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Question

What is the value of c if value of determinant is 16 ?
∣∣ ∣ ∣ ∣∣0−1−2−310−5−6250−c36c0∣∣ ∣ ∣ ∣∣

A
113
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B
1
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C
7
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D
None of these
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Solution

The correct options are
A 1
C 7
Consider, ∣ ∣ ∣ ∣01231056250c36c0∣ ∣ ∣ ∣
R3R32R2,R4R43R2
=∣ ∣ ∣ ∣012310560510c+1206c+1518∣ ∣ ∣ ∣
=(1)∣ ∣123510c+126c+1518∣ ∣
C2C22C1
∣ ∣10350c+126c+318∣ ∣
=(c+3)2
Now, (c+3)2=16
c+3=±4
c=1,7

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