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JEE ADVANCED 2015 PAPER 2 CODE 3
Physics
1. A monochromatic beam of light is incident at 60π on one face of an equilateral prism of refractive index π
and emerges from the opposite face making an angle π(π) with the normal (see the figure). For π = β3
15. Consider a uniform spherical charge distribution of radius π 1 centred at the origin O. In this distribution, a
spherical cavity of radius π 2, centred at π with distance ππ = π = π 1 β π 2 (see figure) is made. If the
electric field inside the cavity at position π is οΏ½βοΏ½ (π ), then the correct statement(s) is (are)
(A) οΏ½βοΏ½ is uniform, its magnitude is independent of π 2 but its direction depends on π
(B) οΏ½βοΏ½ is uniform, its magnitude is depends on π 2 and its direction depends on π
(C) οΏ½βοΏ½ is uniform, its magnitude is dependent of a but its direction depends on π
(D) οΏ½βοΏ½ is uniform and both its magnitude and direction depend on π
Answer Key: (D)
16. In plotting stress versus strain curves for two materials π and π, a student by mistake puts strain on the
π¦-axis and stress on the π₯- axis as shown in the figure. Then the correct statement(s) is(are)
(A) π has more tensile strength than π
(B) π is more ductile than π
(C) π is more brittle than π
(D) The Youngβs modulus of π is more than that of π
Answer Key: (A,B)
SECTION 3 (Maximum Marks: 16)
This section contains TWO Paragraph
Based on each paragraph, there will be TWO questions
Each questions has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these
four options(s) is(are) correct
For each question, darken the bubble(s) corresponding to the correct option(s) in the
ORS
Marking scheme:
+4 If the bubble(s) corresponding to all the correct option(s) is(are) darkened
0 If none of the bubbles is darkened
-2 In all other cases
Paragraph 1 In a thin rectangular metallic strip a constant current πΌ flows along the positive π₯-difection, as shown in the figure. The length, width and thickness of the strip are π, π€ and π, respectively.
A uniform magnetic field οΏ½βοΏ½ is applied on the strip along positive π¦-direction. Due to this the charge carriers experience a net deflection along the π§-direction. This results in accumulation of charge carriers on the surface πππ π and appearance of equal opposite charges on the face opposite to πππ π. A potential difference along the π§-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.
17. Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths
are π€1 and π€2 and thicknesses are π1 and π2, respectively. Two points πΎ and π are symmetrically
located on the opposite faces parallel to the π₯-π¦ plane (see figure). π1 and π2 are the potential differences
between πΎ and π in strips 1 and 2 respectively. Then, for a given current πΌ flowing through them in a
given magnetic field strength π΅, the correct statement(s) is (are)
(A) If π€1 = π€2 and π1 = 2π2, then π2 = 2π1
(B) If π€1 = π€2 and π1 = 2π2, then π2 = π1
(C) If π€1 = 2π€2 and π1 = π2, then π2 = 2π1
(D) If π€1 = 2π€2 and π1 = π2, then π2 = π1
Answer Key: (A,D)
18. Consider two different metallic strips (1 and 2) of same dimensions (length π, width π€and thickness π)
with carrier densities π1 and π2, respectively. Strip 1 is placed in magnetic field π΅1 and strip 2 is placed in
magnetic field π΅2, both along positive π¦-directions. Then π1 and π2 are the potential differences
developed between πΎ and π in strips 1 and 2 respectively.
Assuming that the current πΌ is the same for both strips, the correct option(s) is (are)
(A) If π΅1 = π΅2 and π1 = 2π2, then π2 = 2π1
(B) If π΅1 = π΅2 and π1 = 2π2, then π2 = π1
(C) If π΅1 = 2π΅2 and π1 = π2, then π2 = 0.5π1
(D) If π΅1 = 2π΅2 and π1 = π2, then π2 = π1
Answer Key: (A,C)
Paragraph 2
Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index π1 surrounded by a medium of lower refractive index π2. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media π1 and π2 as shown in the figure. All rays with the angle of incidence π less than a particular value ππ are confined in the medium of refractive index π1. The numerical aperture (NA) of the structure is defined as sin ππ.
19. For two structures namely π1 with π1 =β45
4 and π2 =
3
2, and π2 with π1 =
8
5 and π2 =
7
5 and taking the
refractive index of water to be 4
3 and that of air to be 1, the correct option(s) is (are)
(A) NA of π1 immersed in water is the same as that of π2 immersed in a liquid of refractive index 16
3β15
(B) NA of π1 immersed in liquid of refractive index 6
β15 is the same as that of π2 immersed in water
(C) NA of π1 placed in air is the same as that of π2 immersed in liquid of refractive index 4
β15
(D) NA of π1 placed in air is the same as that of π2 placed in water
Answer Key: (A,C)
20. If two structures of same cross-sectional area, but different numerical apertures ππ΄1 and ππ΄2
(ππ΄2 < ππ΄1) are joined longitudinally, the numerical aperture of the combined structure is
(A) ππ΄1ππ΄2
ππ΄1+ππ΄2
(B) ππ΄1 + ππ΄2
(C) ππ΄1 (D) ππ΄2
Answer Key: (D)
CHEMISTRY
21. The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar
conductivity of a solution of a weak acid HY (0.10 M). If Ξ»Xβ0 β Ξ»Yβ
0 , the difference in their pKa values,
pKa(HX) β pKa(HY) , is (Consider degree of ionization of both acids to << 1)
Answer Key: (3)
22. A closed vessel with rigid walls contains 1 mol of U92238 and 1 mol of air at 298 K. Considering complete
decay of U92238 to Pb82
206 , the ratio of the final pressure to the initial pressure of the system at 298 K is
Answer Key: (9)
23. In dilute aqueous H2SO4 , the complex diaquodioxalatoferrate (II) is oxidized by MnO4β. For this reaction,
the ratio of the rate of change of [H+] to the rate of change of [MnO4β] is
Answer Key: (8)
24. The number of hydroxyl group(s) in Q is
Answer Key: (4)
25. Among the following, the number of reaction(s) that produce(s) benzaldehyde is
SECTION 1 (Maximum Marks: 32)
This section contains EIGHT questions.
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both
inclusive.
For each question, darken the bubble corresponding to the correct integer in the ORS.
Marking scheme:
+4 If the bubble corresponding to the answer is darkened.
0 In all other cases.
Answer Key: (4)
26. In the complex acetylbromidodicarbonylbis(triethylphosphine)iron (II), the number of Fe β C bond (s) is
Answer Key: (3)
27. Among the complex ions, [Co(NH2 β CH2 β CH2 β
NH2)2Cl2]+ , [CrCl2(C2O4)2]
3β , [Fe(H2O)4(OH)2]+, [Fe(NH3)2(CN)4]
β , [Co(NH2 β CH2 β
NH2)2(NH3)(H2O)Cl]2+ , the number of complex ion(s) that show(s) cis-trans isomerism is
Answer Key: (6)
28. Three moles of B2H6 are completely reacted with methanol. The number of moles of boron containing
product formed is
Answer Key: (6)
SECTION 2 (Maximum Marks: 40)
This section contains EIGHT questions.
Each questions has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of
these four options(s) is (are) correct.
For each question, darken the bubble(s) corresponding to all the correct option(s) in
the ORS.
Marking scheme:
+4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened.
0 If none of the bubbles is darkened.
β2 In all other cases.
29. The pair(s) of ions where BOTH the ions are precipitated upon passing H2S gas in presence of dilute HCl,
is (are)
(A) Ba2+, Zn2+
(B) Bi3+, Fe3+
(C) Cu2+, Pb2+
(D) Hg2+, Bi3+
Answer Key: (C,D)
30. Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain
termination, respectively, are
(A) CH3SiCl3 and Si(CH3)4
(B) (CH3)2SiCl2 and (CH3)3SiCl
(C) (CH3)2SiCl2 and CH3SiCl3
(D) SiCl4 and (CH3)3SiCl
Answer Key: (B)
31. When O2 is adsorbed on a metallic surface, electron transfer occurs from the metal to O2. The TRUE
statement(s) regarding this adsorption is(are)
(A) O2 is physisorbed
(B) Heat is released
(C) Occupancy of Ο2pβ of O2 is increased
(D) Bond length of O2 is increased
Answer Key: (B,C,D)
32. One mole of a monoatomic real gas satisfied the equation p(V β b) = RT where b is a constant. The
relationship of interatomic potential V(r) and interatomic distance r for the gas is given by
(A)
(B)
(C)
(D)
Answer Key: (C)
33. In the following reactions, the product S is
(A)
(B)
(C)
(D)
Answer Key: (A)
34. The major product U in the following reactions is
(A)
(B)
(C)
(D)
Answer Key: (B)
35. In the following reactions, the major product W is
(A)
(B)
(C)
(D)
Answer Key: (A)
36. The correct statement(s) regarding,
(i) HClO
(ii) HClO2 (iii) HClO3 and
(iv) HClO4 is are
(A) The number of Cl = O bonds in (ii) and (iii) together is two.
(B) The number of lone pairs of electrons on Cl in (ii) and (iii) together is three.
(C) The hybridization of Cl in (iv) is sp3
(D) Amongst (i) to (iv), the strongest acid (i)
Answer Key: (B,C)
PARAGRAPH 1 In the following reactions
37. Compound X is
(A)
(B)
SECTION 3 (Maximum Marks: 16)
This section contains TWO paragraphs
Based on each paragraph, there will be TWO questions.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these
four options(s) is(are) correct.
For each question, darken the bubbles(s) corresponding to all the correct option(s) in the
ORS.
Marking scheme:
+4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened.
0 If none of the bubbles is darkened.
β2 In all other cases.
(C)
(D)
Answer Key: (C)
38. The major compound Y is
(A)
(B)
(C)
(D)
Answer Key: (D)
PARAGRAPH 2 When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7oC was measured for the beaker and its contents (Expt.1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant (β57.0 kJ molβ1) , this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid (Ka = 2.0 Γ 10β5) was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of 5.6oC was measured.
(Consider heat capacity of all solutions as 4.2 J gβ1 Kβ1 and density of all solutions as 1.0 g mLβ1)
39. Enthalpy of dissociation (in kJ molβ1) of acetic acid obtained from the Expt. 2 is
(A) 1.0
(B) 10.0
(C) 24.5 (D) 51.4
Answer Key: (A)
40. The pH of the solution after Expt. 2 is
(A) 2.8
(B) 4.7
(C) 5.0 (D) 7.0
Answer Key: (B)
Mathematics
41. If πΌ = β« (π9π₯+3 tanβ1 π₯) (12+9π₯2
1+π₯2 )1
0 ππ₯
Where tanβ1 π₯ takes only principal values, then the value of (logπ|1 + πΌ| β 3π
4) is
Answer Key: (9)
42. Let π βΆ β β β be a continuous odd function, which vanishes exactly at one point and π(1) =1
2. Suppose
that πΉ(π₯) = β« π(π‘)π₯
β1ππ‘ for all π₯ β [β1, 2] and πΊ(π₯) = β« π‘|π(π(π‘))|ππ‘
π₯
β1 for all π₯ β [β1, 2]. If
limπ₯β1
πΉ(π₯)
πΊ(π₯)=
1
14, then the value of π (
1
2) is
Answer Key: (7)
43. Suppose that π , π πππ π are three non β coplanar vectors in β3. Let the components of a vector π along (βπ + π + π ), (π β π + π ) πππ (β π β π + π ) are x, y and z, respectively, then the value of 2π₯ + π¦ +
π§ is
Answer Key: (9)
44. For any integer π, let πΌπ = cos (ππ
7) + π sin (
ππ
7) , π€βπππ π = ββ1. The value of the expression
β |πΌπ+1βπΌπ|12π=1
β |πΌ4πβ1βπΌ4πβ2|3π=1
is
Answer Key: (4)
45. Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the
sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh terms lies in
between 130 and 140, then the common difference of this A.P. is
Answer Key: (9)
46. The coefficient of π₯9 in the expansion of (1 + π₯) (1 + π₯2) (1 + π₯3)β¦β¦(1 + π₯100) is
Answer Key: (8)
SECTION 1 (Maximum Marks: 32)
This section contains EIGHT questions
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive
For each question, darken the bubble corresponding to the correct integer in the ORS
Marking scheme:
+4 If the bubble corresponding to the answer is darkened
0 In all other cases
47. Suppose that the foci of the ellipse π₯2
9+
π¦2
5= 1 are (π1, 0) πππ (π2, 0) where π1 > 0 πππ π2 < 0. Let
π1 πππ π2 be two parabolas with a common vertex at (0, 0) and with foci at (π!, 0)πππ (2π2, 0),
respectively. Let π1 be a tangent to π1 which passes through (2π2, 0)πππ π2 be a tangent to π2 which
passes through (π1, 0). If π1 is the slope of π1 πππ π2 is the slope of π2, then the value of (1
π12 + π2
2) is
Answer Key: (4)
48. Let m and n be two positive integers greater than 1. If limπΌβ0
(πcos (πΌπ )βπ
πΌπ) = β(
π
2)
then the value of π
π is
Answer Key: (2)
49. The option(s) with the value of a and L that satisfy the following equation is(are)
PARAGRAPH 1 Let π1 πππ π2 be the number of red and black balls, respectively, in box I. Let π3πππ π4 be the number of red and black balls, respectively, in box II.
PARAGRAPH 2 Let πΉ βΆ β β β be a thrice differentiable function. Suppose that πΉ(1) = 0, πΉ(3) = β4 and πΉβ²(π₯) < 0
all π₯ β (1
2, 3). Let π(π₯) = π₯πΉ(π₯) for all π₯ β β.