Given a,b,c are in A.P. Then determinant in its simplified form is

\begin{vmatrix} x+1 &x+2 & x+a \\ x+2& x+3&x+b \\ x+3 & x+4 & x+c\end{vmatrix} =?

 

  • Option 1)

    x^{3}+3ax+7c

  • Option 2)

    0

  • Option 3)

    15

  • Option 4)

    10x^{2}+5x+2c

 

Answers (1)

As learnt in

 

Property of determinant -

If two rows ( or two columns ) in a determinant have corresponding elements that are equal , the value of determinant is equal to zero 

-

 

 

 

When the numbers of row are in AP, then the value of determinant = 0 


Option 1)

x^{3}+3ax+7c

This solution is incorrect

Option 2)

0

This solution is correct

Option 3)

15

This solution is incorrect

Option 4)

10x^{2}+5x+2c

This solution is incorrect

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