JEE Advanced 2014: Paper 1
Text of page 1
JEE(ADVANCED) – 2014 PAPER-1 Code-1
Questions with Answers
PART – 1 PHYSICS
SECTION – 1 (One or More Than One Options Correct Type)
This section contains 10 multiple choice type questions. Each question has four
choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct.
1. At time tt = 0, terminal A in the circuit shown in the figure is connected to B by a keyand an
(ωωωω), with II0 = 1Aand ω = 500 rad s-1 starts flowing in it with
alternating current II(tt) = II0 cos
7ππ
the initial direction shown in the figure. At t = , the key is switched from B to D. Now
6ωω
onwards only A and D are connected. A total charge Q flows from the battery to charge the
capacitor fully. If C=20µF, R= 10 Ω and the battery is ideal with emf of 50V, identify the correct
statement (s).
B D
A
50 V
C=20 µF
R=10 Ω
7ππ
(A) Magnitude of the maximum charge on the capacitor before tt = is 1 × 10−3 C.
6ωω
7ππ
(B) The current in the left part of the circuit just before tt = is clockwise.
6ωω
(C) Immediately after A is connected to D, the current in R is 10A.
(D) Q = 2 × 10−3 C.
Answer (C) and (D)
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2. A light source, which emits two wavelengths λλ1 = 400 nnnn and λλ2 = 600 nnnn, is used in a
Young’s double slit experiment. If recorded fringe widths for λλ1 andλλ2 areββ1 andββ2 © number of
fringes for them within a distance yon one side of the central maximum are m1 and m2,
respectively, then
(A)ββ2 > ββ1
(B)mm1 > mm2
(C) From the central maximum, 3 maximum of λ2 overlaps with 5 minimum of λ1
rd th
(D)The angular separation of fringes for λ1 is greater than λ2
Answer: (A), (B) and (C)
3. One end of a taut string of length 3m along the x axis is fixed at x=0.The speed of the waves in
the string is 100 mmss −1 . The other end of the string is vibrating in the y direction so that
stationary waves are set up in the string. The possible waveform(s) of these stationary waves
is(are)
ππππ 50ππππ
(A)yy(tt) = AA sin cos
6 3
ππππ 100ππππ
(B)yy(tt) = AA sin cos
3 3
5ππππ 250ππππ
(C) yy(tt) = AA sin cos 3
6
5ππππ
(D) yy(tt) = AA sin cos 250ππππ
2
Answer: (A) , (C) and (D)
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4. A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that
covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor
is C while that of the portion with dielectric in between is C1. When the capacitor is charged, the
plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The
electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct
option/options, ignoring edge effects.
Q1 E1
Q2 E2
EE1
(A) =1
EE2
EE1 1
(B) =
EE2 KK
QQ1 3
(C) =
QQ2 KK
CC 2+KK
(D) =
CC1 KK
Answer: (A) and (D)
5. LetEE1 (rr), EE2 (rr) and EE3 (rr) be the respective electric fields at a distance r from a point charge
Q, an infinitely long wire with constant linear charge density λ, and an infinite plane with
uniform surface charge density σ. If EE1 (rr0 ) = EE2 (rr0 ) = EE3 (rr0 ) at a given distance r0, then
(A)QQ = 4σσσσrr02
λλ
(B)rr0 =
2ππππ
(C) EE1 (rr0 ⁄2)= 2EE2 (rr0 ⁄2)
(D)EE2 (rr0 ⁄2)=4EE3 (rr0 ⁄2)
Answer: (C)
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6. A student is performing an experiment using a resonance column and a tuning fork of
frequency 244ss −1 . He is told that the air in the tube has been replaced by another gas (assume
that the column remains filled with the gas). If the minimum height at which resonance occurs is
(0.350 ± 0.005) mm, the gas in the tube is
⁄ ⁄
(Useful information:√167RRRR = 640 JJ1⁄2 mole−1 2 ;√140RRRR = 590 JJ1⁄2 mole−1 2 .The molar
10
masses Min grams are given in the options. Take the values of � for each gas as given there.)
MM
10 7
(
(A)Neon MM = 20, �
20
=
10
)
10 3
(
(B) Nitrogen MM = 28,�
28
= )
5
10 9
(
(C) Oxygen MM = 32, �
32
=
16
)
10 17
(
(D)Argon MM = 36, �
36
=
32
)
Answer: (D)
7. Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to
raise the temperature of 0.5kgwater by 40K. This heater is replaced by a new heater having two
wires of the same material, each of length L and diameter 2d.The way these wires are connected
is given in the options. How much time in minutes will it take to raise the temperature of the
same amount of water by 40 K?
(A)4 if wires are in parallel
(B) 2 if wires are in series
(C)1 if wires are in series
(D)0.5 if wires are in parallel
Answer : (B) and (D)
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8. In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium
making an angle θ with the horizontal floor. The coefficient of friction between the wall and the
ladder is μμ1 and that between the floor and the ladder is μμ2 . The normal reaction of the wall on
the ladder is N1 and that of the floor is N2. If the ladder is about to slip, then
µ1
θ
µ2
mmmm
(A)μμ1 = 0 μμ2 ≠ 0andNN2 tanθθ =
2
mmmm
(B) μμ1 ≠ 0 μμ2 = 0andNN1 tanθθ =
2
mmmm
(C)μμ1 ≠ 0 μμ2 ≠ 0andNN2 =
1+μμ1 μμ2
mmmm
(D)μμ1 = 0 μμ2 ≠ 0andNN1 tanθθ =
2
Answer: (C) and (D)
9. A transparent thin film of uniform thickness and refractive index n1= 1.4 is coated on the
convex spherical surface of radius Rat one end of a long solid glass cylinder of refractive index
n2 = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing
through the film from air to glass get focused at distance f1 from the film, while rays of light
traversing from glass to air get focused at distance f2 from the film. Then
n1
Air n2
(A) |ff1 | =3R
(B)|ff1 | = 2.8R
(C)|ff2 | =2R
(D)|ff2 | = 1.4R
Answer: (A) and (C)
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10. Two ideal batteries of emfV1 and V2 and three resistancesR1, R2 andR3 are connected as
shown in the figure. The current in resistanceR2 would be zero if
V1 R1
R2
V2
R3
(A)VV1 = VV2 andRR1 = RR2 = RR3
(B) VV1 = VV2 andRR1 = 2RR2 = RR3
(C) VV1 = 2VV2 and 2RR1 = 2RR2 = RR3
(D)2VV1 = VV2 and2RR1 = RR2 = RR3
Answer: (A), (B) and (D)
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SECTION – 2 (One Integer Value Correct Type)
This section contains 10 questions. Each question, when worked out will result in
one integer from 0 to 9 (both inclusive).
11. Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30°
and 60° with respect to the horizontal respectively as shown in figure. The speed of A is
100√3 mmmm −1 . At time tt = 0 ss, an observer in A finds B at a distance of 500 m. This observer
sees B moving with a constant velocity perpendicular to the line of motion of A. If at tt = tt0 , A
just escapes being hit by B, tt0 in seconds is
A
B
30o 60o
Answer: 5
12. During Searle’s experiment, zero of the Vernier scale lies between 3.20 × 10−2 mm and
3.25 × 10−2 mm of the main scale. The 20th division of the Vernier scale exactly coincides with
one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero
of the Vernier scale still lies between 3.20 × 10−2 mm and 3.25 × 10−2 mm of the main scale but
now the 45th division of Vernier scale coincides with one of the main scale divisions. The length
of the thin metallic wire is 2 m and its cross-sectional area is 8 × 10−7 mm2 . The least count of the
Vernier scale is 1.0 × 10−5 mm. The maximum percentage error in the Young’s modulus of the
wire is
Answer: 4
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13. A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal
frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along
the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see
figure). One second after applying the forces, the angular speed of the disc in rrrrrrss −1 is
F
X
o
Y
F
Z
F
Answer: 2
14. Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving
with speed u between the wires in the same plane at a distance X1 from one of the wires. When
the wires carry current of magnitude I in the same direction, the radius of curvature of the path of
the point charge is R1. In contrast, if the currents I in the two wires have directions opposite to
XX0 RR
each other, the radius of curvature of the path is R2. If = 3, the value of RR1 is
XX
1 2
Answer: 3
15. To find the distance d over which a signal can be seen clearly in foggy conditions, a railways
engineer uses dimensional analysis and assumes that the distance depends on the mass density ρ
of the fog, intensity (power/area) SS of the light from the signal and its frequency f. The engineer
finds that ddisproportionaltoSS 1⁄nn . The value of nn is
Answer: 3
16. A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990
2nn
Ω resistance, it can be converted into a voltmeter of range 0 – 30 V. If connected to a Ω
249
resistance, it becomes an ammeter of range 0 – 1.5 A. The value ofnn is
Answer: 5
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17. Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A
block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always
parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the
block when it reaches Q is (nn × 10)Joules. The value of n is (take acceleration due to gravity =
10 mmss −2 )
Q
4m
90o
O 3m P
Answer : 5
18. A rocket is moving in a gravity free space with a constant acceleration of 2 mmss −2 along +x
direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the
left end of the chamber in +x direction with a speed of 0.3 mmss −1 relative to the rocket. At the
same time, another ball is thrown in –x direction with a speed of 0.2 mmss −1 from its right end
relative to the rocket. The time in seconds when the two balls hit each other is
a = 2 ms ̶ 2
0.3 ms ̶ 1 0.2 ms ̶ 1 x
4m
Answer : 2 OR 8
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19. A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its
axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the
platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure).
Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in
opposite directions. After leaving the platform, the balls have horizontal speed of 9 mmmm −1 with
respect to the ground. The rotational speed of the platform inrrrrrrss −1 after the balls leave the
platform is
Answer: 4
20. A thermodynamic system is taken from an initial state i with internal energy UUii = 100 JJ to
the final state f along two different paths iaf and ibf, as schematically shown in the figure. The
work done by the system along the paths af, ib and bf are WWaaaa = 200 JJ, WWiiii = 50 JJ and WWbbbb =
100 JJ respectively. The heat supplied to the system along the path iaf, ib and bf are QQiiiiii , QQiiii and
QQbbbb respectively. If the internal energy of the system in the state b is UUbb = 200 JJ and QQiiiiii =
500 JJ, the ratio QQbbbb /QQiiii is
a f
P
i b
V
Answer : 2
Text of page 11
PART – 2 CHEMISTRY
SECTION – 1 (One or More Than One Options Correct Type)
This section contains 10 multiple choice type questions. Each question has four
choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct.
21. The correct combination of names for isomeric alcohols with molecular formula
C4H10O is/are
(A) tert-butanol and 2-methylpropan-2-ol
(B) tert-butanol and 1, 1-dimethylethan-1-ol
(C) n-butanol and butan-1-ol
(D) isobutyl alcohol and 2-methylpropan-1-ol
Answer: (A), (C) and (D)
22. he reactivity of compound Z with different halogens under appropriate conditions is
given below:
The observed pattern of electrophilic substitution can be explained by
(A) the steric effect of the halogen
(B) the steric effect of the tert-butyl group
(C) the electronic effect of the phenolic group
(D) the electronic effect of the tert-butyl group
Answer: (A), (B) and (C)
Text of page 12
23. In the reaction shown below, the major product(s) formed is/are
(A)
(B)
(C)
(D)
Answer : (A)
Text of page 13
24. An ideal gas in a thermally insulated vessel at internal pressure = P1, volume = V1
and absolute temperature = T1 expands irreversibly against zero external pressure, as
shown in the diagram. The final internal pressure, volume and absolute temperature of
the gas are P2, V2 and T2, respectively. For this expansion,
(A) q = 0
(B) T2 = T1
(C) P2V2 = P1V1
γ γ
(D) P2V2 = P1V1
Answer (A), (B) and (C)
Text of page 14
25. Hydrogen bonding plays a central role in the following phenomena:
(A) Ice floats in water.
(B) Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions.
(C) Formic acid is more acidic than acetic acid.
(D) Dimerisation of acetic acid in benzene.
Answer : (A), (B) and (D)
26. In a galvanic cell, the salt bridge
(A) does not participate chemically in the cell reaction.
(B) stops the diffusion of ions from one electrode to another.
(C) is necessary for the occurrence of the cell reaction.
(D) ensures mixing of the two electrolytic solutions.
Answer: (A) and (C) or only (A)
27. Upon heating with Cu2S, the reagent(s) that give copper metal is/are
(A) CuFeS2
(B) CuO
(C) Cu2O
(D) CuSO4
Answer: (B), (C) and (D)
Text of page 15
28. The correct statement(s) for orthoboric acid is/are
(A) It behaves as a weak acid in water due to self ionization.
(B) Acidity of its aqueous solution increases upon addition of ethylene glycol.
(C) It has a three dimensional structure due to hydrogen bonding.
(D) It is a weak electrolyte in water.
Answer: (B) and (D)
29. For the reaction:
I – + ClO3– + H2SO4 → Cl – + HSO4– + I2
The correct statement(s) in the balanced equation is/are:
–
(A) Stoichiometric coefficient of HSO4 is 6.
(B) Iodide is oxidized.
(C) Sulphur is reduced.
(D) H2O is one of the products.
Answer: (A), (B) and (D) OR (A) and (D)*
*- Due to a minor error in option (B) in the Hindi Version, Answer (A) and (D) will also be accepted
as correct.
30. The pair(s) of reagents that yield paramagnetic species is/are
(A) Na and excess of NH3
(B) K and excess of O2
(C) Cu and dilute HNO3
(D) O2 and 2-ethylanthraquinol
Answer : (A), (B) and (C)
Text of page 16
31. Consider all possible isomeric ketones, including stereoisomers, of MW = 100. All
these isomers are independently reacted with NaBH4 (NOTE: stereoisomers are also
reacted separately). The total number of ketones that give a racemic product(s) is/are
Answer: 5
32. A list of species having the formula XZ4 is given below.
XeF4, SF4, SiF4, BF4–, BrF4–, [Cu(NH3)4]2+, [FeCl4]2–, [CoCl4]2– and [PtCl4]2–.
Defining shape on the basis of the location of X and Z atoms, the total number of
species having a square planar shape is
Answer: 4
33. Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi2S3 and SnS2, the total number of
BLACK coloured sulfides is
Answer: 6 OR 7
34. The total number(s) of stable conformers with non-zero dipole moment for the
following compound is (are)
Answer: 3
Text of page 17
35. Consider the following list of reagents:
Acidified K2Cr2O7, alkaline KMnO4, CuSO4, H2O2, Cl2, O3, FeCl3, HNO3 and Na2S2O3.
The total number of reagents that can oxidise aqueous iodide to iodine is
Answer: 7
36.The total number of distinct naturally occurring amino acids obtained by
complete acidic hydrolysis of the peptide shown below is
Answer: 1
37. In an atom, the total number of electrons having quantum numbers nn = 4, |mmll | =
1 and mmss = − 1�2 is
Answer: 6
23
38. If the value of Avogadro number is 6.023 × 10 mol–1 and the value of Boltzmann
constant is 1.380 × 10–23J K–1, then the number of significant digits in the calculated
value of the universal gas constant is
Text of page 18
Answer: 4
39. A compound H2X with molar weight of 80 g is dissolved in a solvent having density of
0.4 g ml –1. Assuming no change in volume upon dissolution, the molality of a 3.2
molar solution is
Answer: 8
2+
40. MX2 dissociates into M and X– ions in an aqueous solution, with a degree of
dissociation (α) of 0.5. The ratio of the observed depression of freezing point of the
aqueous solution to the value of the depression of freezing point in the absence of ionic
dissociation is
Answer: 2
Text of page 19
PART – 3 MATHEMATICS
SECTION – 1 (One or More Than One Options Correct Type)
This section contains 10 multiple choice type questions. Each question has four
choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct.
41. Let MM and NN be two 3 × 3 matrices such that MMMM = NNNN. Further, if MM ≠ NN 2 and MM2 = NN 4 , then
(A) determinant of (MM2 + MMNN 2 ) is 0
(B) there is a 3 × 3 non-zero matrix UU such that (MM2 + MMNN 2 )UU is the zero matrix
(C) determinant of (MM2 + MMNN 2 ) ≥ 1
(D) for a 3 × 3 matrix UU, if (MM2 + MMNN 2 )UU equals the zero matrix then UU is the zero matrix
Answer: (A), (B)
42. For every pair of continuous functions ff, gg: [0, 1] → ℝ such that
max {ff(xx): xx ∈ [0,1]} = max {gg(xx): xx ∈ [0,1]},
the correct statement(s) is(are) :
(A) (ff(cc)) 2 + 3ff(cc) = (gg(cc)) 2 + 3gg(cc) for some cc ∈ [0, 1]
(B) (ff(cc)) 2 + ff(cc) = (gg(cc)) 2 + 3gg(cc) for some cc ∈ [0, 1]
(C) (ff(cc)) 2 + 3ff(cc) = (gg(cc)) 2 + gg(cc) for some cc ∈ [0, 1]
(D) (ff(cc)) 2 = (gg(cc)) 2 for some cc ∈ [0, 1]
Answer: (A), (D)
Text of page 20
43. Let ff: (0, ∞) → ℝ be given by
xx
1 dddd
ff(xx) = � ee −�tt+ tt � .
1 tt
xx
Then
(A) ff(xx) is monotonically increasing on [1, ∞)
(B) ff(xx) is monotonically decreasing on (0, 1)
1
(C) ff(xx) + ff � � = 0, for all xx ∈ (0, ∞)
xx
(D) ff(2xx ) is an odd function of xx on ℝ
Answer: (A), (C), (D)
44. Let aa ∈ ℝ and let ff: ℝ → ℝ be given by
ff(xx) = xx 5 − 5xx + aa.
Then
(A) ff(xx) has three real roots if aa > 4
(B) ff(xx) has only one real root if aa > 4
(C) ff(xx) has three real roots if aa < −4
(D) ff(xx) has three real roots if −4 < aa < 4
Answer: (B), (D)
Text of page 21
45. Let ff: [aa, bb] → [1, ∞) be a continuous function and let gg: ℝ → ℝ be defined as
0 if xx < aa,
⎧
⎪ xx
⎪� ff(tt)dddd if aa ≤ xx ≤ bb,
gg(xx) = aa
⎨
⎪ bb
⎪ � ff(tt)dddd if xx > bb.
⎩ aa
Then
(A) gg(xx) is continuous but not differentiable at aa
(B) gg(xx) is differentiable on ℝ
(C) gg(xx) is continuous but not differentiable at bb
(D) gg(xx) is continuous and differentiable at either aa or bb but not both
Answer: (A), (C)
ππ ππ
46. Let ff: (− , ) → ℝ be given by
2 2
ff(xx) = (log(sec xx + tan xx))3 .
Then
(A) ff(xx) is an odd function
(B) ff(xx) is a one-one function
(C) ff(xx) is an onto function
(D) ff(xx) is an even function
Answer: (A), (B) and (C)
Text of page 22
47. From a point PP(λλ, λλ, λλ), perpendiculars PPPP and PPPP are drawn respectively on the lines yy = xx, zz = 1
and yy = −xx, zz = −1. If PP is such that ∠QQQQQQ is a right angle, then the possible value(s) of λλ is(are)
(A) √2
(B) 1
(C) −1
(D) −√2
Answer: (C)
ππ
48. Let xx⃗, yy⃗ and zz⃗ be three vectors each of magnitude √2 and the angle between each pair of them is .
3
If aa⃗ is a nonzero vector perpendicular to xx⃗ and yy⃗ × zz⃗ and bb�⃗ is a nonzero vector perpendicular to yy⃗ and
zz⃗ × xx⃗, then
(A) bb�⃗ = (bb�⃗ ∙ zz⃗)(zz⃗ − xx⃗)
(B) aa⃗ = (aa⃗ ∙ yy⃗)(yy⃗ − zz⃗)
(C) aa⃗ ∙ bb�⃗ = − (aa⃗ ∙ yy⃗) (bb�⃗ ∙ zz⃗)
(D) aa⃗ = (aa⃗ ∙ yy⃗)(zz⃗ − yy⃗)
Answer: (A), (B) and (C)
49. A circle SS passes through the point (0, 1) and is orthogonal to the circles (xx − 1)2 + yy 2 = 16 and
xx 2 + yy 2 = 1. Then
(A) radius of SS is 8
(B) radius of SS is 7
(C) centre of SS is (−7, 1)
(D) centre of SS is (−8, 1)
Answer: (B), (C)
Text of page 23
50. Let MM be a 2 × 2 symmetric matrix with integer entries. Then MM is invertible if
(A) the first column of MM is the transpose of the second row of MM
(B) the second row of MM is the transpose of the first column of MM
(C) MM is a diagonal matrix with nonzero entries in the main diagonal
(D) the product of entries in the main diagonal of MM is not the square of an integer
Answer: (C), (D)
bb
51. Let aa, bb, cc be positive integers such that is an integer. If aa, bb, cc are in geometric progression and the
aa
arithmetic mean of aa, bb, cc is bb + 2, then the value of
aa2 + aa − 14
aa + 1
is
Answer: 4
52. Let nn ≥ 2 be an integer. Take nn distinct points on a circle and join each pair of points by a line
segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the
number of red and blue line segments are equal, then the value of nn is
Answer: 5
53. Let nn1 < nn2 < nn3 < nn4 < nn5 be positive integers such that nn1 + nn2 + nn3 + nn4 + nn5 = 20. Then
the number of such distinct arrangements (nn1 , nn2 , nn3 , nn4 , nn5 ) is
Answer: 7
Text of page 24
54. Let ff: ℝ → ℝ and gg: ℝ → ℝ be respectively given by ff(xx) = |xx| + 1 and gg(xx) = xx 2 + 1. Define
ℎ: ℝ → ℝ by
max {ff(xx), gg(xx)} if xx ≤ 0,
ℎ(xx) = �
min {ff(xx), gg(xx)} if xx > 0.
The number of points at which ℎ(xx) is not differentiable is
Answer: 3
55. The value of
1
dd 2
� 4xx 3 � 2 (1 − xx 2 )5 � dddd
ddxx
0
is
Answer: 2
56. The slope of the tangent to the curve (yy − xx 5 )2 = xx(1 + xx 2 )2 at the point (1, 3) is
Answer: 8
57. The largest value of the nonnegative integer aa for which
1−xx
−aaaa + sin(xx − 1) + aa 1−√xx 1
lim � � =
xx→1 xx + sin(xx − 1) − 1 4
is
Answer: 0 (zero)
Text of page 25
58. Let ff: [0, 4ππ] → [0, ππ] be defined by ff(xx) = cos −1 (cos xx). The number of points xx ∈ [0, 4ππ] satisfying
the equation
10 − xx
ff(xx) =
10
Is
Answer: 3
59. For a point PP in the plane, let dd1 (PP) and dd2 (PP) be the distances of the point PP from the lines
xx − yy = 0 and xx + yy = 0 respectively. The area of the region RR consisting of all points PP lying in the first
quadrant of the plane and satisfying 2 ≤ dd1 (PP) + dd2 (PP) ≤ 4 , is
Answer: 6
ππ
60. Let aa, ���⃗ and ��⃗
���⃗ bb, cc be three non-coplanar unit vectors such that the angle between every pair of them is
3
pp 2 + 2qq 2 + rr 2
. If aa ���⃗ + bb�⃗ × ��⃗
���⃗ × bb ���⃗ + qqbb�⃗ + rrcc��⃗, where pp, qq and rr are scalars, then the value of
cc = ppaa is
qq 2
Answer: 4
Official key not published for this paper.
Page 1 of 25
Source: Organising IIT for the year. Question paper published by Organising IIT for the year.