Page 1
SECTION 1 (Maximum Marks : 18)
? Section contains SIX (06) questions.
? The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9. BOTH INCLUSIVE.
? For each question, enter the correct integer corresponding to the answer 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 integer is entered;
Zero Marks : 0 If 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 dk m Ù k j 0 l s 9 r d] , d , dy va d i w .k k Z a d gS A nk s uk s a l fE efyr gS A
• i z R ; s d i z ' u ds fy, ] m Ù k j nt Z dj us ds fy, fufnZ "V L F k k u i j ek m l vk S j vk W u L Øh u vk H k k l h ¼ opq Z vy½ l a [ ; k R ed dh i s M dk
m i ; k s x dj ds m Ù k j ds vuq : i l gh i w .k k Z a d nt Z dj s a 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 large square container with thin transparent vertical walls and filled with water (refractive index
4
3
)
is kept on a horizontal table. A student holds a thin straight wire vertically inside the water
12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this
corner, another student sees two images of the wire, located symmetrically on each side of the line of
sight as shown. The separation (in cm) between these images is ____________.
i r yh i k j n' k h Z Å/ok Z /k j nh ok j k s a ds l k F k , d cM + k oxk Z dk j i k = k gS r F k k i k uh ¼ vi or Z uk a d
4
3
½ l s H k j k gS ] t k s , d {k S fr t V s cy i j j [ k k
gS A , d fo| k F k h Z fp= k k uq l k j bl ds , d dk s us l s 12 cm i k uh ds vU nj Å/ok Z /k j : i l s , d i r ys l h /k s r k j dk s i dM + s (hold) j [ k r k
gS A bl dk s us l s r k j i j ns [ k r s g q , ] vU ; fo | k F k h Z r k j ds nk s çfr fcE ck s a dk s ns [ k r k gS ] t k s fn[ k k ; s uq l k j n` ' ; j s [ k k ds çR ; s d r j Q (side)
l efer : i l s fL F k r gS A bu i z fr fcE ck s a ds ch p nw j h (cm es a ) gS a &
Page 2
SECTION 1 (Maximum Marks : 18)
? Section contains SIX (06) questions.
? The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9. BOTH INCLUSIVE.
? For each question, enter the correct integer corresponding to the answer 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 integer is entered;
Zero Marks : 0 If 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 dk m Ù k j 0 l s 9 r d] , d , dy va d i w .k k Z a d gS A nk s uk s a l fE efyr gS A
• i z R ; s d i z ' u ds fy, ] m Ù k j nt Z dj us ds fy, fufnZ "V L F k k u i j ek m l vk S j vk W u L Øh u vk H k k l h ¼ opq Z vy½ l a [ ; k R ed dh i s M dk
m i ; k s x dj ds m Ù k j ds vuq : i l gh i w .k k Z a d nt Z dj s a 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 large square container with thin transparent vertical walls and filled with water (refractive index
4
3
)
is kept on a horizontal table. A student holds a thin straight wire vertically inside the water
12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this
corner, another student sees two images of the wire, located symmetrically on each side of the line of
sight as shown. The separation (in cm) between these images is ____________.
i r yh i k j n' k h Z Å/ok Z /k j nh ok j k s a ds l k F k , d cM + k oxk Z dk j i k = k gS r F k k i k uh ¼ vi or Z uk a d
4
3
½ l s H k j k gS ] t k s , d {k S fr t V s cy i j j [ k k
gS A , d fo| k F k h Z fp= k k uq l k j bl ds , d dk s us l s 12 cm i k uh ds vU nj Å/ok Z /k j : i l s , d i r ys l h /k s r k j dk s i dM + s (hold) j [ k r k
gS A bl dk s us l s r k j i j ns [ k r s g q , ] vU ; fo | k F k h Z r k j ds nk s çfr fcE ck s a dk s ns [ k r k gS ] t k s fn[ k k ; s uq l k j n` ' ; j s [ k k ds çR ; s d r j Q (side)
l efer : i l s fL F k r gS A bu i z fr fcE ck s a ds ch p nw j h (cm es a ) gS a &
Sol. (Official Answer Bonus : Marks to all)
Probable Answer : 3 or 4 or 5
(for 3)
When ray is normally incident
h ? apparent depth
2
12
h
=
3
4
1
h =
2
9
So, distance between images will be 3 cm.
Page 3
SECTION 1 (Maximum Marks : 18)
? Section contains SIX (06) questions.
? The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9. BOTH INCLUSIVE.
? For each question, enter the correct integer corresponding to the answer 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 integer is entered;
Zero Marks : 0 If 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 dk m Ù k j 0 l s 9 r d] , d , dy va d i w .k k Z a d gS A nk s uk s a l fE efyr gS A
• i z R ; s d i z ' u ds fy, ] m Ù k j nt Z dj us ds fy, fufnZ "V L F k k u i j ek m l vk S j vk W u L Øh u vk H k k l h ¼ opq Z vy½ l a [ ; k R ed dh i s M dk
m i ; k s x dj ds m Ù k j ds vuq : i l gh i w .k k Z a d nt Z dj s a 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 large square container with thin transparent vertical walls and filled with water (refractive index
4
3
)
is kept on a horizontal table. A student holds a thin straight wire vertically inside the water
12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this
corner, another student sees two images of the wire, located symmetrically on each side of the line of
sight as shown. The separation (in cm) between these images is ____________.
i r yh i k j n' k h Z Å/ok Z /k j nh ok j k s a ds l k F k , d cM + k oxk Z dk j i k = k gS r F k k i k uh ¼ vi or Z uk a d
4
3
½ l s H k j k gS ] t k s , d {k S fr t V s cy i j j [ k k
gS A , d fo| k F k h Z fp= k k uq l k j bl ds , d dk s us l s 12 cm i k uh ds vU nj Å/ok Z /k j : i l s , d i r ys l h /k s r k j dk s i dM + s (hold) j [ k r k
gS A bl dk s us l s r k j i j ns [ k r s g q , ] vU ; fo | k F k h Z r k j ds nk s çfr fcE ck s a dk s ns [ k r k gS ] t k s fn[ k k ; s uq l k j n` ' ; j s [ k k ds çR ; s d r j Q (side)
l efer : i l s fL F k r gS A bu i z fr fcE ck s a ds ch p nw j h (cm es a ) gS a &
Sol. (Official Answer Bonus : Marks to all)
Probable Answer : 3 or 4 or 5
(for 3)
When ray is normally incident
h ? apparent depth
2
12
h
=
3
4
1
h =
2
9
So, distance between images will be 3 cm.
For 4 or 5
We will use formula :
2 3
'
2 2 3/2
n hcos
h
(n Sin )
?
?
? ?
1
htan h' tan ? ? ? ? ?
? For this situation ? = 45°
1
4
.sin 1.sin 45
3
? ? ?
1
3
sin
4 2
? ?
1
32 ? ? ?
1
tan 0.62 ? ? ?
n = 4/3
45 ? ? ?
12
h
2
?
2
3/2
2 2
4 12 1
.
3
2 2 2
h' 3.7cm
4 1
3
2
? ?
? ?
? ?
? ? ?
? ?
? ? ? ?
? ? ?
? ? ? ?
? ?
? ? ? ?
? ?
12
.0.62 3.7 1 1.56cm
2
? ? ? ? ?
12 1 h'
y
2 2 2
? ?
? ? ?
? ?
? ?
?
? ? Answer 2y 12 h' . 2
? ?
? ? ? ? ?
? ?
?
12 5.26 2 4.56 ? ? ? ?
Answer : 4 or 5
Page 4
SECTION 1 (Maximum Marks : 18)
? Section contains SIX (06) questions.
? The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9. BOTH INCLUSIVE.
? For each question, enter the correct integer corresponding to the answer 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 integer is entered;
Zero Marks : 0 If 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 dk m Ù k j 0 l s 9 r d] , d , dy va d i w .k k Z a d gS A nk s uk s a l fE efyr gS A
• i z R ; s d i z ' u ds fy, ] m Ù k j nt Z dj us ds fy, fufnZ "V L F k k u i j ek m l vk S j vk W u L Øh u vk H k k l h ¼ opq Z vy½ l a [ ; k R ed dh i s M dk
m i ; k s x dj ds m Ù k j ds vuq : i l gh i w .k k Z a d nt Z dj s a 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 large square container with thin transparent vertical walls and filled with water (refractive index
4
3
)
is kept on a horizontal table. A student holds a thin straight wire vertically inside the water
12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this
corner, another student sees two images of the wire, located symmetrically on each side of the line of
sight as shown. The separation (in cm) between these images is ____________.
i r yh i k j n' k h Z Å/ok Z /k j nh ok j k s a ds l k F k , d cM + k oxk Z dk j i k = k gS r F k k i k uh ¼ vi or Z uk a d
4
3
½ l s H k j k gS ] t k s , d {k S fr t V s cy i j j [ k k
gS A , d fo| k F k h Z fp= k k uq l k j bl ds , d dk s us l s 12 cm i k uh ds vU nj Å/ok Z /k j : i l s , d i r ys l h /k s r k j dk s i dM + s (hold) j [ k r k
gS A bl dk s us l s r k j i j ns [ k r s g q , ] vU ; fo | k F k h Z r k j ds nk s çfr fcE ck s a dk s ns [ k r k gS ] t k s fn[ k k ; s uq l k j n` ' ; j s [ k k ds çR ; s d r j Q (side)
l efer : i l s fL F k r gS A bu i z fr fcE ck s a ds ch p nw j h (cm es a ) gS a &
Sol. (Official Answer Bonus : Marks to all)
Probable Answer : 3 or 4 or 5
(for 3)
When ray is normally incident
h ? apparent depth
2
12
h
=
3
4
1
h =
2
9
So, distance between images will be 3 cm.
For 4 or 5
We will use formula :
2 3
'
2 2 3/2
n hcos
h
(n Sin )
?
?
? ?
1
htan h' tan ? ? ? ? ?
? For this situation ? = 45°
1
4
.sin 1.sin 45
3
? ? ?
1
3
sin
4 2
? ?
1
32 ? ? ?
1
tan 0.62 ? ? ?
n = 4/3
45 ? ? ?
12
h
2
?
2
3/2
2 2
4 12 1
.
3
2 2 2
h' 3.7cm
4 1
3
2
? ?
? ?
? ?
? ? ?
? ?
? ? ? ?
? ? ?
? ? ? ?
? ?
? ? ? ?
? ?
12
.0.62 3.7 1 1.56cm
2
? ? ? ? ?
12 1 h'
y
2 2 2
? ?
? ? ?
? ?
? ?
?
? ? Answer 2y 12 h' . 2
? ?
? ? ? ? ?
? ?
?
12 5.26 2 4.56 ? ? ? ?
Answer : 4 or 5
2. A train with cross-sectional area S
t
is moving with speed v
t
inside a long tunnel of cross-sectional
area S
0
(S
0
= 4S
t
). Assume that almost all the air (density ?) in front of the train flows back between
its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar.
Take the ambient pressure and that inside the train to be p
0
. If the pressure in the region between
the sides of the train and the tunnel walls is p, then
2
0 t
7
p p v
2N
? ? ? . The value of N is _________.
S
t
vuq çL F k &dk V {k s = k Q y dh , d V ª s u] S
0
(S
0
= 4S
t
) vuq i z L F k &dk V {k s = k Q y dh , d yE ch l q j a x ds vU nj v
t
pk y l s xfr ek u
gS A ek uk fd V ª s u ds l k eus yxH k x i w j h gok ¼ ? k uR o ? ?½ bl ds ck t q vk s (sides) r F k k l q j a x dh nh ok j k s a ds ch p ok i l cgr h gS A l k F k
gh ] V ª s u ds l k i s {k gok dk i z ok g fL F k j r F k k i V yh ; gS A V ª s u ds vU nj O ; k i d (ambient) nk c ?
0
ys r s gS A ; fn V ª s u dh ck t q vk s r F k k
l q j a x dh nh ok j k s a ds ch p {k s = k es a nk c p gS ] r c
2
0 t
7
p p v
2N
? ? ? gS A r c N dk ek u gS &
Sol. 9
A
2
= 3S
t
Equation of continuity
v
t
4S
t
= 3S
t
v
v =
3
4
v
t
Using Bernoulli's equation
P
0
+
2
1
?v
t
2
= P +
2
1
?
2
t
v
3
4
?
?
?
?
?
?
P
0
– P =
18
7
?v
t
2
Now compare from given value
N = 9
Page 5
SECTION 1 (Maximum Marks : 18)
? Section contains SIX (06) questions.
? The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9. BOTH INCLUSIVE.
? For each question, enter the correct integer corresponding to the answer 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 integer is entered;
Zero Marks : 0 If 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 dk m Ù k j 0 l s 9 r d] , d , dy va d i w .k k Z a d gS A nk s uk s a l fE efyr gS A
• i z R ; s d i z ' u ds fy, ] m Ù k j nt Z dj us ds fy, fufnZ "V L F k k u i j ek m l vk S j vk W u L Øh u vk H k k l h ¼ opq Z vy½ l a [ ; k R ed dh i s M dk
m i ; k s x dj ds m Ù k j ds vuq : i l gh i w .k k Z a d nt Z dj s a 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 large square container with thin transparent vertical walls and filled with water (refractive index
4
3
)
is kept on a horizontal table. A student holds a thin straight wire vertically inside the water
12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this
corner, another student sees two images of the wire, located symmetrically on each side of the line of
sight as shown. The separation (in cm) between these images is ____________.
i r yh i k j n' k h Z Å/ok Z /k j nh ok j k s a ds l k F k , d cM + k oxk Z dk j i k = k gS r F k k i k uh ¼ vi or Z uk a d
4
3
½ l s H k j k gS ] t k s , d {k S fr t V s cy i j j [ k k
gS A , d fo| k F k h Z fp= k k uq l k j bl ds , d dk s us l s 12 cm i k uh ds vU nj Å/ok Z /k j : i l s , d i r ys l h /k s r k j dk s i dM + s (hold) j [ k r k
gS A bl dk s us l s r k j i j ns [ k r s g q , ] vU ; fo | k F k h Z r k j ds nk s çfr fcE ck s a dk s ns [ k r k gS ] t k s fn[ k k ; s uq l k j n` ' ; j s [ k k ds çR ; s d r j Q (side)
l efer : i l s fL F k r gS A bu i z fr fcE ck s a ds ch p nw j h (cm es a ) gS a &
Sol. (Official Answer Bonus : Marks to all)
Probable Answer : 3 or 4 or 5
(for 3)
When ray is normally incident
h ? apparent depth
2
12
h
=
3
4
1
h =
2
9
So, distance between images will be 3 cm.
For 4 or 5
We will use formula :
2 3
'
2 2 3/2
n hcos
h
(n Sin )
?
?
? ?
1
htan h' tan ? ? ? ? ?
? For this situation ? = 45°
1
4
.sin 1.sin 45
3
? ? ?
1
3
sin
4 2
? ?
1
32 ? ? ?
1
tan 0.62 ? ? ?
n = 4/3
45 ? ? ?
12
h
2
?
2
3/2
2 2
4 12 1
.
3
2 2 2
h' 3.7cm
4 1
3
2
? ?
? ?
? ?
? ? ?
? ?
? ? ? ?
? ? ?
? ? ? ?
? ?
? ? ? ?
? ?
12
.0.62 3.7 1 1.56cm
2
? ? ? ? ?
12 1 h'
y
2 2 2
? ?
? ? ?
? ?
? ?
?
? ? Answer 2y 12 h' . 2
? ?
? ? ? ? ?
? ?
?
12 5.26 2 4.56 ? ? ? ?
Answer : 4 or 5
2. A train with cross-sectional area S
t
is moving with speed v
t
inside a long tunnel of cross-sectional
area S
0
(S
0
= 4S
t
). Assume that almost all the air (density ?) in front of the train flows back between
its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar.
Take the ambient pressure and that inside the train to be p
0
. If the pressure in the region between
the sides of the train and the tunnel walls is p, then
2
0 t
7
p p v
2N
? ? ? . The value of N is _________.
S
t
vuq çL F k &dk V {k s = k Q y dh , d V ª s u] S
0
(S
0
= 4S
t
) vuq i z L F k &dk V {k s = k Q y dh , d yE ch l q j a x ds vU nj v
t
pk y l s xfr ek u
gS A ek uk fd V ª s u ds l k eus yxH k x i w j h gok ¼ ? k uR o ? ?½ bl ds ck t q vk s (sides) r F k k l q j a x dh nh ok j k s a ds ch p ok i l cgr h gS A l k F k
gh ] V ª s u ds l k i s {k gok dk i z ok g fL F k j r F k k i V yh ; gS A V ª s u ds vU nj O ; k i d (ambient) nk c ?
0
ys r s gS A ; fn V ª s u dh ck t q vk s r F k k
l q j a x dh nh ok j k s a ds ch p {k s = k es a nk c p gS ] r c
2
0 t
7
p p v
2N
? ? ? gS A r c N dk ek u gS &
Sol. 9
A
2
= 3S
t
Equation of continuity
v
t
4S
t
= 3S
t
v
v =
3
4
v
t
Using Bernoulli's equation
P
0
+
2
1
?v
t
2
= P +
2
1
?
2
t
v
3
4
?
?
?
?
?
?
P
0
– P =
18
7
?v
t
2
Now compare from given value
N = 9
3. Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch
as shown in the figure. Charged oil drops of density 900 kg m
–3
are released through a tiny hole at
the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to
apply a voltage of 200 V across the discs. As a result, an oil drop of radius 8×10
–7
m stops moving
vertically and floats between the discs. The number of electrons present in this oil drop is ________.
(neglect the buoyancy force, take acceleration due to gravity =10 ms
–2
and charge on an electron
(e) = 1.6×10
–19
C)
0.01 m nw jh l s i ` F k d~ nk s cM + h o ` Ù k h ; pdfr ; k ¡ fp= k k uq l k j ,d fL op ds ek /; e l s , d cS V ª h l s t k s M + h t k r h gS A 900 kg m
–3
? k uR o dh
vk os f' k r r s y dh cw U ns a Åi j h pdr h ds ds U nz i j , d N k s V s fN nz l s Nk s M + h t k r h gS A ,d ck j t c dq N r s y dh cw U ns a l h ek U r os x çk Ir dj
ys r h gS ] r c pdr h ; k s a ds fl jk s a i j 200 V dh ok s Y V r k i z nk u djus ds fy, fL op cU n fd; k t k r k gS A i fj.k k eL o: i ] 8×10
–7
m f= k T ; k
dh ,d r s y cw U n Å/o k Z /k j xfr cU n dj r h gS r F k k pdr h ; k s a ds ch p pyk ; ek u (floats) gS A bl r s y cw U n es a m i fL F k r bys D V ª k W uk s a dh
l a [ ; k gS ¼ m R i yk o u cy ux.; g S ] xq : R o h ; R oj.k =10 ms
–2
r F k k bys D V ª k W u i j vk os ' k (e) = 1.6×10
–19
C)
Sol. 6
qE = mg ....(i)
q = ne
V = Ed ? E =
V
d
from equation (i)
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