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NDA Continuity and Differentiability questions with solutions

Continuity and differentiability of functions. 16 questions from our 2016–2025 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

NDA 2025

The function f(x)=begincasesax+3,&x≤2\x^2-1,&x>2endcases is continuous at x=2 if a is equal toNDA 2025 Maths · medium
A function continuous on a closed interval [a,b] attains its maximum value on [a,b]. 2. A function continuous on an open interval (a,b) attains its…NDA 2025 Maths · medium

NDA 2024

The function f(x)=begincases(x^2-9)/(x-3),&x≠3\\[4pt] k,&x=3endcases is continuous at x=3.NDA 2024 Maths · easy
Let f(x)=begincasesxsin 1/x,&x≠0\\[4pt] 0,&x=0endcases. 1. f is continuous at x=0. 2. f is differentiable at x=0.NDA 2024 Maths · hard

NDA 2023

The function f(x)=|x-1| is differentiable at x=1. 2. If f is continuous on [a,b], then f'(c)=0 for some c∈(a,b).NDA 2023 Maths · hard

NDA 2021

The sum of two continuous functions is continuous. 2. The product of two discontinuous functions is always discontinuous.NDA 2021 Maths · medium

NDA 2020

The function f(x)=(x^2-5x+6)/(x-2) for x≠2 and f(2)=k is continuous at x=2. Then k equalsNDA 2020 Maths · easy
Let f(x)=|x|^3. 1. f is twice differentiable at x=0. 2. f'(0)=0 and f''(0)=0.NDA 2020 Maths · hard
Every continuous function is differentiable. 2. Every differentiable function is continuous.NDA 2020 Maths · easy

NDA 2019

The function f(x)=begincases2x+a,&x<1\\5,&x=1\\3x-b,&x>1endcases is continuous at x=1. The value of a+b isNDA 2019 Maths · easy
The function f(x)=(1-cos 4x)/(x^2 for x≠0 is made continuous at x=0 by defining f(0) equal toNDA 2019 Maths · medium
Every function that is continuous on a closed interval [a,b] is bounded on [a,b]. 2. If lim x→ af(x) exists, then f is continuous at x=a.NDA 2019 Maths · medium

NDA 2017

Let f(x)=(e^3x-1)/(2x) for x≠0 and f(0)=k. If f is continuous at x=0, then k equalsNDA 2017 Maths · easy
The number of points at which f(x)=|x-1|+|x-2| is not differentiable isNDA 2017 Maths · easy
Let f(x)=x^2 for x≤1 and f(x)=ax+b for x>1. If f is differentiable at x=1, then b equalsNDA 2017 Maths · hard

NDA 2016

The function f(x)=|x| is continuous at x=0. 2. The function f(x)=|x| is differentiable at x=0.NDA 2016 Maths · easy