Practice Questions

Q87.Given the data at 25∘C, Ag + I−⟶AgI + e−; E∘= 0.152 V Ag ⟶Ag+ + e−; E∘= −0.800 V What is the value of log Ksp for AgI ? RT = 0.059 (2.303 F V) (1) −8.12 (2) +8.612 (3) −37.83 (4) −16.13

Q88.Resistance of a conductivity cell filled with a solution of an electrolyte of concentration 0.1M is 100Ω . The conductivity of this solution is 1.29 S m−1 . Resistance of the same cell when filled with 0.2M of the same solution is 520Ω . The molar conductivity of 0.02M solution of the electrolyte will be (1) 124 × 10−4 S m2 mol−1 (2) 1240 × 10−4 S m2 mol−1 (3) 1.24 × 10−4 S m2 mol−1 (4) 12.4 × 10−4 S m2 mol−1 JEE Main 2006 JEE Main Previous Year Paper

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

Q90.Rate of a reaction can be expressed by Arrhenius equation as: k = Ae−E/RT In this equation, E represents (1) the energy above which all the colliding (2) the energy below which colliding molecules will molecules will react not react (3) the total energy of the reacting molecules at a (4) the fraction of molecules with energy greater temperature, T than the activation energy of the reaction

Q91.The following mechanism has been proposed for the reaction of NO with Br2 to form NOBr : NO(g) + Br2( g) ⇌NOBr2( g) NOBr2( g) + NO(g) ⟶2NOBr(g) If the second step is the rate determining step, the order of the reaction with respect to NO(g) is (1) 1 (2) 0 (3) 3 (4) 2

Q92.In Langmuir’s model of adsorption of a gas on a solid surface (1) the rate of dissociation of adsorbed molecules (2) the adsorption at a single site on the surface may from the surface does not depend on the surface involve multiple molecules at the same time covered (3) the mass of gas striking a given area of surface is (4) the mass of gas striking a given area of surface is proportional to the pressure of the gas independent of the pressure of the gas

Q93.Which of the following chemical reactions depicts the oxidizing behaviour of H2SO4 ? (1) 2HI + H2SO4 ⟶I2 + SO2 + 2H2O (2) Ca(OH)2 + H2SO4 ⟶CaSO4 + 2H2O (3) NaCl + H2SO4 ⟶NaHSO4 + HCl (4) 2PCl5 + H2SO4 ⟶2POCl3 + 2HCl + SO2Cl2

Q94.What products are expected from the disproportionation reaction of hypochlorous acid? (1) HClO3 and Cl2O (2) HClO2 and HClO4 (3) HCl and Cl2O (4) HCl and HClO3

Q95.Lanthanoid contraction is caused due to (1) the appreciable shielding on outer electrons by 4f (2) the appreciable shielding on outer electrons by 5d electrons from the nuclear charge electrons from the nuclear charge (3) the same effective nuclear charge from Ce to Lu (4) the imperfect shielding on outer electrons by 4f electrons from the nuclear charge

Q96.The IUPAC name for the complex [Co (NO2)(NH3)5]Cl2 is JEE Main 2006 JEE Main Previous Year Paper (1) nitrito-N-pentaamminecobalt (III) chloride (2) nitrito-N-pentaamminecobalt (II) chloride (3) pentaammine nitrito- N -cobalt (II) chloride (4) pentaammine nitrito- N -cobalt (III) chloride

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

Q98.In Fe(CO)5 , the Fe −C bond possesses (1) π-character only (2) both σ and π characters (3) ionic character (4) σ-character only

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

Q1. A particle is moving eastwards with a velocity of 5 m/s in 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is (1) 1 m/s2 towards north-east (2) 21 m/s2 towards north. √2 (3) zero (4) 1 m/s2 towards north-west √2

Q2. Out of the following pair, which one does NOT have identical dimensions is (1) angular momentum and Planck's constant (2) impulse and momentum (3) moment of inertia and moment of a force (4) work and torque

Q3. The relation between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is (1) −2abv2 (2) 2bv3 (3) −2av3 (4) 2av2

Q4. A car starting from rest accelerates at the rate f through a distance S , then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then (1) S = ft (2) S = 1/6ft2 (3) S = 1/2ft2 (4) None of these

Q5. A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s2 . He reaches the ground with a speed of 3 m/s. At what height, did he bail out? (1) 91 m (2) 182 m (3) 293 m (4) 111 m

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

Q8. A projectile can have the same range R for two angles of projection. If t1 and t2 be the times of flights in the two cases, then the product of the two time of flights is proportional to (1) R2 (2) 1/R2 (3) 1/R (4) R

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

Q10.A smooth block is released at rest on a 45∘ incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is JEE Main 2005 JEE Main Previous Year Paper 1 − n2 (1) μk = 1 − n21 (2) μk = √1 1 − n2 (3) μs = 1 − n21 (4) μs = √1

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

Q12.A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration a to keep the block stationary. Then a is equal to (1) g/ tan α (2) g cosec α (3) g (4) g tan α