Q61.If a ∈ R and the equation −3(x − [x])2 + 2(x − [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval (1) (−2, −1) (2) ( −∞, −2) ∪(2,∞) (3) (−1, 0) ∪(0, 1) (4) (1, 2)
What This Question Tests
This question tests the understanding of the fractional part function and its properties within a quadratic equation, requiring the analysis of conditions for its roots to avoid integral solutions.
Concepts Tested
Formulas Used
{x} = x - [x]
Quadratic formula for roots
📚 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.
9.18 — For Fixed Distance S Between Object And Screen, The Lens Equation
Physics Class 12 · Chapter 9
9.18 For fixed distance s between object and screen, the lens equation does not give a real solution for u or v if f is greater than s/4. Therefore, fmax = 0.75 m.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Fractional part function, roots of quadratic equation
- Year
- 2014
- Shift
- 06 Apr
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Quadratic Equations
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