# If ( )( )( ) ( )( )( ) 2 22 222 222 222 abc abc a b c k a b c, 0 111 abc +l +l +l = l l ¹ -l -l -l then k is equal to:

Question:

If

$$\left|\begin{array}{ccc} \mathrm{a}^{2} & \mathrm{~b}^{2} & \mathrm{c}^{2} \\ (\mathrm{a}+\lambda)^{2} & (\mathrm{~b}+\lambda)^{2} & (\mathrm{c}+\lambda)^{2} \\ (\mathrm{a}-\lambda)^{2} & (\mathrm{~b}-\lambda)^{2} & (\mathrm{c}-\lambda)^{2} \end{array}\right|=\mathrm{k} \lambda\left|\begin{array}{ccc} \mathrm{a}^{2} & \mathrm{~b}^{2} & \mathrm{c}^{2} \\ \mathrm{a} & \mathrm{b} & \mathrm{c} \\ 1 & 1 & 1 \end{array}\right|, \lambda \neq 0$$

then $\mathrm{k}$ is equal to:

1. $4 \lambda a b c$

2. $-4 \lambda a b c$

3. $4 \lambda^{2}$

4. $-4 \lambda^{2}$

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Matrices and Determinants chapter.
JEE Main Previous Year Online April 12, 2014

Solution:

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