Test Index

VITEEE 2019 Paper

Section: Mathematics

© examsnet.com

Question : 95 of 125

Marks: +1, -0

If a, b, c are in A. P., then the value of

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

is:

3
-3
0
None of these

Solution:

Given a, b, c are in A.P.

∴ 2b = a + c.....(i)

Now,

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

[Applying

R_2 \rightarrow 2 R_2

]

= \frac{1}{2} \begin{vmatrix} x+1 & x+2 & x+a \\ 2x+4 & 2x+6 & 2x+2b \\ x+3 & x+4 & x+c \end{vmatrix}

= \frac{1}{2} \begin{vmatrix} x+1 & x+2 & x+a \\ 2x+4 & 2x+6 & 2x+(a+c) \\ x+3 & x+4 & x+c \end{vmatrix}

[using equation (i)]

= \frac{1}{2} \begin{vmatrix} x+1 & x+2 & x+a \\ 0 & 0 & 0 \\ x+3 & x+4 & x+c \end{vmatrix} = 0

[Applying

R_2 \rightarrow R_2 - (R_1 + R_3)

]

© examsnet.com

Go to Question:

Prev Question

Next Question