Q62.Let for some real numbers α and β, a = α −iβ . If the system of equations 4ix + (1 + i)y = 0 and ¯8(cos 2π3 + i sin 2π3 )x + ay = 0 has more than one solution then αβ is equal to (1) 2 −√3 (2) 2 + √3 (3) −2 + √3 (4) −2 −√3
What This Question Tests
Requires setting the determinant of the coefficient matrix to zero for a homogeneous system to have more than one solution, involving calculations with complex numbers and trigonometric values.
Concepts Tested
Formulas Used
Determinant of coefficient matrix = 0 for non-trivial solutions
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📋 Question Details
- Chapter
- Matrices & Determinants
- Topic
- System of Linear Equations
- Year
- 2022
- Shift
- 27 Jun Shift 2
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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