Test: Continuity and Differentiability- Assertion & Reason Type Questions
8 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Continuity and Differentiability- Assertion & Reason Type Questions
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion: If y = sin-1 
then 
Reason: 
then 
= 2θ
= 2 sin-1 3x
A is true. R is false.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : |sin x| is continuous for all x ∈ R.
Reason : sin x and |x| are continuous in R.
Consider the functions f(x) = sin x and g(x) = |x| both of which are continuous in R.
gof(x) = g(f(x)) = g(sin x) = |sin x |.
Since f(x) and g(x) are continuous in R, gof(x) is also continuous in R.
Hence A is true.
R is the correct explanation of A.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : A continuous function is always differentiable.
Reason : A differentiable function is always continuous.
A differentiable function is always continuous. Hence R is true.
A continuous function need not be always differentiable.
For example, |x| is continuous at x = 0, but not differentiable at x = 0.
Hence A is false.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : f(x) = tan2 x is continuous at x = π/2
Reason : g(x) = x2 is continuous at x = π/2.
Hence R is true.
f(x) = tan2 x is not defined when x = π/2.
Therefore f(π/2) does not exist and hence f(x) is not continuous at x = π/2.
A is false.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : f(x) = [x] is not differentiable at x = 2.
Reason : f(x) = [x] is not continuous at x = 2.
So f(x) is not continuous at x = 2. Hence R is true.
A differentiable function is always continuous.
Since f(x) = [x] is not continuous at x = 2, it is also not differentiable at x = 2.
Hence A is true.
R is the correct explanation of A.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Consider the function
which is continuous at x = 0.
Assertion (A): The value of k is – 3.
This is the definition for modulus function and hence true.
Hence R is true.
Since f is continuous at x = 0,
Here f(0) = 3,
∴ -k = 3 or k = -3
Hence A is true.
R is the correct explanation of A.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): |sin x| is continuous at x = 0.
Reason (R): |sin x| is differentiable at x = 0.
Hence A is true.
At x = 0, LHD ≠ RHD.
So f(x) is not differentiable at x = 0.
Hence R is false.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Consider the function
which is continuous at x = 2.
Assertion (A): The value of k is 0.Reason (R): f(x) is continuous at x = a, if
∴ R is true.
∴ k = 7
Hence A is false.
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