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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:
= 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) = tan^{2} x is continuous at x = π/2
Reason : g(x) = x^{2} is continuous at x = π/2.
Hence R is true.
f(x) = tan^{2} 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.
209 videos218 docs139 tests

209 videos218 docs139 tests
