Question
Let p=(x+y+z) and q=xyz. If vmatrix x & 1 & 1 \\ 1 & y & 1 \\ 1 & 1 & z vmatrix is positive, then which one of the following is correct ?
NDA
Mathematics
Determinants
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. q>p
- B. q+1>p
- C. q+2>p
- D. q+2 p
Answer
C. q+2>p
Step-by-step solution
Expanding the given determinant along the first row and setting it greater than zero: x(yz - 1) - 1(z - 1) + 1(1 - y) > 0 xyz - x - z + 1 + 1 - y > 0 xyz - (x + y + z) + 2 > 0 Substituting p = x + y + z and q = xyz: q - p + 2 > 0 q + 2 > p Answer: q+2>p
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