JEE Advanced 2018 Question Paper paper1 JEE Notes | EduRev

JEE : JEE Advanced 2018 Question Paper paper1 JEE Notes | EduRev

 Page 1


JEE (Advanced) 2018                                 Paper 1 
 1/12 
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   :  +??   If only (all) the correct option(s) is (are) chosen. 
Partial Marks     :  +??  If all the four options are correct but ONLY three options are chosen. 
Partial Marks     :  +??  If three or more options are correct but ONLY two options are chosen, both of  
which are correct options. 
Partial Marks     :  +??  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 : -??   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 ?? at a distance ?? from a fixed point ?? is given by 
?? (?? ) = ?? ?? 2
/2, where ?? is a positive constant of appropriate dimensions. This particle is 
moving in a circular orbit of radius ?? about the point ?? . If ?? is the speed of the particle and 
?? is the magnitude of its angular momentum about ?? , which of the following statements is 
(are) true? 
 
(A)   ?? = v
?? 2?? ??       
        
(B)  ?? = v
?? ?? ??      
        
(C)  ?? = v???? ?? 2
         
 
       
(D)  ?? = v
????
2
 ?? 2
  
 
 
 
 
Page 2


JEE (Advanced) 2018                                 Paper 1 
 1/12 
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   :  +??   If only (all) the correct option(s) is (are) chosen. 
Partial Marks     :  +??  If all the four options are correct but ONLY three options are chosen. 
Partial Marks     :  +??  If three or more options are correct but ONLY two options are chosen, both of  
which are correct options. 
Partial Marks     :  +??  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 : -??   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 ?? at a distance ?? from a fixed point ?? is given by 
?? (?? ) = ?? ?? 2
/2, where ?? is a positive constant of appropriate dimensions. This particle is 
moving in a circular orbit of radius ?? about the point ?? . If ?? is the speed of the particle and 
?? is the magnitude of its angular momentum about ?? , which of the following statements is 
(are) true? 
 
(A)   ?? = v
?? 2?? ??       
        
(B)  ?? = v
?? ?? ??      
        
(C)  ?? = v???? ?? 2
         
 
       
(D)  ?? = v
????
2
 ?? 2
  
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 2/12 
Q.2  
Consider a body of mass 1.0 ???? at rest at the origin at time ?? = 0. A force  ?? ?
= (???? ?? ^ + ?? ?? ^ ) 
is applied on the body, where ?? = 1.0 ?? ?? -1
 and ?? = 1.0 ?? . The torque acting on the body 
about the origin at time ?? = 1.0 ?? is ?? ?. Which of the following statements is (are) true? 
 
(A) |?? ?| =
1
3
?? ?? 
 
(B) The torque ?? ?  is in the direction of the unit vector  + ?? ^
 
 
(C) The velocity of the body at ?? = 1 ?? is v ? ? =
1
2
(?? ^ + 2?? ^ ) ?? ?? -1
 
 
(D) The magnitude of displacement of the body at ?? = 1 ?? is  
1
6
 ?? 
 
 
 
 
 
Q.3  A uniform capillary tube of inner radius ?? 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 ?? . The angle of contact between water and the wall of the capillary 
tube is ?? .  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 ?? 
(B) For a given material of the capillary tube, h is independent of ?? 
(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 ?? 
 
 
  
 
 
 
 
 
 
Page 3


JEE (Advanced) 2018                                 Paper 1 
 1/12 
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   :  +??   If only (all) the correct option(s) is (are) chosen. 
Partial Marks     :  +??  If all the four options are correct but ONLY three options are chosen. 
Partial Marks     :  +??  If three or more options are correct but ONLY two options are chosen, both of  
which are correct options. 
Partial Marks     :  +??  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 : -??   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 ?? at a distance ?? from a fixed point ?? is given by 
?? (?? ) = ?? ?? 2
/2, where ?? is a positive constant of appropriate dimensions. This particle is 
moving in a circular orbit of radius ?? about the point ?? . If ?? is the speed of the particle and 
?? is the magnitude of its angular momentum about ?? , which of the following statements is 
(are) true? 
 
(A)   ?? = v
?? 2?? ??       
        
(B)  ?? = v
?? ?? ??      
        
(C)  ?? = v???? ?? 2
         
 
       
(D)  ?? = v
????
2
 ?? 2
  
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 2/12 
Q.2  
Consider a body of mass 1.0 ???? at rest at the origin at time ?? = 0. A force  ?? ?
= (???? ?? ^ + ?? ?? ^ ) 
is applied on the body, where ?? = 1.0 ?? ?? -1
 and ?? = 1.0 ?? . The torque acting on the body 
about the origin at time ?? = 1.0 ?? is ?? ?. Which of the following statements is (are) true? 
 
(A) |?? ?| =
1
3
?? ?? 
 
(B) The torque ?? ?  is in the direction of the unit vector  + ?? ^
 
 
(C) The velocity of the body at ?? = 1 ?? is v ? ? =
1
2
(?? ^ + 2?? ^ ) ?? ?? -1
 
 
(D) The magnitude of displacement of the body at ?? = 1 ?? is  
1
6
 ?? 
 
 
 
 
 
Q.3  A uniform capillary tube of inner radius ?? 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 ?? . The angle of contact between water and the wall of the capillary 
tube is ?? .  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 ?? 
(B) For a given material of the capillary tube, h is independent of ?? 
(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 ?? 
 
 
  
 
 
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 3/12 
Q.4  In the figure below, the switches ?? 1
 and ?? 2
 are closed simultaneously at ?? = 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 ?? in the middle wire reaches its maximum magnitude ?? ??????
 at  time 
?? = ?? .  Which of the following statements is (are) true? 
 
 
(A) ?? ?????? =
?? 2?? (B)  ?? ?????? =
?? 4??    (C) ?? =
?? ?? ln 2 (D) ?? =
2?? ?? ln 2 
 
 
 
 
Q.5  Two infinitely long straight wires lie in the ???? -plane along the lines ?? = ±?? . The wire 
located at ?? = +?? carries a constant current ?? 1
 and the wire located at ?? = -?? carries a 
constant current ?? 2
. A circular loop of radius ?? is suspended with its centre at (0, 0, v3?? ) 
and in a plane parallel to the ???? -plane. This loop carries a constant current ?? 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 +?? ^ direction. Which of the following statements regarding the magnetic field ?? ? ?
 is (are) 
true? 
 
(A) If ?? 1
= ?? 2
, then ?? ? ?
 cannot be equal to zero at the origin (0, 0, 0) 
 
(B) If ?? 1
> 0 and ?? 2
< 0, then ?? ? ?
 can be equal to zero at the origin (0, 0, 0) 
 
(C) If ?? 1
< 0 and ?? 2
> 0, then ?? ? ?
 can be equal to zero at the origin (0, 0, 0) 
 
(D) If ?? 1
= ?? 2
, then the ?? -component of the magnetic field at the centre of the loop is (-
?? 0 
?? 2?? )   
 
 
 
 
 
 
Page 4


JEE (Advanced) 2018                                 Paper 1 
 1/12 
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   :  +??   If only (all) the correct option(s) is (are) chosen. 
Partial Marks     :  +??  If all the four options are correct but ONLY three options are chosen. 
Partial Marks     :  +??  If three or more options are correct but ONLY two options are chosen, both of  
which are correct options. 
Partial Marks     :  +??  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 : -??   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 ?? at a distance ?? from a fixed point ?? is given by 
?? (?? ) = ?? ?? 2
/2, where ?? is a positive constant of appropriate dimensions. This particle is 
moving in a circular orbit of radius ?? about the point ?? . If ?? is the speed of the particle and 
?? is the magnitude of its angular momentum about ?? , which of the following statements is 
(are) true? 
 
(A)   ?? = v
?? 2?? ??       
        
(B)  ?? = v
?? ?? ??      
        
(C)  ?? = v???? ?? 2
         
 
       
(D)  ?? = v
????
2
 ?? 2
  
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 2/12 
Q.2  
Consider a body of mass 1.0 ???? at rest at the origin at time ?? = 0. A force  ?? ?
= (???? ?? ^ + ?? ?? ^ ) 
is applied on the body, where ?? = 1.0 ?? ?? -1
 and ?? = 1.0 ?? . The torque acting on the body 
about the origin at time ?? = 1.0 ?? is ?? ?. Which of the following statements is (are) true? 
 
(A) |?? ?| =
1
3
?? ?? 
 
(B) The torque ?? ?  is in the direction of the unit vector  + ?? ^
 
 
(C) The velocity of the body at ?? = 1 ?? is v ? ? =
1
2
(?? ^ + 2?? ^ ) ?? ?? -1
 
 
(D) The magnitude of displacement of the body at ?? = 1 ?? is  
1
6
 ?? 
 
 
 
 
 
Q.3  A uniform capillary tube of inner radius ?? 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 ?? . The angle of contact between water and the wall of the capillary 
tube is ?? .  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 ?? 
(B) For a given material of the capillary tube, h is independent of ?? 
(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 ?? 
 
 
  
 
 
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 3/12 
Q.4  In the figure below, the switches ?? 1
 and ?? 2
 are closed simultaneously at ?? = 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 ?? in the middle wire reaches its maximum magnitude ?? ??????
 at  time 
?? = ?? .  Which of the following statements is (are) true? 
 
 
(A) ?? ?????? =
?? 2?? (B)  ?? ?????? =
?? 4??    (C) ?? =
?? ?? ln 2 (D) ?? =
2?? ?? ln 2 
 
 
 
 
Q.5  Two infinitely long straight wires lie in the ???? -plane along the lines ?? = ±?? . The wire 
located at ?? = +?? carries a constant current ?? 1
 and the wire located at ?? = -?? carries a 
constant current ?? 2
. A circular loop of radius ?? is suspended with its centre at (0, 0, v3?? ) 
and in a plane parallel to the ???? -plane. This loop carries a constant current ?? 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 +?? ^ direction. Which of the following statements regarding the magnetic field ?? ? ?
 is (are) 
true? 
 
(A) If ?? 1
= ?? 2
, then ?? ? ?
 cannot be equal to zero at the origin (0, 0, 0) 
 
(B) If ?? 1
> 0 and ?? 2
< 0, then ?? ? ?
 can be equal to zero at the origin (0, 0, 0) 
 
(C) If ?? 1
< 0 and ?? 2
> 0, then ?? ? ?
 can be equal to zero at the origin (0, 0, 0) 
 
(D) If ?? 1
= ?? 2
, then the ?? -component of the magnetic field at the centre of the loop is (-
?? 0 
?? 2?? )   
 
 
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 4/12 
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 
 
 
 
  
Page 5


JEE (Advanced) 2018                                 Paper 1 
 1/12 
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   :  +??   If only (all) the correct option(s) is (are) chosen. 
Partial Marks     :  +??  If all the four options are correct but ONLY three options are chosen. 
Partial Marks     :  +??  If three or more options are correct but ONLY two options are chosen, both of  
which are correct options. 
Partial Marks     :  +??  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 : -??   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 ?? at a distance ?? from a fixed point ?? is given by 
?? (?? ) = ?? ?? 2
/2, where ?? is a positive constant of appropriate dimensions. This particle is 
moving in a circular orbit of radius ?? about the point ?? . If ?? is the speed of the particle and 
?? is the magnitude of its angular momentum about ?? , which of the following statements is 
(are) true? 
 
(A)   ?? = v
?? 2?? ??       
        
(B)  ?? = v
?? ?? ??      
        
(C)  ?? = v???? ?? 2
         
 
       
(D)  ?? = v
????
2
 ?? 2
  
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 2/12 
Q.2  
Consider a body of mass 1.0 ???? at rest at the origin at time ?? = 0. A force  ?? ?
= (???? ?? ^ + ?? ?? ^ ) 
is applied on the body, where ?? = 1.0 ?? ?? -1
 and ?? = 1.0 ?? . The torque acting on the body 
about the origin at time ?? = 1.0 ?? is ?? ?. Which of the following statements is (are) true? 
 
(A) |?? ?| =
1
3
?? ?? 
 
(B) The torque ?? ?  is in the direction of the unit vector  + ?? ^
 
 
(C) The velocity of the body at ?? = 1 ?? is v ? ? =
1
2
(?? ^ + 2?? ^ ) ?? ?? -1
 
 
(D) The magnitude of displacement of the body at ?? = 1 ?? is  
1
6
 ?? 
 
 
 
 
 
Q.3  A uniform capillary tube of inner radius ?? 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 ?? . The angle of contact between water and the wall of the capillary 
tube is ?? .  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 ?? 
(B) For a given material of the capillary tube, h is independent of ?? 
(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 ?? 
 
 
  
 
 
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 3/12 
Q.4  In the figure below, the switches ?? 1
 and ?? 2
 are closed simultaneously at ?? = 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 ?? in the middle wire reaches its maximum magnitude ?? ??????
 at  time 
?? = ?? .  Which of the following statements is (are) true? 
 
 
(A) ?? ?????? =
?? 2?? (B)  ?? ?????? =
?? 4??    (C) ?? =
?? ?? ln 2 (D) ?? =
2?? ?? ln 2 
 
 
 
 
Q.5  Two infinitely long straight wires lie in the ???? -plane along the lines ?? = ±?? . The wire 
located at ?? = +?? carries a constant current ?? 1
 and the wire located at ?? = -?? carries a 
constant current ?? 2
. A circular loop of radius ?? is suspended with its centre at (0, 0, v3?? ) 
and in a plane parallel to the ???? -plane. This loop carries a constant current ?? 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 +?? ^ direction. Which of the following statements regarding the magnetic field ?? ? ?
 is (are) 
true? 
 
(A) If ?? 1
= ?? 2
, then ?? ? ?
 cannot be equal to zero at the origin (0, 0, 0) 
 
(B) If ?? 1
> 0 and ?? 2
< 0, then ?? ? ?
 can be equal to zero at the origin (0, 0, 0) 
 
(C) If ?? 1
< 0 and ?? 2
> 0, then ?? ? ?
 can be equal to zero at the origin (0, 0, 0) 
 
(D) If ?? 1
= ?? 2
, then the ?? -component of the magnetic field at the centre of the loop is (-
?? 0 
?? 2?? )   
 
 
 
 
 
 
JEE (Advanced) 2018                                 Paper 1 
 4/12 
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 
 
 
 
  
JEE (Advanced) 2018                                 Paper 1 
 5/12 
 
SECTION 2 (Maximum Marks: 24) 
? This section contains EIGHT (08) questions.  The answer to each question is a NUMERICAL VALUE. 
? For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to 
the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) using the mouse and the on-
screen virtual numeric keypad in the place designated to enter the answer. 
? Answer to each question will be evaluated according to the following marking scheme: 
Full Marks :  +3 If ONLY the correct numerical value is entered as answer. 
Zero Marks :   0 In all other cases. 
 
 
Q.7  
Two vectors ?? ?
 and ?? ? ?
 are defined as ?? ?
= ?? ?? ^ and ?? ? ?
= ?? (cos ???? ?? ^ + sin ???? ?? ^ ), where ?? is a 
constant and ?? = ?? /6 ?????? ?? -1
.  If |?? ?
+ ?? ? ?
| = v3|?? ?
- ?? ? ?
 |  at time ?? = ?? for the first time, 
the value of ?? , in ?????????????? , is __________. 
 
 
 
 
Q.8  Two men are walking along a horizontal straight line in the same direction. The man in front 
walks at a speed 1.0 ?? ?? -1
 and the man behind walks at a speed 2.0 ?? ?? -1
. A third man is 
standing at a height 12 ?? above the same horizontal line such that all three men are in a 
vertical plane. The two walking men are blowing identical whistles which emit a sound of 
frequency 1430 ???? . The speed of sound in air is 330 ?? ?? -1
. At the instant, when the moving 
men are 10 ?? apart, the stationary man is equidistant from them. The frequency of beats in 
???? , heard by the stationary man at this instant, is __________. 
 
 
 
 
Q.9  A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes 
an  angle 60° with the horizontal. They start to roll without slipping at the same instant of 
time along the shortest path. If the time difference between their reaching the ground is 
(2 - v3) /v10 ?? , then the height of the top of the inclined plane, in ???????????? , is __________. 
Take ?? = 10 ?? ?? -2
. 
 
 
 
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