Kerala Plus Two Chapter 5 Maths important Questions

Chapter 5 of Kerala Plus Two Maths covers continuity and differentiability, two core calculus topics. Questions usually ask students to check continuity at a given point, find an unknown constant, and differentiate trigonometric, inverse trigonometric, implicit, logarithmic, or parametric functions. 

Practising Kerala Plus Two Chapter 5 Maths important questions builds strong analytical skills and improves speed and accuracy. Solving them step by step also helps you manage your time better, so check the Kerala Plus Two timetable and plan your revision around your Maths exam date.

Kerala Plus Two Maths Chapter 5 Important Questions

Here are some important practice questions on Continuity and Differentiability for Kerala Plus Two Maths Chapter 5. Solve each question step by step to improve accuracy and strengthen your preparation. For better exam planning, check the Kerala Plus Two Maths exam pattern and timetable.

Question 1: Let f : R → R be defined by

f(x) = kx + 1, if x ≤ π
f(x) = cos x, if x > π

For what value of k is f continuous?

Answer:
For f(x) to be continuous at x = π, the left-hand limit, the right-hand limit and the value of the function must be equal.

Left-hand limit: lim (x→π⁻) f(x) = lim (x→π⁻) (kx + 1) = kπ + 1

Right-hand limit: lim (x→π⁺) f(x) = lim (x→π⁺) cos x = cos π = −1

Value of the function: f(π) = kπ + 1

Equating the left-hand and right-hand limits:
kπ + 1 = −1
kπ = −2
k = −2/π

Question 2: Discuss the continuity of the function

f(x) = 3x + 1, if x ≤ 3
f(x) = x² + 1, if x > 3

at x = 3.

Answer:
Left-hand limit: lim (x→3⁻) f(x) = lim (x→3⁻) (3x + 1) = 3(3) + 1 = 10

Right-hand limit: lim (x→3⁺) f(x) = lim (x→3⁺) (x² + 1) = 3² + 1 = 10

Value of the function: f(3) = 3(3) + 1 = 10

Since lim (x→3⁻) f(x) = lim (x→3⁺) f(x) = f(3) = 10, the function f(x) is continuous at x = 3.

Question 3: Find dy/dx, if x² + y² + xy = 100.

Answer:
Differentiating both sides with respect to x:

d/dx (x²) + d/dx (y²) + d/dx (xy) = d/dx (100)

2x + 2y (dy/dx) + [x (dy/dx) + y] = 0

(x + 2y) (dy/dx) = −(2x + y)

dy/dx = −(2x + y) / (x + 2y)

Note: These are only a few of the important questions from this chapter. For more practice questions on continuity and differentiability, download the PDF below.

Kerala Board Class 12 Maths Chapter 5 PDF Download

Students can download the Kerala Board Class 12 Maths Chapter 5 PDF for extra practice. The Kerala Class 12 Mathematics Continuity PDF includes questions on continuity, finding unknown constants, and implicit, logarithmic, parametric and second-order differentiation, so you can practise offline. 

Use the link below to get the PDF: 

How Can You Use Kerala Plus Two Maths Chapter 5 Important Questions for Exam Preparation?

Solving practice questions in an organised way makes calculus revision easier. Before you start, check the Kerala Class 12 syllabus so you know which topics to cover. Then follow these steps to prepare well for your board exams:

• Review Core Definitions: Learn the exact conditions for continuity and differentiability before attempting problems. Also revise the Kerala Plus Two Maths Inverse Trigonometric Functions MIQs, as inverse trigonometric functions often appear in differentiation questions.

• Practice Step-by-Step Methods: Write down every intermediate step when solving derivative questions to secure full method marks.

• Identify Weak Areas: Note down topics where errors occur, such as logarithmic differentiation or parametric forms, and re-solve them.

• Time Your Practice: Solve questions under timed conditions using Kerala Plus Two model papers to build exam-day confidence.

Practising Kerala Plus Two Chapter 5 Maths important questions helps you understand continuity and differentiability concepts and improve problem-solving skills. Revise the solutions and practise the PDF questions to prepare for your board exams.