# NCERT Solutions for Class 12 maths chapter 6

NCERT solutions for class 12 Maths chapter 6 exercise 6.5, 6.4, 6.3, 6.2, 6.1 Applications of Derivatives (rate of change, increasing decreasing, approximation, tangent normal and maxima minima) in PDF form to free download. 12th * NCERT solutions* of other subjects,

*books, revisions books, assignments, chapter tests based on applications of derivatives class xii,*

**NCERT***questions are in PDF.*

**previous year’s board papers**## NCERT solutions for class 12 Maths chapter 6

**Class 12 Maths Solutions – Applications of derivatives**

**Class 12 Maths Solutions – Applications of derivatives**

**NCERT Chapter to study online and answers given in the end of ncert books.**

**NCERT Chapter to study online and answers given in the end of ncert books.**

*These books are very good for revision and more practice. These book are also confined to NCERT Syllabus.*

*These books are very good for revision and more practice. These book are also confined to NCERT Syllabus.*

**Assignments for practice**

**Assignments for practice**

**Mixed Chapter Tests**

Chapter 5 & 6

**Level 1 Test 1 **

**Level 2 Test 1 **

**Level 3 Test 1 Test 2**

#### Previous Years Questions

- The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. Find the rate at which its area increases, when side is 10 cm long. [CBSE Sample Paper 2017]
- The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm. [Delhi 2017]
- The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm? [Delhi 2015]
- Determine for what values of x, the function f(x) = x^3 + 1/x^3, where x ≠ 0, is strictly increasing or strictly decreasing. [CBSE Sample Paper 2017]
- Show that the function f(x) = 4x^3 – 18x^2 + 27x – 7 is always increasing on R. [Delhi 2017]
- Find the interval in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing. [Delhi 2016]
- Find the point on the curve y = x^3 – 11x + 5 at which the tangent is y = x – 11. [CBSE Sample Paper 2017]
- Find the equation of tangents to the curve y = cos(x + y), where x lies in [- 2π, 2π], that are parallel to the line x + 2y = 0. [Foreign 2016]
- Find the shortest distance between the line x – y + 1 = 0 and the curve y^2 = x. [CBSE Sample Paper 2017]
- If the sum of lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of the triangle is maximum, when the angle between them is π/3. [Delhi 2017]
- 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. Also find maximum volume in terms of volume of the sphere. [Delhi 2016]
- The sum of the surface areas of a cuboid with sides x, 2x and x/3 and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if x is equal to three times the radius of the sphere. Also find the minimum value of the sum of their volumes. [Foreign 2016]
- A tank with rectangular base and rectangular sides open at the top is to be constructed so that its depth is 3 m and volume is 75 cubic meter. If building of tank costs ₹ 100 per square metre for the base and ₹ 50 per square meters for the sides, find the cost of least expensive tank. [Delhi 2015C]
- A point on the hypotenuse of a right triangle is at distances ‘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. [Delhi 2015C]
- Find the local maxima and local minima, of the function f(x) = sin x – cos x, 0 < x < 2π. Also find the local maximum and local minimum values. [Delhi 2015]