Karnataka 2nd PUC Maths Chapter 6 Important Questions 2027: Application of Derivatives

Karnataka 2nd PUC Maths Chapter 6 Important Questions 2027 cover important concepts from Application of Derivatives, including rate of change of quantities, increasing and decreasing functions, critical and stationary points, and maxima and minima. Students can practise MCQs, revise key derivative-based concepts, and solve previous-year CET questions for exam preparation.

The Application of Derivatives chapter includes questions based on derivatives, rates of change, intervals of increase and decrease, and maximum and minimum values. Practising these questions can help students understand the concepts and apply the required formulas while solving exam questions.

Before starting Chapter 6, students should first check the Karnataka 2nd PUC Syllabus 2026-27 to understand the prescribed topics and then review the Karnataka 2nd PUC Exam Pattern 2027 to understand the question structure and marking scheme. 

Karnataka 2nd PUC Maths Chapter 6 Application of Derivatives Important Questions and Answers

The following Application of Derivatives Questions and Answers are based on the chapter-wise Mathematics CET material released for 2026-27. The source includes questions on rate of change, increasing and decreasing functions, and maxima and minima, with questions labelled as Easy, Average, and Difficult.

Along with chapter-wise practice, solving the [Karnataka 2nd PUC Previous Year Question Papers] can help students understand recurring question patterns and the types of problems asked in examinations. 

Q1. A circular plate of radius 5 cm is heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. The rate at which its area is increasing, when the radius is 5.2 cm, is:

(A) 5.05π cm²/sec
(B) 5.2π cm²/sec
(C) 0.52π cm²/sec
(D) 27.4π cm²/sec

Answer: (C) 0.52π cm²/sec

Q2. The sides of an equilateral triangle are increasing at the rate of 4 cm/sec. The rate at which its area is increasing, when the side is 14 cm, is:

(A) 42 cm²/sec
(B) 7√3 cm²/sec
(C) 28√3 cm²/sec
(D) 14√3 cm²/sec

Answer: (C) 28√3 cm²/sec

Q3. The rate of change of the surface area of a sphere of radius r, when the radius is increasing at the rate of 2 cm/sec, is proportional to:

(A) 1/r²
(B) 1/r
(C) r²
(D) r

Answer: (D) r

Q4. If the distance s metres travelled by a particle in time t is given by s = t³ − 3t², then the velocity of the particle when the acceleration is zero, in m/sec, is:

(A) 3
(B) −2
(C) −3
(D) 2

Answer: (C) −3

Q5. If s = 60t − 5t² denotes the distance covered by a particle in time t, then the distance it covers before coming to rest is:

(A) 120
(B) 720
(C) 240
(D) 180

Answer: (D) 180 units

These Application of Derivatives PYQs and practice questions cover rate of change concepts involving particles, geometric figures, and changing quantities. The source includes previous-year CET questions from topics such as rate of change and applications of derivatives.

Important Topics in Karnataka 2nd PUC Maths Chapter 6: Application of Derivatives

The important topics from the provided Application of Derivatives material include rate of change, increasing and decreasing functions, critical points, stationary points, maxima and minima, and related applications.

• Rate of Change of Quantities

Revise the derivative as the rate of change of one quantity with respect to another. The source includes applications involving velocity, acceleration, changing areas, volumes, radii, and distances.

• Increasing and Decreasing Functions

Learn the conditions for determining whether a function is increasing or decreasing using its first derivative. If f′(x) is positive throughout an interval, the function is increasing; if f′(x) is negative, the function is decreasing.

• Critical and Stationary Points

A critical point occurs when f′(c) = 0 or when f′(c) does not exist, while a stationary point is a point where f′(c) = 0. Practise questions that require identifying these points before applying maxima or minima tests.

• Maxima and Minima

Revise local and global maximum and minimum values, turning points, and the first and second derivative tests. The source also includes application-based questions involving maximum area, minimum distance, maximum volume, and other optimisation problems.

• Absolute Maximum and Minimum Values

Practise finding the absolute maximum and minimum values of functions over a given closed interval. The source includes questions involving polynomial functions and functions defined on specific intervals.

Increasing and Decreasing Functions Questions

The Increasing and Decreasing Functions Questions in the chapterwise material test the use of derivatives to determine intervals where a function increases or decreases.

Q1. The interval in which the function f(x) = x³ − 6x² + 9x + 10 is increasing is:

(A) [1, 3]
(B) (−∞, 1) ∪ (3, ∞)
(C) (−∞, 1) ∪ [3, ∞)
(D) (−∞, 1] ∪ [3, ∞)

Answer: (B) (−∞, 1) ∪ (3, ∞)

Q2. The function f(x) = x + cos x, x ∈ [0, π], is:

(A) increasing
(B) decreasing
(C) constant
(D) f′(x) > 0, ∀ x ∈ [0, π]

Answer: (A) increasing

Q3. The value of x for which 2x³ − 9x² + 12x + 2 is decreasing is:

(A) 1 < x < 2
(B) x < 1 or x > 2
(C) −2 < x < −1
(D) x < −2 or x > −1

Answer: (A) 1 < x < 2

Q4. The function f(x) = tan⁻¹x is:

(A) An increasing function
(B) A decreasing function
(C) Neither increasing nor decreasing
(D) A constant function

Answer: (A) An increasing function

The source contains 20 questions under Increasing and Decreasing Functions, including KCET questions from 2024 and 2025 and questions involving polynomial, trigonometric, logarithmic, and inverse trigonometric functions.

Maxima and Minima Important Questions

The Maxima and Minima Questions focus on local and global extreme values, critical points, first and second derivative tests, and optimisation-based applications.

Q1. The minimum value of 1 − sin x is:

(A) 0
(B) −1
(C) 1
(D) 2

Answer: (A) 0

Q2. If x + y = 12, then the minimum value of x² + y² is:

(A) 72
(B) 144
(C) 48
(D) 36

Answer: (A) 72

Q3. The maximum value of log x/x, x ∈ (0, ∞), is:

(A) 1/e
(B) 2/e
(C) e
(D) 1

Answer: (A) 1/e

Q4. If y = (x − a)² + (x − b)² + (x − c)², then y is minimum when x is equal to:

(A) (a + b + c)/2
(B) (a + b + c)/3
(C) a + b + c
(D) 2(a + b + c)

Answer: (B) (a + b + c)/3

Q5. The number of points of local maxima and local minima of the function f(x) = 3x³ + 6x² + 4x + 7 is:

(A) 1
(B) 2
(C) 3
(D) 0

Answer: (B) 2

The provided material contains 31 questions under Maxima and Minima, including questions on local extrema, absolute maximum and minimum values, optimisation, and application-based problems.

Application of Derivatives Important Questions PDF

The Application of Derivatives Important Questions PDF contains chapter-wise Mathematics CET questions for Karnataka 2nd PUC. It includes questions on rate of change of quantities, increasing and decreasing functions, and maxima and minima. The material also provides answer keys for the practice questions.

Students can use the PDF to practise Application of Derivatives MCQs, revise important concepts, and solve questions based on different levels of difficulty.

Students should also keep track of the Karnataka 2nd PUC Mid Term Time Table 2026 while planning their revision schedule and completing important chapters on time. 

How to Prepare for Karnataka 2nd PUC Maths Chapter 6: Application of Derivatives

A simple 5-step plan can help students revise Application of Derivatives effectively:

1. Revise derivative concepts first – Make sure the basic differentiation rules are clear before solving application-based questions.

2. Practise rate of change questions – Solve problems involving velocity, acceleration, area, volume, and changing dimensions.

3. Focus on increasing and decreasing functions – Practise finding f′(x) and identifying the intervals where a function increases or decreases.

4. Revise maxima and minima tests – Learn how critical and stationary points are used with the first and second derivative tests.

5. Solve CET and previous-year questions – Practise the questions provided in the chapter-wise material to become familiar with different question types.

Students preparing for school-level tests can also refer to the Karnataka 2nd PUC Mid Term Question Paper to practise questions under timed conditions and assess their preparation. 

Karnataka 2nd PUC Maths Chapter 6 Important Questions 2027 cover important concepts from Application of Derivatives, including rate of change, increasing and decreasing functions, and maxima and minima. Regular practice of the Application of Derivatives Question Bank can help students revise these concepts and apply them while solving exam questions.

PW provides Karnataka 2nd PUC exam content, including Karnataka Board Exam Blogs, sample papers, mock tests, guidance sessions, and more. Students can also explore Karnataka 2nd PUC Online Coaching for exam preparation.