Test Index

UPSC NDA Math Model Paper 10

Question : 15 of 120

Marks: +1, -0

Calculate

\begin{vmatrix} x & y-2 & x-y+2 \\ a & b-2 & a-b+2 \\ p & q-2 & p-q+2 \end{vmatrix}

Solution:

D=\begin{vmatrix} x & y-2 & x-y+2 \\ a & b-2 & a-b+2 \\ p & q-2 & p-q+2 \end{vmatrix}

D=\begin{vmatrix} x & y-2 & x \\ a & b-2 & a \\ p & q-2 & p \end{vmatrix}

+\begin{vmatrix} x & y-2 & -y+2 \\ a & b-2 & -b+2 \\ p & q-2 & -q+2 \end{vmatrix}

In first Column 1 and 3 are same so its value is zero

D = 0+\begin{vmatrix} x & y-2 & -(y-2) \\ a & b-2 & -(b-2) \\ p & q-2 & -(q-2) \end{vmatrix}

D = -\begin{vmatrix} x & y-2 & (y-2) \\ a & b-2 & (b-2) \\ p & q-2 & (q-2) \end{vmatrix}

The column 2 and 3 are same so the value is zero⇒ D = 0

Go to Question:

Prev Question

Next Question