JEE Advanced 2010 Paper 2
Q. 1 The complex showing a spin-only magnetic moment of 2.82 B.M is
A. A
B. B
C. C
D. D
Q. 2 The species having pyramidal shape is
A. A
B. B
C. C
D. D
Q. 3 Choose the correct option
A. A
B. B
C. C
D. D
Q. 4 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 5 The packing efficiency of the two-dimensional square unit cell shown below is
A. 39.27%
B. 68.02%
C. 74.05%
D. 78.54%
Q. 6 Assuming that Hund’s rule is violated. the bond order and magnetic nature of the diatomic molecule B₂ is
A. 1 and diamagnetic
B. 1 and paramagnetic
C. 0 and diamagnetic
D. 0 and paramagnetic
Q. 7 The total number of diprotic acids among the following is
Q. 8 Total number of geometrical isomers for the complex is
Q. 9 Among the following. the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn Tl, Na, Ti
Q. 10 Silver (atomic weight = 108 g/mol) has a density of 10.5 g cm-³. The number of silver atoms on a surface of area 10⁻¹² m² can be expressed in scientific notation as y x 10ˣ. The value of x is
Q. 11 One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is Wₛ and that along the dotted line path is W. then the integer closest to the ratio W/Wₛ is
Questions: 12 – 14
Two aliphatic aldehydes P and Q react in the presence of aqueous K₂CO₃ to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below
Q. 12 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 13 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 14 Choose the correct option:
A. A
B. B
C. C
D. D
Questions: 15 – 17
The hydrogen-like species Li²⁺ is in a spherically symmetric state S₁ with one radial node. Upon absorbing light the ion undergoes transition to a state S₂. The state S₂ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
Q. 15 The state S₁ is
A. 1s
B. 2s
C. 2p
D. 3s
Q. 16 Energy of the state S₁ in units of the hydrogen atom ground state energy is
A. 0.75
B. 1.50
C. 2.25
D. 4.50
Q. 17 The orbital angular momentum quantum number of the state S₂ is
A. 0
B. 1
C. 2
D. 3
Q. 18 Match the reactions in Column I with appropriate options in Column II.
A. A – r, s ; B – t ; C – p, q ; D – r
B. A – q, s ; B – t ; C – p, q ; D – r
C. A – p, q ; B – t ; C – q, s ; D – r
D. A – r, s ; B – r ; C – p, q ; D – t
Q. 19 All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.
A. A – p, s ; B – p, q, r, t ; C – p, q ; D – p
B. A – p, s ; B – p, q, r, t ; C – p, q ; D – p, r
C. A – p, q ; B – p, q, r, t ; C – p, s ; D – p
D. A – p, r ; B – p, q, r, t ; C – p, q ; D – p, s
Q. 20 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 21 Let S = {1. 2. 3. 4}. The total number of unordered pairs of disjoint subsets of S is equal to
A. 25
B. 34
C. 42
D. 41
Q. 22 Choose the correct option:
A. 1
B. 1/3
C. 1/2
D. 1/e
Q. 23 If the distance of the point P(1, -2, 1) from the plane x + 2y – 22 = a. where a > 0, is 5, then the foot of the perpendicular from P to the plane is
A. (8/3, 4/3, -7/3)
B. (4/3, -4/3, 1/3)
C. (1/3, 2/3, 10/3)
D. (2/3, -1/3, 5/2)
Q. 24 Two adjacent sides of a parallelogram ABCD are given by
AB =2i + 10j + 11k and AD = -i + 2j + 2k
The side AD is rotated by an acute angle a in the plane of the parallelogram so that AD becomes AD’. If AD’ makes a right angle with the side AB. then the cosine of the angle a is given by
A. 8/9
B. √17/9
C. 1/9
D. 4√5/9
Q. 25 A signal which can be green or red with probability 4/5 and 1/5 respectively. is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is
A. 3/5
B. 6/7
C. 20/23
D. 9/20
Q. 26 Two parallel chords of a circle of radius 2 are at a distance √3 +1 apart. If the chords subtend at the center angles of π/k and 2π/k where k > 0, then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k]
Q. 27 Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15√3. If ∠ACB is obtuse and if r denotes the radius of the incircle of the triangle. then r² is equal to
Q. 28 Answer the following:
Q. 29 Answer the following:
Q. 30 Answer the following:
Questions: 31 – 33
Consider the polynomial
f(x) = 1 + 2x + 3x² + 4x³
Let s be the sum of all distinct real roots of fix) and let t = |s|.
Q. 31 The real number s lies in the interval
A. (-1/4, 0)
B. (-11, -3/4)
C. (-3/4, -1/2)
D. (0, 1/4)
Q. 32 The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t, lies in the interval
A. (3/4, 3)
B. (24/64, 11/16)
C. (9, 10)
D. (0, 21/64)
Q. 33 The function f ‘(x) is
A. increasing in (-t, -1/4) and decreasing in (-1/4, t)
B. decreasing in (-t, -1/4) and increasing in (-1/4, t)
C. increasing in (-t, t)
D. decreasing in (-t, t)
Questions: 34 – 36
Tangents are drawn from the point P(3, 4) to the ellipse x²/9 + y²/4 = 1 touching the ellipse at points A and B.
Q. 34 The coordinates of A and B are
A. (3, 0) and (0, 2)
B. (-8/5, 2√161/15) and (-9/5, 8/5)
C. (-8/5, 2√161/15) and (0, 2)
D. (3, 0) and (-9/5, 8/5)
Q. 35 The orthocenter of the triangle PAB is
A. (5, 8/7)
B. (7/5, 25/8)
C. (11/5, 8/5)
D. (8/25, 7/5)
Q. 36 The equation of the locus of the point whose distances from the point P and the line AB are equal is
A. 9x² + y² – 6xy – 54x – 62y + 241 = 0
B. x² + 9y² + 6xy – 54x + 62y – 241 = 0
C. 9x² + 9y² – 6xy – 54x – 62y – 241 = 0
D. x² + y² – 2xy + 27x + 31y – 120 = 0
Q. 37 Match the statements in Column-I with those in Column-II.
[Note: Here z takes values in the complex plane and Im z and Re z denote respectively, the imaginary part and the real part of z.]
A. A – p, r; B – q ; C – p, s, t ; D – q, r, s, t
B. A – p, r, s, t ; B – p ; C – p, s, t ; D – q, r
C. A – q, r; B – p ; C – p, s, t ; D – q, r, s, t
D. A – q, r ; B – p ; C – s, t ; D – r, s, t
Q. 38 Match the statements in Column-I with those in Column-II.
A. A – t ; B – p, r ; C – q, s ; D – r
B. A – t ; B – q, s ; C – p, r ; D – r
C. A – r ; B – p, r ; C – q, s ; D – t
D. A – r ; B – q, s ; C – p, r ; D – t
Q. 39 A Vernier caliper has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers. the least count is
A. 0.02 mm
B. 0.05 mm
C. 0.1 mm
D. 0.2 mm
Q. 40 A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the Wire is 50 N and the speed of sound is 320 m/s. the mass of the string is
A. 5 grams
B. 10 grams
C. 20 grams
D. 40 grams
Q. 41 A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is
A. virtual and at a distance of 16 cm from the mirror
B. real and at a distance of 16 cm from the mirror
C. Virtual and at a distance of 20 cm from the mirror
D. real and at a distance of 20 cm from the mirror
Q. 42 A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is
A. 4.50 J
B. 7.50 J
C. 5.06 J
D. 14.06 J
Q. 43 A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81π/7 x 10⁵ V/m. When the field is switched off, the drop is observed to fall with terminal velocity 2 x 10⁻³ m/s. Given g = 9.8 m/s²,. viscosity of the air = 1.8 x 10⁻⁵ Ns m-² and the density of oil = 900 kg/m³, the magnitude of q is
A. 1.6 x 10⁻¹⁹ C
B. 3.2 x 10⁻¹⁹ C
C. 4.8 x 10⁻¹⁹ C
D. 8.0 x 10⁻¹⁹ C
Q. 44 A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells held together by pressing them with force F (see figure). F is proportional to
A. A
B. B
C. C
D. D
Q. 45 A diatomic ideal gas is compressed adiabatically to 1/32 of its initial volume. In the initial temperature of the gas is Tᵢ (in Kelvin) and the final temperature is aTᵢ. the value of a is
Q. 46 At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?
[Take ln 5 = 1.6, ln 3 = 1.1]
Q. 47 Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from 25/3 m to 50/7 m in 30 seconds. What is the speed of the object in km per hour ?
Q. 48 A large glass slab (μ = 5/ 3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ?
Q. 49 To determine the half life of a radioactive element. a student plots a graph of ln|dN(t)/dt| versus t. Here dN(t)/dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is Years
Questions: 50 – 52
When liquid medicine of density ρ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the chopper is pressed. a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
Q. 50 If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r <
A. 2πrT
B. 2πRT
C. 2πr²T/R
D. 2πR²T/r
Q. 51 If r = 5 x 10^(-4) ρ =10 kg/m³. g=10 m/s², T=0.11N/m, the radius of the drop when it detaches from the dropper is approximately
A. 1.4 x 10-³ m
B. 3.3 x 10-³ m
C. 2.0 x 10-³ m
D. 4.1 x 10-³ m
Q. 52 After the drop detaches. its surface energy is
A. 1.4 x 10⁻⁶ J
B. 2.7 x 10⁻⁶ J
C. 5.4 x 10⁻⁶ J
D. 8.1 x 10⁻⁶ J
Questions: 53 – 55
The key feature of Bohr’s theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr’s quantization condition.
Q. 53 A diatomic molecule has moment of inertia I. By Bohr’s quantization condition its rotational energy in the nth level (n = 0 is not allowed) is
A. 1/n² x (h²/(8π²I))
B. 1/n x (h²/(8π²I))
C. n x (h²/(8π²I))
D. n² x (h²/(8π²I))
Q. 54 It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to 4/π x 10¹¹ Hz. Then the moment of inertia of CO molecule about its center of mass is close to (Take h = 2 x 10³⁴ J s)
A. 2.76 x 10⁻⁴⁶ kg m²
B. 1.87 x 10⁻⁴⁶ kg m²
C. 4.67 x 10⁻⁴⁷ kg m²
D. 1.17 x 10⁻⁴⁷ kg m²
Q. 55 In a CO molecule. the distance between C (mass = 12 a.m.u.) and 0 (mass = 16 a.m.u.) where 1 a.m.u = (5/3) x 10⁻²⁷ is close to
A. 2.4 x 10⁻¹⁰ m
B. 1.9 x 10⁻¹⁰ m
C. 1.3 x 10⁻¹⁰ m
D. 4.4 x 10⁻¹¹ m
Q. 56 Two transparent media of refractive indices μ₁ and μ₃ have a solid lens shaped transparent material of refractive index μ₂ between them as shown in figures in Column II. A traversing these media is also shown in the figures. In Column I different relationship between μ₁, μ₂ and μ₃ are given. Match them to the ray diagrams shown in Column
A. A – p, r ; B – q, s, t ; C – p, r, t ; D – q, s
B. A – q, s ; B – q, s, t ; C – p, r, t ; D – p, r
C. A – p, r ; B – p, r, t ; C – q, s, t ; D – q, s
D. A – q, s ; B – q, s, t ; C – p, r, t ; D – p, r
Q. 57 You are given many resistances. capacitors and inductors. These are connected to variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V₁ and V₂. (indicated in circuits) are related as shown in column I. Match the two
A. A – r, s, t ; B – q, r, s, t ; C – p, q; D – q, r, s, t
B. A – r, t ; B – r, s, t ; C – p, q; D – q, r, s, t
C. A – s, t ; B – q, r, s, t ; C – p, q; D – q, r, s
D. A – r, s, t ; B – q, r ; C – p, q; D – q, r
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | B | D | C | C | D | A | 6 | 3 | 2 | 7 |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | 2 | B | A | D | B | C | B | A | A | D |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | D | B | A | B | C | 3 | 3 | 1 | 0 | 4 |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | C | A | B | D | C | A | C | A | D | B |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | B | C | D | A | 4 | 2 | 3 | 6 | 8 | C |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | |||
| Answer | A | B | D | B | C | A | A |