Practice Questions

Q25.A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is (1) 1/2( K −1)CV2 (2) CV2( K −1)/K (3) (K −1)CV2 (4) zero

Q71.Identify the incorrect statement among the following (1) Ozone reacts with SO2 to give SO3 (2) Silicon reacts with NaOH(aq) in the presence of air to give Na2SiO3 and H2O (3) Cl2 reacts with excess of NH3 to give N2 and (4) Br2 reacts with hot and strong NaOH solution to HCl give NaBr, NaBrO4 and H2O

Q13.Four point masses, each of value m, are placed at the corners of a square ABCD of side ℓ. The moment of inertia through A and parallel to BD is (1) mℓ2 (2) 2 mℓ2 (3) 3mℓ2 (4) 3 mℓ2

Q89.A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will (1) remain unchanged (2) triple (3) increase by a factor of 4 (4) double

Q97.Nickel (Z = 28) combines with a uninegative monodentate ligand X− to form a paramagnetic complex [NiX4]2− . The number of unpaired electron(s) in the nickel and geometry of this complex ion are, respectively (1) one, tetrahedral (2) two, tetrahedral (3) one, square planar (4) two, square planar

Q6. Two points A and B move from rest along a straight line with constant acceleration f and f ' respectively. If A takes m sec. more than B and describes ' n ' units more than B in acquiring the same speed then (1) (f −f ′)m2 = ff ′n (2) (f + f ′)m2 = ff ′n (3) 2 1 (f + f ′)m = ff ′n2 (4) (f ′ −f)n = 21 ff ′m2

Q7. A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance (1) 2H (2) H A−B A+B (3) H (4) H 2(A+B) A−B

Q9. A particle is projected from a point O with velocity u at an angle of 60∘ with the horizontal. When it is moving in a direction at right angles to its direction at O , its velocity then is given by (1) u (2) u 3 2 (3) 2u (4) u 3 √3

Q11.The upper half of an inclined plane with inclination ϕ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by (1) 2 sin ϕ (2) 2 cos ϕ (3) 2 tan ϕ (4) tan ϕ

Q23.A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the JEE Main 2005 JEE Main Previous Year Paper location of P with respect to C (1) 2 3 ℓ (2) 23 ℓ (3) 4 ℓ (4) ℓ 3

Q81.An organic compound having molecular mass 60 is found to contain C = 20%, H = 6.67% and N = 46.67% while rest is oxygen. On heating it gives NH3 alongwith a solid residue. The solid residue give violet colour with alkaline copper sulphate solution. The compound is (1) CH3NCO (2) CH3CONH2 (3) (NH2)2CO (4) CH3CH2CONH2

Q11.A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to (1) x3 (2) ex (3) x (4) loge x

Q23.Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius R around the sun will be proportional to (1) R( n+12 ) (2) R( n−12 ) (3) Rn (4) R( n−22 )

Q42.Four charges equal to −Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is (1) −Q4 (1 + 2√2) (2) −Q2 (1 + 2√2) (3) −Q2 (1 + 2√2) (4) Q2 (1 + 2√2)

Q58.In a uniform magnetic field of induction B a wire in the form of semicircle of radius r rotates about the diameter of the circle with angular frequency ω. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R the mean power generated per period of rotation is (1) Bπr2ω (2) (Bπr2ω)2 2R 2R (3) (Bπrω)2 (4) (Bπrω2)2 2R 8R

Q65.A plane convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object? (1) 20 cm (2) 30 cm (3) 60 cm (4) 80 cm

Q75.For a transistor amplifier in common emitter configuration having load impedance of 1kΩ (hfe = 50 and hoe = 25 ) the current gain is (1) −5.2 (2) −15.7 (3) −24.8 (4) −48.78

Q89.The maximum number of 90∘ angles between bond pair of electrons is observed in (1) dsp 3 hybridization (2) sp3 d2 hybridization (3) dsp2 hybridization (4) sp3 d hybridization

Q7. Two particles start simultaneously from the same point and move along two straight lines, one with uniform → velocity →u and the other from rest with uniform acceleration f . Let α be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time. (1) u cos α (2) u sin α f f (3) f cos α (4) u sin α. u

Q9. Two stones are projected from the top of a cliff h metres high, with the same speed u, so as to hit the ground at the same spot. If one of the stones is projected at an angle θ to the horizontal then the θ equals (1) u√2gh (2) √2ugh (3) 2 g√uh (4) 2 h√ug

Q21.A particle performing uniform circular motion has angular frequency is doubled \& its kinetic energy halved, then the new angular momentum is (1) L (2) 2 L 4 (3) 4 L (4) L2

Q53.A thin rectangular magnet suspended freely has a period of oscillation equal to T . Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T ′ , the ratio TT ′ is (1) 1 (2) 1 2√2 2 (3) 2 (4) 1 4

Q44.If a charge q is placed at the centre of the line joining two equal charges Q such that the system is in equilibrium then the value of q is (1) Q/2 (2) −Q/2 (3) Q/4 (4) −Q/4

Q83.Which of the following are arranged in an increasing order of their bond strengths ? (1) O−2 < O2 < O+2 < O2−2 (2) O2−2 < O−2 < O2 < O+2 (3) O−2 < O2−2 < O2 < O+2 (4) O+2 < O2 < O−2 < O2−2

Q99.For the reactions, C + O2 ⟶CO2; ΔH = −393 J 2Zn + O2 ⟶2ZnO; ΔH = −412 J (1) carbon can oxidise Zn (2) oxidation of carbon is not feasible (3) oxidation of Zn is not feasible (4) Zn can oxidise carbon Q100.Which of the following is a redox reaction ? (1) NaCl + KNO3 →NaNO3 + KCl (2) CaC2O4 + 2HCl →CaCl2 + H2C2O4 (3) Mg(OH)2 + 2NH4Cl →MgCl2 + 2NH4OH (4) Zn + 2AgCN →2Ag + Zn(CN)2 Q101. KO2 (potassium super oxide) is used in oxygen cylinders in space and submarines because it (1) absorbs CO2 and increases O2 content (2) eliminates moisture (3) absorbs CO2 (4) produces ozone. JEE Main 2002 JEE Main Previous Year Paper Q102.A metal M readily forms its sulphate MSO4 which is water - soluble. It forms its oxide MO which becomes inert on heating. It forms an insoluble hydroxide M(OH)2 which is soluble in NaOH solution. Then M is (1) Mg (2) Ba (3) Ca (4) Be Q103.Alum helps in purifying water by (1) forming Si complex with clay particles (2) sulphate part which combines with the dirt and removes it (3) coagulating the mud particles (4) making mud water soluble Q104.Arrangement of (CH3)3 −C−, (CH3)2 −CH−, CH3 −CH2 - when attached to benzyl or an unsaturated group in increasing order of inductive effect is (1) (CH3)3 −C−< (CH3)2 −CH−< CH3 −CH2(2) CH3 −CH2−< (CH3)2−< CH−< (CH3)3 −C− (3) (CH3)2 −CH−< (CH3)3 −C−< CH3, −CH2(4) (CH3)3 −C−< CH3 −CH2 −(CH3)2 −CH− Q105.A similarity between optical and geometrical isomerism is that (1) each forms equal number of isomers for a given (2) If in a compound one is present then so is the compound other (3) both are included in stereoisomerism (4) they have no similarity Q106.Which of the following does not show geometrical isomerism? (1) 1, 2-dichloro - 1- pentene (2) 1, 3 - dichloro - 2- pentene (3) 1, 1- dichloro - 1- pentene (4) 1, 4 - dichloro - 2- pentene Q107.Which of the following compounds has wrong IUPAC name ? (1) (2) (3) (4) Q108.Which of these will not react with acetylene ? (1) NaOH (2) ammonical AgNO3 (3) Na (4) HCl Q109.In which of the following species is the underlined carbon having sp3 hybridisation? (1) (2) (3) (4) Q110.Racemic mixture is formed by mixing two JEE Main 2002 JEE Main Previous Year Paper (1) isomeric compounds (2) chiral compounds (3) meso compounds (4) optical isomers Q111.Na and Mg crystallize in BCC and FCC type crystals respectively, then the number of atoms of Na and Mg present in the unit cell of their respective crystal is (1) 4 and 2 (2) 9 and 14 (3) 14 and 9 (4) 2 and 4 Q112.Freezing point of an aqueous solution is (−0.186)∘C. Elevation of boiling point of the same solution is Kb = 0.512∘C, Kf = 1.86∘C, find the increase in boiling point. (1) 0.186∘C (2) 0.0512∘C (3) 0.092∘C (4) 0.2372∘C Q113.With increase of temperature, which of these changes? (1) molality (2) weight fraction of solute (3) fraction of solute present in water (4) mole fraction Q114.In mixture A and B component show -ve deviation as (1) ΔVmix > 0 (2) ΔHmix < 0 (3) A - B interaction is weaker than A - A and B - B (4) A - B interaction is stronger than A - A and B - B interaction interaction Q115.Conductivity (unit Siemen’s S) is directly proportional to area of the vessel and the concentration of the solution in it and is inversely proportional to the length of the vessel then the unit of the constant of proportionality is (1) Sm mol−1 (2) Sm2 mol−1 (3) S−2 m2 mol (4) S2 m2 mol−2 Q116.EMF of a cell in terms of reduction potential of its left and right electrodes is (1) E = Eleft −Eright (2) E = Eleft + Eright (3) E = Eright −Eleft (4) E = −(Eright + Eleft ) Q117.If ϕ denotes reduction potential, then which is true ? (1) E cell 0 = ϕright −ϕleft (2) E0cell = ϕleft + ϕright (3) E0cell = ϕleft −ϕright (4) E0cell = −(ϕleft + ϕright ) Q118.What will be the emf for the given cell Pt |H2 (P1)|H+(aq)||H2 (P2) ∣Pt (1) RT f log P1P2 (2) RT2f log P1P2 (3) RT f log P2P1 (4) none of these Q119.Which of the following reaction is possible at anode? (1) 2Cr3+ + 7H2O →Cr2O2−7 + 14H+ (2) F2 →2 F− (3) (1/2)O2 + 2H+ →H2O (4) none of these Q120.When the sample of copper with zinc impurity is to be purified by electrolysis, the appropriate electrodes are (1) cathode - pure zinc anode - pure copper (2) cathode - impure sample anode - pure copper (3) cathode - impure zinc anode - impure sample (4) cathode - pure copper anode - impure sample JEE Main 2002 JEE Main Previous Year Paper Q121.Units of rate constant of first and zero order reactions in terms of molarity M unit are respectively (1) sec−1, Msec−1 (2) sec−1, M (3) Msec −1, sec−1 (4) M, sec−1 Q122.For the reaction A + 2B →C , rate is given by R = [A][B]2 then the order of the reaction is (1) 3 (2) 6 (3) 5 (4) 7 Q123.The differential rate law for the reaction H2 + I2 →2HI is (1) −d[H2]dt = −d[I2]dt = −d[HI]dt (2) d[H2]dt = d[I2]dt = 12 1 d[Hl]dt 1 d[H2] (3) 2 dt = 12 d[I2]dt = −d[HI]dt (4) −2 d[H2]dt = −2 d[I2]dt = d[HI]dt Q124.If half-life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64 grams is (1) 16 grams (2) 2 grams (3) 32 grams (4) 8 grams Q125.The integrated rate equation is Rt = log C0 −log Ct . The straight line graph is obtained by plotting (1) time vs log Ct (2) time1 vs Ct (3) time vs Ct (4) time1 vs Ct1 Q126.The formation of gas at the surface of tungsten due to adsorption is the reaction of order (1) 0 (2) 1 (3) 2 (4) insufficient data Q127.Aluminium is extracted by the electrolysis of (1) bauxite (2) alumina (3) alumina mixed with molten cryolite (4) molten cryolite Q128.The metal extracted by leaching with a cyanide is (1) Mg (2) Ag (3) Cu (4) Na Q129.Cyanide process is used for the extraction of (1) barium (2) aluminium (3) boron (4) silver Q130.When H2 S is passed through Hg2 S we get (1) HgS (2) HgS + Hg2 S (3) Hg2 S (4) Hg2 S2 Q131.In XeF2, XeF4, XeF6 the numebr of lone pairs of Xe are respectively (1) 2, 3, 1 (2) 1, 2, 3 (3) 4, 1, 2 (4) 3, 2, 1 Q132.In case of nitrogen, NCl3 is possible but not NCl5 while in case of phosphorous, PCl3 as well as PCl5 are possible. It is due to JEE Main 2002 JEE Main Previous Year Paper (1) availability of vacant d orbitals in P but not in N (2) lower electronegativity of P than N (3) lower tendency of H - bond formation in P than (4) occurrence of P in solid while N in gaseous state N at room temperature Q133.Number of sigma bonds in P4O10 is (1) 6 (2) 7 (3) 17 (4) 16 Q134.Most common oxidation states of Ce (cerium) are (1) +2, +3 (2) +2, +4 (3) +3, +4 (4) +3, +5 Q135.Arrange Ce+3, La+3, Pm+3 and Yb+3 in increasing order of their ionic radii (1) Yb+3 < Pm+3 < Ce+3 < La+3 (2) Ce+3 < Yb+3 < Pm+3 < La+3 (3) Yb+3 < Pm+3 < La+3 < Ce+3 (4) Pm+3 < La+3 < Ce+3 < Yb+3 Q136.Which of the following ions has the maximum magnetic moment ? (1) Mn+2 (2) Fe+2 (3) Ti+2 (4) Cr+2 Q137.Which is the correct order of ionic sizes ? (Atomic Number : Ce = 58, Sn = 50, Yb = 70 and Lu = 71) (1) Ce > Sn > Yb > Lu (2) Sn > Ce > Lu > Yb (3) Lu > Yb > Sn > Ce (4) Sn > Yb > Ce > Lu Q138.When KMnO4 acts as an oxidising agent and ultimately forms [MnO4]−1, MnO2, Mn2O3, Mn+2 then the number of electrons transferred in each case respectively is (1) 4, 3, 1, 5 (2) 1, 5, 3, 7 (3) 1, 3, 4, 5 (4) 3, 5, 7, 1 Q139.A square planar complex is formed by hybridisation of which atomic orbitals ? (1) s, px, py, dyz (2) s, px, py, dx2−y2 (3) s, px, py, dz2 (4) s, py, pz, dxy Q140.The type of isomerism present in nitropentamine chromium (III) chloride is (1) optical (2) linkage (3) ionization (4) polymerisation Q141.The most stable ion is (1) [Fe(OH)3]3− (2) [Fe(Cl)6]3− (3) [Fe(CN)6]3− (4) [Fe(H2O)6]3+ Q142. CH3 −Mg −Br is an organo metallic compound due to (1) Mg −Br bond (2) C - Mg bond (3) C - Br bond (4) C −H bond Q143.What is the product when acetylene reacts with hypochlorous acid ? (1) CH3COCl (2) ClCH2CHO (3) Cl2CHCHO (4) ClCHCOOH JEE Main 2002 JEE Main Previous Year Paper Q144.The reaction: (CH3)3C −Br ⟶(CH3)3H2O −C −OH (1) elimination reaction (2) substitution reaction (3) free radical reaction (4) displacement reaction Q145.On vigorous oxidation by permanganate solution (CH3)2C = CH −CH2 −CHO gives (1) (2) (3) (4) Q146. CH3CH2COOH ⟶Cl2 A alc.⟶KOH B . What is B ? red P (1) CH3CH2COCl (2) CH3CH2CHO (3) CH2 = CHCOOH (4) ClCH2CH2COOH Q147.When primary amine reacts with chloroform in ethanoic KOH then the product is (1) an isocyanide (2) an aldehyde (3) a cyanide (4) an alcohol Q148.Polymer formation from monomers starts by (1) condensation reaction between monomers (2) coordinate reaction between monomers (3) conversion of monomer to monomer ions by (4) hydrolysis of monomers protons Q149. The compound is used as (1) antiseptic (2) antibiotic (3) analgesic (4) pesticide Q150.RNA is different from DNA because RNA contains (1) ribose sugar and thymine (2) ribose sugar and uracil (3) deoxyribose sugar and thymine (4) deoxyribose sugar and uracil JEE Main 2002 JEE Main Previous Year Paper Q151.The functional group, which is found in amino acid is (1) COOH group (2) NH2 group (3) CH3 group (4) both (a) and (b) Q152.If a, b, c are distinct +ve real numbers and a2 + b2 + c2 = 1 then ab + bc + ca is (1) less than 1 (2) equal to 1 (3) greater than 1 (4) any real no. Q153.If α ≠β but α2 = 5α −3 and β2 = 5β −3 then the equation having α/β and β/α as its roots is (1) 3x2 −19x + 3 = 0 (2) 3x2 + 19x −3 = 0 (3) 3x2 −19x −3 = 0 (4) x2 −5x + 3 = 0 Q154.Difference between the corresponding roots of x2 + ax + b = 0 and x2 + bx + a = 0 is same and a ≠b, then (1) a + b + 4 = 0 (2) a + b - 4 = 0 (3) a - b - 4 = 0 (4) a - b + 4 = 0 Q155.Product of real roots of the equation t2x2 + |x| + 9 = 0 (1) is always positive (2) is always negative (3) does not exist (4) none of these Q156.If p and q are the roots of the equation x2 + px + q = 0, then (1) p =1, q = -2 (2) p = 0, q = 1 (3) p = -2, q = 0 (4) p = -2, q = 1 Q157.If 2a + 3b + 6c = 0(a, b, c ∈R) then the quadratic equation ax2 + bx + c = 0 has (1) at least one root in [0, 1] (2) at least one root in [2, 3] (3) at least one root in [4, 5] (4) none of these Q158. z and w are two non zero complex no.s such that |z| = |w| and Arg z + Arg w = π then z equals –– (1) W (2) - W (3) W (4) - W Q159.If |z −4| < |z −2|, its solution is given by (1) Re(z) > 0 (2) Re(z) < 0 (3) Re (z) > 3 (4) Re(z) > 2 Q160.The locus of the centre of a circle which touches the circle |z −z1| = a and |z −z2| = b externally ( z, z1 and z2 are complex numbers) will be (1) an ellipse (2) a hyperbola (3) a circle (4) none of these Q161.Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are (1) 216 (2) 375 (3) 400 (4) 720 Q162.Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed) is JEE Main 2002 JEE Main Previous Year Paper (1) 125 (2) 105 (3) 375 (4) 625 Q163.Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4, 6 and 7 without repetition. Total number of such numbers are (1) 312 (2) 3125 (3) 120 (4) 216 Q164.If 1, log9 (31−x + 2), log3 (4.3x −1) are in A.P. then x equals (1) log3 4 (2) 1 + log3 4 (3) 1 - log3 4 (4) log4 3 Q165.The value of 21/4, 41/8, 81/6 + … … ∞ is (1) 1 (2) 2 (3) 3/2 (4) 4 Q166.Fifth term of a GP is 2, then the product of its 9 terms is (1) 256 (2) 512 (3) 1024 (4) none of these Q167.Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is (1) 5 (2) 3/5 (3) 8/5 (4) 1/5 Q168. 13 −23 + 33 −43 + … . +93 = (1) 425 (2) -425 (3) 475 (4) -475 Q169.The sum of integers from 1 to 100 that are divisible by 2 or 5 is (1) 3000 (2) 3050 (3) 3600 (4) 3250 Q170.If an = √7 + √7 + √7 + … . having n radical signs then by methods of mathematical induciton which is true (1) an > 7∀n ≥1 (2) an > 7∀n ≥1 (3) an < 4∀n ≥1 (4) an < 3∀n ≥1 Q171.The coefficients of xp and xq in the expansion of (1 + x)p+q are (1) equal (2) equal with opposite signs (3) reciprocals of each other (4) none of these Q172.If the sum of the coefficients in the expansion of (a + b)n is 4096 , then the greatest coefficient in the expansion is (1) 1594 (2) 792 (3) 924 (4) 2924 Q173.The positive integer just greater than (1 + 0.0001)10000 is JEE Main 2002 JEE Main Previous Year Paper (1) 4 (2) 5 (3) 2 (4) 3 Q174. r and n are positive integers r > 1, n > 2 and coefficient of (r + 2)th term and 3rth term in the expansion of (1 + x)2n are equal, then n equals (1) 3r (2) 3r + 1 (3) 2r (4) 2r + 1 Q175.The period of sin2 θ is (1) π2 (2) π (3) 2π (4) π/2 Q176.The number of solution of tan x + sec x = 2 cos x in [0, 2π) is (1) 2 (2) 3 (3) 0 (4) 1 Q177.A triangle with vertices (4, 0), (-1, -1), (3, 5) is (1) isosceles and right angled (2) isosceles but not right angled (3) right angled but not isosceles (4) neither right angled nor isoceles Q178.The sides of a triangle are 3x + 4y, 4x+37 and 5x + 57 where x, y > 0 then the triangle is (1) right angled (2) obtuse angled (3) equilateral (4) none of these Q179.If the pair of lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 intersect on the y - axis then (1) 2fgh = bg2 + ch2 (2) bg2 ≠ch2 (3) abc = 2fgh (4) none of these Q180.The point of lines represented by 3ax2 + 5xy + (a2 −2)y2 = 0 and perpendicular to each other for (1) two values of a (2) ∀a (3) for one value of a (4) for no values of a Q181.Locus of mid point of the portion between the axes of x cos α + y sin α = p where p is constant is (1) x2 + y2 = 4 (2) x2 + y2 = 4p2 p2 (3) 1 + 1 = 2 (4) 1 + 1 = 4 x2 y2 p2 x2 y2 p2 Q182.If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure 450 at the major segment of the circle then value of m is (1) 2 ± √2 (2) −2 ± √2 (3) −1 ± √2 (4) none of these Q183.The centres of a set of circles, each of radius 3 , lie on the circle x2 + y2 = 25. The locus of any point in the set is (1) 4 ≤x2 + y2 ≤64 (2) x2 + y2 ≤25 (3) x2 + y2 ≥25 (4) 3 ≤x2 + y2 ≤9 Q184.The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x2 + y2 = 9 is JEE Main 2002 JEE Main Previous Year Paper , −√2) (1) ( 21 , 12 ) (2) ( 12 (3) ( 23 , 12 ) (4) ( 12 , 32 ) Q185.Two common tangents to the circle x2 + y2 = 2a2 and parabola y2 = 8ax are (1) x = ±(y + 2a) (2) y = ±(x + 2a) (3) x = ±(y + a) (4) y = ±(x + a) Q186. (1) 1 (2) -1 (3) zero (4) does not exist Q187. (1) e4 (2) e2 (3) e3 (4) 1 Q188.Let f(x) = 4 and f ′(x) = 4. Then Limx→2 xf(2)−2f(x)x−2 is given by (1) 2 (2) -2 (3) -4 (4) 3 Q189. 1p + 2p + 3p + … + np Limn→∞ np+1 is (1) 1 (2) 1 p+1 1−p (3) p 1 − p−11 (4) p+21 denotes greatest integer less than or equal to x) Q190. Limx→0 log xn−[x][x] , n ∈N([x] (1) has value -1 (2) has value 0 (3) has value 1 (4) does not exist Q191.If f(1) = 1, f ′(1) = 2, then Limx→1 √f(x)−1 is √x−1 (1) 2 (2) 4 (3) 1 (4) 1/2 Q192.In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls? (1) 73 (2) 65 (3) 68 (4) 74 Q193.The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is JEE Main 2002 JEE Main Previous Year Paper (1) x2 + y2 = 9a2 (2) x2 + y2 = 16a2 (3) x2 + y2 = 4a2 (4) x2 + y2 = a2 Q194.In a triangle with sides a, b, c, r1 > r2 > r3 (which are the ex-radii) then (1) a > b > c (2) a < b < c (3) a > b and b < c (4) a < b and b > c Q195. log l p 1 l, m, n are the pth , qth and rth term of a G.P. all positive, then log m q 1 equals log n r 1 (1) -1 (2) 2 (3) 1 (4) 0 Q196. a b ax + b If a > 0 discriminant of ax2 + 2bx + c is -ve, then b c bx + c is ax + b bx + c 0 (1) +ve (2) (ac −b2) (ax2 + 2bx + c) (3) -ve (4) 0 Q197. cot−1(√cos α) = tan−1(√cos α) = x, then sin x = (1) tan2 ( α2 ) (2) cot2 ( α2 ) (3) tan α (4) cot ( α2 ) Q198.The domain of sin−1 [log3(x/3)] is (1) [1, 9] (2) [-1,9] (3) [-9, 1] (4) [-9, -1] Q199.Which one is not periodic (1) |sin 3x| + sin2 x (2) cos √x + cos2 x (3) cos 4x + tan2 x (4) cos 2x + sin x Q200.If f(x + y) = f(x) ⋅f(y)∀x ⋅y and f(5) = 2, f ′(0) = 3 then f ′(5) is (1) 0 (2) 1 (3) 6 (4) 2 Q201.f is defined in [-5, 5] as f(x) = x if x is rational and = -x is irrational. Then (1) f(x) is continuous at every x, except x = 0 (2) f(x) is discontinuous at every x, except x = 0 (3) f(x) is continuous everywhere (4) f(x) is discontinuous everywhere n d2y dy (1 + x2) dx2 + x dx is Q202.If y = (x + √1 + x2) , then (1) n2y (2) −n2y (3) −y (4) 2x2y Q203.The maximum distance from origin of a point on the curve x = a sin t −b sin ( atb ) y = a cos t −b cos ( atb ), both a, b > 0 is (1) a - b (2) a + b (3) √a2 + b2 (4) √a2 −b2 JEE Main 2002 JEE Main Previous Year Paper Q204. ∫10π0 | sin x|dx is (1) 20 (2) 8 (3) 10 (4) 18 xdx then Limn→∞n [In + In−2] equals Q205. In = ∫π/40 tann (1) 1/2 (2) 1 (3) ∞ (4) zero is Q206. ∫ 0√2 [x2]dx (1) 2 −√2 (2) 2 + √2 (3) √2 −1 (4) √2 −2 Q207. ∫π−π 2x(1+sin1+cos2 xx) dx is (1) π2 (2) π2 4 (3) zero (4) π 2 Q208.If y = f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 square unit with the axes then ∫20 xf ′(x)dx is (1) 3/2 (2) 1 (3) 5/4 (4) -3/4 Q209.The area bounded by the curves y = ln x, y = ln |x|, y = | ln x| and y = | ln ||x| is (1) 4 sq. units (2) 6 sq. units (3) 10 sq. units (4) none of these d3y Q210.The order and degree of the differential equation 2/3 are + 3 dx = 4 dx3 (1 dy ) (1) (1, 32 ) (2) (3, 1) (3) (3, 3) (4) (1, 2) Q211.The solution of the equation d2y = e−2x dx2 (1) e−2x (2) e−2x 4 4 + cx + d (3) 4 1 e−2x + cx2 + d (4) 14 e−4x + cx + d Q212. f(x) and g(x) are two differentiable functions on [0, 2] such that f ′′(x) −g′′(x) = 0 f ′(1) = 2g′(1) = 4f(2) = 3g(2) = 9 then f(x) −g(x) at x = 3/2 is (1) 0 (2) 2 (3) 10 (4) 5 Q213.If |→a| = 4, |→b| = 2 and the angle between →a and →b is π/6 then (→a × →b)2 = 2 is equal to (1) 48 (2) 16 (3) →a (4) none of these Q214. If →a,→b, →c are vectors such that |→a→b→c| = 4 then (1) 16 (2) 64 (3) 4 (4) 8 JEE Main 2002 JEE Main Previous Year Paper Q215.If →a,→b, →c are vectors such that →a + →b + →c = 0 and |→a| = 7, |→b| = 5, |→c| = 3 then angle between vector →b and →c is (1) 60∘ (2) 30∘ (3) 45∘ (4) 90∘ Q216.If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a ⋅b + b. c + c. a| , given that →a + →b + →c = 0 (1) 25 (2) 50 (3) -25 (4) -50 Q217. 3λ→c + 2μ(→a × →b) = 0 then (1) 3λ + 2μ = 0 (2) 3λ = 2μ (3) λ = μ (4) λ + μ = 0 Q218. →a = 3^i −5^j and →b = 6^i + 3^j are two vectors and →c is a vector such that →c = →a × →b then |→a| : |→b| : |→c| (1) √34 : √45 : √39 (2) √34 : √45 : 39 (3) 34 : 39 : 45 (4) 39 : 35 : 34 Q219.If →a × →b = →b × →c = →c × →a then →a + →b + →c = (1) abc (2) -1 (3) 0 (4) 2 Q220.The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. The magnitude of the two forces are (1) 13, 5 (2) 12, 6 (3) 14, 4 (4) 11, 7 Q221.A plane which passes through the point (3, 2, 0) and the line x−41 = y−75 = z−44 is (1) x - y + z = 1 (2) x + y + z = 5 (3) x + 2y - z = 1 (4) 2x - y + z = 5 Q222.The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π/4 with plane x + y = 3 are (1) 1, √2, 1 (2) 1, 1, √2 (3) 1, 1, 2 (4) √2, 1, 1 Q223.A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 2 1 , 13 and 14 . Probability that the problem is solved is (1) 3 (2) 1 4 2 (3) 2 (4) 1 3 3 Q224. A and B are events such that P(A ∪B) = 3/4, P(A ∩B) = 1/4, P(¯A) = 2/3 then P(¯A ∩B) is (1) 5/12 (2) 3/8 (3) 5/8 (4) 1/4 Q225.A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is JEE Main 2002 JEE Main Previous Year Paper (1) 8/3 (2) 3/8 (3) 4/5 (4) 5/4 JEE Main 2002 JEE Main Previous Year Paper