MATHS
         BOOKS NCERT MATHS (ENGLISH)
                 DETERMINANTS
  Short Answer Type Questions
             2
           ∣               ∣
            x −x+1 x−1
   1. evaluate: ∣          ∣
           ∣  x +1    x +1∣
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                ∣ a + x    y       z   ∣
                ∣                      ∣ 
    2. evaluate: ∣ x     a +y      z   ∣ 
                ∣                      ∣
                ∣  x       y     a +z∣
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                         2     2
                  0    xy   xz
                ∣                ∣
                ∣                ∣ 
                   2           2
    3. evaluate:  x y   0    yz
                ∣                ∣ 
                ∣                ∣
                   2     2
                ∣ x z  zy     0 ∣
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                ∣  3x    −x+y −x+z∣
                ∣                          ∣ 
    4. evaluate: ∣ x − y    3y      z − y ∣ 
                ∣                          ∣
                ∣ x − z   y − z       3z   ∣
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                   x +4       x        x
                  ∣                         ∣
                  ∣                         ∣ 
     5. evaluate:    x      x +4       x
                  ∣                         ∣
                  ∣  x        x      x +4∣
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                   a −b−c           2a            2a
                  ∣                                      ∣
                  ∣                                      ∣ 
     6. evaluate:      2b       b − c − a         2b
                  ∣                                      ∣
                  ∣    2c            2c       c − a − b∣
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                      2 2
                   ∣ y z    yz   y + z ∣
                   ∣                    ∣ 
                      2 2
     7. prove that:∣                    ∣ = 0
                     z x    zx z+x
                   ∣                    ∣
                      2 2
                   ∣ x y    xy x+y∣
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                 y + z    z      y
                ∣                    ∣
                ∣                    ∣ 
    8. prove that: z    z + x    x     =4xyz
                ∣                    ∣ 
                ∣                    ∣
                ∣  y      x    x +y∣
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    9. Using properties of determinants, prove that 3 2 (a 1) 3 3
    1 2a 1 a 2 1 a 2a 2a
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    10.     If     A+B+C=0,      then      prove      that
           1    cosC cosB
        ⎡                    ⎤
    Det cosC      1    cosA    =0
        ⎢                    ⎥
        ⎣                    ⎦
         cosB cosA       1
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