JEE Advanced 2020 Question Paper - 1 with Solutions | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


__________________________________________________________________________________________________
SECTION 1 (Maximum Marks : 18)
• This section contains SIX (06) questions.
• Each question has FOUR options. ONLY ONE of these four options is the correct answer.
• For each question, choose the option corresponding to the correct answer.
• Answer to each question will be evaluated according to the following marking scheme :
Full marks : +3 If ONLY the correct option is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –1 In all other cases.
H k k x -1 (vf/k dr e va d: 18)
• bl H k k x es a N% (06) i z ' u ' k k fey gS A
• i z R ; s d i z ' u ds pk j fodY i gS A bu pk j fodY i k s a es a l s ds oy , d gh l gh m Ù k j gS A
• i z R ; s d i z ' u ds fy, ] l gh m Ù k j ds vuq : i fodY i pq fu, A
• i z R ; s d i z ' u ds m Ù k j dk ew Y ; k a du fuE ufyf[ k r va d i ) fr ds vuq l k j fd; k t k , xk A
i w .k Z va d : +3  ds oy l gh fodY i pq uk t k r k gS A
' k w U ; va d :  0   ; fn dk s bZ fodY i ugh pq uk t k r k gS A ¼ vF k k Z r ~ i z ' u dk m Ù k j ugh fn; k gk s ½
_ .k k R ed va d : –1  vU ; l H k h fL F k fr ; k s a es a A
___________________________________________________________________________________________________
1. A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end
of the plank is now lifted so that it gets tilted making an angle ? from the horizontal as shown in the
figure below. The maximum value of ? so that the football does not start rolling down the plank
satisfies (figure is schematic and not drawn to scale)
R f= k T ; k dh , d Q q V ck W y {k S fr t : i l s j [ k s , d r [ r s i j cus r (r < R) f= k T ; k ds , d fNæ i j j [ k h t k r h gS a A r [ r s dk , d fl j k
vc m B k ; k (lifted) t k r k gS r k fd ; g fp= k k uq l k j {k S fr t l s ? dk s .k cuk r s gq , >q dr k gS A ? dk vf/k dr e ek u r k fd Q q V ck W y r [ r s
ds uh ps yq <+ duk i z k j a H k ugh a dj r h gS ] l a r q "V dj r k gS ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) 
r
sin
R
? ? (B) 
r
tan
R
? ? (C) 
r
sin
2R
? ? (D) 
r
cos
2R
? ?
Page 2


__________________________________________________________________________________________________
SECTION 1 (Maximum Marks : 18)
• This section contains SIX (06) questions.
• Each question has FOUR options. ONLY ONE of these four options is the correct answer.
• For each question, choose the option corresponding to the correct answer.
• Answer to each question will be evaluated according to the following marking scheme :
Full marks : +3 If ONLY the correct option is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –1 In all other cases.
H k k x -1 (vf/k dr e va d: 18)
• bl H k k x es a N% (06) i z ' u ' k k fey gS A
• i z R ; s d i z ' u ds pk j fodY i gS A bu pk j fodY i k s a es a l s ds oy , d gh l gh m Ù k j gS A
• i z R ; s d i z ' u ds fy, ] l gh m Ù k j ds vuq : i fodY i pq fu, A
• i z R ; s d i z ' u ds m Ù k j dk ew Y ; k a du fuE ufyf[ k r va d i ) fr ds vuq l k j fd; k t k , xk A
i w .k Z va d : +3  ds oy l gh fodY i pq uk t k r k gS A
' k w U ; va d :  0   ; fn dk s bZ fodY i ugh pq uk t k r k gS A ¼ vF k k Z r ~ i z ' u dk m Ù k j ugh fn; k gk s ½
_ .k k R ed va d : –1  vU ; l H k h fL F k fr ; k s a es a A
___________________________________________________________________________________________________
1. A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end
of the plank is now lifted so that it gets tilted making an angle ? from the horizontal as shown in the
figure below. The maximum value of ? so that the football does not start rolling down the plank
satisfies (figure is schematic and not drawn to scale)
R f= k T ; k dh , d Q q V ck W y {k S fr t : i l s j [ k s , d r [ r s i j cus r (r < R) f= k T ; k ds , d fNæ i j j [ k h t k r h gS a A r [ r s dk , d fl j k
vc m B k ; k (lifted) t k r k gS r k fd ; g fp= k k uq l k j {k S fr t l s ? dk s .k cuk r s gq , >q dr k gS A ? dk vf/k dr e ek u r k fd Q q V ck W y r [ r s
ds uh ps yq <+ duk i z k j a H k ugh a dj r h gS ] l a r q "V dj r k gS ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) 
r
sin
R
? ? (B) 
r
tan
R
? ? (C) 
r
sin
2R
? ? (D) 
r
cos
2R
? ?
Sol. A
 
r
sin
R
? ?
on the verge of rolling 'mg' passes through point of contact.
2. A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate
about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc
away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is
schematic and not drawn to scale)
, Y ; q fefu; e ¼ , d vpq E cdh ; i nk F k Z ½ dh cuh , d gY dh  pdr h {k S fr t : i l s j [ k h t k r h gS r F k k fp= k k uq l k j bl ds v{k ds i fj r %
? k w eus ds fy, L or U = k gS A , d i z cy (strong) pq E cd pdr h ds Åi j , d fcU nq i j bl ds v{k l s nw j Å/ok Z /k j j [ k h t k r h gS A pdr h
ds v{k ds i fj r % pq E cd dk s ? k q ek us i j pdr h ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) rotate in the direction opposite to the direction of magnet’s motion
(B) rotate in the same direction as the direction of magnet’s motion
(C) not rotate and its temperature will remain unchanged
(D) not rotate but its temperature will slowly rise
(A) pq E cd dh xfr dh fn' k k ds foi fj r fn' k k es a ? k w es xh
(B) pq E cd dh xfr dh fn' k k ds l ek u fn' k k es a ? k w es xh
(C) ugh a ? k w es xh r F k k bl dk r k i ek u vi fj ofr Z r j gs xk
(D) ? k w es xh ys fdu bl dk r k i ek u /k h j s &/k h j s c<+ s xk
Page 3


__________________________________________________________________________________________________
SECTION 1 (Maximum Marks : 18)
• This section contains SIX (06) questions.
• Each question has FOUR options. ONLY ONE of these four options is the correct answer.
• For each question, choose the option corresponding to the correct answer.
• Answer to each question will be evaluated according to the following marking scheme :
Full marks : +3 If ONLY the correct option is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –1 In all other cases.
H k k x -1 (vf/k dr e va d: 18)
• bl H k k x es a N% (06) i z ' u ' k k fey gS A
• i z R ; s d i z ' u ds pk j fodY i gS A bu pk j fodY i k s a es a l s ds oy , d gh l gh m Ù k j gS A
• i z R ; s d i z ' u ds fy, ] l gh m Ù k j ds vuq : i fodY i pq fu, A
• i z R ; s d i z ' u ds m Ù k j dk ew Y ; k a du fuE ufyf[ k r va d i ) fr ds vuq l k j fd; k t k , xk A
i w .k Z va d : +3  ds oy l gh fodY i pq uk t k r k gS A
' k w U ; va d :  0   ; fn dk s bZ fodY i ugh pq uk t k r k gS A ¼ vF k k Z r ~ i z ' u dk m Ù k j ugh fn; k gk s ½
_ .k k R ed va d : –1  vU ; l H k h fL F k fr ; k s a es a A
___________________________________________________________________________________________________
1. A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end
of the plank is now lifted so that it gets tilted making an angle ? from the horizontal as shown in the
figure below. The maximum value of ? so that the football does not start rolling down the plank
satisfies (figure is schematic and not drawn to scale)
R f= k T ; k dh , d Q q V ck W y {k S fr t : i l s j [ k s , d r [ r s i j cus r (r < R) f= k T ; k ds , d fNæ i j j [ k h t k r h gS a A r [ r s dk , d fl j k
vc m B k ; k (lifted) t k r k gS r k fd ; g fp= k k uq l k j {k S fr t l s ? dk s .k cuk r s gq , >q dr k gS A ? dk vf/k dr e ek u r k fd Q q V ck W y r [ r s
ds uh ps yq <+ duk i z k j a H k ugh a dj r h gS ] l a r q "V dj r k gS ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) 
r
sin
R
? ? (B) 
r
tan
R
? ? (C) 
r
sin
2R
? ? (D) 
r
cos
2R
? ?
Sol. A
 
r
sin
R
? ?
on the verge of rolling 'mg' passes through point of contact.
2. A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate
about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc
away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is
schematic and not drawn to scale)
, Y ; q fefu; e ¼ , d vpq E cdh ; i nk F k Z ½ dh cuh , d gY dh  pdr h {k S fr t : i l s j [ k h t k r h gS r F k k fp= k k uq l k j bl ds v{k ds i fj r %
? k w eus ds fy, L or U = k gS A , d i z cy (strong) pq E cd pdr h ds Åi j , d fcU nq i j bl ds v{k l s nw j Å/ok Z /k j j [ k h t k r h gS A pdr h
ds v{k ds i fj r % pq E cd dk s ? k q ek us i j pdr h ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) rotate in the direction opposite to the direction of magnet’s motion
(B) rotate in the same direction as the direction of magnet’s motion
(C) not rotate and its temperature will remain unchanged
(D) not rotate but its temperature will slowly rise
(A) pq E cd dh xfr dh fn' k k ds foi fj r fn' k k es a ? k w es xh
(B) pq E cd dh xfr dh fn' k k ds l ek u fn' k k es a ? k w es xh
(C) ugh a ? k w es xh r F k k bl dk r k i ek u vi fj ofr Z r j gs xk
(D) ? k w es xh ys fdu bl dk r k i ek u /k h j s &/k h j s c<+ s xk
Sol. B
by lenz's law, the disc also tries to move in same direction because in the backward part of disc the
flux reduces as magnet moves and as there is change in magnetic flux, so there is eddy current
production which leads to production of heat.
3. A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on
a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale
on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it
moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has
moved 50 cm, the position of the scale will look like (figures are schematic and not drawn to scale)
20 cm O ; k l ds , d Nk s V s j k s yj es a 10 cm ¼ uh ps ck ; h a vk s j fp= k ns f[ k ; s ½ O ; k l dh , d /k q j h (axle) gS A ; g , d {k S fr t Q ' k Z i j gS
r F k k ,d eh V j i S ek uk b l dh /k q jh i j {k S fr t : i l s fL F k r gS ] ft l es a /k q jh ds f' k [ k j i j ¼ nk ; h a vk s j ns f[ k ; s ½ i S ek us dk ,d fduk jk (edge)
gS A vc i S ek us dk s /k q j h i j /k h js &/k h j s /k ds yk t k r k gS r k fd ; g /k q j h i j fcuk fQ l ys pys ] r F k k j k s yj fcuk fQ l ys yq <+ duk i z k j a H k dj r k
gS A j k s yj ds 50 cm pyus ds i ' pk r ~ i S ek us dh fL F k fr fuE u r j g fn[ k k bZ ns xh ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) (B) 
(C) (D) 
Page 4


__________________________________________________________________________________________________
SECTION 1 (Maximum Marks : 18)
• This section contains SIX (06) questions.
• Each question has FOUR options. ONLY ONE of these four options is the correct answer.
• For each question, choose the option corresponding to the correct answer.
• Answer to each question will be evaluated according to the following marking scheme :
Full marks : +3 If ONLY the correct option is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –1 In all other cases.
H k k x -1 (vf/k dr e va d: 18)
• bl H k k x es a N% (06) i z ' u ' k k fey gS A
• i z R ; s d i z ' u ds pk j fodY i gS A bu pk j fodY i k s a es a l s ds oy , d gh l gh m Ù k j gS A
• i z R ; s d i z ' u ds fy, ] l gh m Ù k j ds vuq : i fodY i pq fu, A
• i z R ; s d i z ' u ds m Ù k j dk ew Y ; k a du fuE ufyf[ k r va d i ) fr ds vuq l k j fd; k t k , xk A
i w .k Z va d : +3  ds oy l gh fodY i pq uk t k r k gS A
' k w U ; va d :  0   ; fn dk s bZ fodY i ugh pq uk t k r k gS A ¼ vF k k Z r ~ i z ' u dk m Ù k j ugh fn; k gk s ½
_ .k k R ed va d : –1  vU ; l H k h fL F k fr ; k s a es a A
___________________________________________________________________________________________________
1. A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end
of the plank is now lifted so that it gets tilted making an angle ? from the horizontal as shown in the
figure below. The maximum value of ? so that the football does not start rolling down the plank
satisfies (figure is schematic and not drawn to scale)
R f= k T ; k dh , d Q q V ck W y {k S fr t : i l s j [ k s , d r [ r s i j cus r (r < R) f= k T ; k ds , d fNæ i j j [ k h t k r h gS a A r [ r s dk , d fl j k
vc m B k ; k (lifted) t k r k gS r k fd ; g fp= k k uq l k j {k S fr t l s ? dk s .k cuk r s gq , >q dr k gS A ? dk vf/k dr e ek u r k fd Q q V ck W y r [ r s
ds uh ps yq <+ duk i z k j a H k ugh a dj r h gS ] l a r q "V dj r k gS ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) 
r
sin
R
? ? (B) 
r
tan
R
? ? (C) 
r
sin
2R
? ? (D) 
r
cos
2R
? ?
Sol. A
 
r
sin
R
? ?
on the verge of rolling 'mg' passes through point of contact.
2. A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate
about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc
away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is
schematic and not drawn to scale)
, Y ; q fefu; e ¼ , d vpq E cdh ; i nk F k Z ½ dh cuh , d gY dh  pdr h {k S fr t : i l s j [ k h t k r h gS r F k k fp= k k uq l k j bl ds v{k ds i fj r %
? k w eus ds fy, L or U = k gS A , d i z cy (strong) pq E cd pdr h ds Åi j , d fcU nq i j bl ds v{k l s nw j Å/ok Z /k j j [ k h t k r h gS A pdr h
ds v{k ds i fj r % pq E cd dk s ? k q ek us i j pdr h ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) rotate in the direction opposite to the direction of magnet’s motion
(B) rotate in the same direction as the direction of magnet’s motion
(C) not rotate and its temperature will remain unchanged
(D) not rotate but its temperature will slowly rise
(A) pq E cd dh xfr dh fn' k k ds foi fj r fn' k k es a ? k w es xh
(B) pq E cd dh xfr dh fn' k k ds l ek u fn' k k es a ? k w es xh
(C) ugh a ? k w es xh r F k k bl dk r k i ek u vi fj ofr Z r j gs xk
(D) ? k w es xh ys fdu bl dk r k i ek u /k h j s &/k h j s c<+ s xk
Sol. B
by lenz's law, the disc also tries to move in same direction because in the backward part of disc the
flux reduces as magnet moves and as there is change in magnetic flux, so there is eddy current
production which leads to production of heat.
3. A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on
a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale
on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it
moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has
moved 50 cm, the position of the scale will look like (figures are schematic and not drawn to scale)
20 cm O ; k l ds , d Nk s V s j k s yj es a 10 cm ¼ uh ps ck ; h a vk s j fp= k ns f[ k ; s ½ O ; k l dh , d /k q j h (axle) gS A ; g , d {k S fr t Q ' k Z i j gS
r F k k ,d eh V j i S ek uk b l dh /k q jh i j {k S fr t : i l s fL F k r gS ] ft l es a /k q jh ds f' k [ k j i j ¼ nk ; h a vk s j ns f[ k ; s ½ i S ek us dk ,d fduk jk (edge)
gS A vc i S ek us dk s /k q j h i j /k h js &/k h j s /k ds yk t k r k gS r k fd ; g /k q j h i j fcuk fQ l ys pys ] r F k k j k s yj fcuk fQ l ys yq <+ duk i z k j a H k dj r k
gS A j k s yj ds 50 cm pyus ds i ' pk r ~ i S ek us dh fL F k fr fuE u r j g fn[ k k bZ ns xh ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) (B) 
(C) (D) 
Sol. B
v R 0 ? ? ?
v R ? ?
v
v 20
20
? ? ? ? ?
Velocity of point (A) = v+ ?r
v
v 10
20
? ? ?
3v
1.5v
2
? ?
so distance moved by point of contact
= 1.5×50 cm = 75 cm
4. A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure,
its two ends are connected to two wires and it is hanging by those wires with its plane being
vertical. The wires are connected to a capacitor with charge Q through a switch. The coil is in a
horizontal uniform magnetic field B
0
 parallel to the plane of the coil. When the switch is closed, the
capacitor gets discharged through the coil in a very short time. By the time the capacitor is
discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the
discharge time is so short that the coil has hardly rotated during this time)
R f= k T ; k r F k k N Q s j k s a dh ,d o` Ù k k dk j dq .M yh dk ux.; i z fr jk s /k gS A l k a ds fr d fp= k es a fn[ k k ; s uq l k j] bl ds nk s fl js nk s r k jk s a l s t k s M + s t k r s
gS r F k k ; g m u r k j k s a } k jk yV dk ; k t k r k g S ] ft l dk r y Å/ok Z /k j gk s A r k j ,d fL op ds ek /; e l s vk os ' k Q ds l k F k , d
l a /k k fj= k l s t k s M + s t k r s gS A dq .M yh b l ds ¼ L o; a ds ½ r y ds l ek uk U r j {k S fr t l e: i pq E cdh ; {k s = k B
0
 es a gS A t c fL op cU n fd; k t k r k
gS ] r c l a /k k fj = k cgq r vY i l e; es a dq .M yh l s fujk os f' k r gk s r k gS A t c r d l a /k k fj= k i w .k Z : i l s fujk os f' k r gk s r k gS ] r c r d dq .M yh } k jk
i z k Ir dk s .k h ; l a os x dk i fjek .k gk s xk ¼ ek uk fd fujk os ' k u l e; br uk vY i gS fd dq .M yh bl l e; ds nk S j k u eq f' dy l s ? k w er h  gS A ½ &
B
0
(A) 
2
0
2
NQB R
?
(B) 
2
0
NQB R ? (C) 
2
0
2 NQB R ? (D) 
2
0
4 NQB R ?
Page 5


__________________________________________________________________________________________________
SECTION 1 (Maximum Marks : 18)
• This section contains SIX (06) questions.
• Each question has FOUR options. ONLY ONE of these four options is the correct answer.
• For each question, choose the option corresponding to the correct answer.
• Answer to each question will be evaluated according to the following marking scheme :
Full marks : +3 If ONLY the correct option is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –1 In all other cases.
H k k x -1 (vf/k dr e va d: 18)
• bl H k k x es a N% (06) i z ' u ' k k fey gS A
• i z R ; s d i z ' u ds pk j fodY i gS A bu pk j fodY i k s a es a l s ds oy , d gh l gh m Ù k j gS A
• i z R ; s d i z ' u ds fy, ] l gh m Ù k j ds vuq : i fodY i pq fu, A
• i z R ; s d i z ' u ds m Ù k j dk ew Y ; k a du fuE ufyf[ k r va d i ) fr ds vuq l k j fd; k t k , xk A
i w .k Z va d : +3  ds oy l gh fodY i pq uk t k r k gS A
' k w U ; va d :  0   ; fn dk s bZ fodY i ugh pq uk t k r k gS A ¼ vF k k Z r ~ i z ' u dk m Ù k j ugh fn; k gk s ½
_ .k k R ed va d : –1  vU ; l H k h fL F k fr ; k s a es a A
___________________________________________________________________________________________________
1. A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end
of the plank is now lifted so that it gets tilted making an angle ? from the horizontal as shown in the
figure below. The maximum value of ? so that the football does not start rolling down the plank
satisfies (figure is schematic and not drawn to scale)
R f= k T ; k dh , d Q q V ck W y {k S fr t : i l s j [ k s , d r [ r s i j cus r (r < R) f= k T ; k ds , d fNæ i j j [ k h t k r h gS a A r [ r s dk , d fl j k
vc m B k ; k (lifted) t k r k gS r k fd ; g fp= k k uq l k j {k S fr t l s ? dk s .k cuk r s gq , >q dr k gS A ? dk vf/k dr e ek u r k fd Q q V ck W y r [ r s
ds uh ps yq <+ duk i z k j a H k ugh a dj r h gS ] l a r q "V dj r k gS ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) 
r
sin
R
? ? (B) 
r
tan
R
? ? (C) 
r
sin
2R
? ? (D) 
r
cos
2R
? ?
Sol. A
 
r
sin
R
? ?
on the verge of rolling 'mg' passes through point of contact.
2. A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate
about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc
away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is
schematic and not drawn to scale)
, Y ; q fefu; e ¼ , d vpq E cdh ; i nk F k Z ½ dh cuh , d gY dh  pdr h {k S fr t : i l s j [ k h t k r h gS r F k k fp= k k uq l k j bl ds v{k ds i fj r %
? k w eus ds fy, L or U = k gS A , d i z cy (strong) pq E cd pdr h ds Åi j , d fcU nq i j bl ds v{k l s nw j Å/ok Z /k j j [ k h t k r h gS A pdr h
ds v{k ds i fj r % pq E cd dk s ? k q ek us i j pdr h ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) rotate in the direction opposite to the direction of magnet’s motion
(B) rotate in the same direction as the direction of magnet’s motion
(C) not rotate and its temperature will remain unchanged
(D) not rotate but its temperature will slowly rise
(A) pq E cd dh xfr dh fn' k k ds foi fj r fn' k k es a ? k w es xh
(B) pq E cd dh xfr dh fn' k k ds l ek u fn' k k es a ? k w es xh
(C) ugh a ? k w es xh r F k k bl dk r k i ek u vi fj ofr Z r j gs xk
(D) ? k w es xh ys fdu bl dk r k i ek u /k h j s &/k h j s c<+ s xk
Sol. B
by lenz's law, the disc also tries to move in same direction because in the backward part of disc the
flux reduces as magnet moves and as there is change in magnetic flux, so there is eddy current
production which leads to production of heat.
3. A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on
a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale
on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it
moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has
moved 50 cm, the position of the scale will look like (figures are schematic and not drawn to scale)
20 cm O ; k l ds , d Nk s V s j k s yj es a 10 cm ¼ uh ps ck ; h a vk s j fp= k ns f[ k ; s ½ O ; k l dh , d /k q j h (axle) gS A ; g , d {k S fr t Q ' k Z i j gS
r F k k ,d eh V j i S ek uk b l dh /k q jh i j {k S fr t : i l s fL F k r gS ] ft l es a /k q jh ds f' k [ k j i j ¼ nk ; h a vk s j ns f[ k ; s ½ i S ek us dk ,d fduk jk (edge)
gS A vc i S ek us dk s /k q j h i j /k h js &/k h j s /k ds yk t k r k gS r k fd ; g /k q j h i j fcuk fQ l ys pys ] r F k k j k s yj fcuk fQ l ys yq <+ duk i z k j a H k dj r k
gS A j k s yj ds 50 cm pyus ds i ' pk r ~ i S ek us dh fL F k fr fuE u r j g fn[ k k bZ ns xh ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
(A) (B) 
(C) (D) 
Sol. B
v R 0 ? ? ?
v R ? ?
v
v 20
20
? ? ? ? ?
Velocity of point (A) = v+ ?r
v
v 10
20
? ? ?
3v
1.5v
2
? ?
so distance moved by point of contact
= 1.5×50 cm = 75 cm
4. A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure,
its two ends are connected to two wires and it is hanging by those wires with its plane being
vertical. The wires are connected to a capacitor with charge Q through a switch. The coil is in a
horizontal uniform magnetic field B
0
 parallel to the plane of the coil. When the switch is closed, the
capacitor gets discharged through the coil in a very short time. By the time the capacitor is
discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the
discharge time is so short that the coil has hardly rotated during this time)
R f= k T ; k r F k k N Q s j k s a dh ,d o` Ù k k dk j dq .M yh dk ux.; i z fr jk s /k gS A l k a ds fr d fp= k es a fn[ k k ; s uq l k j] bl ds nk s fl js nk s r k jk s a l s t k s M + s t k r s
gS r F k k ; g m u r k j k s a } k jk yV dk ; k t k r k g S ] ft l dk r y Å/ok Z /k j gk s A r k j ,d fL op ds ek /; e l s vk os ' k Q ds l k F k , d
l a /k k fj= k l s t k s M + s t k r s gS A dq .M yh b l ds ¼ L o; a ds ½ r y ds l ek uk U r j {k S fr t l e: i pq E cdh ; {k s = k B
0
 es a gS A t c fL op cU n fd; k t k r k
gS ] r c l a /k k fj = k cgq r vY i l e; es a dq .M yh l s fujk os f' k r gk s r k gS A t c r d l a /k k fj= k i w .k Z : i l s fujk os f' k r gk s r k gS ] r c r d dq .M yh } k jk
i z k Ir dk s .k h ; l a os x dk i fjek .k gk s xk ¼ ek uk fd fujk os ' k u l e; br uk vY i gS fd dq .M yh bl l e; ds nk S j k u eq f' dy l s ? k w er h  gS A ½ &
B
0
(A) 
2
0
2
NQB R
?
(B) 
2
0
NQB R ? (C) 
2
0
2 NQB R ? (D) 
2
0
4 NQB R ?
Sol. B
after closing switch, within fraction of seconds entire charge flows through coil and produces
impulsive torque.
dt L ? ? ?
?
NBIAdt L ? ?
?
2
NB R Q L ? ? ?
2
0
NQB R L ? ? ?
5. A parallel beam of light strikes a piece of transparent glass having cross section as shown in the
figure below. Correct shape of the emergent wavefront will be (figures are schematic and not
drawn to scale)
i z dk ' k dk , d l ek uk U r j i q a t fp= k k uq l k j vuq i z L F k dk V j [ k us ok ys i k j n' k h Z dk a p ds , d V q dM + s i j V dj k r k gS A fuxZ r r j a xk xz dk l gh
vk dk j gk s xk ¼ fp= k l k a ds fr d gS r F k k i S ek us l s j s [ k k a fdr ugh a gS ½
Air
Light
Glass
Air
(A) (B) (C) (D)