Q. The value of $∣ ∣ 1^{2} 2^{2} 3^{2} 2^{2} 3^{2} 4^{2} 3^{2} 4^{2} 5^{2} ∣ ∣$ is:

2207 224 KEAMKEAM 2001 Report Error

A

8

B

$- 8$

C

400

D

1

E

0

Solution:

$∣ ∣ 1^{2} 2^{2} 3^{2} 2^{2} 3^{2} 4^{2} 3^{2} 4^{2} 5^{2} ∣ ∣$ $= ∣ ∣ 149491691625 ∣ ∣ = ∣ ∣ 149357579 ∣ ∣$ $C_{2} \to C_{2} - C_{1} an d C_{3} \to C_{3} - C_{2}$ $= ∣ ∣ 149357222 ∣ ∣$ $C_{3} \to C_{3} - C_{2}$ $= ∣ ∣ 135322200 ∣ ∣$ $R_{2} \to R_{2} - R_{1} R_{3} \to R_{3} - R_{2}$ $= 2 ∣ ∣ 3522 ∣ ∣ = 2 (6 - 10) = - 8$