# Class 12 continuity and differentiability multiple choice

# 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

**Answer (c)**

**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

**Answer (a)**

**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

**Answer (d)**

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

(a) 1 (b) 2

(c) 3 (d) None of these

**Answer (d)**

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

(a) 3 (b) 2

(c) 1 (d) 1.5

**Answer (b)**

**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

**Answer (c)**

**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}

**Answer (a)**

**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

**Answer (b)**

**9.) The function** **is discontinuous at**

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

(c) Exactly three points (d) No point

**Answer (c)**

**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

**Answer (a)**

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

(a) 3 (b) 5

(c) 2 (d) 8

**Answer (d)**

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

(a)

(b)

(c)

(d)

**Answer (b)**

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

(a) (b)

(c) (d)

**Answer (a)**

**14.) If** ,** then** **is**

(a) (b)

(c) (d)

**Answer (a)**

**15.) If** , **then** **is**

(a)

(b)

(c)

(d)

**Answer (c)**

**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

**Answer (b)**

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

(a) (b)

(c) (d)

**Answer (a)**

**18.) If** **and** , then ** is**

(a) 1/2 (b) x

(c) (d) 1

**Answer (d)**

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

(a) 0 (b) 1

(c) 1/2 (d) ∞

**Answer (b)**

**20.) If** , then **is equal to**

(a) (b)

(c) (d)

**Answer (a)**