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Question

If pλ4+qλ3+rλ2+sλ+t=∣ ∣ ∣λ2+3λλ1λ+3λ2+12+5λλ3λ23λ+43λ∣ ∣ ∣
then p is equal to

A
5
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B
8
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C
3
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D
2
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Solution

The correct option is B 8
We divide LHS by λ4 and C1 by λ2 ,C2 by λ and C3 by λ on the RHS to obtain ,
p+q(1λ)+r(1λ)2+s(1λ)3+t(1λ)4
=∣ ∣ ∣1+3/λ11/λ1+3/λ1+1/λ22/λ+513/λ13/λ21+4/λ23∣ ∣ ∣
taking limit as λ we get
p=∣ ∣111151113∣ ∣=∣ ∣111040002∣ ∣=8 ---------[using R2R2R1,R3R3R1]

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