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  • Provide solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 18

Provide solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 18

Answers (1)

Answer:

Correct option (a)

Hint:

If a,b,c are in A.P \Rightarrow 2b=a+c

Given:

If a,b,c are in A.P

        Let \: \: \Delta= \begin{vmatrix} x+2 &x+3 &x+2a \\ x+3 &x+4 &x+2b \\ x+4 &x+5 &x+2c \end{vmatrix}

We have to find the value of given determinant \Delta

Solution:

        \Delta= \begin{vmatrix} x+2 &x+3 &x+2a \\ x+3 &x+4 &x+2b \\ x+4 &x+5 &x+2c \end{vmatrix}

If a,b,c are in A.P \Rightarrow 2b=a+c

        \Rightarrow \Delta= \begin{vmatrix} x+2 &x+3 &x+2a \\ x+3 &x+4 &x+a+c \\ x+4 &x+5 &x+2c \end{vmatrix}

Applying R1→R1-R2 ; R3→R3-R2

        \Rightarrow \Delta= \begin{vmatrix} -1 &-1 &a-c \\ x+3 &x+4 &x+a+c \\ 1 &1 &c-a \end{vmatrix}

Applying R1→R1+R3

        \Rightarrow \Delta= \begin{vmatrix} 0 &0 &0 \\ x+3 &x+4 &x+a+c \\ 1 &1 &c-a \end{vmatrix}

Here R1 is zero

        \Rightarrow \Delta= 0

Hence \: \: \begin{vmatrix} x+2 &x+3 &x+2a \\ x+3 &x+4 &x+2b \\ x+4 &x+5 &x+2c \end{vmatrix}=0

Posted by

Gurleen Kaur

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