Q77. x + 1 x x If x x + λ x = 89 (103x + 81), then λ, λ3 are the roots of the equation x x x + λ2 (1) 4x2 + 24x −27 = 0 (2) 4x2 −24x −27 = 0 (3) 4x2 + 24x + 27 = 0 (4) 4x2 −24x + 27 = 0
What This Question Tests
This problem involves evaluating a 3x3 determinant to form a cubic equation, finding a relationship for λ, and then constructing a quadratic equation whose roots are λ and λ^3.
Concepts Tested
Formulas Used
Determinant expansion
Sum and product of roots of a cubic equation
📚 NCERT Sections This Tests
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
3.26 — The Decomposition Of Hydrocarbon Follows The Equation
Chemistry Class 11 · Chapter 3
3.26 The decomposition of hydrocarbon follows the equation k = (4.5 × 1011s–1) e-28000K/T Calculate Ea. 87 Chemical Kinetics Reprint 2025-26
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
📋 Question Details
- Chapter
- Determinants
- Topic
- Properties of determinants
- Year
- 2023
- Shift
- 11 Apr Shift 2
- Q Number
- Q77
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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