Continuity And Differentiability Mock Tests

25 questions available

Continuity And Differentiability Mock Test 1

Questions: 25

Sample Questions

Class 12 Mathematics

The function f : R → R defined by f(x) = [x], where [x] is the greatest integer ≤ x, is:

A continuous everywhere

B continuous only at integer points

C continuous only at non-integer points

D neither continuous nor differentiable at any integer point

Class 12 Mathematics

The function f(x) = |x − 1|, x ∈ R is:

A differentiable everywhere but not continuous at x = 1

B continuous everywhere but not differentiable at x = 1

C neither continuous nor differentiable at x = 1

D both continuous and differentiable at x = 1

Class 12 Mathematics

The derivative of sin⁻¹(2x√(1 − x²)) with respect to sin⁻¹x, where −1/√2 < x < 1/√2, is:

A 1

B 2

C 3

D 1/2

Class 12 Mathematics

If y = eˣ sin x, then dy/dx is:

A eˣ(sin x + cos x)

B eˣ(sin x − cos x)

C eˣ sin x + cos x

D eˣ cos x

Class 12 Mathematics

The function f(x) = |x − 2| + |x − 3| is differentiable at:

A x = 2 only

B x = 3 only

C all x ∈ ℝ except x = 2 and x = 3

D all x ∈ ℝ

Class 12 Mathematics

The function f(x) = |x − 1| is:

A differentiable at x = 1

B continuous but not differentiable at x = 1

C neither continuous nor differentiable at x = 1

D differentiable everywhere

Class 12 Mathematics

The function f(x) = cos(x²) is:

A a continuous function

B a discontinuous function

C a periodic function

D a one-one function

Class 12 Mathematics

If y = eˣ · sin x, then dy/dx equals:

A eˣ(sin x + cos x)

B eˣ(sin x − cos x)

C eˣ sin x

D eˣ cos x

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