Docstoc

t15

Document Sample
t15 Powered By Docstoc
					                                            g~j ( I                  ) RvZxq AsK

1| †h †Kvb wØNvZ mgxKi‡Yi g~jØq n‡Z mgxKiYwU MVb Ki
ev MVb c×wZ eb©bv Ki|
                                                                      A_ev,
   †Kvb wØNvZ mgxKi‡Yi g~jØq                                                                         I                   n‡j †`LvI †h
mgxKiYwU n‡e-
   x 2    x    0        ev, x -(g~j؇qi †hvMdj) x + g~j؇qi ¸bdj = 0
                                              2




2|  Ges  hw`, ax bx  c =0 mgxKi‡Yi g~jØq nq, Z‡e wb‡gœv³
                                  2




AsK¸‡jvi gvb wbb©q Ki|
                                                                                 2
  (i)    (ii)          2
                                2   (iii)      4   7
                                                            7 4   (iv)       
                                                                                              (v) 1      3
                                                                                                                  
                                                                                                                      1
                                                                                                                      3
                                                                                  

  (vi)    4
                4   (vii)  .         . 1
                                      1
                                                       (viii)      2
                                                                             
                                                                           2   2     (ix) 
                                                                                          2               3
                                                                                                               3    (x)    2
                                                                                                                                    2   
                                                                                                                                          2




3| hw`               Ges  ,              x 2  px  q  0          mgxKi‡Yi g~jØq nq, Zvn‡j Ggb
                                                                                                                  1
GKwU mgxKiY wbY©q Ki hvi g~jØq 1 Ges                                                         2
                                                                                                                  2

4| hw`             I ,   x 2  px  q  0            mgxKi‡Yi g~jØq nq, Zvn‡j Ggb GKwU
mgxKiY MVb Ki hvi g~jØq h_vµ‡g  I                                                   2           2




5| hw`  I  ,             ax 2 bx  c  0                mgxKi‡Yi g~jØq nq, Z‡e Ggb GKwU
mgxKiY MVb Ki hvi g~jØq
  (i)  ,
      
                 
                 
                       (ii)       1
                                a  b
                                             ,      1
                                                  a  b

6| hw`  I  ,                x 2  px  q  0          mgxKi‡Yi g~jØq nq, Z‡e Ggb GKwU
mgxKiY MVb Ki hvi g~jØq h_vµ‡g                                                                            Ges
                          nq|
7|          cx 2 bx  a  0          mgxKi‡Yi g~jØq                                              I            nq, Z‡e Giƒc wØNvZ
mgxKiY wbY©q Ki hvi g~j¸‡jv n‡jv-
                    1            1                                                                         1       1       1              1           1
            (i)     
                            ,    
                                       (ii)        
                                                         ,    
                                                                   (iii)     1       ,    1    (iv)      
                                                                                                                 
                                                                                                                     
                                                                                                                         ,   
                                                                                                                                      (v)      2
                                                                                                                                                    ,   2
                                                                                                                                                             (vi)
1               1
   3
        ,    3

                      1                           1
            (vii)    ,               
                                              

8| Ggb GKwU wØNvZ mgxKiY wbY©q Ki hvi g~j¸‡jv n‡jv-
        (i) 6, 7 (ii)                             5 3       ,    5 3      (iii)          3i 2   ,    3i 2            (iv)     4i 2     ,       4i 2    (v)
        p q        ,           p q

                            p q              p q
            (vi)
                            p q              p q


9| 2x 4x  1  0 mgxKi‡Yi g~jØq h_vµ‡g
            2
                                                                                                                  I           n‡j Ggb GKwU
mgxKiY MVb Ki hvi g~jØq h_vµ‡g                                                                         2
                                                                                                                 Ges        2 

10| hw`  ,  h_vµ‡g x 2x  3  0 mgxKi‡Yi g~jØq nq, Zvn‡j wb‡Pi
                                                              2




g~jØq¸‡jv †_‡K mgxKiY¸‡jv wbY©q Ki-
                                                                                                             1          1
                (i)   3 ,             3           (ii)        2  3   ,       3  2    (iii)         1          1

11| hw`                 2 x 2 5 x  6  0             nq Ges  I                         Dnvi `ywU g~j nq Zvn‡j,
                (i)    2
                             2     (ii)    4
                                                   4   (iii)    Gi gvb wbY©q Ki|
                                                                        3   3




12| 2x 3x  7  0 mgxKi‡Yi g~jØq h_vµ‡g  I  n‡j wb‡Pi ivwk¸‡jvi
                2




gvb wbY©qKi|
            (i)  .        1
                                  . 1   (ii)       2
                                                                   
                                                               2   2      
                                                                                2
13| k - Gi gvb wbY©q Ki, hw`-
       (i) 2x 3x  k  0 mgxKi‡Yi g~jØq ci¯úi mgvb nq,
                  2




      (ii) x 4x  k  0 mgxKi‡Yi GKwU g~j 21  3  nq,
              2




      (iii) x 6x  k  0 mgxKi‡Yi GKwU g~j
                  2
                                                            3i 2   nq,
      (iv) x 6x  k  0 mgxKi‡Yi GKwU g~j Ab¨wUi wظb nq,
                  2




14| Ggb GKwU kZ© wba©vib Ki †h,                                 ax 2 bx  c  0     mgxKi‡Yi
GKwU g~j Ab¨wUi n ¸‡bi mgvb n‡e|
15| Ggb GKwU kZ© wba©vib Ki †h,                                 ax 2 bx  c  0     mgxKi‡Yi
g~j؇qi cv_©K¨ 5 nq|
16| hw`               ax 2 bx  c  0     mgxKi‡Yi g~j؇qi AbycvZ r nq, Z‡e †`LvI
†h    r  1  b 2 ev rb 2  acr  12
        r         ac

17| hw`                an 2 bn  c  0     mgxKi‡Yi g~j؇qi AbycvZ            m:n    nq, Z‡e
cÖgvY Ki †h,                    mnb 2  acm  n 2

18| hw`           ax 2 bx  c  0       mgxKi‡Yi g~j؇qi AbycvZ        p:q   nq, Z‡e †`LvI
†h,     ac p  q 2 b 2 pq

19| hw`                 ax 2 bx  c  0    mgxKi‡Yi g~j؇qi AbycvZ           3: 4   nq, Zvn‡j
cªgvY Ki †h, 12b  49ac           2




20|| hw` px qx  q  0 mgxKi‡Yi g~j؇qi AbycvZ
                       2
                                                                        m:n   nq, Z‡e †`LvI
†h,         m
            n
              
                n
                m
                  
                              q
                              p
                                0


21| hw`               bx 2 cx  c  0     mgxKi‡Yi g~j `yBwU      ,        n‡j †`LvI †h,
       c
         0
       b

				
DOCUMENT INFO
Shared By:
Tags:
Stats:
views:0
posted:7/3/2012
language:
pages:4