JEE Advanced 2008 Paper 2
Q. 1 A particle P starts from the point z₀ = 1 + 2i, where i = √-1 It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1. From z1 the particle moves √2 units in the direction of the vector î + ĵ and then it moves through an angle π/2 in anticlockwise direction on a circle with centre at origin, to reach a point z₂. The point z₂ is given by
A. 6 + 7i
B. − 7 + 6i
C. 7 + 6i
D. − 6 + 7i
Q. 2 Let the function g: (−∞, ∞) → (-π/2, π/2) be given by g(n) = 2tan⁻¹ (eⁿ) − π/2 . Then, g is
A. even and is strictly increasing in (0, ∞)
B. odd and is strictly decreasing in (−∞, ∞)
C. odd and is strictly increasing in (−∞, ∞)
D. neither even nor odd, but is strictly increasing in (−∞, ∞)
Q. 3 Consider a branch of the hyperbola x² − 2y² − 2√2x – 4√2y – 6 = 0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is
A. 1 – √(2/3)
B. √(3/2) – 1
C. 1 + √(2/3)
D. √(3/2) + 1
Q. 4 The area of the region between the curves y = √((1 + sinx)/cosx) and y = √((1 – sinx)/cosx) bounded by the lines x = 0 and x = π/4 is
A. (A)
B. (B)
C. (C)
D. (D)
Q. 5 Consider three points P = (−sin(β − α), − cosβ), Q = (cos(β − α), sinβ) and R = (cos(β − α + θ), sin(β − θ)), where 0 < α, β, θ < π/4. Then
A. P lies on the line segment RQ
B. Q lies on the line segment PR
C. R lies on the line segment QP
D. P, Q, R are non-collinear
Q. 6 An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is
A. 2, 4 or 8
B. 3, 6 or 9
C. 4 or 8
D. 5 or 10
Q. 7 Let two non-collinear unit vectors â and b̂ form an acute angle. A point P moves so that at any time t the position vector O̅P̅ (where O is the origin) is given by âcos t + b̂sin t. When P is farthest from origin O, let M be the length of O̅P̅ and û be the unit vector along O̅P̅. Then,
A. û = (â + b̂)/|â + b̂| and M = (1 + â.b̂̂ )^½
B. û = (â – b̂)/|â – b̂| and M = (1 + â.b̂̂ )^½
C. û = (â + b̂)/|â + b̂| and M = (1 + 2â.b̂̂ )^½
D. û = (â – b̂)/|â – b̂| and M = (1 + 2â.b̂̂ )^½
Q. 8 Let I = ∫(e^x)/(e^(4x) + e^(2x) +1)dx, J = ∫(e^(-x))/(e^(-4x) + e^(-2x) +1)dx. Then, for an arbitrary constant C, the value of J − I equals
A. 1/2 log((e^(4x) – e^(2x) +1)/(e^(4x) + e^(2x) +1)) + C
B. 1/2 log((e^(2x) + e^(x) +1)/(e^(2x) – e^(x) +1)) + C
C. 1/2 log((e^(2x) – e^(x) +1)/(e^(2x) + e^(x) +1)) + C
D. 1/2 log((e^(4x) + e^(2x) +1)/(e^(4x) – e^(2x) +1)) + C
Q. 9 Let g(x) = log(f(x)) where f(x) is a twice differentiable positive function on (0, ∞) such that f(x + 1) = x f(x). Then, for N = 1, 2, 3, …,
g′′ (N + (1/2)) – g′′ (1/2) =
A. -4{1 + 1/9 + 1/25 + ….. + 1/((2N – 1)²)}
B. 4{1 + 1/9 + 1/25 + ….. + 1/((2N – 1)²)}
C. -4{1 + 1/9 + 1/25 + ….. + 1/((2N + 1)²)}
D. 4{1 + 1/9 + 1/25 + ….. + 1/((2N + 1)²)}
Q. 10 Suppose four distinct positive numbers a₁, a₂, a₃, a₄ are in G.P. Let b₁ = a₁, b₂ = b₁ + a₂, b₃ = b₂ + a₃ and b₄ = b₃ + a₄.
STATEMENT−1 : The numbers b₁, b₂, b₃, b₄ are neither in A.P. nor in G.P.
And STATEMENT−2 : The numbers b₁, b₂, b₃, b₄ are in H.P.
A. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is a correct explanation for STATEMENT−1
B. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is NOT a correct explanation for STATEMENT−1.
C. STATEMENT−1 is True, STATEMENT−2 is False
D. STATEMENT−1 is False, STATEMENT−2 is True
Q. 11 Let a, b, c, p, q be real numbers. Suppose α, β are the roots of the equation x² + 2px + q = 0 and α, 1/β are the roots of the equation ax² + 2bx + c = 0, where β² ∉{−1, 0, 1}. STATEMENT−1 : (p² − q) (b² − ac) ≥ 0
And
STATEMENT−2 : b ≠ pa or c ≠ qa
A. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is a correct explanation for STATEMENT−1
B. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is NOT a correct explanation for STATEMENT−1.
C. STATEMENT−1 is True, STATEMENT−2 is False
D. STATEMENT−1 is False, STATEMENT−2 is True
Q. 12 Consider
L1 : 2x + 3y + p − 3 = 0
L2 : 2x + 3y + p + 3 = 0,
where p is a real number, and C : x² + y² + 6x − 10y + 30 = 0.
STATEMENT – 1 : If line L₁ is a chord of circle C, then line L₂ is not always a diameter of circle C.
and
STATEMENT – 2 : If line L₁ is a diameter of circle C, then line L₂ is not a chord of circle C.
A. STATEMENT – 1 is True, STATEMENT – 2 is True; STATEMENT – 2 is a correct explanation for STATEMENT – 1
B. STATEMENT – 1 is True, STATEMENT – 2 is True; STATEMENT – 2 is NOT a correct explanation for STATEMENT – 1.
C. STATEMENT – 1 is True, STATEMENT – 2 is False
D. STATEMENT – 1 is False, STATEMENT – 2 is True
Q. 13 Let a solution y = y(x) of the differential equation x√(x² – 1) dy – y√(y² – 1) dx = 0 satisfy y(2) = 2/√3
STATEMENT−1 : y(x) = sec(sec⁻¹x – π/6)
And
STATEMENT−2 : y(x) is given by 1/y = 2√3/x – √(1 – (1/x²))
A. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is a correct explanation for STATEMENT−1
B. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is NOT a correct explanation for STATEMENT−1.
C. STATEMENT−1 is True, STATEMENT−2 is False
D. STATEMENT−1 is False, STATEMENT−2 is True
Q. 14 Which of the following is true?
A. (2 + a)² f′′(1) + (2 − a)² f′′(−1) = 0
B. (2 – a)² f′′(1) – (2 + a)² f′′(−1) = 0
C. f′(1) f′(−1) = (2 − a)²
D. f′(1) f′(−1) = -(2 + a)²
Q. 15 Which of the following is true?
A. f(x) is decreasing on (−1, 1) and has a local minimum at x = 1
B. f(x) is increasing on (−1, 1) and has a local maximum at x = 1
C. f(x) is increasing on (−1, 1) but has neither a local maximum nor a local minimum at x = 1
D. f(x) is decreasing on (−1, 1) but has neither a local maximum nor a local minimum at x = 1
Q. 16 which of the following is true?
A. g′(x) is positive on (−∞, 0) and negative on (0, ∞)
B. g′(x) is negative on (−∞, 0) and positive on (0, ∞)
C. g′(x) changes sign on both (−∞, 0) and (0, ∞)
D. g′(x) does not change sign on (−∞, ∞)
Questions: 17 – 19
Consider the line
L1 : (x+1)/3 = (y+2)/1 = (z+1)/2
L2 : (x-2)/1 = (y+2)/2 = (z-3)/3
Q. 17 The unit vector perpendicular to both L1 and L2 is
A. (-î + 7ĵ + 7k̂)/√99
B. (-î – 7ĵ + 5k̂)/5√3
C. (-î + 7ĵ + 5k̂)/5√3
D. (7î – 7ĵ – k̂)/√99
Q. 18 The shortest distance between L₁ and L₂ is
A. 0
B. 17/√3
C. 41/5√3
D. 17/5√3
Q. 19 The distance of the point (1, 1, 1) from the plane passing through the point (−1, −2, −1) and whose normal is perpendicular to both the lines L₁ and L₂ is
A. 2/√75
B. 7/√75
C. 13/√75
D. 23/√75
Q. 20 Consider the lines given by
L1 : x + 3y − 5 = 0
L2 : 3x − ky − 1 = 0
L3 : 5x + 2y − 12 = 0
Match the Statements / Expressions in Column I with the Statements / Expressions in
Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4
matrix given in the ORS.
A. A – s; B – p,q; C – r; D – p, q, s
B. A – s, t; B – p; C – q, r; D – p, s
C. A – s; B – p,q, r; D – p, q, s
D. A – s; B – p; C – r; D – p, q
Q. 21 Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
A. A – s; B – p,q; C – r; D – p, q, s
B. A – s; B – p; C – r; D – p, q
C. A – r; B – q, s; C – r, s; D – p, r
D. A – s; B – p,q, r; D – p, q, s
Q. 22 Consider all possible permutations of the letters of the word ENDEANOEL.
Match the Statements / Expressions in Column I with the Statements / Expressions in
Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4
matrix given in the ORS.
A. A – s; B – p,q, r; D – p, q, s
B. A – s; B – p; C – r; D – p, q
C. A – s; B – p,q; C – r; D – p, q, s
D. A – p; B – s; C – q; D -q
Q. 23 Consider a system of three charges q/3, q/3 and -2q/3 placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60°
A. The electric field at point O is q/(8πε0(R²)) directed along the negative x-axis
B. The potential energy of the system is zero
C. The magnitude of the force between the charges at C and B is (q²)/(54πε0(R²))
D. The potential at point O is q/(12πε0R)
Q. 24 A radioactive sample S₁ having an activity 5μCi has twice the number of nuclei as another sample S₂ which has an activity of 10 μCi. The half lives of S₁ and S₂ can be
A. 20 years and 5 years, respectively
B. 20 years and 10 years, respectively
C. 10 years each
D. 5 years each
Q. 25 A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap –shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is
A. √(3)π/50 ĵ m/s
B. -√(3)π/50 ĵ m/s
C. √(3)π/50 î m/s
D. -√(3)π/50 î m/s
Q. 26 A block (B) is attached to two unstretched springs S₁ and S₂ with spring constants k and 4k, respectively (see figure I). The other ends are attached to identical supports M₁ and M₂ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is
A. 4
B. 2
C. 1/2
D. 1/4
Q. 27 A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle θ at which the speed of the bob is half of that at A, satisfie
A. θ = π/4
B. π/4 < θ < π/2
C. π/2 < θ < 3π/4
D. 3π/4 < θ < π
Q. 28 A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,
A. air from end 1 flows towards end 2. No change in the volume of the soap bubbles
B. air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases
C. no changes occurs
D. air from end 2 flows towards end 1. volume of the soap bubble at end 1 increases
Q. 29 A vibrating string of certain length l under a tension T resonates with a mode
corresponding to the first overtone (third harmonic) of an air column of length 75 cm
inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is
A. 344
B. 336
C. 117.3
D. 109.3
Q. 30 A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is d/3 initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is
A. (A)
B. (B)
C. (C)
D. (D)
Q. 31 A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are n0, n0/2, n0/6 and n0/8, respectively. The angle of incidence θ for which the beam just misses entering Region IV is
A. sin^(-1)(3/4)
B. sin^(-1)(1/8)
C. sin^(-1)(1/4)
D. sin^(-1)(1/3)
Q. 32
STATEMENT-1
For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.
and
STATEMENT-2
If the observer and the object are moving at velocities V̅1 and V̅2 respectively with
reference to a laboratory frame, the velocity of the object with respect to the observer is V̅2 – V̅1.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct
explanation for STATEMENT-1
C. STATEMENT -1 is True, STATEMENT-2 is False
D. STATEMENT -1 is False, STATEMENT-2 is True
Q. 33
STATEMENT-1
It is easier to pull a heavy object than to push it on a level ground.
and
STATEMENT-2
The magnitude of frictional force depends on the nature of the two surfaces in contact.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct
explanation for STATEMENT-1
C. STATEMENT -1 is True, STATEMENT-2 is False
D. STATEMENT -1 is False, STATEMENT-2 is True
Q. 34 STATEMENT-1
For practical purposes, the earth is used as a reference at zero potential in electrical
circuits.
and
STATEMENT-2
The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by Q/(4πε0R)
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct
explanation for STATEMENT-1
C. STATEMENT -1 is True, STATEMENT-2 is False
D. STATEMENT -1 is False, STATEMENT-2 is True
Q. 35
STATEMENT-1
The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
and
STATEMENT-2
Soft iron has a high magnetic permeability and cannot be easily magnetized or
demagnetized.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct
explanation for STATEMENT-1
C. STATEMENT -1 is True, STATEMENT-2 is False
D. STATEMENT -1 is False, STATEMENT-2 is True
Questions: 36 – 38
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R.
The charge density ρ (r) [charge per unit volume] is dependent only on the radial
distance r from the centre of the nucleus as shown in figure The electric field is
only along rhe radial direction.
Q. 36 The electric field at r = R is
A. independent of a
B. directly proportional to a
C. directly proportional to a²
D. inversely proportional to a
Q. 37 For a = 0, the value of d (maximum value of ρ as shown in the figure) is
A. (3Ze)/(4πR³)
B. (3Ze)/(πR³)
C. (4Ze)/(3πR³)
D. (Ze)/(3πR³)
Q. 38 The electric field within the nucleus is generally observed to be linearly dependent on r. This implies.
A. a = 0
B. a = R/2
C. a = R
D. a = 2R/3
Questions: 39 – 41
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity V̅₀ = V₀ î . The coefficient of friction is μ.
Q. 39 The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is
A. −kx
B. −2kx
C. −2kx /3
D. −4kx /3
Q. 40 The centre of mass of the disk undergoes simple harmonic motion with angular frequency ω equal to
A. √(k/M)
B. √(2k/M)
C. √(2k/3M)
D. √(4k/3M)
Q. 41 The maximum value of V0 for which the disk will roll without slipping is
A. μg√(M/k)
B. μg√(M/2k)
C. μg√(3M/k)
D. μg√(5M/2k)
Q. 42 Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graph given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
A. A – s; B – p,q, r; D – p, q, s
B. A – s; B – p,q; C – r; D – p, q, s
C. A – s; B – p; C – r; D – p, q
D. A – p, s; B – q, r, s; C – s; D – q
Q. 43 An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
A. A – p, q, r, s; B – q; C – p, q, r, s; D – p, q, r, s
B. A – p, s; B – q, r, s; C – s; D – q
C. A – s; B – p; C – r; D – p, q
D. A – s; B – p,q, r; D – p, q, s
Q. 44 Column I Contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
A. A – s; B – p,q; C – r; D – p, q, s
B. A – s, t; B – p; C – q, r; D – p, s
C. A – q; B – p, r; C – p, s; D – q, s
D. A – p, s; B – q, r, s; C – s; D – q
Q. 45 The correct stability order for the following species is
A. (II) > (IV) > (I) > (III)
B. (I) > (II) > (III) > (IV)
C. (II) > (I) > (IV) > (III)
D. (I) > (III) > (II) > (IV)
Q. 46 Cellulose upon acetylation with excess acetic anhydride/H2SO4 (catalytic) gives cellulose triacetate whose structure is
A. (A)
B. (B)
C. (C)
D. (D)
Q. 47 In the following reaction sequence, the correct structures of E, F and G are
A. (A)
B. (B)
C. (C)
D. (D)
Q. 48 Among the following the coloured compound is
A. CuCl
B. K₃[Cu(CN)₄]
C. CuF₂
D. [Cu(CH₃CN)₄]BF₄
Q. 49 Both [Ni(CO)₄] and [Ni(CN)₄]⁻² are diamagnetic. The hybridization of nickel in these complexes, respectively, are
A. sp₃, sp₃
B. sp₃, dsp₂
C. dsp₂, sp₃
D. dsp₂, dsp₂
Q. 50 The IUPAC name of [Ni(NH₃)₄][NiCl₄] is
A. Tetrachloronickel (II) – tetraamminenickel (II)
B. Tetraamminenickel (II) – tetrachloronickel (II)
C. Tetraamminenickel (II) – tetrachloronickelate (II)
D. Tetrachloronickel (II) – tetraamminenickelate (0)
Q. 51 Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate 0.01 mol of H₂ gas at the cathode is (1 Faraday = 96500 C mol⁻¹)
A. 9.65 × 10⁴ sec
B. 19.3 × 10⁴ sec
C. 28.95 × 10⁴ sec
D. 38.6 × 10⁴ sec
Q. 52 Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is
A. (A)
B. (B)
C. (C)
D. (D)
Q. 53 Solubility product constant (Ksp) of salts of types MX, MX2 and M3X at temperature ‘T’ are 4.0 × 10⁻⁸, 3.2 × 10⁻¹⁴ and 2.7 × 10⁻¹⁵, respectively. Solubilities (mole dm⁻³)) of the salts at temperature ‘T’ are in the order
A. MX > MX₂ > M₃X
B. M₃X > MX₂ > MX
C. MX₂ > M₃X > MX
D. MX > M₃X > MX₂
Q. 54
STATEMENT-1: Aniline on reaction with NaNO₂/HCl at 0°C followed by coupling with β- naphthol gives a dark blue coloured precipitate.
and
STATEMENT-2: The colour of the compound formed in the reaction of aniline with
NaNO₂/HCl at 0°C followed by coupling with β-naphthol is due to the extended conjugation.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct
explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Q. 55 STATEMENT-1: [Fe(H₂O)₅NO]SO₄ is paramagnetic.
and
STATEMENT-2: The Fe in [Fe(H₂O)₅NO]SO₄ has three unpaired electrons.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct
explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Q. 56
STATEMENT-1: The geometrical isomers of the complex [M(NH₃)₄Cl₂] are optically inactive. and
STATEMENT-2: Both geometrical isomers of the complex [M(NH₃)₄Cl₂] possess axis of symmetry
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct
explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Q. 57 STATEMENT-1: There is a natural asymmetry between converting work to heat and converting heat to work.
and
STATEMENT-2: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct
explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Questions: 58 – 60
A tertiary alcohol H upon acid catalysed dehydration gives a product I. Ozonolysis of I leads to compounds J and K. Compound J upon reaction with KOH gives benzyl alcohol and a compound L, whereas K on reaction with KOH gives only M,
Q. 58 Compound H is formed by the reaction of (see figure 2)
A. (A)
B. (B)
C. (C)
D. (D)
Q. 59 The structure of compound I is (see figure 3)
A. (A)
B. (B)
C. (C)
D. (D)
Q. 60 The structures of compounds J, K and L, respectively, are (see figure 4)
A. (A)
B. (B)
C. (C)
D. (D)
Questions: 61 – 63
In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A spacefilling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assumer radius of every sphere to be ‘r’.
Q. 61 The number of atoms on this HCP unit cell is
A. 4
B. 6
C. 12
D. 17
Q. 62 The volume of this HCP unit cell is
A. 24√2 r³
B. 16√2 r³
C. 12√2 r³
D. (64/3√3) r³
Q. 63 The empty space in this HCP unit cell is
A. 74%
B. 47.6%
C. 32%
D. 26%
Q. 64 Match the compounds in Column I with their characteristic test(s)/ reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix gives in the ORS.
A. A – r; B – p, q; C – p, q, r; D – p
B. A – s; B – p,q, r; D – p, q, s
C. A – p, s; B – q, r, s; C – s; D – q
D. A – r, s; B – p, q; C – p, q, r; D – p, s
Q. 65 Match the conversions in Column I with the type(s) of reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
A. A – s; B – p,q, r; D – p, q, s
B. A – p, s; B – q, r, s; C – s; D – q
C. A – p; B – q; C – p, r; D – p, s
D. A – r; B – p, q; C – p, q, r; D – p
Q. 66 Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
A. A – q, r; B – p, q, r, s; C – p, q, r; D – p, q
B. A – s; B – p,q; C – r; D – p, q, s
C. A – s; B – p,q, r; D – p, q, s
D. A – r; B – p, q; C – p, q, r; D – p
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | D | C | B | B | D | D | A | C | A | C |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | B | C | C | A | A | B | B | D | C | A |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | C | D | C | A | A | C | D | B | A | A |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | B | B | B | A | C | A | B | C | D | D |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | C | D | A | C | D | A | C | C | B | C |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | B | A | D | D | A | B | A | B | A | D |
| Question | 61 | 62 | 63 | 64 | 65 | 66 | ||||
| Answer | B | A | D | A | C | A |