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The number of values of k for which the linear equations  4x+ky+2z=0, kx+4y+z=0, 2x+2y+z=0  possess a non-zero solution is 

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b
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c
3
d
2

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detailed solution

Correct option is D

The condition for a homogeneous system of equations to have a non-zero solution is Δ=0⇒4k2k41221=0⇒4[2]−k[k−2]+2[2k−8]=0⇒8−k2+2k+4k−16=0⇒k2−6k+8=0 ⇒k=2,4


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