Q88.A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then ( π4 + 1)k is equal to
What This Question Tests
This is an optimization problem where the sum of areas of a square and a circle, formed from a fixed length of wire, needs to be minimized using calculus.
Concepts Tested
Formulas Used
Area of square = s²
Area of circle = πr²
Circumference of circle = 2πr
Perimeter of square = 4s
📚 NCERT Sections This Tests
8.1 — Figure 8.5 Shows A Capacitor Made Of Two Circular Plates Each Of
Physics Class 11 · Chapter 8
8.1 Figure 8.5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A. (a) Calculate the capacitance and the rate of change of potential difference between the plates. (b) Obtain the displacement current across the plates. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain. FIGURE 8.5
4.4 — A Horizontal Overhead Power Line Carries A Current Of 90 A In East To
Physics Class 11 · Chapter 4
4.4 A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?
4.8 — A Closely Wound Solenoid 80 Cm Long Has 5 Layers Of Windings Of 400
Physics Class 11 · Chapter 4
4.8 A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Maxima and Minima
- Year
- 2021
- Shift
- 26 Aug Shift 1
- Q Number
- Q88
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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