# Multiple choice (Continuity and differentiability)

Choose and write the correct option in the following question:(continuity and differentiability multiple choice)

1.) The function f:R → R given by f(x) = -|x – 1| is

(a) Continuous as well as differentiable at x = 1

(b) Not continuous but differentiable at x = 1

(c) Continuous but not differentiable at x = 1

(d) Neither continuous nor differentiable at x = 1

2.) The function is

(a) Continuous everywhere but not differentiable at x = 1

(b) Continuous and differentiable everywhere

(c) Not continuous at x= 0

(d) None of these

3.) The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at

(a) 4                         (b) 2

(c) 1                           (d) None of these

4.) The number of points at which the function is not continuous  is

(a) 1                           (b) 2

(c) 3                           (d) None of these

5.) The function is continuous at x = 0 then the value of k is

(a) 3                             (b) 2

(c) 1                              (d) 1.5

6.) If the function f defined by , is continuous at x =π/2, then the value of

(a) 2                              (b) 3

(c) 6                              (d) -6

7.) The function f(x) = cot x is discontinuous on the set

(a) {x = nπ: n∈ Z}           (b) {x = 2nπ: n∈ Z}

(c) {x = (2nπ+1)π/2: n∈ Z}   (d) {x = nπ/2: n∈ Z}

8.)Let f(x) = |sin x|. then

(a) f is everywhere differentiable.

(b) f is everywhere continuous but not differentiable at x = nπ: n∈Z

(c) f is everywhere continuous but not differentiable at x =(2n + 1)π/2, n∈ Z.

(d) None of these

9.) The function is discontinuous at

(a) Exactly one point              (b) Exactly two points

(c) Exactly three points         (d)  No point

10.) If , where x ≠ 0, thenthe value of the function f at x = 0, so that the function is

(a) 0                     (b)  -1

(c) 1                       (d) None of these

11.) The function is continuous at x = 0 for the value of k, as

(a) 3                   (b) 5

(c) 2                    (d) 8

12.) If , then which of the following question is true ?

(a)

(b)

(c)

(d)

13.) Differential of w.r.t. , is

(a)        (b)

(c)   (d)

14.) If , then is

(a)            (b)

(c)                     (d)

15.) If , then is

(a)

(b)

(c)

(d)

16.) The set of points where the functions f given by f(x) = |x – 3| cos x is differentiable is

(a) R                          (b) R – {3}

(c) (0, ∞)                  (d) None of these

17.) Differential coefficient of w.r.t. x is

(a)             (b)

(c)                              (d)

18.) If and , then is

(a) 1/2                                           (b) x

(c)         (d) 1

19.) If , then the value of at x = π/4 is

(a) 0                      (b) 1

(c) 1/2                   (d) ∞

20.) If , then is equal to

(a)           (b)

(c)             (d)

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