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Q u e s t i o n 	 1
P A R T 	 - 	 I 	 ( P H Y S I C S )
T h e 	 r o o t 	 m e a n 	 s q u a r e 	 s p e e d 	 o f 	 s m o k e 	 p a r t i c l e s 	 o f 	 m a s s 	 5 	 × 1 0
- 1 7
k g 	 i n
t h e i r 	 B r o w n i a n 	 m o t i o n 	 i n 	 a i r 	 a t 	 N T P 	 i s 	 a p p r o x i m a t e l y .
[ G i v e n 	 k = 1 . 3 8 × 1 0
- 2 3
J K
- 1
	 ]
O p t i o n s :
A . 	 6 0 m m 	 s
- 1
B . 	 1 2 m m 	 s
- 1
C . 	 1 5 m m 	 s
- 1
D . 	 3 6 m m 	 s
- 1
A n s w e r : 	 C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 2
T h e 	 e q u a t i o n 	 o f 	 a 	 p a r t i c l e 	 e x e c u t i n g 	 s i m p l e 	 h a r m o n i c 	 m o t i o n 	 i s 	 g i v e n 	 b y
x = s i n p t +
1
3
m . 	 A t 	 t = 1 s , 	 t h e 	 s p e e d 	 o f 	 p a r t i c l e 	 w i l l 	 b e 	 ( G i v e n 	 :
p = 3 . 1 4 	 )
O p t i o n s :
A . 	 0 c m 	 s
- 1
B . 	 1 5 7 c m 	 s
- 1
C . 	 2 7 2 c m 	 s
- 1
D . 	 3 1 4 c m 	 s
- 1
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
( )
VITEEE Paper - 2022
Physics
Page 2


Q u e s t i o n 	 1
P A R T 	 - 	 I 	 ( P H Y S I C S )
T h e 	 r o o t 	 m e a n 	 s q u a r e 	 s p e e d 	 o f 	 s m o k e 	 p a r t i c l e s 	 o f 	 m a s s 	 5 	 × 1 0
- 1 7
k g 	 i n
t h e i r 	 B r o w n i a n 	 m o t i o n 	 i n 	 a i r 	 a t 	 N T P 	 i s 	 a p p r o x i m a t e l y .
[ G i v e n 	 k = 1 . 3 8 × 1 0
- 2 3
J K
- 1
	 ]
O p t i o n s :
A . 	 6 0 m m 	 s
- 1
B . 	 1 2 m m 	 s
- 1
C . 	 1 5 m m 	 s
- 1
D . 	 3 6 m m 	 s
- 1
A n s w e r : 	 C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 2
T h e 	 e q u a t i o n 	 o f 	 a 	 p a r t i c l e 	 e x e c u t i n g 	 s i m p l e 	 h a r m o n i c 	 m o t i o n 	 i s 	 g i v e n 	 b y
x = s i n p t +
1
3
m . 	 A t 	 t = 1 s , 	 t h e 	 s p e e d 	 o f 	 p a r t i c l e 	 w i l l 	 b e 	 ( G i v e n 	 :
p = 3 . 1 4 	 )
O p t i o n s :
A . 	 0 c m 	 s
- 1
B . 	 1 5 7 c m 	 s
- 1
C . 	 2 7 2 c m 	 s
- 1
D . 	 3 1 4 c m 	 s
- 1
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
( )
VITEEE Paper - 2022
Physics
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 3
F o l l o w i n g 	 a r e 	 e x p r e s s i o n s 	 f o r 	 f o u r 	 p l a n e 	 s i m p l e 	 h a r m o n i c 	 w a v e s
( i ) 	 y
1
= A c o s 2 p n
1
t +
x
?
1
( i i ) 	 y
2
= A c o s 2 p n
1
t +
x
?
1
+ p
( i i i ) 	 y
3
= A c o s 2 p n
2
t +
x
?
2
( i v ) 	 y
4
= A c o s 2 p n
2
t -
x
?
2
T h e 	 p a i r s 	 o f 	 w a v e s 	 w h i c h 	 w i l l 	 p r o d u c e 	 d e s t r u c t i v e 	 i n t e r f e r e n c e 	 a n d
s t a t i o n a r y 	 w a v e s 	 r e s p e c t i v e l y 	 i n 	 a 	 m e d i u m , 	 a r e
O p t i o n s :
A . 	 ( i i i , 	 i v ) , 	 ( i , 	 i i )
B . 	 ( i , 	 i i i ) , 	 ( i i , 	 i v )
C . 	 ( i , 	 i v ) , 	 ( i i , 	 i i i )
D . 	 ( i , 	 i i ) , 	 ( i i i , 	 i v )
A n s w e r : 	 D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 4
I f 	 a 	 c h a r g e 	 q 	 i s 	 p l a c e d 	 a t 	 t h e 	 c e n t r e 	 o f 	 a 	 c l o s e d 	 h e m i s p h e r i c a l 	 n o n -
c o n d u c t i n g 	 s u r f a c e , 	 t h e 	 t o t a l 	 f l u x 	 p a s s i n g 	 t h r o u g h 	 t h e 	 f l a t 	 s u r f a c e 	 w o u l d
b e 	 :
O p t i o n s :
A . 	 z e r o
B . 	
q
2 e
0
( )
( )
( )
( )
Page 3


Q u e s t i o n 	 1
P A R T 	 - 	 I 	 ( P H Y S I C S )
T h e 	 r o o t 	 m e a n 	 s q u a r e 	 s p e e d 	 o f 	 s m o k e 	 p a r t i c l e s 	 o f 	 m a s s 	 5 	 × 1 0
- 1 7
k g 	 i n
t h e i r 	 B r o w n i a n 	 m o t i o n 	 i n 	 a i r 	 a t 	 N T P 	 i s 	 a p p r o x i m a t e l y .
[ G i v e n 	 k = 1 . 3 8 × 1 0
- 2 3
J K
- 1
	 ]
O p t i o n s :
A . 	 6 0 m m 	 s
- 1
B . 	 1 2 m m 	 s
- 1
C . 	 1 5 m m 	 s
- 1
D . 	 3 6 m m 	 s
- 1
A n s w e r : 	 C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 2
T h e 	 e q u a t i o n 	 o f 	 a 	 p a r t i c l e 	 e x e c u t i n g 	 s i m p l e 	 h a r m o n i c 	 m o t i o n 	 i s 	 g i v e n 	 b y
x = s i n p t +
1
3
m . 	 A t 	 t = 1 s , 	 t h e 	 s p e e d 	 o f 	 p a r t i c l e 	 w i l l 	 b e 	 ( G i v e n 	 :
p = 3 . 1 4 	 )
O p t i o n s :
A . 	 0 c m 	 s
- 1
B . 	 1 5 7 c m 	 s
- 1
C . 	 2 7 2 c m 	 s
- 1
D . 	 3 1 4 c m 	 s
- 1
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
( )
VITEEE Paper - 2022
Physics
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 3
F o l l o w i n g 	 a r e 	 e x p r e s s i o n s 	 f o r 	 f o u r 	 p l a n e 	 s i m p l e 	 h a r m o n i c 	 w a v e s
( i ) 	 y
1
= A c o s 2 p n
1
t +
x
?
1
( i i ) 	 y
2
= A c o s 2 p n
1
t +
x
?
1
+ p
( i i i ) 	 y
3
= A c o s 2 p n
2
t +
x
?
2
( i v ) 	 y
4
= A c o s 2 p n
2
t -
x
?
2
T h e 	 p a i r s 	 o f 	 w a v e s 	 w h i c h 	 w i l l 	 p r o d u c e 	 d e s t r u c t i v e 	 i n t e r f e r e n c e 	 a n d
s t a t i o n a r y 	 w a v e s 	 r e s p e c t i v e l y 	 i n 	 a 	 m e d i u m , 	 a r e
O p t i o n s :
A . 	 ( i i i , 	 i v ) , 	 ( i , 	 i i )
B . 	 ( i , 	 i i i ) , 	 ( i i , 	 i v )
C . 	 ( i , 	 i v ) , 	 ( i i , 	 i i i )
D . 	 ( i , 	 i i ) , 	 ( i i i , 	 i v )
A n s w e r : 	 D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 4
I f 	 a 	 c h a r g e 	 q 	 i s 	 p l a c e d 	 a t 	 t h e 	 c e n t r e 	 o f 	 a 	 c l o s e d 	 h e m i s p h e r i c a l 	 n o n -
c o n d u c t i n g 	 s u r f a c e , 	 t h e 	 t o t a l 	 f l u x 	 p a s s i n g 	 t h r o u g h 	 t h e 	 f l a t 	 s u r f a c e 	 w o u l d
b e 	 :
O p t i o n s :
A . 	 z e r o
B . 	
q
2 e
0
( )
( )
( )
( )
C . 	
q
4 e
0
D . 	
q
2 p e
0
A n s w e r : 	 A
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 5
T h e 	 e l e c t r i c 	 p o t e n t i a l 	 V ( x ) 	 i n 	 a 	 r e g i o n 	 a r o u n d 	 t h e 	 o r i g i n 	 i s 	 g i v e n 	 b y
V ( x ) = 4 x
2
	 v o l t s . 	 T h e 	 e l e c t r i c 	 c h a r g e 	 e n c l o s e d 	 i n 	 a 	 c u b e 	 o f 	 1 m 	 s i d e 	 w i t h
i t s 	 c e n t r e 	 a t 	 t h e 	 o r i g i n 	 i s 	 ( i n 	 c o u l o m b )
O p t i o n s :
A . 	 8 e
0
B . 	 - 4 e
0
C . 	 0
D . 	 - 8 e
0
A n s w e r : 	 D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 6
A 	 h e a t e r 	 c o i l 	 i s 	 c u t 	 i n t o 	 t w o 	 e q u a l 	 p a r t s 	 a n d 	 o n l y 	 o n e 	 p a r t 	 i s 	 n o w 	 u s e d 	 i n
t h e 	 h e a t e r . 	 T h e 	 h e a t 	 g e n e r a t e d 	 w i l l 	 n o w 	 b e
O p t i o n s :
A . 	 f o u r 	 t i m e s
B . 	 d o u b l e d
C . 	 h a l v e d
D . 	 o n e 	 f o u r t h
A n s w e r : 	 B
S o l u t i o n :
Page 4


Q u e s t i o n 	 1
P A R T 	 - 	 I 	 ( P H Y S I C S )
T h e 	 r o o t 	 m e a n 	 s q u a r e 	 s p e e d 	 o f 	 s m o k e 	 p a r t i c l e s 	 o f 	 m a s s 	 5 	 × 1 0
- 1 7
k g 	 i n
t h e i r 	 B r o w n i a n 	 m o t i o n 	 i n 	 a i r 	 a t 	 N T P 	 i s 	 a p p r o x i m a t e l y .
[ G i v e n 	 k = 1 . 3 8 × 1 0
- 2 3
J K
- 1
	 ]
O p t i o n s :
A . 	 6 0 m m 	 s
- 1
B . 	 1 2 m m 	 s
- 1
C . 	 1 5 m m 	 s
- 1
D . 	 3 6 m m 	 s
- 1
A n s w e r : 	 C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 2
T h e 	 e q u a t i o n 	 o f 	 a 	 p a r t i c l e 	 e x e c u t i n g 	 s i m p l e 	 h a r m o n i c 	 m o t i o n 	 i s 	 g i v e n 	 b y
x = s i n p t +
1
3
m . 	 A t 	 t = 1 s , 	 t h e 	 s p e e d 	 o f 	 p a r t i c l e 	 w i l l 	 b e 	 ( G i v e n 	 :
p = 3 . 1 4 	 )
O p t i o n s :
A . 	 0 c m 	 s
- 1
B . 	 1 5 7 c m 	 s
- 1
C . 	 2 7 2 c m 	 s
- 1
D . 	 3 1 4 c m 	 s
- 1
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
( )
VITEEE Paper - 2022
Physics
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 3
F o l l o w i n g 	 a r e 	 e x p r e s s i o n s 	 f o r 	 f o u r 	 p l a n e 	 s i m p l e 	 h a r m o n i c 	 w a v e s
( i ) 	 y
1
= A c o s 2 p n
1
t +
x
?
1
( i i ) 	 y
2
= A c o s 2 p n
1
t +
x
?
1
+ p
( i i i ) 	 y
3
= A c o s 2 p n
2
t +
x
?
2
( i v ) 	 y
4
= A c o s 2 p n
2
t -
x
?
2
T h e 	 p a i r s 	 o f 	 w a v e s 	 w h i c h 	 w i l l 	 p r o d u c e 	 d e s t r u c t i v e 	 i n t e r f e r e n c e 	 a n d
s t a t i o n a r y 	 w a v e s 	 r e s p e c t i v e l y 	 i n 	 a 	 m e d i u m , 	 a r e
O p t i o n s :
A . 	 ( i i i , 	 i v ) , 	 ( i , 	 i i )
B . 	 ( i , 	 i i i ) , 	 ( i i , 	 i v )
C . 	 ( i , 	 i v ) , 	 ( i i , 	 i i i )
D . 	 ( i , 	 i i ) , 	 ( i i i , 	 i v )
A n s w e r : 	 D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 4
I f 	 a 	 c h a r g e 	 q 	 i s 	 p l a c e d 	 a t 	 t h e 	 c e n t r e 	 o f 	 a 	 c l o s e d 	 h e m i s p h e r i c a l 	 n o n -
c o n d u c t i n g 	 s u r f a c e , 	 t h e 	 t o t a l 	 f l u x 	 p a s s i n g 	 t h r o u g h 	 t h e 	 f l a t 	 s u r f a c e 	 w o u l d
b e 	 :
O p t i o n s :
A . 	 z e r o
B . 	
q
2 e
0
( )
( )
( )
( )
C . 	
q
4 e
0
D . 	
q
2 p e
0
A n s w e r : 	 A
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 5
T h e 	 e l e c t r i c 	 p o t e n t i a l 	 V ( x ) 	 i n 	 a 	 r e g i o n 	 a r o u n d 	 t h e 	 o r i g i n 	 i s 	 g i v e n 	 b y
V ( x ) = 4 x
2
	 v o l t s . 	 T h e 	 e l e c t r i c 	 c h a r g e 	 e n c l o s e d 	 i n 	 a 	 c u b e 	 o f 	 1 m 	 s i d e 	 w i t h
i t s 	 c e n t r e 	 a t 	 t h e 	 o r i g i n 	 i s 	 ( i n 	 c o u l o m b )
O p t i o n s :
A . 	 8 e
0
B . 	 - 4 e
0
C . 	 0
D . 	 - 8 e
0
A n s w e r : 	 D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 6
A 	 h e a t e r 	 c o i l 	 i s 	 c u t 	 i n t o 	 t w o 	 e q u a l 	 p a r t s 	 a n d 	 o n l y 	 o n e 	 p a r t 	 i s 	 n o w 	 u s e d 	 i n
t h e 	 h e a t e r . 	 T h e 	 h e a t 	 g e n e r a t e d 	 w i l l 	 n o w 	 b e
O p t i o n s :
A . 	 f o u r 	 t i m e s
B . 	 d o u b l e d
C . 	 h a l v e d
D . 	 o n e 	 f o u r t h
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 7
I n 	 a 	 r e g i o n , 	 s t e a d y 	 a n d 	 u n i f o r m 	 e l e c t r i c 	 a n d 	 m a g n e t i c 	 f i e l d s 	 a r e 	 p r e s e n t .
T h e s e 	 t w o 	 f i e l d s 	 a r e 	 p a r a l l e l 	 t o 	 e a c h 	 o t h e r . 	 A 	 c h a r g e d 	 p a r t i c l e 	 i s
r e l e a s e d 	 f r o m 	 r e s t 	 i n 	 t h i s 	 r e g i o n . 	 T h e 	 p a t h 	 o f 	 t h e 	 p a r t i c l e 	 w i l l 	 b e 	 a
O p t i o n s :
A . 	 h e l i x
B . 	 s t r a i g h t 	 l i n e
C . 	 e l l i p s e
D . 	 c i r c l e
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 8
A n 	 o b j e c t 	 i s 	 t h r o w n 	 v e r t i c a l l y 	 u p w a r d s . 	 A t 	 i t s 	 m a x i m u m 	 h e i g h t , 	 w h i c h 	 o f
t h e 	 f o l l o w i n g 	 q u a n t i t y 	 b e c o m e s 	 z e r o 	 ?
O p t i o n s :
A . 	 M o m e n t u m
B . 	 P o t e n t i a l 	 e n e r g y
C . 	 A c c e l e r a t i o n
D . 	 F o r c e
A n s w e r : 	 A
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 9
T h e 	 s e l f 	 i n d u c e d 	 e m f 	 o f 	 a 	 c o i l 	 i s 	 2 5 	 v o l t s . 	 W h e n 	 t h e 	 c u r r e n t 	 i n 	 i t 	 i s
c h a n g e d 	 a t 	 u n i f o r m 	 r a t e 	 f r o m 	 1 0 A 	 t o 	 2 5 	 A 	 i n 	 1 	 s , 	 t h e 	 c h a n g e 	 i n 	 t h e
Page 5


Q u e s t i o n 	 1
P A R T 	 - 	 I 	 ( P H Y S I C S )
T h e 	 r o o t 	 m e a n 	 s q u a r e 	 s p e e d 	 o f 	 s m o k e 	 p a r t i c l e s 	 o f 	 m a s s 	 5 	 × 1 0
- 1 7
k g 	 i n
t h e i r 	 B r o w n i a n 	 m o t i o n 	 i n 	 a i r 	 a t 	 N T P 	 i s 	 a p p r o x i m a t e l y .
[ G i v e n 	 k = 1 . 3 8 × 1 0
- 2 3
J K
- 1
	 ]
O p t i o n s :
A . 	 6 0 m m 	 s
- 1
B . 	 1 2 m m 	 s
- 1
C . 	 1 5 m m 	 s
- 1
D . 	 3 6 m m 	 s
- 1
A n s w e r : 	 C
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 2
T h e 	 e q u a t i o n 	 o f 	 a 	 p a r t i c l e 	 e x e c u t i n g 	 s i m p l e 	 h a r m o n i c 	 m o t i o n 	 i s 	 g i v e n 	 b y
x = s i n p t +
1
3
m . 	 A t 	 t = 1 s , 	 t h e 	 s p e e d 	 o f 	 p a r t i c l e 	 w i l l 	 b e 	 ( G i v e n 	 :
p = 3 . 1 4 	 )
O p t i o n s :
A . 	 0 c m 	 s
- 1
B . 	 1 5 7 c m 	 s
- 1
C . 	 2 7 2 c m 	 s
- 1
D . 	 3 1 4 c m 	 s
- 1
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
( )
VITEEE Paper - 2022
Physics
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 3
F o l l o w i n g 	 a r e 	 e x p r e s s i o n s 	 f o r 	 f o u r 	 p l a n e 	 s i m p l e 	 h a r m o n i c 	 w a v e s
( i ) 	 y
1
= A c o s 2 p n
1
t +
x
?
1
( i i ) 	 y
2
= A c o s 2 p n
1
t +
x
?
1
+ p
( i i i ) 	 y
3
= A c o s 2 p n
2
t +
x
?
2
( i v ) 	 y
4
= A c o s 2 p n
2
t -
x
?
2
T h e 	 p a i r s 	 o f 	 w a v e s 	 w h i c h 	 w i l l 	 p r o d u c e 	 d e s t r u c t i v e 	 i n t e r f e r e n c e 	 a n d
s t a t i o n a r y 	 w a v e s 	 r e s p e c t i v e l y 	 i n 	 a 	 m e d i u m , 	 a r e
O p t i o n s :
A . 	 ( i i i , 	 i v ) , 	 ( i , 	 i i )
B . 	 ( i , 	 i i i ) , 	 ( i i , 	 i v )
C . 	 ( i , 	 i v ) , 	 ( i i , 	 i i i )
D . 	 ( i , 	 i i ) , 	 ( i i i , 	 i v )
A n s w e r : 	 D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 4
I f 	 a 	 c h a r g e 	 q 	 i s 	 p l a c e d 	 a t 	 t h e 	 c e n t r e 	 o f 	 a 	 c l o s e d 	 h e m i s p h e r i c a l 	 n o n -
c o n d u c t i n g 	 s u r f a c e , 	 t h e 	 t o t a l 	 f l u x 	 p a s s i n g 	 t h r o u g h 	 t h e 	 f l a t 	 s u r f a c e 	 w o u l d
b e 	 :
O p t i o n s :
A . 	 z e r o
B . 	
q
2 e
0
( )
( )
( )
( )
C . 	
q
4 e
0
D . 	
q
2 p e
0
A n s w e r : 	 A
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 5
T h e 	 e l e c t r i c 	 p o t e n t i a l 	 V ( x ) 	 i n 	 a 	 r e g i o n 	 a r o u n d 	 t h e 	 o r i g i n 	 i s 	 g i v e n 	 b y
V ( x ) = 4 x
2
	 v o l t s . 	 T h e 	 e l e c t r i c 	 c h a r g e 	 e n c l o s e d 	 i n 	 a 	 c u b e 	 o f 	 1 m 	 s i d e 	 w i t h
i t s 	 c e n t r e 	 a t 	 t h e 	 o r i g i n 	 i s 	 ( i n 	 c o u l o m b )
O p t i o n s :
A . 	 8 e
0
B . 	 - 4 e
0
C . 	 0
D . 	 - 8 e
0
A n s w e r : 	 D
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 6
A 	 h e a t e r 	 c o i l 	 i s 	 c u t 	 i n t o 	 t w o 	 e q u a l 	 p a r t s 	 a n d 	 o n l y 	 o n e 	 p a r t 	 i s 	 n o w 	 u s e d 	 i n
t h e 	 h e a t e r . 	 T h e 	 h e a t 	 g e n e r a t e d 	 w i l l 	 n o w 	 b e
O p t i o n s :
A . 	 f o u r 	 t i m e s
B . 	 d o u b l e d
C . 	 h a l v e d
D . 	 o n e 	 f o u r t h
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 7
I n 	 a 	 r e g i o n , 	 s t e a d y 	 a n d 	 u n i f o r m 	 e l e c t r i c 	 a n d 	 m a g n e t i c 	 f i e l d s 	 a r e 	 p r e s e n t .
T h e s e 	 t w o 	 f i e l d s 	 a r e 	 p a r a l l e l 	 t o 	 e a c h 	 o t h e r . 	 A 	 c h a r g e d 	 p a r t i c l e 	 i s
r e l e a s e d 	 f r o m 	 r e s t 	 i n 	 t h i s 	 r e g i o n . 	 T h e 	 p a t h 	 o f 	 t h e 	 p a r t i c l e 	 w i l l 	 b e 	 a
O p t i o n s :
A . 	 h e l i x
B . 	 s t r a i g h t 	 l i n e
C . 	 e l l i p s e
D . 	 c i r c l e
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 8
A n 	 o b j e c t 	 i s 	 t h r o w n 	 v e r t i c a l l y 	 u p w a r d s . 	 A t 	 i t s 	 m a x i m u m 	 h e i g h t , 	 w h i c h 	 o f
t h e 	 f o l l o w i n g 	 q u a n t i t y 	 b e c o m e s 	 z e r o 	 ?
O p t i o n s :
A . 	 M o m e n t u m
B . 	 P o t e n t i a l 	 e n e r g y
C . 	 A c c e l e r a t i o n
D . 	 F o r c e
A n s w e r : 	 A
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 9
T h e 	 s e l f 	 i n d u c e d 	 e m f 	 o f 	 a 	 c o i l 	 i s 	 2 5 	 v o l t s . 	 W h e n 	 t h e 	 c u r r e n t 	 i n 	 i t 	 i s
c h a n g e d 	 a t 	 u n i f o r m 	 r a t e 	 f r o m 	 1 0 A 	 t o 	 2 5 	 A 	 i n 	 1 	 s , 	 t h e 	 c h a n g e 	 i n 	 t h e
e n e r g y 	 o f 	 t h e 	 i n d u c t a n c e 	 i s :
O p t i o n s :
A . 	 7 4 0 J
B . 	 4 3 7 . 5 J
C . 	 5 4 0 J
D . 	 6 3 7 . 5 J
A n s w e r : 	 B
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 1 0
A l t e r n a t i n g 	 c u r r e n t 	 c a n 	 n o t 	 b e 	 m e a s u r e d 	 b y 	 D . C . 	 a m m e t e r 	 b e c a u s e
O p t i o n s :
A . 	 A v e r a g e 	 v a l u e 	 o f 	 c u r r e n t 	 f o r 	 c o m p l e t e 	 c y c l e 	 i s 	 z e r o
B . 	 A . C . 	 C h a n g e s 	 d i r e c t i o n
C . 	 A . C . 	 c a n 	 n o t 	 p a s s 	 t h r o u g h 	 D . C . 	 A m m e t e r
D . 	 D . C . 	 A m m e t e r 	 w i l l 	 g e t 	 d a m a g e d .
A n s w e r : 	 A
S o l u t i o n :
S o l u t i o n :
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Q u e s t i o n 	 1 1
T h e 	 m a g n e t i c 	 f i e l d 	 o f 	 a 	 p l a n e 	 e l e c t r o m a g n e t i c 	 w a v e 	 i s 	 g i v e n 	 b y :
?
B
= 2 × 1 0
- 8
s i n ( 0 . 5 × 1 0
3
x + 1 . 5 × 1 0
1 1
t )
^
j
T . 	
T h e 	 a m p l i t u d e 	 o f 	 t h e 	 e l e c t r i c 	 f i e l d 	 w o u l d 	 b e :
O p t i o n s :
A . 	 6 V m
- 1
	 a l o n g 	 x - a x i s
B . 	 3 V m
- 1
	 a l o n g 	 z - a x i s
C . 	 6 V m
- 1
	 a l o n g 	 z - a x i s
D . 	 2 × 1 0
- 8
V m
- 1
	 a l o n g 	 z - a x i s

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