Consider the following statements in respect of the determinant ∆=\left|\begin{array}{ccc}k(k+2) & 2 k+1 & 1 \ 2 k+1 & k+2 & 1 \ 3 & 3 & 1 |\end{array} I. ∆ is positive if k>0. II. ∆ is negative if k< 0. III. ∆ is zero if k=0. How many of the statements given above are correct?

UPSC NDA I 2025 Mathematics Paper

Question : 9 of 120

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Consider the following statements in respect of the determinant
∆=|

|
I. ‌‌∆ is positive if k>0.
II. ‌‌∆ is negative if k<0.
III. ∆ is zero if k=0.
How many of the statements given above are correct?

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k2−1	1
k−1	1

k2−1	2k+1
k−1	k+2