Q51.The set of all real values of λ for which the quadratic equation (λ2 + 1)x2 −4λx + 2 = 0 always have exactly one root in the interval (0, 1) is : (1) (−3, −1) (2) (0, 2) (3) (1, 3] (4) (2, 4]
What This Question Tests
This question tests the analytical understanding of root location for a quadratic equation within a specific interval, requiring evaluation of the function at endpoints and considering boundary cases.
Concepts Tested
Formulas Used
f(x) = ax² + bx + c
f(x₁)f(x₂) < 0 (for one root between x₁ and x₂)
Discriminant D = b² - 4ac
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
5.16 — Draw Figure To Show The Splitting Of D Orbitals In An Octahedral Crystal Field.
Chemistry Class 11 · Chapter 5
5.16 Draw figure to show the splitting of d orbitals in an octahedral crystal field.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
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.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Location of Roots
- Year
- 2020
- Shift
- 03 Sep Shift 2
- Q Number
- Q51
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Quadratic Equations
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