The correct option is B 1
∣∣
∣∣y+zxyz+xzxx+yyz∣∣
∣∣=(x+y+z)∣∣
∣∣211z+xzxx+yyz∣∣
∣∣by R1→R1+R2+R3=(x+y+z)∣∣
∣∣111xzxxyz∣∣
∣∣; by C1→C1−C2=(x+y+z).{(z2−xy)−(xz−x2)+(xy−xz)}=(x+y+z)(x−z)2⇒k=1.
Trick : Put x=1, y=2, z=3, then
∣∣
∣∣512431323∣∣
∣∣=5(7)−1(12−3)+2(8−9)=35−9−2=24 and (x+y+z)(x−z)2=(6)(−2)2=24
∴k=2424=1.