JEE (Advanced) 2018 Paper 1
JEE (ADVANCED) 2018 PAPER 1
PART-I PHYSICS
SECTION 1 (Maximum Marks: 24)
This section contains SIX (06) questions.
Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
For each question, choose the correct option(s) to answer the question.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +𝟒 If only (all) the correct option(s) is (are) chosen.
Partial Marks : +𝟑 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +𝟐 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +𝟏 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : −𝟐 In all other cases.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option) ,without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in -2 marks.
Q.1 The potential energy of a particle of mass 𝑚 at a distance 𝑟 from a fixed point 𝑂 is given by
𝑉(𝑟) = 𝑘𝑟 2 /2, where 𝑘 is a positive constant of appropriate dimensions. This particle is
moving in a circular orbit of radius 𝑅 about the point 𝑂. If 𝑣 is the speed of the particle and
𝐿 is the magnitude of its angular momentum about 𝑂, which of the following statements is
(are) true?
𝑘
(A) 𝑣 = √2𝑚 𝑅
𝑘
(B) 𝑣 = √𝑚 𝑅
(C) 𝐿 = √𝑚𝑘 𝑅 2
𝑚𝑘
(D) 𝐿 = √ 𝑅2
2
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,JEE (Advanced) 2018 Paper 1
Q.2 Consider a body of mass 1.0 𝑘𝑔 at rest at the origin at time 𝑡 = 0. A force 𝐹⃗ = (𝛼𝑡 𝑖̂ + 𝛽 𝑗̂)
is applied on the body, where 𝛼 = 1.0 𝑁𝑠 −1 and 𝛽 = 1.0 𝑁. The torque acting on the body
about the origin at time 𝑡 = 1.0 𝑠 is 𝜏⃗. Which of the following statements is (are) true?
1
(A) |𝜏⃗| = 3 𝑁 𝑚
(B) The torque 𝜏⃗ is in the direction of the unit vector + 𝑘̂
1
⃗⃗ = 2 (𝑖̂ + 2𝑗̂) 𝑚 𝑠 −1
(C) The velocity of the body at 𝑡 = 1 𝑠 is v
1
(D) The magnitude of displacement of the body at 𝑡 = 1 𝑠 is 𝑚
6
Q.3 A uniform capillary tube of inner radius 𝑟 is dipped vertically into a beaker filled with water.
The water rises to a height ℎ in the capillary tube above the water surface in the beaker. The
surface tension of water is 𝜎. The angle of contact between water and the wall of the capillary
tube is 𝜃. Ignore the mass of water in the meniscus. Which of the following statements is
(are) true?
(A) For a given material of the capillary tube, ℎ decreases with increase in 𝑟
(B) For a given material of the capillary tube, ℎ is independent of 𝜎
(C) If this experiment is performed in a lift going up with a constant acceleration, then ℎ
decreases
(D) ℎ is proportional to contact angle 𝜃
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,JEE (Advanced) 2018 Paper 1
Q.4 In the figure below, the switches 𝑆1 and 𝑆2 are closed simultaneously at 𝑡 = 0 and a current
starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive
force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between
the inductors. The current 𝐼 in the middle wire reaches its maximum magnitude 𝐼𝑚𝑎𝑥 at time
𝑡 = 𝜏. Which of the following statements is (are) true?
𝑉 𝑉 𝐿 2𝐿
(A) 𝐼𝑚𝑎𝑥 = (B) 𝐼𝑚𝑎𝑥 = (C) 𝜏 = ln 2 (D) 𝜏 = ln 2
2𝑅 4𝑅 𝑅 𝑅
Q.5 Two infinitely long straight wires lie in the 𝑥𝑦-plane along the lines 𝑥 = ±𝑅. The wire
located at 𝑥 = +𝑅 carries a constant current 𝐼1 and the wire located at 𝑥 = −𝑅 carries a
constant current 𝐼2 . A circular loop of radius 𝑅 is suspended with its centre at (0, 0, √3𝑅)
and in a plane parallel to the 𝑥𝑦-plane. This loop carries a constant current 𝐼 in the clockwise
direction as seen from above the loop. The current in the wire is taken to be positive if it is
in the +𝑗̂ direction. Which of the following statements regarding the magnetic field 𝐵 ⃗⃗ is (are)
true?
⃗⃗ cannot be equal to zero at the origin (0, 0, 0)
(A) If 𝐼1 = 𝐼2, then 𝐵
⃗⃗ can be equal to zero at the origin (0, 0, 0)
(B) If 𝐼1 > 0 and 𝐼2 < 0, then 𝐵
⃗⃗ can be equal to zero at the origin (0, 0, 0)
(C) If 𝐼1 < 0 and 𝐼2 > 0, then 𝐵
𝜇0 𝐼
(D) If 𝐼1 = 𝐼2, then the 𝑧-component of the magnetic field at the centre of the loop is (− )
2𝑅
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, JEE (Advanced) 2018 Paper 1
Q.6 One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure
(where V is the volume and T is the temperature). Which of the statements below is (are)
true?
(A) Process I is an isochoric process
(B) In process II, gas absorbs heat
(C) In process IV, gas releases heat
(D) Processes I and III are not isobaric
4/12
JEE (ADVANCED) 2018 PAPER 1
PART-I PHYSICS
SECTION 1 (Maximum Marks: 24)
This section contains SIX (06) questions.
Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
For each question, choose the correct option(s) to answer the question.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +𝟒 If only (all) the correct option(s) is (are) chosen.
Partial Marks : +𝟑 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +𝟐 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +𝟏 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : −𝟐 In all other cases.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option) ,without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in -2 marks.
Q.1 The potential energy of a particle of mass 𝑚 at a distance 𝑟 from a fixed point 𝑂 is given by
𝑉(𝑟) = 𝑘𝑟 2 /2, where 𝑘 is a positive constant of appropriate dimensions. This particle is
moving in a circular orbit of radius 𝑅 about the point 𝑂. If 𝑣 is the speed of the particle and
𝐿 is the magnitude of its angular momentum about 𝑂, which of the following statements is
(are) true?
𝑘
(A) 𝑣 = √2𝑚 𝑅
𝑘
(B) 𝑣 = √𝑚 𝑅
(C) 𝐿 = √𝑚𝑘 𝑅 2
𝑚𝑘
(D) 𝐿 = √ 𝑅2
2
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,JEE (Advanced) 2018 Paper 1
Q.2 Consider a body of mass 1.0 𝑘𝑔 at rest at the origin at time 𝑡 = 0. A force 𝐹⃗ = (𝛼𝑡 𝑖̂ + 𝛽 𝑗̂)
is applied on the body, where 𝛼 = 1.0 𝑁𝑠 −1 and 𝛽 = 1.0 𝑁. The torque acting on the body
about the origin at time 𝑡 = 1.0 𝑠 is 𝜏⃗. Which of the following statements is (are) true?
1
(A) |𝜏⃗| = 3 𝑁 𝑚
(B) The torque 𝜏⃗ is in the direction of the unit vector + 𝑘̂
1
⃗⃗ = 2 (𝑖̂ + 2𝑗̂) 𝑚 𝑠 −1
(C) The velocity of the body at 𝑡 = 1 𝑠 is v
1
(D) The magnitude of displacement of the body at 𝑡 = 1 𝑠 is 𝑚
6
Q.3 A uniform capillary tube of inner radius 𝑟 is dipped vertically into a beaker filled with water.
The water rises to a height ℎ in the capillary tube above the water surface in the beaker. The
surface tension of water is 𝜎. The angle of contact between water and the wall of the capillary
tube is 𝜃. Ignore the mass of water in the meniscus. Which of the following statements is
(are) true?
(A) For a given material of the capillary tube, ℎ decreases with increase in 𝑟
(B) For a given material of the capillary tube, ℎ is independent of 𝜎
(C) If this experiment is performed in a lift going up with a constant acceleration, then ℎ
decreases
(D) ℎ is proportional to contact angle 𝜃
2/12
,JEE (Advanced) 2018 Paper 1
Q.4 In the figure below, the switches 𝑆1 and 𝑆2 are closed simultaneously at 𝑡 = 0 and a current
starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive
force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between
the inductors. The current 𝐼 in the middle wire reaches its maximum magnitude 𝐼𝑚𝑎𝑥 at time
𝑡 = 𝜏. Which of the following statements is (are) true?
𝑉 𝑉 𝐿 2𝐿
(A) 𝐼𝑚𝑎𝑥 = (B) 𝐼𝑚𝑎𝑥 = (C) 𝜏 = ln 2 (D) 𝜏 = ln 2
2𝑅 4𝑅 𝑅 𝑅
Q.5 Two infinitely long straight wires lie in the 𝑥𝑦-plane along the lines 𝑥 = ±𝑅. The wire
located at 𝑥 = +𝑅 carries a constant current 𝐼1 and the wire located at 𝑥 = −𝑅 carries a
constant current 𝐼2 . A circular loop of radius 𝑅 is suspended with its centre at (0, 0, √3𝑅)
and in a plane parallel to the 𝑥𝑦-plane. This loop carries a constant current 𝐼 in the clockwise
direction as seen from above the loop. The current in the wire is taken to be positive if it is
in the +𝑗̂ direction. Which of the following statements regarding the magnetic field 𝐵 ⃗⃗ is (are)
true?
⃗⃗ cannot be equal to zero at the origin (0, 0, 0)
(A) If 𝐼1 = 𝐼2, then 𝐵
⃗⃗ can be equal to zero at the origin (0, 0, 0)
(B) If 𝐼1 > 0 and 𝐼2 < 0, then 𝐵
⃗⃗ can be equal to zero at the origin (0, 0, 0)
(C) If 𝐼1 < 0 and 𝐼2 > 0, then 𝐵
𝜇0 𝐼
(D) If 𝐼1 = 𝐼2, then the 𝑧-component of the magnetic field at the centre of the loop is (− )
2𝑅
3/12
, JEE (Advanced) 2018 Paper 1
Q.6 One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure
(where V is the volume and T is the temperature). Which of the statements below is (are)
true?
(A) Process I is an isochoric process
(B) In process II, gas absorbs heat
(C) In process IV, gas releases heat
(D) Processes I and III are not isobaric
4/12
