PrepWiser › Learn › Mathematics › Continuity & DifferentiabilityContinuity & Differentiability — JEE Main PYQs & Practice Questions Continuity & Differentiability is a Mathematics chapter in the JEE Main syllabus. This page brings together 94 previous-year and practice questions on Continuity & Differentiability, organised into 3 topics: Continuity at a Point, Types of Discontinuities and Differentiability. Most questions come with a step-by-step solution you can work through free in PrepWiser.
Download Continuity & Differentiability JEE Main PYQs as a free PDF
Revise this chapter: Revision notes · Formula sheet
Chapter weightage : how many questions each chapter had per shift in the 2024–26 papers.
Continuity at a Point Let f: R → R be a function given by f(x)= (1-cos 2 x)/x², x < 0 ; α, x=0, ; (β √(1-cos… Let α ∈ R be such that the function f(x) = { (cos ⁻¹(1 - { x} ²)sin ⁻¹(1 - { x} ))/({ x}… Let f(x) = x.[ x/2 ], for -10< x < 10, where [t] denotes the greatest integer function… Let [t] denote the greatest integer less than or equal to t. If the function f(x)={b²… If f(x)={(a|x|+x²-2(sin |x|)(cos |x|))/x, ,x≠ 0; b, ,x=0 is continuous at x=0, then a+b… Let f:( - π/4,π/4 ) → R be defined as f(x) = { (1 + |sin x|)^(3a/(|sin x|)), ,, - π/4 <… If the function f(x)={2/x{sin (k₁+1) x+sin (k₂-1) x}, x<0; 4, x=0; 2/x log ₑ((2+k₁… Let [t] denote the greatest integer less than or equal to t. Let f:[0, ∞) → R be a… Let f(x)={x³+8;, x<0,; x²-4;, x≥ 0, and g(x)={(x-8)^(1/3);, x<0,; (x+4)^(1/2);, x≥ 0… If the function f(x) = { (log ₑ(1 - x + x²) + log ₑ(1 + x + x²))/(sec x - cos x), ,, x ∈… Let a function f : R → R be defined as f(x) = { sin x - eˣ, if, x ≤ 0; a + [ - x], if, 0… If the function f(x)= (72ˣ-9ˣ-8ˣ+1)/(√2-√(1+cos x)), x ≠ 0 ; a log ₑ 2 log ₑ 3 , x=0 is… If the function f(x) = (cos (sin x) - cos x)/x⁴ is continuous at each point in its… Let f : R → R and g : R → R be defined as f(x) = { x + a,, x < 0; |x - 1|,, x ≥ 0 and… If the function ƒ defined on ( - 1/3,1/3 ) by f(x) = { 1/xlog ₑ( (1 + 3x)/(1 - 2x) )… Consider the function where P(x) is a polynomial such that P'' (x) is always a constant… Let f : R → R be defined as f(x) = { 2 sin ( - (π x)/2 ),if x < - 1; |ax² + x + b|, if -… Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1)… Let f(x)=[x²-x]+|-x+[x]|, where x ∈ ℝ and [t] denotes the greatest integer less than or… Let a, b ∈ R, b ∈ 0, Define a function f(x) = { a sin π/2(x - 1),, for x ≤ 0; (tan 2x -… Types of Discontinuities Differentiability If f(x) = { 1/|x|, ; |x| ≥ 1; ax² + b, ; |x| < 1 is differentiable at every point of the… The number of points, at which the function f(x)=max{6x,2+3x²}+|x-1|cos |x²-1/4|,x∈… Let f(x) = { (sin (x - [x]))/(x - [x]), , x ∈ ( - 2, - 1); max { 2x,3[|x|]}, , |x| < 1… Let α, β ∈ ℝ be such that the function f(x)= 2 α(x²-2)+2 β x , x<1 ; (α+3) x+(α-β) , x ≥… Let f:[0,∞ ) → [0,3] be a function defined by f(x) = { max { sin t:0 ≤ t ≤ x} ,, 0 ≤ x ≤… Let f:R → R be a function defined by : f(x) = { max { t³ - 3t} t ≤ x, ;, x ≤ 2; x² + 2x… Let f(x)={eˣ⁻¹, ,x<0; x²-5x+6, ,x≥ 0 and g(x)=f(|x|)+|f(x)|. If the number of points… Let f : R → R be a function defined by f(x) = max x, x². Let S denote the set of all… Let a function g : [ 0, 4 ] → R be defined as g(x) = { max _(0 ≤ t ≤ x) { t³ - 6t² + 9t… Let the function, f(x)= -3 ax²-2, x<1 ; a²+b x, x ≥ 1 be differentiable for all x ∈ R… Let the function f(x)=(x²-1)|x²-a x+2|+cos |x| be not differentiable at the two points… The number of points, at which the function f(x) = | 2x + 1 | - 3| x + 2 | + | x² + x -… Let f, g : R → R be two real valued functions defined as f(x) = { - |x + 3|, ,, x < 0… Let f:[0,3] → R be defined by f(x) = min { x - [x],1 + [x] - x} where [x] is the… Let a ∈ ℤ and [t] be the greatest integer ≤ t. Then the number of points, where the… A function f is defined on [-3, 3] as f(x) = { min { |x|,2 - x²} ,, - 2 ≤ x ≤ 2; [|x|]… If the function f( x ) = { k₁( x - π )² - 1,, x ≤ π; k₂cos x,, x > π is twice… The number of points, where the function f: R → R, f(x)=|x-1| cos |x-2| sin… Let f be any function defined on R and let it satisfy the condition : |f(x) - f(y)| ≤… Consider the function f:(0,2) → R defined by f(x)=x/2+2/x and the function g(x) defined… More Mathematics chapters Frequently asked questions How many Continuity & Differentiability questions are there for JEE Main? PrepWiser has 94 Continuity & Differentiability questions for JEE Main, grouped into 3 topics such as Continuity at a Point, Types of Discontinuities and Differentiability.
Are these Continuity & Differentiability questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Continuity & Differentiability questions? Open any Continuity & Differentiability question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.