Q85.If the point on the curve y2 = 6x, nearest to the point (3, 32 ) is (α, β), then 2(α + β) is equal to _________.
What This Question Tests
This problem requires finding the point on a given curve that is nearest to a fixed point, which is a classic application of derivatives for minimization of distance.
Concepts Tested
Formulas Used
Distance formula: D² = (x2-x1)² + (y2-y1)²
Derivative for minimization: d(D²)/dx = 0
📚 NCERT Sections This Tests
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.
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?
2.3 — Two Charges 2 Mc And –2 Mc Are Placed At Points A And B 6 Cm
Physics Class 11 · Chapter 2
2.3 Two charges 2 mC and –2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Distance minimization
- Year
- 2021
- Shift
- 20 Jul Shift 2
- Q Number
- Q85
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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