Page 52 - Mathematics Class - XII

Case-Study Based Questions
Case-Study Based Questions

A function f (x) is said to be continuous at x = c, if the function is defined at x = c and if the value of the
function at x = c equals to the limit of the function at x = c i.e. lim( )fx fc
( )
x c
If the function f (x) is not continuous at x = c, we can say that f is discontinuous at c and c is called the point
of discontinuity of f.
Based upon the above paragraph, answer the questions given below
1. The number of points of discontinuity of f (x) in [3, 7] is

(a) 4 (b) 5 (c) 6 (d) 8
2. Suppose f and g are two real functions continuous at a real number c then:
(a) f + g is continuous at x = c (b) f + g is discontinuous at x = c

(c) f + g may or may not be continuous at x = c (d) None of these
3. Find the value of k, sothat the given function f (x) is continuous at x = 5.

kx 1 , x 5 3 1 4 9
fx() (a) (b) (c) (d)
3 x 5 , x 5 5 5 5 5
4. Find the value of k, sothat the given function f (x) is continuous at x = 2.

kx , x 2 1 3 11
2
fx() (a) 1 (b) 4 (c) 4 (d) 4
, 3 x 2

Assertion-Reason Based Questions
Assertion-Reason Based Questions

Directions for Questions 1 to 3: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false. (d) A is false but R is true.

Q. 1. Assertion (A) : f (x) = [x] greatest integer function is not differentiable at x = 2.
Reason (R) : The greatest integer function is not continuous at any integer.

,
12 x 13 if x 3
Q. 2. Assertion (A) : The function fx() is differentiable at x = 3
2
2 x 5 , if x 3
Reason (R) : The function f (x) is differentiable at x = c of its domain if
left hand derivative of f at c = right hand derivative of f at c.

Q. 3. Assertion (A) : f (x) = | x – 1| + | x – 2| is continuous but not differentiable at x = 1, 2
Reason (R) : Every differentiable function is continuous.

Answers

Case-Study Based Questions: 1. (a) 2. (a) 3. (d) 4. (c)
Assertion-Reason Based Questions: 1. (a) 2. (a) 3. (b)

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