Ch 6 Miscellaneous Exercise (Last Part) | Application of Derivatives Class 12 | NCERT | Faiz Sir скачать в хорошем качестве

Ch 6 Miscellaneous Exercise (Last Part) | Application of Derivatives Class 12 | NCERT | Faiz Sir

इस वीडियो में Class 12 Maths – Chapter 6: Application of Derivatives (NCERT) के Miscellaneous Exercise का LAST PART विस्तार से समझाया गया है। 📘 Infinix Classes Maths by Faiz Sir पर यह लेक्चर बोर्ड परीक्षा, स्कूल एग्ज़ाम और competitive exams के लिए बहुत महत्वपूर्ण है। 🔹 इस वीडियो में क्या पढ़ाया गया है? इस भाग में maximum–minimum, optimization problems, prove based questions, और rate of change जैसे high-weightage सवाल पूरे concept के साथ समझाए गए हैं: ✔ Circle और Square के area optimization ✔ Window design for maximum light ✔ Triangle hypotenuse minimum length proof ✔ Local maxima, minima & point of inflexion ✔ Absolute maximum & minimum values ✔ Cone, Cylinder & Sphere से जुड़े maximum volume problems ✔ Increasing function का proof ✔ MCQ based rate of change question 📌 Covered Questions (NCERT – Chapter 6): Q.7 to Q.16 (Miscellaneous Exercise – Last Part) 👉 यह वीडियो CBSE Board Exam 2025, School Tests, और Concept clarity के लिए बहुत उपयोगी है। अगर आपको यह वीडियो पसंद आए तो 👍 Like करें | 🔔 Subscribe करें | 📤 Share करें #applicationofderivatives #class12maths #chapter6maths #miscellaneousexercise #ncertmaths #cbseclass12 #MaximumMinimum #OptimizationProblems #calculusclass12 #faizsir #infinixclasses #boardexampreparation #mathsbyfaizsir #DerivativesMaths application of derivatives class 12, chapter 6 maths class 12, miscellaneous exercise application of derivatives, class 12 maths ncert solutions, application of derivatives miscellaneous questions, maximum and minimum problems class 12, optimization problems calculus, cbse class 12 maths chapter 6, ncert class 12 maths solutions, faIz sir maths, infinix classes maths, calculus class 12 hindi, application of derivatives full chapter, board exam maths preparation, class 12 maths important questions, application of derivatives last part, miscellaneous exercise chapter 6 maths MISCELLANEOUS EXERCISE ON CHAPTER 6 7. The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. 8. A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening. 9. A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is (𝒂^(𝟐/𝟑)+ 𝒃^(𝟐/𝟑) )^(𝟑/𝟐). 10. Find the points at which the function f given by f (x) = (x – 2)4 (x + 1)3 has (i) local maxima (ii) local minima (iii) point of inflexion 11. Find the absolute maximum and minimum values of the function f given by f(x) = cos2x + sin x, x ∈ [0, π] 12. Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 𝟒𝒓/𝟑. 13. Let f be a function defined on [a, b] such that f′(x) is greater than 0, for all x ∈ (a, b). Then prove that f is an increasing function on (a, b). 14. Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 𝟐𝑹/√𝟑 . Also find the maximum volume. 15. Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle α is one-third that of the cone and the greatest volume of cylinder is 𝟒/𝟐𝟕 𝝅𝒉^𝟑 〖𝒕𝒂𝒏〗^𝟐 𝜶. 16. A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of (A) 1 m/h (B) 0.1 m/h (C) 1.1 m/h (D) 0.5 m/h