Q99.How many EDTA (ethylenediaminetetraacetic acid) molecules are required to make an octahedral complex with a Ca2+ ion? (1) six (2) three (3) one (4) two Q100. HBr reacts with CH2 = CH −OCH3 under anhydrous conditions at room temperature to give (1) CH3CHO and CH3Br (2) BrCH2CHO and CH3OH (3) BrCH2 −CH2 −OCH3 (4) H3C −CHBr −OCH3 Q101. CH3Br + Nu−⟶CH3 −Nu + Br− The decreasing order of the rate of the above reaction with nucleophiles (Nu−)A to D is [Nu−= (A)PhO− , (B) AcO− , (C) HO− , (D) CH3O−] (1) D > C > A > B (2) D > C > B > A (3) A > B > C > D (4) B > D > C > A Q102.Fluorobenzene (C6H5 F) can be synthesized in the laboratory (1) by heating phenol with HF and KF (2) from aniline by diazotisation followed by heating the diazonium salt with HBF4 (3) by direct fluorination of benzene with F2 gas (4) by reacting bromobenzene with NaF solution Q103. The structure of the major product formed in the following reaction is JEE Main 2006 JEE Main Previous Year Paper (1) (2) (3) (4) Q104.Reaction of trans-2-phenyl-1-bromocyclopentane on reaction with alcoholic KOH produces (1) 4-phenylcyclopentene (2) 2-phenylcyclopentene (3) 1-phenylcyclopentene (4) 3-phenylcyclopentene Q105.The structure of the compound that gives a tribromo derivative on treatment with bromine water is (1) (2) (3) (4) Q106.Phenyl magnesium bromide reacts with methanol to give (1) a mixture of anisole and Mg(OH)Br (2) a mixture of benzene and Mg(OMe)Br (3) a mixture of toluene and Mg(OH)Br (4) a mixture of phenol and Mg(Me)Br Q107.Among the following the one that gives positive iodoform test upon reaction with I2 and NaOH is (1) CH3CH2CH(OH)CH2CH3 (2) C6H5CH2CH2OH (3) (4) PhCHOHCH3 JEE Main 2006 JEE Main Previous Year Paper Q108. The electrophile involved in the above reaction is (1) (2) dichlorocarbene (: CCl2) (3) (4) Q109.The correct order of increasing acid strength of the compounds is (a) CH3CO2H (b) MeOCH2CO2H (c) CF3CO2H (d) (1) b < d < a < c (2) d < a < c < b (3) d < a < b < c (4) a < d < c < b Q110.The term anomers of glucose refers to (1) isomers of glucose that differ in configurations (2) a mixture of (D)-glucose and (L)-glucose at carbons one and four (C −1 and C −4) (3) enantiomers of glucose (4) isomers of glucose that differ in configuration at carbon one (C −1) Q111.The pyrimidine bases present in DNA are (1) cytosine and adenine (2) cytosine and guanine (3) cytosine and thymine (4) cytosine and uracil Q112.If the roots of the quadratic equation x2 + px + q = 0 are tan 30∘ and tan 15∘ , respectively then the value of 2 + q −p is (1) 2 (2) 3 (3) 0 (4) 1 Q113.All the values of m for which both roots of the equations x2 −2mx + m2 −1 = 0 are greater than −2 but less than 4 , lie in the interval (1) −2 < m < 0 (2) m > 3 (3) −1 < m < 3 (4) 1 < m < 4 Q114.If z2 + z + 1 = 0, where z is a complex number, then the value of 1 2 1 2 1 2 1 2 + + + + + + ⋯+ + (z z ) (z2 z2 ) (z3 z3 ) (z6 z6 ) JEE Main 2006 JEE Main Previous Year Paper (1) 18 (2) 54 (3) 6 (4) 12 Q115.At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is (1) 5040 (2) 6210 (3) 385 (4) 1110 Q116.The value of ∑10k=1 (sin 2kπ11 + i cos 2kπ11 ) is (1) i (2) 1 (3) -1 (4) -i p2 a6 equals , p ≠q , then = q2Q117.Let a1, a2, a3, … be terms of an A.P. If a1+a2+⋯+aqa1+a2+⋯ap a21 (1) 41 (2) 7 11 2 (3) 2 (4) 11 7 41 Q118.If a1, a2, … , an are in H.P., then the expression a1a2 + a2a3 + … + an−1an is equal to (1) n (a1 −an) (2) (n −1) (a1 −an) (3) na1an (4) (n −1)a1an Q119.If the expansion in powers of x of the function 1 is a0 + a1x + a2x2 + a3x3 + …, then an is (1−ax)(1−bx) (1) bn−an (2) an−bn b−a b−a (3) an+1−bn+1 (4) bn+1−an+1 b−a b−a Q120.For natural numbers m, n if (1 −y)m(1 + y)n = 1 + a1y + a2y2 + …, and a1 = a2 = 10 then (m, n) is (1) (20, 45) (2) (35, 20) (3) (45, 35) (4) (35, 45) Q121.The number of values of x in the interval [0, 3π] satisfying the equation 2 sin2 x + 5 sin x −3 = 0 is (1) 4 (2) 6 (3) 1 (4) 2 Q122.If 0 < x < π and cos x + sin x = 21 , then tan x is (1) (1−√7) (2) (4−√7) 4 3 (3) −(4+√7)3 (4) (1+√7)4 Q123.A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is (1) x + y = 7 (2) 3x − 4y + 7 = 0 (3) 4x + 3y = 24 (4) 3x + 4y = 25 Q124.The two lines x = ay + b, z = cy + d; and x = a′y + b′, z = c′y + d′ are perpendicular to each other if (1) aa′ + cc′ = −1 (2) aa′ + cc′ = 1 (3) a′a + c′c = −1 (4) a′a + c′c = 1 JEE Main 2006 JEE Main Previous Year Paper Q125.If (a, a2) falls inside the angle made by the lines y = x2 , x > 0 and y = 3x, x > 0 , then a belongs to (1) (0, 12 ) (2) (3, ∞) (3) ( 12 , 3) (4) (−3, −12 ) Q126.If the lines 3x −4y −7 = 0 and 2x −3y −5 = 0 are two diameters of a circle of area 49π square units, the equation of the circle is (1) x2 + y2 + 2x −2y −47 = 0 (2) x2 + y2 + 2x −2y −62 = 0 (3) x2 + y2 −2x + 2y −62 = 0 (4) x2 + y2 −2x + 2y −47 = 0 Q127.Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of 2π at its centre is 3 (1) x2 + y2 = −3 (2) x2 + y2 = 1 (3) x2 + y2 = 274 (4) x2 + y2 = 94 Q128.The locus of the vertices of the family of parabolas y = a3x23 + a2x2 −2a is (1) xy = 10564 (2) xy = 43 (3) xy = 1635 (4) xy = 10564 Q129.Angle between the tangents to the curve y = x2 −5x + 6 at the points (2, 0) and (3, 0) is (1) π (2) π 2 2 (3) π (4) π 6 4 Q130.In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is (1) 3 (2) 1 5 2 (3) 4 (4) 1 5 √5 Q131.Suppose a population A has 100 observations 101, 102, … , 200 , and another population B has 100 observations 151, 152, … , 250 . If VA and VB represent the variances of the two populations, respectively, then VA is VB (1) 1 (2) 9/4 (3) 4/9 (4) 2/3 Q132.A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is (1) 3 x2 (2) 2 √x38 (3) 21 x2 (4) πx2 Q133.Let W denote the words in the English dictionary. Define the relation R by : R = {(x, y) ∈W × W ∣ the words x and y have at least one letter in common } . Then R is (1) not reflexive, symmetric and transitive (2) reflexive, symmetric and not transitive (3) reflexive, symmetric and transitive (4) reflexive, not symmetric and transitive Q134.If A and B are square matrices of size n × n such that A2 −B2 = (A −B)(A + B), then which of the following will be always true? JEE Main 2006 JEE Main Previous Year Paper (1) A = B (2) AB = BA (3) either of A or B is a zero matrix (4) either of A or B is an identity matrix and B = a, b ∈N . ThenQ135.Let A = (13 24 ) (a0 0b ), (1) there cannot exist any B such that AB = BA (2) there exist more than one but finite number of B’s such that AB = BA (3) there exists exactly one B such that AB = BA (4) there exist infinitely many B’s such that AB = BA Q136.The set of points where f(x) = 1+|x|x is differentiable is (1) (−∞, 0) ∪(0, ∞) (2) (−∞, −1) ∪(−1, ∞) (3) (−∞, ∞) (4) (0, ∞) Q137.If xm ⋅yn = (x + y)m+n , then dxdy is (1) xy (2) x+yxy (3) xy (4) x y Q138.If x is real, the maximum value of 3x2+9x+17 is 3x2+9x+7 (1) 1/4 (2) 41 (3) 1 (4) 17/7 Q139.The function f(x) = x2 + x2 has a local minimum at (1) x = 2 (2) x = −2 (3) x = 0 (4) x = 1 dx isQ140.The value of the integral, ∫63 √9−x+√x√x (1) 1/2 (2) 3/2 (3) 2 (4) 1 Q141. ∫π0 xf(sin x)dx is equal to (1) π ∫π0 f(cos x)dx (2) π ∫π0 f(sin x)dx (3) π 2 ∫π/20 f(sin x)dx (4) π ∫π/20 f(cos x)dx Q142. ∫−π/2−3π/2 [(x + π)3 + cos2(x + 3π)]dx is equal to (1) π4 (2) π4 32 32 + π2 (3) π (4) π 2 4 −1 a > 1 , where [x] denotes the greatest integer not exceeding x isQ143.The value of ∫a1 [x]f ′(x)dx, (1) af(a) −{f(1) + f(2) + … + f([a])} (2) [a]f(a) −{f(1) + f(2) + … + f([a])} (3) [a]f([a]) −{f(1) + f(2) + … + f(a)} (4) af([a]) −{f(1) + f(2) + … + f(a)} Q144.The differential equation whose solution is Ax2 + By2 = 1, where A and B are arbitrary constants is of (1) second order and second degree (2) first order and second degree (3) first order and first degree (4) second order and first degree JEE Main 2006 JEE Main Previous Year Paper −−Q145. → → 1 ABC is a triangle, right angled at A . The resultant of the forces acting along AB, AC with magnitudes AB −→ and 1 respectively is the force along AD , where D is the foot of the perpendicular from A onto BC. The AC magnitude of the resultant is (1) AB2+AC 2 (2) (AB)(AC) (AB)2(AC)2 AB+AC (3) AB 1 + AC1 (4) AD1 –––– Q146.If (a × b) × –c = –a × (b × –c), where –a, b and –c are any three vectors such that –a ⋅b ≠0, b ⋅–c ≠0, then a and c are (1) inclined at an angle of π/3 between them (2) inclined at an angle of π/6 between them (3) perpendicular (4) parallel Q147.A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then θ is (1) 90∘ (2) 120∘ (3) 45∘ (4) 60∘ Q148.The values of a, for which the points A, B, C with position vectors 2^i −^j + ^k,^i −3^j −5^k and a^i −3^j + ^k respectively are the vertices of a right-angled triangle with C = π2 are (1) 2 and 1 (2) −2 and −1 (3) −2 and 1 (4) 2 and −1 Q149.The image of the point (−1, 3, 4) in the plane x − 2y = 0 is (1) (−173 , −193 , 4) (2) (15, 11, 4) (3) (−173 , −193 , 1) (4) none of these Q150.At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10-minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is (1) 6 (2) 5 5e 6 (3) 6 (4) 6 55 e5 JEE Main 2006 JEE Main Previous Year Paper