Easy2Siksha.com
   2021
/  

(





)
 : 3   :100
 :     ,            
           

1.         :
(a)     (b)      (c)    (d)
 
(6¼ × 4 = 25)
2.(a) 



 


(b)  :
󰇛󰇜󰇛󰇜 w.r.t.
(c)          ?     
  :
Easy2Siksha.com



(6 + 6 + 13 = 25)

3.()      -     
   
()       :
x
2
3
4
5
6
7
8
f
2
4
6
2
3
2
1
(18 + 7 = 25)
4.()           :

0–10
1020
2030
3040
5060
  
5
6
9
15
6
()                 
        ?

5.()           ,
        
(b)            :

10
11
12
13
14
15

3
5
10
8
5
1
6.()            
         
Easy2Siksha.com
()        :
X
-4
5
6
7
9
12

2
3
4
6
5
8

7.    ?         
 ,          
8.   ,          , 33    
    :
 ()
10
15
20
25
30
35
  ()
35.3
32.4
29.2
26.1
23.2
20.5
Easy2Siksha.com
   2021
/  

(





)
 : 3   :100
 :     ,            
           

1.         :
(a)     (b)      (c)    (d)
 
: ,             
 ,              ,   ,
 , ,  ,            
           ,  
       ,   ,  ,   
  
      ,        
        
(a)   
                
              
 :
Easy2Siksha.com

                 
          ,      
      
  ?
    (     )      
  :
1.       
2.        
  ,    " "        
  
 
              :
󰇣
󰇤
 1:   
2×2   :
1 → 4  
2   → −3
3   → −2
4   → 1
        :
󰇣


󰇤
 2:    
    -  :
Easy2Siksha.com
󰇛󰇜󰇣


󰇤
 
  -           
             , 
      
(b)    
               
     :
󰇣
󰇤
      ,      
              -   
     
     ?
               
      

:
󰇣
󰇤
 :
Easy2Siksha.com
   
          -     
    ,      -    
   ?
       
        
     
,             

()   
          
                
     ,       
󰇟
󰇠
(2    3   )
󰇣


󰇤
(    ₹50 ,    ₹10 )
     ,     
   
      :
      =
     

󰇛󰇜󰇛󰇜

Easy2Siksha.com
    ₹130 
  
    ,   :

       .
 
                  ,
  
( (d)  **
 ,         
      ,              
            

      :
  ,            

      ,      
Easy2Siksha.com
?
:
 (1,2) =  (2,1)
 (1,3) =  (3,1)
 (2,3) =  (3,2)
         
  
          :

 
 
 
              
󷄧󼿒
     ,             , 
    
              

             
           ,    
   
          , 
    
     ,  ,      
                  
         
Easy2Siksha.com
2.(a) 



 


(b)  :
󰇛󰇜󰇛󰇜 w.r.t.
(c)          ?     
  :



:     :          
          ,     
    
 ()  



 1:       :

󰇛
󰇜

 2:     








 :





Easy2Siksha.com
 ()  
󰇛󰇜󰇛󰇜
 1:      :
󰇛
󰇜󰇛
󰇜
󰇛󰇜󰇛󰇜

   :
󰇛
󰇜

 2:     




 :



 ()   
             :
󰇛󰇜


 1:  
     
󰆒
󰇛󰇜

󰇛

󰇜
󰆒
󰇛󰇜

 2:  
󰆒
󰇛󰇜


 6    :

 :
󰇛󰇜󰇛󰇜
Easy2Siksha.com
 ,   :

 3:   
󰆒󰆒
󰇛󰇜

󰇛
󰇜
:
󰆒󰆒
󰇛󰇜󰇛󰇜󰇛negative → maximum󰇜
:
󰆒󰆒
󰇛󰇜󰇛󰇜󰇛positive → minimum󰇜
 4:     
:
󰇛󰇜󰇛󰇜
󰇛󰇜
󰇛󰇜

 , x = 1    = -3 
:
󰇛󰇜󰇛󰇜
󰇛󰇜
󰇛󰇜

 , x = 6    = -128
        ( )
1.    :
󰆒
󰇛󰇜
2.        
󰆒
󰇛󰇜
3.       :
o   ,   
󰆒󰆒
󰇛󰇜
o   ,   
󰆒󰆒
󰇛󰇜
4.             
 

()





Easy2Siksha.com
()



()  :󰇛󰇜


o   = 
o   = 
󷷑󷷒󷷓󷷔  :         ,  -
                
  ""      ,   ,      

3.()      -     
   
()       :
x
2
3
4
5
6
7
8
f
2
4
6
2
3
2
1

:(a)  
󷄧󼿒   
  (),      ,         
       
  :
󷷑󷷒󷷓󷷔  =      ÷   
 (   ):

:
=  
=     
=   
   :
Easy2Siksha.com


:
= 
=     
󷷑󷷒󷷓󷷔:      40, 50, 60, 70  80   :
  = 300,    = 5
  = 300 ÷ 5 = 60
          60 
󷄧󼿒    ()
                  
     
1.        
                 
2.        
   ,          
,       
3.    
               
     
4.        
 , ,          
 
5.    
Easy2Siksha.com
           ,   
   
󽆱     ()
      ,      
1.    
         ,     
󷷑󷷒󷷓󷷔: = 40, 45, 50, 55, 100
          
2.        
       ,      
3.            
 ,          
4.      
-         
:     = 2.4,      2.4    !
󽇐    
        
1.      
          
󰇛
󰇜
            
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2.   
                 
       
3.  
      , ,      ,  
  
󷷑󷷒󷷓󷷔   5   ,   5   
4.        
    ,         
        
()    
󷄧󼿒   ?
  ()            
    :
 
 
 
  
              
   :
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Antilog


 1:  
x
f
 x
f  x
2
2
0.3010
0.6020
3
4
0.4771
1.9084
4
6
0.6021
3.6126
5
2
0.6990
1.3980
6
3
0.7782
2.3346
7
2
0.8451
1.6902
8
1
0.9031
0.9031
 2:    


 3:   
Antilog


Antilog󰇛󰇜
   :

󷄧󼿒 
󷷑󷷒󷷓󷷔  = 4.19 ()
󽇐
              
    ,        ,    
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   ,           - 
   
 , ,            
       ,        4.19  
4.()           :

0–10
1020
2030
3040
5060
  
5
6
9
15
6
()                 
        ?
: ()       
     :

010
1020
2030
3040
4050
5060
6070
  
5
6
9
15
7
6
4
 1:  
 
       :
0–10 → 5
10–20 → 15
20–30 → 25
30–40 → 35
40–50 → 45
50–60 → 55
60–70 → 65
 2:  (f) 
(x)   



(x)
f
fx
010
5
5
25
1020
15
6
90
2030
25
9
225
3040
35
15
525
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4050
45
7
315
5060
55
6
330
6070
65
4
260

 3:    





 ,  ≈ 34.04
 4:     
x
5
15
25
35
45
55
65
f
5
6
9
15
7
6
4
\
x \
29.04
19.04
9.04
0.96
10.96
20.96
30.96

x \
145.20
114.24
81.36
14.40
76.72
125.76
123.84

 5:    






 :    ≈ 13.11
 ()        
 
:  ( )     
   
     
-              
 
:         
     
  ()   
,            
  ,        
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   ?
        :
o        ,      
o          
o             
 ,       ,   
       

         = 13.11
:
o   ,  , 
o   ,        ,   

 : ,          
     

5.()           ,
        
(b)            :

10
11
12
13
14
15

3
5
10
8
5
1
:󷄧󼿒(a)   
           
               
      ,      
              
,     

 ,               
 ,     

       
Easy2Siksha.com
󷷑󷷒󷷓󷷔:
           
    ,        

    

     :
1.  
2.     
3.     
         ,        
    
󷄧󼿒     ( -)
Easy2Siksha.com
                  
󹵙󹵚󹵛󹵜   ?
       :
      
        
  ,        :
       
      
    
 
󹵍󹵉󹵎󹵏󹵐,     
     :
󷷑󷷒󷷓󷷔 <  < 
Easy2Siksha.com
?
              
    
       
 ,         
󷄧󼿒     ( -)
Easy2Siksha.com
      ( )       

   
󹵙󹵚󹵛󹵜   ?
     :
     
      
  :       ,       , 
          

 
󹵍󹵉󹵎󹵏󹵐,     
     :
󷷑󷷒󷷓󷷔 <  < 
:
        
      
,     
󷄧󼿒  
  
  

 

 <  < 
 

 <  < 
Easy2Siksha.com
󷄧󼿒()  '  
       
󹵙󹵚󹵛󹵜:
     :


 
,        ,      :

           ,        
󷄧󼿒  


10
3
11
5
12
10
13
8
14
5
15
1
󷄧󼿒 1:    
    :



  :
X
f

10
3
30
11
5
55
12
10
120
Easy2Siksha.com
13
8
104
14
5
70
15
1
15
   :


:




󷄧󼿒 2:   
        ,   
:
󷷑󷷒󷷓󷷔 10  
󷷑󷷒󷷓󷷔  = 12
,

󷄧󼿒 3:     
      :

󰇛󰇜

          (-- ),    
  :

Easy2Siksha.com
󷄧󼿒 4:  '










󷄧󼿒 
󷷑󷷒󷷓󷷔     = +0.23
󷄧󼿒
   ,      :
󷷑󷷒󷷓󷷔       
  :
  -      
     
  
,      ,    
󷄧󼿒
              
               
       ,       
     
,               
     
  ,          ,   
     , +0.23,         
,    
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6.()            
         
()        :
X
-4
5
6
7
9
12

2
3
4
6
5
8
:  
               
       ,          
      ,         , 
       
󷷑󷷒󷷓󷷔    :              
 -      
  
:             
(  ,       )
 :,             
 :        ,      
     
:-       (   
   )
  
1.  :         
o :          
2.  :      
o :    
3.  :      
o :     
4.  :             (
 = +1  -1)
5.  :          
     
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1.   :    ;       
   
2.      (r):
o         
o :
󰇛󰇜󰇛󰇜
󰇛󰇜
󰇛󰇜
3.   :
o             
o :

󰇛
󰇜
 =  
4.   :
o       
o    
(b)      
   :
X
-4
5
6
7
9
12

2
3
4
6
5
8
  X  Y        :
X  Y   (X  Y  )
X  Y   (Y  X   )
 1:    







 2:      
X

X - X
Y - Ȳ
(X - X)(Y - Ȳ)
(X - X)^2
(Y - Ȳ)^2
Easy2Siksha.com
-4
2
-9.83
-2.67
26.26
96.6
7.13
5
3
-0.83
-1.67
1.39
0.69
2.79
6
4
0.17
-0.67
-0.11
0.03
0.45
7
6
1.17
1.33
1.56
1.37
1.77
9
5
3.17
0.33
1.05
10.05
0.11
12
8
6.17
3.33
20.56
38.07
11.09
󰇛
󰇜󰇛
󰇜
󰇛
󰇜

󰇛
󰇜

 3:  
Y  X  :

󰇛
󰇜󰇛
󰇜
󰇛
󰇜



X  Y  :

󰇛
󰇜󰇛
󰇜
󰇛
󰇜



 4:  
Y  X  :

󰇛
󰇜
󰇛󰇜

X  Y  :

󰇛
󰇜
󰇛󰇜


:     
:, , , , 
:  ,  ,  ,  
       :
o Y  X  :
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o X  Y  :

7.    ?         
 ,          
:   
           ( ,   ) 
                
            100    100 
                
  :
   120 ,           
20%    
  90 ,   10%    
    ,       , 
                
  
    
1.  :
              
       
2.  :
 -              
3.  :
   100   ,       
4.   :
     ,   ,     
       
,     ,          -   
   "" ( )    "" ()
    
Easy2Siksha.com
       ,       : 
   
  
             
                  
:
95
95
95
,      ,         

 ,    ,          
  -    
 :
   
      
      
       
:
         ,           
,           
󷷑󷷒󷷓󷷔     -   
  
           ( )  
            :
  ₹5000
  ₹3000
  ₹500
Easy2Siksha.com
     ,            
         ,       
      
 :
   
     
         
     
 :
   ()
   ()
              
       

 
 

     
  
   

 
 

  
 

 

      
  

     
 
    

󷷑󷷒󷷓󷷔 :
            ,  
        
     
                
               
    
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1.  
               
  :
 (  )
( )
        ,     
󷷑󷷒󷷓󷷔          
2.   
         
  :
     A   B     ,    (B  A
)      
 :
 ,   


:
  2020  2024    
,         
󷷑󷷒󷷓󷷔       
3.   
              ,
      
  :
 ×   = 
               
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  ?
           
󷷑󷷒󷷓󷷔         ,     
   ?
   ,            
            
 
           :




  ,             
     ,          

            
                  
 :
              
 
          
               
   ,      
            
      ,         ,
 ,            
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8.   ,          , 33    
    :
 ()
10
15
20
25
30
35
  ()
35.3
32.4
29.2
26.1
23.2
20.5
:               
           ,      
     33             
          
1.   
 ()
10
15
20
25
30
35
  ()
35.3
32.4
29.2
26.1
23.2
20.5
 33          
2.  1:       
 5-5        
  , .
   

3.  2:      
          
 (x)
y ()
Δy
Δ²y
Δ³y
Δ⁴y
Δ⁵y
10
35.3
-2.9
0.3
-0.2
0.1
-0.1
15
32.4
-3.2
0.1
-0.1
0.0
20
29.2
-3.1
0.0
-0.1
25
26.1
-2.9
-0.1
30
23.2
-2.7
35
20.5
4.  3:     
 :

󰇛󰇜

󰇛󰇜󰇛󰇜

:
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=   (10     → 35.3)

, , ,




5.  4:   







     :
󰇛󰇜󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜󰇛󰇜
󰇛󰇜
󰇛󰇜󰇛󰇜󰇛󰇜

󰇛󰇜
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜

󰇛󰇜
6.  5:    
 :
 :
 :


 :


 :



 :



7.  6:   


 
33         :
 years
   
Easy2Siksha.com
             30  35    
   ,   33            
            ,        
 
       33        22.37      
  30  (23.2 )  35  (20.5 )         
              
        ,     