Easy2Siksha.com
   2021
/  

( -)
 : 3  
:75
:     ,            
         
1.      -    - AL  DL 
   
2.       AL  DL    ?
3.    :
(i) 
(ii) 
(iii)  
(iv)  
4.      ?         
Easy2Siksha.com
5.               
 
6.       ?      

7.            
  
8.         (r)       
   ?
   2021
/  

( -)
 : 3   :75
:     ,            
         
1.      -    - AL  DL 
   
::        
         ,       -
       ,           -
Easy2Siksha.com
       ,           
    ,           , "!    
  "
      ?      ""   ,  ""
  ,     "  "   ?
        
         ( , , , , ) 
   (      ,  ,      ) 
        ,         
 
                 
                
-,    ,           ,   
  
           :
1.          ?
2.           ?
3.             ?
      ,         
 ,   ()   -  
  (AL):         
  (  AL  AT      )       
            
              
  :
         
       
            
           
  ,         :
Easy2Siksha.com
"     50%      "
50% ?  -       -    
    , ,        
  50%      
     
   48         (  
 )
      -    
           
               
  ():    ()
       ,     :
             ?
     ,     ()      
  , DL  JND   :
"              "
      :
  1     ,        
 , "     "?
     10  ,         
       — 11, 12,  15?
       2   ,        
  ?
        -        
         
  :   
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              
  
                 
  ,      
 :
      ;      
      
  ,   :
  (ΔI)    (I)    
  , ΔI / I = K,  ΔI =          ,
I =    , K =  (    )
        
󷄧󷄫  100     ,  5          
  10     ,  5         
     500     
,    ,          
󷄧󷄬            ,      
       ,         

               , 
  
  :     
  ,           :
            
   ?      ,         
-    ,  -  
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  :
      
     ,    
      
 :
            
                
                

   
         :
            ?
,                   
  
        ,   ?
    :
󷄧󽇄    
    :
󷄧󽇄    
-       :
󷄧󽇄             

              
       ,          
 ,    -       ,  
               
    ,  ,  ,  ,  
                  
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,                 
   -           
2.       AL  DL    ?
:󷶪󷶫     AL  DL  
         ,       
                - 
         , ",      "      
  (AL)             
                 
      , "      ?"    
        ,   , ",       "
        (DL)         
    
AL  DL       ,        
                
             (Method of Limits)
󷘹󷘴󷘵󷘶󷘷󷘸   ?
            ,  
            -  
          ,       
  
󷷑󷷒󷷓󷷔  :              
              
󷈷󷈸󷈹󷈺󷈻󷈼     (AL)  
  (AL)              50% 
         (Method of Limits)     
  
1.  
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              
  -      
        ""  󷷑󷷒󷷓󷷔:   0
             15    

2.  
             
  -       
  ""           󷷑󷷒󷷓󷷔: 
        -        
       
3.   
           
    (""  )      (""  ) 
  
4.   
     (     )    
      
󷷑󷷒󷷓󷷔    : AL   ,         
      
󷈷󷈸󷈹󷈺󷈻󷈼     ()  
  (),     ()    ,    
         
1.  
       (  , 50   )
2.  
 -         
      ""  󷷑󷷒󷷓󷷔:   - 
          , "      "
3.  
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 -       
      ""  󷷑󷷒󷷓󷷔:     
         , "     "
4.   
       
      ,    
5.   
      
    ()   
󷷑󷷒󷷓󷷔  :  ,            
   
󹶓󹶔󹶕󹶖󹶗󹶘  
                
    
 ,             -
         , ",       "  
     (AL)
 ,  50          
          55    ,  
 , ",    "     (DL) 
     ,            
  
󷈷󷈸󷈹󷈺󷈻󷈼   
    
:       
:   (, , , )      
󽀼󽀽󽁀󽁁󽀾󽁂󽀿󽁃   
  :         ""  "" 
 :-        
   :     ""  ""   
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󷷑󷷒󷷓󷷔      ,        
   
󷇮󷇭 
               
  :
  (AL):        
  ():           

         ,     
    ,         
       
3.    :
(i) 
(ii) 
(iii)  
(iv)  
:󼩏󼩐󼩑:        
               ,  
            ,    
              ,      
            
󷘹󷘴󷘵󷘶󷘷󷘸  ?
 ,                
              
󷷑󷷒󷷓󷷔    :              
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                   ,
          ,       
  ,         
󷈷󷈸󷈹󷈺󷈻󷈼   
:    ;        
-  :-    -     , 
-     
  :          ,     
 
  :   ,    (  )

󷷑󷷒󷷓󷷔            
       
󼩺󼩻     
             ,     
 ,     -     
1.  ( )
             
       ,          
   
    
󷷑󷷒󷷓󷷔:                 
     
2. 
       
 :       󷷑󷷒󷷓󷷔:    
         
 :       󷷑󷷒󷷓󷷔:    
     
,        
3.   
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          󷷑󷷒󷷓󷷔:    
    ,        
4.  ( )
-            
      
            
󷷑󷷒󷷓󷷔:               
  
5.   
-               
               
    ( )       
󷷑󷷒󷷓󷷔:         ,       
           
6.  
            ,      
 󷷑󷷒󷷓󷷔:            , 
      
7.  
      
,        
      ,      

󷷑󷷒󷷓󷷔:                
   
8.    
      
  ,             
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  ,             
󷷑󷷒󷷓󷷔:               
9. 
            ,  -   
󷷑󷷒󷷓󷷔:          ,     
  
10. -  
-           󷷑󷷒󷷓󷷔:  
         
󹶓󹶔󹶕󹶖󹶗󹶘  
                 
     
   ,        
  ,            

  ,             
      
 ,      ,      
                 
󷈷󷈸󷈹󷈺󷈻󷈼       
         :
     
           
       
         
         
󷷑󷷒󷷓󷷔                 
    
󷇮󷇭 
Easy2Siksha.com
          , , , ,
  ,  , , ,       
     ,          
                
           ,   
 
4.      ?         
:   : , ,     
 
            ,      
          ?        
               
        ,       
             : , ,
              
(i)    
        ,          
          ?       
               
        
                ,
               
   
  
             :
Easy2Siksha.com
󷄧󷄫               , 
    ,      ,         

󷄧󷄬             , 
   ,       ,       

󷄧󷄭         ,      
   , "         "   ,
     ,   
   ?
         ,        
          ?        
      ,      ,      
      ,             
    
(ii)    
         ,       
     
               
 
                    
                  
          
  
      :
󷄧󷄫 :                 
  ,    ,    ,       
󷄧󷄬:                
    ,            

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 -     ?
      , “       !”   
   ?              , 
 ,    ,           
      ,          

(iii)         
-               
              
         ,     
           
                 
,      
     
󷄧󷄫  :            : 
       – VIBGYOR (, , , , , , )
󷄧󷄬 :              
:      :
  -   -    
, , , , , , , 
󷄧󷄭  :              
   :         
󷄧󷄮 :             ",
, "    ,               -
  !
󷄰󷄯  -      : 987654321  987-654-
321       
      ?
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     ,         
       
(iv)     
              ,  
        
                
  
     ""          
             
   
   
     
 
 
  
     
       ,        
     ?
   ,           
                 
          ,     

         ,          
        ,         
  ,         ,    
           
              
            ,   ,   
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       ,          
 !
5.               
 
:              
 
             ,    
              ,     
        ,         ,  
               
     ,        
           ,   ,  
  ,              
      ,     ,  ,     
   
    
1. - 
                 
         ,         
      ,   ""      
       
2.    
   -     ,     ,
   ,      -      
    ;      
3.      
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              :
1.    
2.     
3.     
4.   
5.            
           
4.      ,      
         ,       
      ,             
   ,  ,     
5.     
              
    ,           
   ,         ,    
       
6.        
-    -          
        ,         
   ,               
 -  ,   ,        
             "!"   
    
7.      
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               
  ,   ,    -     
  , ,        
8.     
                 
    -     ,  
   ,            
   ""  
        — ""         
 ?
 , ""            ,
,                
 ""  ,                
  
   , ,           
  ,  -             :
1.       
(i)       
  -         ,      
   -             
    ,           
           
(ii)    
             ,     
 -                
         
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(iii)       
       , , , , 
       -    -  
   
2.        ( )
-                  
  ,                
  
(i)     
         ,         
  ,               
  ,           
(ii)       
-                  
                
(iii)     
                
       
       
                 
                 
             ,  
       ,          
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                 ,  
           
       ?
       ,       :
   
   
       
       
       
     

             ,
   ,         
, , ,      
          
   ,           , 
               
,       :        
  ,            
6.       ?      

:󼩏󼩐󼩑 :   
       -       
,  ,    ,      -,     
""  " "           
           
Easy2Siksha.com
             
    ,            
,       
󷘹󷘴󷘵󷘶󷘷󷘸   ?
 ,             ,
              
󷷑󷷒󷷓󷷔    :            
      
  :
" "      ,   ,    
       -        
""     ,      
        ,       
󷈷󷈸󷈹󷈺󷈻󷈼   
    :  -      ,  
       
  :          
    :       
  
  :          

󷷑󷷒󷷓󷷔    , ,         
 
󼩺󼩻   
              
   ,         
1.   
            
       
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     ,     
  
󷷑󷷒󷷓󷷔:                ,    
   
           
2. 
       -    
             
          
󷷑󷷒󷷓󷷔: ""    ,  ,       
              
3. 
          
         ,       
 
            
󷷑󷷒󷷓󷷔:         ,        
              
4. 
         
       
   ,       
󷷑󷷒󷷓󷷔:   ""  " "      ,     
  
5.     
         
      ,        
         
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󷷑󷷒󷷓󷷔:      " "   ,    ,   

6. 
       
        
       ,        
󷷑󷷒󷷓󷷔: ""   ,            , 
    - 
7.   
     
  ( , , )    
  (, )    
󷷑󷷒󷷓󷷔:     ,       "" 
 
8.   
                
             
󷷑󷷒󷷓󷷔:         , ,    
 
󹶓󹶔󹶕󹶖󹶗󹶘  
             
   -     , , 
       
   ,            
       ,      
         
   ,  -        ,   
   
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        ""    
             
,              
                
   
󷈷󷈸󷈹󷈺󷈻󷈼      
  :    ;     
:              
:       
:           

:      
󷇮󷇭 
             ,
, , , ,   ,    
 ,             ,  
              
7.            
  
:󷈷󷈸󷈹󷈺󷈻󷈼  ?
                 
           ,    :
       
     
          
  :
   ,         
Easy2Siksha.com
      ,         
   
               
  
,                 
   
󹵙󹵚󹵛󹵜   ?
     , ,  ,    
        :
 
  
 
 
  ,             
                
       
󷘹󷘴󷘵󷘶󷘷󷘸  
                 -
   
󷄧󷄫 
                   
        
󽆤:
  ,      
         
        
󽇐    :
Easy2Siksha.com
      
          
  0    (0  +1  )
   ,   +1       ,   0   
󷄧󷄬 
                ,  

󽆤:
       
        
        
󽇐    :
     
      
  0  -1   
    -1  ;   0  
󷄧󷄭 () 
-,                 
󽆤:
    
     
     
󽇐    :
      
    
  0 
Easy2Siksha.com
       
󼪍󼪎󼪏󼪐󼪑󼪒󼪓      
     ,          
󷄧󷄮 
            ,     
󽆤:
   (+1)
:            
   (–1)
:               
󽇐 :
     
  100%  
        
󷄰󷄯   
-    ,   
󽆤 
       ,    :
  
   (  )
󽆤 
      :
   
Easy2Siksha.com
  
󹵱󹵲󹵵󹵶󹵷󹵳󹵴󹵸󹵹󹵺       
󷄧󷄱 
             ,  
 
󽆤:
           
󽇐 :
   
 
       
󷄧󷄲- () 
          ,   - 
󽆤:
 ,      
   ,            
   
󽇐 :
 
  
       
󹵍󹵉󹵎󹵏󹵐     ?
Easy2Siksha.com
            ,     
    :
    (    )
  (       )
  ( )
             
󼩏󼩐󼩑    
1.    ,     :     
        -   ,      
2.  -1  +1   
3.       
4.      
5.      
󷄧󼿒
                
      ,         ,   
        , , , ,
       
, , , , , ,   -    
,               
   
8.         (r)       
   ?
:󹵍󹵉󹵎󹵏󹵐  (r)    
                  
           :      
Easy2Siksha.com
  ,                 
?     (r)  
                
 ,               
    
󷘹󷘴󷘵󷘶󷘷󷘸   ?
  ( r    )       :
  : (    )   (   
  )
  :  -1  +1   
󷷑󷷒󷷓󷷔:
 r = +0.9 ,           

 r = -0.8 ,            
 r = 0 ,     
󷈷󷈸󷈹󷈺󷈻󷈼  
              ( X  Y) 
         
  :
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
:
   
    
     
         
󷷑󷷒󷷓󷷔  : r = (X  Y  ) ÷ (    )
󼩺󼩻      r     
          
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 1:   
      󷷑󷷒󷷓󷷔: 5       (X)   
 (Y)

  (X)
 ()
2
40

4
50

6
60

8
70
10
80
 2:    
X  Y    


   :
󰇛 󰇜 
󰇛    󰇜 
 3:   
          



2
40
-4
-20

4
50
-2
-10

6
60
0
0

8
70
+2
+10
10
80
+4
+20
 4:    
      


-20
80

-10
20

0
0

+10
20
+20
80
󰇛
󰇜󰇛
󰇜 
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 5:    
   -  

󰇛

󰇜
󰇛

󰇜
16
400

4
100

0
0

4
100
16
400
󰇛
󰇜
󰇛
󰇜

 6:   
     :
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇜

 




 7:    
, r = 1 ,               
     -       
󹶓󹶔󹶕󹶖󹶗󹶘  
 ,              ,  
               
  r      r = 0.85          
   :            
 ,     
          :      
   
󷈷󷈸󷈹󷈺󷈻󷈼    
        
      ,  
        
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   :, , , 
󽀼󽀽󽁀󽁁󽀾󽁂󽀿󽁃
  ()   
     
, -      
󷷑󷷒󷷓󷷔:           (    
 ,       ),  r       
󷇮󷇭 
  (r)             
    , :
1.  
2.    
3.   
4.    
5.  
6.   
7.    
                 
   
              
       ,      