9 JEE Main 2025 Continuity and Differentiability previous-year questions with verified answers and step-by-step solutions.
These are the JEE Main 2025 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 the function f(x)= (x²+1 ) |x²-a x+2 |+ |x| be not differentiable at the two points x=α=2 and x=β. Then the distanc…
Let m and n be the number of points at which the function f(x)= \x, x³, x⁵, … ., x²¹ x R, is not differentiable and not…
Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the func…
The number of points of discontinuity of the function f(x)= [x²2 ]-[x], x [0,4], where [·] denotes the greatest integer…
Let f(x)= cases(1+ax)¹ / x & , x 0 \ 1+b & , x=0 \ (x+4)¹ / ²-2(x+c)¹ / ³-2 & ,cases be continuous at x=0. Then e^a b c…
Let f(x) be a real differentiable function such that f(0)=1 and f(x+y)=f(x) fⁱme(y)+fⁱme(x) f(y) for all x, y R. Then ₌…
Let the function, f(x)= cases-3 a x²-2, & x 1 \ a²+b x, & x 1cases be differentiable for all x R, where a1, b R. If the…
If the function f(x)= \arrayl(2)/(x) (k₁+1 ) x+ (k₂-1 ) x x 0 \ 4, x=0 \ (2)/(x) e ((2+k₁ x)/(2+k₂ x) ), x0array . is c…
Let f(x)= \arraylc3 x, & x 0 \ \1+x+[x], x+2[x] & 0 ≤ x ≤ 2 \ 5, & x2,array . where [.] denotes greatest integer functi…