Q79.The least value of the product xyz (such that x, y and z are positive real numbers) for which the determinant x 1 1 1 y 1 is non-negative is 1 1 z (1) −1 (2) −16√2 (3) −8 (4) −2√2
What This Question Tests
This question requires calculating a 3x3 determinant and setting it to be non-negative. It then involves using the AM-GM inequality to relate the product xyz to the sum x+y+z, leading to a cubic inequality. The positive real number constraint on x,y,z contradicts the negative options, indicating a potential ambiguity in the problem's formulation or intended scope (if x,y,z could be any real numbers).
Concepts Tested
Formulas Used
det(A)
(x+y+z)/3 >= (xyz)^(1/3)
📚 NCERT Sections This Tests
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2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
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📋 Question Details
- Chapter
- Determinants
- Topic
- Evaluation of Determinants
- Year
- 2015
- Shift
- 10 Apr Online
- Q Number
- Q79
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants; Class 11 Mathematics Ch 6: Linear Inequalities
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