (4) [Co(NH3)5Cl]2+ ( R-= alkyl group, en = ethylenediamine) Q139.The correct order of magnetic moments (spin only values in B.M.) among is JEE Main 2004 JEE Main Previous Year Paper (1) [MnCl4]2−> [CoCl4]−2 > [Fe(CN)6]−4 (2) [Fe(CN)6]−4 > [CoCl4]2−> [MnCl4]2− (3) [Fe(CN)6]4−> [MnCl4]2−> [CoCl4]2− (4) [MnCl4]2−> [Fe(CN)6]4−> [CoCl4]2− (Atomic numbers: Mn = 25; Fe = 26, Co = 27 ) Q140.The compound formed on heating chlorobenzene with chloral in the presence concentrated sulphuric acid is (1) gammexene (2) hexachloroethane (3) Freon (4) DDT Q141.Acetyl bromide reacts with excess of CH3Mgl followed by treatment with a saturated solution of NH4Cl given (1) acetone (2) acetyl iodide (3) 2- methyl -2-propanol (4) acetamide Q142.Among the following compound which can be dehydrated very easily is (1) (2) (3) (4) Q143.Which one of the following reduced with zinc and hydrochloric acid to give the corresponding hydrocarbon? (1) Ethyl acetate (2) Butan -2-one (3) Acetamide (4) Acetic acid Q144.Consider the acidity of the carboxylic acids: (1) PhCOOH (2) O −NO2C6H4COOH (3) p −NO2C6H4COOH (4) m −NO2C6H4COOH Q145.On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is (1) CH3COOC2H5 + NaCl (2) CH3Cl + C2H5COONa (3) CH3COCl + C2H5OH + NaOH (4) CH3COONa + C2H5OH Q146.Which of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid? (1) Phenol (2) Benzoic acid (3) Butanal (4) Benzaldehyde Q147.Which of the following is the strongest base? JEE Main 2004 JEE Main Previous Year Paper (1) < smiles>Nc1ccccc1 < /smiles> (2) < smiles>NCc1ccccc1 < /smiles> (3) < smiles>Cc1ccccc1N < /smiles> (4) < smiles>CNc1ccccc1 < /smiles> Q148.Identify the correct statements regarding enzymes (1) Enzymes are specific biological catalysts that (2) Enzymes are specific biological catalysts that the can normally function at very high temperature posses well - defined active sites (T ∼1000 K) (3) Enzymes are specific biological catalysts that (4) Enzymes are normally heterogeneous catalysts can not be poisoned that are very specific in their action Q149.Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories? (1) A co- enzyme (2) An antibiotic (3) An enzyme (4) A hormone Q150.Which one of the following statements is false? (1) Raoult's law states that the vapour pressure of a (2) Two sucrose solutions of same molality prepared components over a solution is proportional to its in different solvents will have the same freezing mole fraction point depression (3) The correct order of osmotic pressure for 0.01M (4) The osmotic pressure (π) = MRT, where M is aqueous solution of each compound is the molarity of the solution BaCl2 > KCl > CH3COOH > sucrose Q151.Which base is present in RNA but not in DNA? (1) Uracil (2) Thymine (3) Guanine (4) Cytosine Q152.Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation (1) x2 + 18x + 16 = 0 (2) x2 −18x −16 = 0 (3) x2 + 18x −16 = 0 (4) x2 −18x + 16 = 0 Q153.If (1 −p) is a root of quadratic equation x2 + px + (1 −p) = 0 , then its roots are (1) 0,1 (2) −1, 2 (3) 0, −1 (4) −1, 1 Q154.If one root of the equation x2 + px + 12 = 0 is 4 , while the equation x2 + px + q = 0 has equal roots, then the value of ' q ' is (1) 49 (2) 4 4 (3) 3 (4) 12 Q155.Let z, w be complex numbers such that ¯z + i ¯w = 0 and arg zw = π. Then arg z equals (1) π (2) 5π 4 4 (3) 3π (4) π 4 2 JEE Main 2004 JEE Main Previous Year Paper Q156.If z = x −iy and z 31 = p + iq , then ( xp + yq ) is equal to (p2+q2) (1) 1 (2) −2 (3) 2 (4) −1 Q157.If z2 −1 = |z|2 + 1 , then z lies on (1) the real axis (2) an ellipse (3) a circle (4) the imaginary axis. Q158.How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order? (1) 120 (2) 480 (3) 360 (4) 240 Q159.The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is (1) 5 (2) 8C3 (3) 38 (4) 21 Q160.Let Tr be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, m ≠n, Tm = n1 and Tn = m1 , then a −d equals (1) 0 (2) 1 (3) 1 (4) m 1 + n1 mn when n isQ161.The sum of the first n terms of the series 12 + 2 ⋅22 + 32 + 2 ⋅42 + 52 + 2 ⋅62 + … is n(n+1)22 even. When n is odd the sum is (1) 3n(n+1) (2) n2(n+1) 2 2 (3) n(n+1)2 (4) n(n+1) 2 4 [ 2 ] Q162.The sum of series 2! 1 + 4!1 + 6!1 + … is (1) (e2−1) (2) (e−1)2 2 2e (3) (e2−1) (4) (e2−2) 2e e Q163.If u = √a2 cos2 θ + b2 sin2 θ + √a2 sin2 θ + b2 cos2 θ, then the difference between the maximum and minimum values of u2 is given by (1) 2 (a2 + b2) (2) 2√a2 + b2 (3) (a + b)2 (4) (a −b)2 Q164.Let S(K) = 1 + 3 + 5 + … + (2K −1) = 3 + K 2 . Then which of the following is true? (1) S(1) is correct (2) Principle of mathematical induction can be used to prove the formula (3) S(K) ≠S(K + 1) (4) S(K) ⇒S(K + 1) Q165.The coefficient of the middle term in the binomial expansion in powers of x of (1 + αx)4 and of (1 −αx)6 is the same if α equals (1) −53 (2) 35 (3) −3 (4) 10 10 3 JEE Main 2004 JEE Main Previous Year Paper Q166.The coefficient of xn in expansion of (1 + x)(1 −x)n is (1) (n −1) (2) (−1)n(1 −n) (3) (−1)n−1(n −1)2 (4) (−1)n−1n Q167.If Sn = ∑nr=0 nCr1 and tn = ∑nr=0 nCrr , then Sntn is equal to (1) 2 1 n (2) 12 n −1 (3) n −1 (4) 2n−12 Q168.Let α, β be such that π < α −β < 3π. If sin α + sin β = −2165 and cos α + cos β = −2765 , then the value of α−β is cos 2 (1) − 3 (2) 3 √130 √130 (3) 65 6 (4) −665 Q169.Let A(2, −3) and B(−2, 1) be vertices of a triangle ABC . If the centroid of this triangle moves on the line 2x + 3y = 1 , then the locus of the vertex C is the line (1) 2x + 3y = 9 (2) 2x −3y = 7 (3) 3x + 2y = 5 (4) 3x −2y = 3 Q170.The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is −1 is y (1) x 2 + 3 = −1 and −2x + 1y = −1 (2) x2 −y3 = −1 and −2x + 1y = −1 (3) x 2 + 3y = 1 and x2 + 1y = 1 (4) x2 −y3 = 1 and −2x + 1y = 1 Q171.If one of the lines given by 6x2 −xy + 4cy2 = 0 is 3x + 4y = 0 , then c equals (1) 1 (2) −1 (3) 3 (4) −3 Q172.A line makes the same angle θ, with each of the x and z axis. If the angle β, which it makes with y-axis, is such that sin2 β = 3 sin2 θ, then cos2 θ equals (1) 2 (2) 1 3 5 (3) 3 (4) 2 5 5 Q173.If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre is (1) 2ax + 2by + (a2 + b2 + 4) = 0 (2) 2ax + 2by −(a2 + b2 + 4) = 0 (3) 2ax −2by + (a2 + b2 + 4) = 0 (4) 2ax −2by −(a2 + b2 + 4) = 0 Q174.If the lines 2x + 3y + 1 = 0 and 3x −y −4 = 0 lie along diameters of a circle of circumference 10π, then the equation of the circle is (1) x2 + y2 −2x + 2y −23 = 0 (2) x2 + y2 −2x −2y −23 = 0 (3) x2 + y2 + 2x + 2y −23 = 0 (4) x2 + y2 + 2x −2y −23 = 0 Q175.The intercept on the line y = x by the circle x2 + y2 −2x = 0 is AB . Equation of the circle on AB as a diameter is JEE Main 2004 JEE Main Previous Year Paper (1) x2 + y2 −x −y = 0 (2) x2 + y2 −x + y = 0 (3) x2 + y2 + x + y = 0 (4) x2 + y2 + x −y = 0 Q176.A variable circle passes through the fixed point A(p, q) and touches x -axis. The locus of the other end of the diameter through A is (1) (x −p)2 = 4qy (2) (x −q)2 = 4py (3) (y −p)2 = 4qx (4) (y −q)2 = 4px Q177.If a ≠0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then (1) d2 + (2b + 3c)2 = 0 (2) d2 + (3b + 2c)2 = 0 (3) d2 + (2b −3c)2 = 0 (4) d2 + (3b −2c)2 = 0 Q178.The eccentricity of an ellipse, with its centre at the origin, is 1 . If one of the directrices is x = 4 , then the 2 equation of the ellipse is (1) 3x2 + 4y2 = 1 (2) 3x2 + 4y2 = 12 (3) 4x2 + 3y2 = 12 (4) 4x2 + 3y2 = 1 = e2 , then the values of a and b, are Q179.If limx→∞(1 + xa + x2b ) 2x (1) a ∈R, b ∈= (2) a = 1, b ∈R––– (3) a ∈R, b = 2 (4) a = 1 and b = 2– Q180.Let f(x) = 1−tan4x−πx , x ≠π4 , x ∈[0, π2 ]. If f(x) is continuous in [0, π2 ], then f ( π4 ) is (1) 1 (2) 1 2 (3) −12 (4) −1 e n is Q181. limn→∞∑nr=1 n1 − (1) e (2) e −1 (3) 1 −e (4) e + 1 Q182.Consider the following statements: Mode can be computed from histogram Median is not independent of change of scale Variance is independent of change of origin and scale. (1) only (a) (2) only (b) (3) only (a) and (b) (4) (a), (b) and (c) Q183.In a series of 2n observations, half of them equal a and remaining half equal −a. If the standard deviation of the observations is 2 , then |a| equals (1) 1 (2) √2 n (3) 2 (4) √2 n Q184.A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60∘ and when he retires 40 meter away from the tree the angle of elevation becomes 30∘ . The breadth of the river is (1) 20 m (2) 30 m (3) 40 m (4) 60 m JEE Main 2004 JEE Main Previous Year Paper Q185.A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively (1) 17 4 km/h and 134 km/h (2) 134 km/h and 174 km/h (3) 17 9 km/h and 139 km/h (4) 139 km/h and 179 km/h Q186.The sides of a triangle are sin α, cos α and √1 + sin α cos α for some 0 < α < π2 . Then the greatest angle of the triangle is (1) 60∘ (2) 90∘ (3) 120∘ (4) 150∘ Q187.Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4} . The relation R is (1) a function (2) reflexive (3) not symmetric (4) transitive Q188. ⎛ 0 0 −1⎞ Let A = 0 −1 0 The only correct statement about the matrix A is ⎝ −1 0 0 ⎠ (1) A is a zero matrix (2) A2 = I (3) A−1 does not exist (4) A = (−1)I , where I is a unit matrix Q189. ⎛ 1 −1 1 ⎞ ⎛ 4 2 2 ⎞ Let A = 2 1 −3 (10)B = −5 0 α . If B ⎝ 1 1 1 ⎠ ⎝ 1 −2 3 ⎠ (1) −2 (2) 5 (3) 2 (4) −1 Q190.If a1, a2, a3, … , an, … . are in G.P., then the value of the determinant log an log an+1 log an+2 log an+3 log an+4 log an+5 , is log an+6 log an+7 log an+8 (1) 0 (2) −2 (3) 2 (4) 1 Q191.The range of the function f(x) = 7−xPx−3 is (1) {1, 2, 3} (2) {1, 2, 3, 4, 5} (3) {1, 2, 3, 4} (4) {1, 2, 3, 4, 5, 6} Q192.If f : R →S , defined by f(x) = sin x −√3 cos x + 1 , is onto, then the interval of S is (1) [0, 3] (2) [−1, 1] (3) [0, 1] (4) [−1, 3] Q193.The graph of the function y = f(x) is symmetrical about the line x = 2 , then (1) f(x + 2) = f(x −2) (2) f(2 + x) = f(2 −x) (3) f(x) = f(−x) (4) f(x) = −f(−x) JEE Main 2004 JEE Main Previous Year Paper Q194.The domain of the function f(x) = sin−1(x−3) is √9−x2 (1) [2, 3] (2) [2, 3) (3) [1, 2] (4) [1, 2) Q195.If x = ey+ey+..10∞, x > 0 , then dxdy is (1) x (2) 1 1+x x (3) 1−x (4) 1+x x x Q196.A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is (1) (2, 4) (2) (2, −4) (3) ( −98 , 29 ) (4) ( 98 , 92 ) Q197.A function y = f(x) has a second order derivative f ′′(x) = 6(x −1). If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x −5 , then the function is (1) (x −1)2 (2) (x −1)3 (3) (x + 1)3 (4) (x + 1)2 Q198.The normal to the curve x = a(1 + cos θ), y = a sin θ at ' θ ' always passes through the fixed point (1) (a, 0) (2) (0, a) (3) (0, 0) (4) (a, a) Q199.If 2a + 3b + 6c = 0 , then at least one root of the equation ax2 + bx + c = 0 lies in the interval (1) (0, 1) (2) (1, 2) (3) (2, 3) (4) (1, 3) Q200.If the sum of the slopes of the lines given by x2 −2cxy −7y2 = 0 is four times their product, then c has the value (1) 1 (2) −1 (3) 2 (4) −2 Q201.If ∫ sin(x−α)sin x dx = Ax + B log sin(x −α) + C , then value of (A, B) is (1) (sin α, cos α) (2) (cos α, sin α) (3) (−sin α, cos α) (4) (−cos α, sin α) Q202. ∫ cos x−sindx x is equal to (1) √2 1 log tan ( x2 −π8 ) + C (2) √21 log cot ( x2 ) + C (3) √2 1 log tan ( x2 −3π8 ) + C (4) √21 log tan ( x2 + 3π8 ) + C dx isQ203.The value of ∫3−2 1 −x2 (1) 28 (2) 14 3 3 (3) 7 (4) 1 3 3 dx isQ204.The value of I = ∫π/20 (sin√1+sinx+cos2xx)2 (1) 0 (2) 1 (3) 2 (4) 3 JEE Main 2004 JEE Main Previous Year Paper A is Q205.If ∫π0 xf(sin x)dx = A ∫π/20 f(sin x)dx, then (1) 0 (2) π (3) π (4) 2π 4 Q206.If f(x) = 1+exex , l1 = ∫f(a)f(−a) xg{x(1 −x)}dx and I2 = ∫f(a)f(−a) g{x(1 −x)}dx then the value of l2l1 is (1) 2 (2) −3 (3) −1 (4) 1 Q207.The area of the region bounded by the curves y = |x −2|, x = 1, x = 3 and the x-axis is (1) 1 (2) 2 (3) 3 (4) 4 Q208.The differential equation for the family of curves x2 + y2 −2ay = 0 , where a is an arbitrary constant is (1) 2 (x2 −y2)y′ = xy (2) 2 (x2 + y2)y′ = xy (3) (x2 −y2)y′ = 2xy (4) (x2 + y2)y′ = 2xy Q209.The solution of the differential equation ydx + (x + x2y)dy = 0 is (1) −1xy = C (2) −1xy + log y = C (3) 1 + log y = C (4) log y = Cx xy Q210.If the straight lines x = 1 + s, y = −3 −λs, z = 1 + λs and x = 2t , y = 1 + t, z = 2 −t with parameters s and t respectively, are co-planar then λ equals (1) −2 (2) −1 (3) −12 (4) 0 Q211.Let →a,→b and →c be three non-zero vectors such that no two of these are collinear. If the vector →a + 2→b is collinear with →c and →b + 3→c is collinear with →a ( λ being some non-zero scalar) then →a + 2→b + 6→c equals (1) λ→a (2) λ→b (3) λ→c (4) 0 Q212.A particle is acted upon by constant forces 4I + J −3k and 3I + J −k which displace it from a point ^i + 2^j + 3^k to the point 5^i + 4^j + ^k. The work done in standard units by the forces is given by (1) 40 (2) 30 (3) 25 (4) 15 –– Q213.If ¯a,¯b, ¯c are non-coplanar vectors and λ is a real number, then the vectors –a + 2b + 3–c, λb + 4–c and (2λ −1)–c are non-coplanar for (1) all values of λ (2) all except one value of λ (3) all except two values of λ (4) no value of λ –––1 . If θ is the acute angle between the Q214.Let –a, b and –c be non-zero vectors such that (–a × b) × –c = 3 |b||–c|–a – vectors b and –c , then sin θ equals (1) 1 (2) √2 3 3 (3) 2 (4) 2√2 3 3 JEE Main 2004 JEE Main Previous Year Paper Q215.With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N . If they act at right angles, then their resultant is 3 N . Then the forces are (1) (2 + √2)N and (2 −√2)N (2) (2 + √3)N and (2 −√3)N (3) (2 + 12 √2)N and (2 −12 √2)N (4) (2 + 12 √3)N and (2 −12 √3)N Q216.In a right angle △ABC, ∠A = 90∘ and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force →F has moments 0,9 and 16 in N cm. units respectively about vertices A, B and C , then magnitude of →F is (1) 3 (2) 4 (3) 5 (4) 9 Q217.Three forces →P, →Q and →R acting along IA, IB and IC, where I is the incentre of a △ABC , are in equilibrium. Then →P : →Q : →R is (1) cos A2 : cos B2 : cos C2 (2) sin A2 : sin B2 : sin C2 (3) sec A2 : sec B2 : sec C2 (4) cosec A2 : cosec B2 : cosec C2 Q218.A velocity 1 4 m/s is resolved into two components along OA and OB making angles 30∘ and 45∘ respectively with the given velocity. Then the component along OB is (1) 8 1 m/s (2) 14 (√3 −1)m/s (3) 41 m/s (4) 18 (√6 −√2)m/s Q219.Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is (1) 3 (2) 5 2 2 (3) 7 (4) 9 2 2 Q220.A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by (1) (3a, 3a, 3a), (a, a, a) (2) (3a, 2a, 3a), (a, a, a) (3) (3a, 2a, 3a), (a, a, 2a) (4) (2a, 3a, 3a), (2a, a, a) Q221.The intersection of the spheres x2 + y2 + z2 + 7x −2y −z = 13 and x2 + y2 + z2 −3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane (1) x −y −z = 1 (2) x −2y −z = 1 (3) x −y −2z = 1 (4) 2x −y −z = 1 –– Q222.Let ¯u, ¯v, ¯w be such that |¯u| = 1, |¯v| = 2, |¯w| = 3 . If the projection ¯v along ¯u is equal to that of w along u and ––––v, w are perpendicular to each other then |u −–v + w| equals (1) 2 (2) √7 (3) √14 (4) 14 Q223.The probability that A speaks truth is 4 , while this probability for B is 3 . The probability that they contradict 5 4 each other when asked to speak on a fact is (1) 3 (2) 1 20 5 (3) 7 (4) 4 20 5 JEE Main 2004 JEE Main Previous Year Paper Q224.A random variable X has the probability distribution: X : 1 2 3 4 5 6 7 8 p(X) : 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05 For the events E = {X is a prime number } and F = {X < 4} , the probability P(E ∪F) is (1) 0.87 (2) 0.77 (3) 0.35 (4) 0.50 Q225.The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is (1) 25637 (2) 219256 (3) 128 (4) 28 256 256 JEE Main 2004 JEE Main Previous Year Paper