Q61.If a, b, c, d and p are distinct real numbers such that (a2 + b2 + c2)p2 −2p(ab + bc + cd) + (b2+ c2 + d2) ≤0, then (1) a, b, c, d are in A.P. (2) ab = cd (3) ac = bd (4) a, b, c, d are in G.P.
What This Question Tests
This question requires algebraic manipulation of a given inequality to reveal it as a quadratic in 'p' and then analyze its discriminant or complete the square to deduce the relationship between the coefficients.
Concepts Tested
Formulas Used
Discriminant (D) = b^2 - 4ac
(x-y)^2 >= 0
📚 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.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
2.5 — A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 · Chapter 2
2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Conditions for real roots
- Year
- 2012
- Shift
- 12 May Online
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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