Continuity & Differentiability: Class 12 Previous Year Questions

Continuity & Differentiability questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. (a) Check whether function f(x) defined as 2 f(x) =           3 , 6 6 3 , ) 3 ( 2 3 x x x x x is continuous at x = 3 or not ? OR (b) If 3(x2 + y2) = 4xy, then find dy dx at   1 2 , 3 2 .
   Board 20262 marksshort answer
2. { } 38. Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as follows : f(x) =         3 , 40 3 0 4, 4 – 2 2 4 x x …
   Board 20264 marksshort answer
3. dy x-y 25. (a) If x= ey, then prove that dx x log x OR 2x-3,-3·x·-2 (b) If f(·) x+1 ,-2<x·0 Check the differentiability of f(x) at x = -2. Page 15 of 24 (6 × 3 = 18) 26. (a) 3a 2(y + 3) - xy dx (b) dx n , , n R, 28.: ae x - y ·0; - x + 2y · 2, x·3, y·4, y·0 I …
   Board 20252 marksshort answer
4. -8, x·5 20. Assertion (A) : f(x) : 2k· x>5 is continuous at x = 5 for k = Reason (R) : For a function f to be continuous at x = a, lim..
   Board 20251 markAssertion-Reason
5. If f(x) = I x I + I x- 1 I, then which of the following is correct ? (A) f(·x) is both continuous and differentiable, at x = O and x = 1. (B) f(x) is differentiable but not continuous, at x = O and x = 1. (C) f(x) is continuous but not differentiable, at x = O…
   Board 20251 markMCQ
6. Page 4 of 23 7. _mZm Xmo _mÌH$ g{Xem| ^a Am¡a ^b Ho$ ~rM H$m H$moU q Bg àH$ma h¡ {H$ sin q = 5 3 h¡ & Vmo ^a . ^b ~am~a h¡ : (A) ± 5 3 (B) ± 4 3 (C) ± 5 4 (D) ± 3 4 666 Page 5 of 23 3. Which of the following statements is true for the function f(x) = 2 x 3, x …
   Board 20241 markMCQ
7. (d2y) (dy)? 25. (a) Ify=ax + b, prove that y dx? dx OR [ax+b·0<x·l If f(·) (b) is a differentiable function in (O, 2), [2x2 - x ; 1 <x<2 then find the values of a and b.
   Board 20232 marksshort answer
8. The function f(·) = xI xlis 15. (A) continuous and differentiable at x = O. (B) continuous but not differentiable at x= O. (C) differentiable but not continuous at x = O. (D) neitherdifferentiablenorcontinuousatx=O. y d
   Board 20231 markMCQ
9. tan x- 13. Anti-derivative of (A) (B) sec2 sec2 log log (C) (D) sec sec
   Board 20231 markMCQ
10. Two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R). Assertion (A): The function f(x) = |x − 6|(cos x) is differentia…
    CBSE practice 2022-231 markAssertion-Reason
11. A function f: R -> R is defined by: Which of the following statements is true about the function at the point x = ln 1 2 ? (a) f(x) is not continuous but differentiable. (b) f(x) is continuous but not differentiable. (c) f(x) is neither continuous nor differen…
    CBSE practice 2023-241 markMCQ
12. The first derivative of a function f(x) is given below. If f(1) = e + 3, find f(x). Show your steps.
    CBSE practice 2021-223 marksshort answer
13. The anti-derivative of a function of the form (3x − 1)f(x), (x ≠ 1 3), is given by 3𝑥4 − 13 3 𝑥3 + 3 2 𝑥2 + 𝐶, where C is the constant of integration. Find the value of f(6). Show your steps.
    CBSE practice 2022-233 marksshort answer

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