28 JEE Main 2021 Continuity and Differentiability previous-year questions with verified answers and step-by-step solutions.
These are the JEE Main 2021 previous-year questions from the Continuity and Differentiability chapter of Mathematics. Each links to a full solution with a verified answer key. To see the whole chapter across all years, visit the Continuity and Differentiability chapter hub.
Let f   :   R → R be a function defined as f x = sin ( a + 1 ) x + sin 2 x 2 x , if   x < 0 b…
Let α ∈ R be such that the function f x = cos - 1 1 - x 2 sin - 1 1 - x x - x 3 , x ≠ 0 α , x = 0…
If the function f x = 1 x log e 1 + x a 1 - x   b                   &…
Let f   :   R → R satisfy the equation f ( x + y ) = f ( x ) · f ( y ) for all x , y ∈ R and…
Let [ t ] denote the greatest integer less than or equal to t . Let f ( x ) = x - [ x ] ,   g ( x ) = 1 - x + [ x…
Let f : - π 4 , π 4 → R be defined as, f x = 1 + sin x 3 a sin x ,    - π 4 < x <…
If the function f x = cos ( sin x ) - cos x x 4 is continuous at each point in its domain and f 0 = 1 k , then k is ___…
Let a function g : 0 , 4 → R be defined as g x = max   t 3 - 6 t 2 + 9 t - 3 0 ≤ t ≤ x , 0 Ͱ…
Let f : R → R be defined as f x = x 3 ( 1 - cos 2 x ) 2 log e 1 + 2 x e - 2 x 1 - x e - x 2 ,    x X…
Consider the function f x = P x sin x - 2 ,   x ≠ 2 , and f x = 7 ,   x = 2 where P x is a polynomial s…
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