JEE (Advanced) 2021 Paper 2
SECTION 1
This section contains SIX (06) questions.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)
is (are) correct answer(s).
For each question, choose the option(s) corresponding to (all) the correct answer(s).
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;
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 unanswered;
Negative Marks : −2 In all other cases.
For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct
answers, then
choosing ONLY (A), (B) and (D) will get +4 marks;
choosing ONLY (A) and (B) will get +2 marks;
choosing ONLY (A) and (D) will get +2marks;
choosing ONLY (B) and (D) will get +2 marks;
choosing ONLY (A) will get +1 mark;
choosing ONLY (B) will get +1 mark;
choosing ONLY (D) will get +1 mark;
choosing no option(s) (i.e. the question is unanswered) will get 0 marks and
choosing any other option(s) will get −2 marks.
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,JEE (Advanced) 2021 Paper 2
Q.1 One end of a horizontal uniform beam of weight 𝑊 and length 𝐿 is hinged on a
vertical wall at point O and its other end is supported by a light inextensible rope.
The other end of the rope is fixed at point Q, at a height 𝐿 above the hinge at point
O. A block of weight 𝛼𝑊 is attached at the point P of the beam, as shown in the
figure (not to scale). The rope can sustain a maximum tension of (2√2)𝑊. Which
of the following statement(s) is(are) correct?
(A) The vertical component of reaction force at O does not depend on 𝛼
(B) The horizontal component of reaction force at O is equal to 𝑊 for 𝛼 = 0.5
(C) The tension in the rope is 2𝑊 for 𝛼 = 0.5
(D) The rope breaks if 𝛼 > 1.5
Q.2 A source, approaching with speed 𝑢 towards the open end of a stationary pipe of
length 𝐿, is emitting a sound of frequency 𝑓𝑠 . The farther end of the pipe is closed.
The speed of sound in air is 𝑣 and 𝑓0 is the fundamental frequency of the pipe. For
which of the following combination(s) of 𝑢 and 𝑓𝑠 , will the sound reaching the pipe
lead to a resonance?
(A) 𝑢 = 0.8𝑣 and 𝑓𝑠 = 𝑓0
(B) 𝑢 = 0.8𝑣 and 𝑓𝑠 = 2𝑓0
(C) 𝑢 = 0.8𝑣 and 𝑓𝑠 = 0.5𝑓0
(D) 𝑢 = 0.5𝑣 and 𝑓𝑠 = 1.5𝑓0
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, JEE (Advanced) 2021 Paper 2
Q.3 For a prism of prism angle 𝜃 = 60°, the refractive indices of the left half and the
right half are, respectively, 𝑛1 and 𝑛2 (𝑛2 ≥ 𝑛1 ) as shown in the figure. The angle
of incidence 𝑖 is chosen such that the incident light rays will have minimum
deviation if 𝑛1 = 𝑛2 = 𝑛 = 1.5. For the case of unequal refractive indices, 𝑛1 = 𝑛
and 𝑛2 = 𝑛 + ∆𝑛 (where ∆𝑛 ≪ 𝑛), the angle of emergence 𝑒 = 𝑖 + ∆𝑒. Which of
the following statement(s) is(are) correct?
(A) The value of ∆𝑒 (in radians) is greater than that of ∆𝑛
(B) ∆𝑒 is proportional to Δ𝑛
(C) Δ𝑒 lies between 2.0 and 3.0 milliradians, if ∆𝑛 = 2.8 × 10−3
(D) Δ𝑒 lies between 1.0 and 1.6 milliradians, if ∆𝑛 = 2.8 × 10−3
Q.4 A physical quantity 𝑆⃗ is defined as 𝑆⃗ = (𝐸⃗⃗ × 𝐵
⃗⃗)/𝜇0 , where 𝐸⃗⃗ is electric field, 𝐵
⃗⃗ is
magnetic field and 𝜇0 is the permeability of free space. The dimensions of 𝑆⃗ are the
same as the dimensions of which of the following quantity(ies) ?
𝐸𝑛𝑒𝑟𝑔𝑦 𝐹𝑜𝑟𝑐𝑒
(A) (B)
𝐶ℎ𝑎𝑟𝑔𝑒 × 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑒𝑛𝑔𝑡ℎ × 𝑇𝑖𝑚𝑒
𝐸𝑛𝑒𝑟𝑔𝑦 𝑃𝑜𝑤𝑒𝑟
(C) (D)
𝑉𝑜𝑙𝑢𝑚𝑒 𝐴𝑟𝑒𝑎
Q.5 A heavy nucleus 𝑁, at rest, undergoes fission 𝑁 → 𝑃 + 𝑄, where 𝑃 and 𝑄 are two
lighter nuclei. Let 𝛿 = 𝑀𝑁 − 𝑀𝑃 − 𝑀𝑄 , where 𝑀𝑃 , 𝑀𝑄 and 𝑀𝑁 are the masses of 𝑃,
𝑄 and 𝑁, respectively. 𝐸𝑃 and 𝐸𝑄 are the kinetic energies of 𝑃 and 𝑄, respectively.
The speeds of 𝑃 and 𝑄 are 𝑣𝑃 and 𝑣𝑄 , respectively. If 𝑐 is the speed of light, which
of the following statement(s) is(are) correct?
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SECTION 1
This section contains SIX (06) questions.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)
is (are) correct answer(s).
For each question, choose the option(s) corresponding to (all) the correct answer(s).
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;
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 unanswered;
Negative Marks : −2 In all other cases.
For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct
answers, then
choosing ONLY (A), (B) and (D) will get +4 marks;
choosing ONLY (A) and (B) will get +2 marks;
choosing ONLY (A) and (D) will get +2marks;
choosing ONLY (B) and (D) will get +2 marks;
choosing ONLY (A) will get +1 mark;
choosing ONLY (B) will get +1 mark;
choosing ONLY (D) will get +1 mark;
choosing no option(s) (i.e. the question is unanswered) will get 0 marks and
choosing any other option(s) will get −2 marks.
1/9
,JEE (Advanced) 2021 Paper 2
Q.1 One end of a horizontal uniform beam of weight 𝑊 and length 𝐿 is hinged on a
vertical wall at point O and its other end is supported by a light inextensible rope.
The other end of the rope is fixed at point Q, at a height 𝐿 above the hinge at point
O. A block of weight 𝛼𝑊 is attached at the point P of the beam, as shown in the
figure (not to scale). The rope can sustain a maximum tension of (2√2)𝑊. Which
of the following statement(s) is(are) correct?
(A) The vertical component of reaction force at O does not depend on 𝛼
(B) The horizontal component of reaction force at O is equal to 𝑊 for 𝛼 = 0.5
(C) The tension in the rope is 2𝑊 for 𝛼 = 0.5
(D) The rope breaks if 𝛼 > 1.5
Q.2 A source, approaching with speed 𝑢 towards the open end of a stationary pipe of
length 𝐿, is emitting a sound of frequency 𝑓𝑠 . The farther end of the pipe is closed.
The speed of sound in air is 𝑣 and 𝑓0 is the fundamental frequency of the pipe. For
which of the following combination(s) of 𝑢 and 𝑓𝑠 , will the sound reaching the pipe
lead to a resonance?
(A) 𝑢 = 0.8𝑣 and 𝑓𝑠 = 𝑓0
(B) 𝑢 = 0.8𝑣 and 𝑓𝑠 = 2𝑓0
(C) 𝑢 = 0.8𝑣 and 𝑓𝑠 = 0.5𝑓0
(D) 𝑢 = 0.5𝑣 and 𝑓𝑠 = 1.5𝑓0
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, JEE (Advanced) 2021 Paper 2
Q.3 For a prism of prism angle 𝜃 = 60°, the refractive indices of the left half and the
right half are, respectively, 𝑛1 and 𝑛2 (𝑛2 ≥ 𝑛1 ) as shown in the figure. The angle
of incidence 𝑖 is chosen such that the incident light rays will have minimum
deviation if 𝑛1 = 𝑛2 = 𝑛 = 1.5. For the case of unequal refractive indices, 𝑛1 = 𝑛
and 𝑛2 = 𝑛 + ∆𝑛 (where ∆𝑛 ≪ 𝑛), the angle of emergence 𝑒 = 𝑖 + ∆𝑒. Which of
the following statement(s) is(are) correct?
(A) The value of ∆𝑒 (in radians) is greater than that of ∆𝑛
(B) ∆𝑒 is proportional to Δ𝑛
(C) Δ𝑒 lies between 2.0 and 3.0 milliradians, if ∆𝑛 = 2.8 × 10−3
(D) Δ𝑒 lies between 1.0 and 1.6 milliradians, if ∆𝑛 = 2.8 × 10−3
Q.4 A physical quantity 𝑆⃗ is defined as 𝑆⃗ = (𝐸⃗⃗ × 𝐵
⃗⃗)/𝜇0 , where 𝐸⃗⃗ is electric field, 𝐵
⃗⃗ is
magnetic field and 𝜇0 is the permeability of free space. The dimensions of 𝑆⃗ are the
same as the dimensions of which of the following quantity(ies) ?
𝐸𝑛𝑒𝑟𝑔𝑦 𝐹𝑜𝑟𝑐𝑒
(A) (B)
𝐶ℎ𝑎𝑟𝑔𝑒 × 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑒𝑛𝑔𝑡ℎ × 𝑇𝑖𝑚𝑒
𝐸𝑛𝑒𝑟𝑔𝑦 𝑃𝑜𝑤𝑒𝑟
(C) (D)
𝑉𝑜𝑙𝑢𝑚𝑒 𝐴𝑟𝑒𝑎
Q.5 A heavy nucleus 𝑁, at rest, undergoes fission 𝑁 → 𝑃 + 𝑄, where 𝑃 and 𝑄 are two
lighter nuclei. Let 𝛿 = 𝑀𝑁 − 𝑀𝑃 − 𝑀𝑄 , where 𝑀𝑃 , 𝑀𝑄 and 𝑀𝑁 are the masses of 𝑃,
𝑄 and 𝑁, respectively. 𝐸𝑃 and 𝐸𝑄 are the kinetic energies of 𝑃 and 𝑄, respectively.
The speeds of 𝑃 and 𝑄 are 𝑣𝑃 and 𝑣𝑄 , respectively. If 𝑐 is the speed of light, which
of the following statement(s) is(are) correct?
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