Continuity and Differentiability

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Question

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Question 1 :

Let f (x) = [n+psinx], x ? (0,π), n ??? Z,p is a prime number and [x] =

the greatest integer less then or equal to x. The number of points at which  f (x) is not differentiable is

1. p
2. p-1
3. 2p+1
4. 2p-1
Answer
6768

Question 2 :

The identity function is:

1. Continuous only at integral points
2. Not continuous everywhere
3. Continuous everywhere
4. None of these
Answer
6769

Question 3 :

The function f (x) = [x] where [x] denotes the greatest integer not greater than x is   

1. continuous for all real value of x
2. continuous only rational value of x
3. continuous for all nonintegral value of x
4. continuous only at positive integral value of x
Answer
6770

Question 4 :

If f (x) = - 2x + a, x  < 2 and

f (x) = x - 1, x > 2 is continuous at x = 2 then a = 0

1. 3
2. 4
3. 5
4. 2
Answer
6771

Question 5 :

If f (x) = 3, when x < 2, and f (x) = kx², when x > 2 is continuous at x = 2, then the value of k is ?

1. 3/4
2. -4/3
3. 2/4
4. none of these
Answer
6772