1
Easy2Siksha
GNDU  -2022
  
  - II
 :    : 100
:               
 
-
1.             
     
2. 
      ?     ?    -
      
-
3. (i)   ?       
(ii)     ,      :

0-10
10-20
20-30
30-40
40-50
50-60
f
8
15
22
20
10
5
2
Easy2Siksha
4. (i)   ? -      
(ii)           :
 


0-10
10-20
20-30
30-40
40-50
50-60
 

12
17
23
39
16
3
-
5. (i)      ,    ?
(ii)            :





52
53
42
60
45
41
38
25
27





65
68
43
38
77
48
30
25
50
6. (i) 
     ?     
(ii)        :

6
2
10
4
8

9
11
5
8
6
3
Easy2Siksha
-
7. (i)          ?
(ii)            :


2010

2010

2011

2011
20
12
30
14

13
13
15
20

12
10
20
15
8
6
10
4

5
8
5
6
8. (i).        -    
(ii)           :

2001
2002
2003
2004
 

38
45
65
68

2005
2006
2007
2008
 

75
87
60
95
4
Easy2Siksha
GNDU  -2022
  
  - II
 :    : 100
:               
 
-
1.             
     
:   ?
                
      ,    ,  ,  ,
               
   -            
 
     ,    
     
       
  :
    
-     
     
      
            
5
Easy2Siksha
  :
     ,           
     :
1.  :           
              
   ,           
                ,  
      
2.  :        '    
                 
            ,   
              
-     :
1.    :
     
      
    
      :     
        -     
 ,            
2.    :
    
      
     
   : -19   ,   
   ,         ,   
       
3. :
      
 
   
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  :            
           
           
4.  :
  
  
  
   : - -     
       '         
  
5. :
  
  
    
  :       
     ()    
6.  :
   
   
   
    :      
              
  :
1.  :         
   '    , 
    
       :        
       ,       

2.   :      ,   
             
 :         
      
     
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3.   :        
         :     
             
4.  :         
     :      
              
  
5.  :         -  
     :       
        
6.   :  -          
  :     '     
       
7.  :           
 :           

- :
          
    :
             
         '  
             
   
      
 
         
  :
   ,     :
         
      '   
       

   
 

 ,     
          
              
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        ,    , -  
   
   
    ,     , 
      ,  , -     
 
2. 
      ?     ?    -
      
:    ?           
                  -
 ,    -  
       
          ,  
      
 
  :
1.   
    ,          
  
 
      : ? ? ?
 : "    
, - 2023"  " 
"   
2.    
     ,     
     '     ( , "
( )", " (₹ )")
         ' 
 
3.   
        (  ,   ,
  )
         (    
)
        
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4.    
       
              
           
5.   
         
               
(  '   )
       
  :
1.           ,     

 
:
    (2023)
   
 150
 175
  325
2.        
 :
:
        (2023)
   
 85% 82% 78%
 83% 86% 82%
 84% 84% 80%
3.            
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:
   2023
          
       
 250 300 50 50 100 50
. 300 275 60 60 120 40
B.Sc 200 225 45 45 90 30
4.      
       -   

:
      
   
0-20 5 5%
21-40 15 15%
41-60 45 45%
61-80 25 25%
81-100 10 10%
  100 100%
5.     -         
:
   (2021-2023)
     
2021 300 250 200 750
2022 325 275 225 825
2023 350 300 250 900
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   :
1.  
     
 
  -        
         
2.  
         
         
     
 
3.  
       
         
-     
   :
1.   
          
  ,     
2.  
     
       
     
3.  
     
     
       
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Easy2Siksha
 :
1.   
,     

  
    
2.  
        
    
      
3.    
        
      
  '  100%    
4.   
  
     
     -    
    
 ,    
 :
  
   
   
  
  
 
 ,      '      
                
   
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Easy2Siksha
-
3. (i)   ?       
(ii)     ,      :

0-10
10-20
20-30
30-40
40-50
50-60
f
8
15
22
20
10
5
ANS:  1:  
                     
   ""  ""             
           , "     ?" 

            
       :
1.    (  )
         ""  
                 
 :       85, 90, 88, 92,  95  
     : (85 + 90 + 88 + 92 + 95) ÷ 5 = 90
:
o      
o         
o     
:
o      ()
o                 
2. 
          
       ,     
    ,        
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Easy2Siksha
:  2, 3, 4, 7, 9    : 2, 3, 4, 7, 9  = 4 ( )
:
o      

o        
 
:
o        
 
o      
3. 
         
    ,  ,    
  
:  2, 3, 3, 4, 4, 4, 5, 6  = 4 (    )
:
o        
o   
o       
:
o           
o      
o     '  

4.   
             
            
:   :  (40% ): 85  (30% ): 92 
 (30% ): 88    = (85 × 0.4) + (92 × 0.3) + (88 × 0.3) = 88
5.  
,  ,       
      n       
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Easy2Siksha
:       10%, 20%,  30%   
 = ((1.1 × 1.2 × 1.3)) - 1
       ' 
 2:     
(ii)     ,      :

0-10
10-20
20-30
30-40
40-50
50-60
f
8
15
22
20
10
5
: ,      
             :
  (X)
 (f)
0-10
8
10-20
15
20-30
22
30-40
20
40-50
10
50-60
5
 , ,     -- 
1. 
 ( )         :
:
     
      
-- :
1.       (x) :        
  :
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Easy2Siksha
        :
o 0-10:
o 10-20:
o 20-30:
o 30-40:
o 40-50:
o 50-60:
2. f, x,     :
  (X)
 (f)
  (x)
0-10
8
5
40
10-20
15
15
225
20-30
22
25
550
30-40
20
35
700
40-50
10
45
450
50-60
5
55
275
3.   :
4.    :
2. 
                , 
 
    :
:
=     
=     
=      
=    
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Easy2Siksha
=  
-- :
1. :
2.  :
3.     :         40 
      
o 0-10:   = 8
o 10-20:   = 8 + 15 = 23
o 20-30:   = 23 + 22 = 45
  20-30  
      40    
4.   :
o (20-30   )
o (20-30    )
o (20-30  )
o ( )
3. 
            ,       
  :
:
=     
=    
=       
=       
=  
-- :
1.     :         
o     22 ,     20-30 .
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Easy2Siksha
2.   :
o (20-30   )
o (20-30  )
o (10-20  )
o (30-40  )
o ( )

:28
:27.73
:27.78
     -        ,  
       
4. (i)   ? -      
(ii)           :
 


0-10
10-20
20-30
30-40
40-50
50-60
 

12
17
23
39
16
3
:  :   
  ?
       
            
             ()        
,       ""  ""  
 , 10          , 
      50       ,  10  90  
           ,     
 
    
  
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Easy2Siksha
       :
1. :                

2. :              
  
 -         ',      
 :
1.    
2.    
1.    
          
       
     :
a) 
                     
 
:
 =    -     
:
     : 15, 20, 25, 30, 35,  : 35 - 15 = 20
:
     '          , 
    
 
b)   ( )
                 
     
:
 = (     ) / (  )
:
    5, 10, 15    (5 + 10 + 15) ÷ 3 = 10
  :|5 - 10|, |10 - 10|, |15 - 10| = 5, 0, 5.   = (5 + 0 + 5)
÷ 3 = 3.33
20
Easy2Siksha
:
      '   ,      
 
c)    
         , 
     
   
:
           
:
 = (     ) / (  )
  (SD):
          '    

       ,         
:
 '  :2, 4, 6. = (2 + 4 + 6) ÷ 3 = 4.  = [(2 - 4)² + (4 - 4)² + (6 - 4)²] ÷ 3 =
(4 + 0 + 4) ÷ 3 = 2.67.   = √2.67 ≈ 1.63
- :
 
  '      ,       
,      ()
2.    
           ,  -  
        
 
a)   
                 
:
   = (   -     ) ÷ (   +     )
:
  10  90 ,     = (90 - 10) ÷ (90 + 10) = 80 ÷ 100 = 0.8
b)   (CV)
CV                  
         
:
CV = (  ÷ ) × 100
21
Easy2Siksha
:
 A: = 50, SD = 5. CV = (5 ÷ 50) × 100 = 10%
 B: = 100, SD = 20. CV = (20 ÷ 100) × 100 = 20%
: B    
  
?
1.    :
 ,        
 
2.   :
 -          , 
  -    
3.  :
 ,  ,           
 
1. :
         (     ), 

   ,          ,  
 
 
2. :
 ,  ,     A  85-90     ,
  B   50-95          , B   
   
3.  :
             
         
 ,    


               ,
 , ,  ,        
 , 
             , ,
   ,           
     
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Easy2Siksha
(ii)           :
 


0-10
10-20
20-30
30-40
40-50
50-60
 

12
17
23
39
16
3
: 2:     
            
 1:   
:N = 110 ΣfX = 3,140 ΣfX² = 107,750
 2: (X
) X
= ΣfX/N = 3,140/110 = 28.55     
 3:    
(σ) : σ = √[(ΣfX²/N) - (X
)²]
σ = √[(107,750/110) - (28.55)²]
σ = √(979.55 - 814.90) σ = √164.65
σ = 12.83  
 4:   (CV)   
CV = (σ/X
) × 100
CV = (12.83/28.55) × 100
CV = 44.94%
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Easy2Siksha
:
1. 12.83      
  , ,    
       28.55      
 
2. 44.94%               
    ':
o CV <25%   
 
o 25-75%     
 
o CV > 75%  
 
  ,    
 ,   -  
    
         :
  -   
-      
-    
-  
-      :
  ,        
 ,       
   ,       
 ,             
     
 ,          ,        
      
            
  
 ,     
      
24
Easy2Siksha
-
5. (i)      ,    ?
(ii)            :





52
53
42
60
45
41
37
38
25
27





65
68
43
38
77
48
35
30
25
50
:  1:   
       ,          
   
      1  10     
 
        (      
 ),         
     ( 
       ),      
    :
   ?                
      ()         ' 
   :
1.      

2.    (           
)
3.     
  
4.      ()        

- :
1. 
-       
25
Easy2Siksha
           
        
2. 
-       
            
             
3. 
-  ( ,    ,  )   '  
  
         
-         
4.  
-         
          
-         
5.  
-      '      
          
       
   :
1. 
     
     

          
2.
    
   
-      
   
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3. 
              
     

           
:
1.  
             
      


  2.Ties
      ,      
     
3.   
      
  
         
   :
1.   
     
-1  +1  
Pearson's correlation     
2.   
 
       
      
 2:       
 ,            
  
,             :
:            :
: 85, 90, 75, 95, 70
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Easy2Siksha
: 88, 85, 80, 92, 75
   :
1.         : 3, 2, 4, 1, 5 : 2, 3, 4, 1, 5
2.  (d)   
3.      (d²)
4.    
5.   : rs = 1 - (6Σ)/(n(n²-1))  n    
      :
+1.0     
 
-1.0     
 
0   

 
     -  
 
  :
0.00  0.19:   
0.20  0.39:  
0.40  0.59:  
0.60  0.79:  
0.80  1.00:   
            , , ,
         -   
          
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(ii)            :





52
53
42
60
45
41
37
38
25
27





65
68
43
38
77
48
35
30
25
50
:    :
   -           
                 
               ,
      ,        
        -- 
1.  
         :
X    :52, 53, 42, 60, 45, 41, 37, 38, 25, 27
Y    :65, 68, 43, 38, 77, 48, 35, 30, 25, 50
      -  (X  Y)       
   
2.   
       ,   X  Y    
        1          
X  :
o   :25, 27, 37, 38, 41, 42, 45, 52, 53, 60
o   :
25 = 1
27 = 2
37 = 3
29
Easy2Siksha
38 = 4
41 = 5
42 = 6
45 = 7
52 = 8
53 = 9
60 = 10
 , X  :8, 9, 6, 10, 7, 5, 3, 4, 1, 2
Y  :
o   :25, 30, 35, 38, 43, 48, 50, 65, 68, 77
o   :
25 = 1
30 = 2
35 = 3
38 = 4
43 = 5
48 = 6
50 = 7
65 = 8
68 = 9
77 = 10
 , Y  :8, 9, 5, 4, 10, 6, 3, 2, 1, 7
3.        
, 
             

 
 
 (d)
d^2
8
8
0
0
9
9
0
0
30
Easy2Siksha
6
5
1
1
10
4
6
36
7
10
-3
9
5
6
-1
1
3
3
0
0
4
2
2
4
1
1
0
0
2
7
-5
25
 ,     (∑d^2):
∑d^2 = 0 + 0 + 1 + 36 + 9 + 1 + 0 + 4 + 0 + 25 = 76
4.       
      (ρ)   :
ρ = 1 - [(6 ∑d^2) / (n(n^2 - 1))]
:
∑d^2 =    
n =    (  , 10)
   :
ρ = 1 - [(6 * 76) / (10(10^2 - 1))]
ρ = 1 - [(456) / (10 * 99)]
ρ = 1 - [456 / 990] ρ = 1 - 0.46 ρ = 0.54
5.    
   -  (ρ) 0.54     X  Y     
    
    ,       X
     , Y       ,    
      
      ,   ,       
  
               
31
Easy2Siksha
               
         ,     (1  )  
     ,     (-1  )     
, 
 0   
 
              ,    
                 
  (        ),       
 ,        ,   - 
            ,   
   '    ,       
      
?
       '    :
        () 
   -  '  
   '  
       
 

               
      , 
  -      
-               
    ,  -        
     
6. (i) 
     ?     
(ii)        :

6
2
10
4
8

9
11
5
8
6
:   :        
            
     
                  ,
   ,      ,     
32
Easy2Siksha
    '          
  
      "  - "     
       :
        
           
        
2.  
   :
1. X  Y     (X    Y    )
2. Y ' X    (Y    X    )
  :
Y = a + bX (Y  X)
X = a + byY (Y  X)
:
'a' Y-  (  Y-    )
'b'   ( X 1      Y   )
3.     
            :
X: 6, 2, 10, 4, 8
Y: 9, 11, 5, 8, 6
 1:    ()
X   (X
) = (6 + 2 + 10 + 4 + 8) ÷ 5 = 30 ÷ 5 = 6
Y (Ȳ) = (9 + 11 + 5 + 8 + 6) ÷ 5 = 39 ÷ 5 = 7.8  
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 2:    
∑=30 ∑=39 ∑=220 ∑=327 ∑=206
 3: 
    :
∑X = 30
∑Y = 39
∑X² = 220
∑Y² = 327
∑XY = 206
n = 5 (  )
 4:     
X (byx) ' Y :
byx = (n∑XY - ∑X∑Y) ÷ (n∑X² - (∑X)²)
= (5(206) - 30×39) ÷ (5(220) - 30²)
= (1030 - 1170) ÷ (1100 - 900)
= -140 ÷ 200 = -0.7
X  Y (bxy) :
bxy = (n∑XY - ∑X∑Y) ÷ (n∑Y² - (∑Y)²)
= (5(206) - 30×39) ÷ (5(327) - 39²)
= -140 ÷ (1635 - 1521) = -140 ÷ 114
= -1.228
 5:     (a)
X ' Y :
a = Ȳ - byx(X)
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= 7.8 - (-0.7)(6)
= 7.8 + 4.2 = 12
X  Y :
a = X - bxy(Ȳ)
= 6 - (-1.228)(7.8)
= 6 + 9.578
= 15.578
 6:  
1. X  Y   : Y = 12 - 0.7X
2. Y  X    : X = 15.578 - 1.228Y
:
     X  Y     
 
X     , Y 0.7   ( )
Y     , X 1.228  ( )   
4.     
       :
1. 
X    Y       (Y = 12 - 0.7X    )
2. 
Y    X       (X = 15.578 - 1.228Y   )
 :
 X = 7,   Y = 12 - 0.7(7) = 7.1
 Y = 10,   X = 15.578 - 1.228(10) = 3.298
5.     
6.    - -        

7.     (X
, Ȳ)   
8. -      '          
 
9.                 
  
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10.  
    -     :
    '   
   '   
    '      
   '     
          
           ' 
          ,  ,  
              
 
-
7. (i)          ?
(ii)            :


2010

2010

2011

2011
20
12
30
14

13
13
15
20

12
10
20
15
8
6
10
4

5
8
5
6
ANS:  :   
   ?
                 
       , ,      
 -             
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  '       
      (   
)        ,           
               
      ,            
    ,  
           
 ,  
          
    
1.  :      
 ,    
  ,      
 
2.  :         ,    
        
3.  :    (    )    
 (     )     
4.  :          ,   
      
   
1.  :         ( , 
 )
2.  : ,          
3.  :        
   
   ,        '  
         
1.     ( )
               
               ,  
,        
:    (CPI)        
         ,     
-     
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  
:
o    ,        
 
o             
    
:    
         
  
          ,          
 '   
2.     
       ,      '  
      , ,   
:   6% ,    , ,    
  6%           (WPI)  
     
  
:
o              

o            
 
:          -     

     ( )   
3.   
              ,
    ,          
     
:   ()       
        
  
:
o        
o   
      '  
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4.      
    ,    -    
           
:  CPI 5%  ,         
   5%           

  
:
o       
 
o        
 
:               
             " "  
5.   
       ,        
       
:            
           
  
:
o         
o         
:               
6.       
  -            ,
            
:     -       
     
  
:
o         
o     
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Easy2Siksha
7.   
   (IPI)       
 ,            
 
    
  
:
o         .
o        
8.    
          ,     
       
:       '    ,
         

             
       ,     ,   
  ,           

              ,
        
 , ,     
    
 
(ii)            :


2010

2010

2011

2011
20
12
30
14

13
13
15
20

12
10
20
15
8
6
10
4

5
8
5
6
40
Easy2Siksha
:     
                
               
       -      
  --            

  (  )

       :
 1: 
            
 :
  (L)
Laspeyres    (2010)         :
:
P1 = 2011  
P0 = 2010  
Q0 = 2010  
  (P)
Paasche    (2011)         :
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Easy2Siksha
:
Q1 = 2011  
 2:   (L)   
      
42
Easy2Siksha
 
          138.87 
43
Easy2Siksha
     

1.  : Laspeyres  Paasche       
2.  :            ,
 138.87        2010  2011     38.87%  
 
8. (i).        -    
(ii)           :

2001
2002
2003
2004
 

38
45
65
68

2005
2006
2007
2008
 

75
87
60
95
:    
                ,   '
  ',   , ,    ,   
 ,      ,         
   
    
         '      
    
          
   
        ,         :  ,
 ,  ,           
        
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1.  (-  )
        ,     
    ,   
      :
  :           
  :          

 :           

    
       -   
 
:
   
10              
 '           ,        
      
 
2.  
      -       '  ,
  '       ,  ,     
              
 
:
       '       
   ,          
    ,          

             
:
                 -
                

   ,      
3.  
              ,   '
                 
    

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:
              
    -,         
     
   ,           
  
  ,  ,      '   
:
         
    ( ),  

    ()  -       
  
     '      
4.  
    -         
           
 
:
         .
-19        
-           

     
  ,    "" 
             
:
         '    .   
   
     
    
          :
1.   :  =  +  +  + 
o             
2.  :   =  ×  ×  × 
o            
 ,  
        ,    
 :
46
Easy2Siksha
            .
           ' -
         
          
  
 :    
          '  :
1. :5  ,        -   
2.  :         '    
            
3.  :             
             
4.  :       
 ,   
   
 
    ,        , , 
      
    
        :
1.  :     ,       
  
2.  :,        
3.   :       

                   -
 ,  ,  ,    -
  
,                 
 ,      ,      
 ,              
   
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Easy2Siksha
(ii)           :

2001
2002
2003
2004
 

38
45
65
68

2005
2006
2007
2008
 

75
87
60
95
:         
    ,               
                  
              ,  

           ,  
   
        
  ,   2001  2008      ( )   :

                 
     '     :
Y=a+bX
:
Y    (   ),
X    () ,
a   (      X=0X = 0X=0),
b   (       )
     
 1:  (X)  
   , 
            
  
  2001, 2002,      , 
X=−3,−2,−1,0,1,2,3,4
48
Easy2Siksha
     0    (2004) 
     

    
 2: a  b   
a  b   :
:
ΣXY: X  Y    ,
ΣX2: X    ,
ΣY:  Y    ,
n:     
49
Easy2Siksha
     
   
         
    
,                
       ,     
    
    
12.27   ()      ₹12.27    66.63 
 (a)   
   X=0X = 0X=0 (  )
50
Easy2Siksha

                  
   '          -  
 (  2007,     ),        ,  
              
    ,    , ,      !
:      Ai      ( )       
        , 
  '         