Assertion (A): $f (x) = sin (π [x])$ is differentiable every where $[]$ is greatest integer function

Reason (R): lf $x = n π \Rightarrow$ $sin x$ $= 0 \forall n \in Z$ then

Both (A) and (R) are true and R is correct explanation for A

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Both (A) and (R) are true and R is not correct explanation for A

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(A) is true (R) is false

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(A) is false (R) is true

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Solution

The correct option is A Both (A) and (R) are true and R is correct explanation for A
$[x]$ is an integer $\forall x ϵ R$
Hence, sin $(π [x]) = 0 \forall x ϵ R$
Hence, $f (x) = 0 \forall x ϵ R$
Hence, $f (x)$ is differentiable everywhere.
The Assertion is correct and the Reason provides the correct explanation for it.

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Assertion (A): f(x)=sin(π[x]) is differentiable every where [ ] is greatest integer functionReason (R): lf x=nπ⇒ sinx =0 ∀ n∈Z then

The correct option is A Both (A) and (R) are true and R is correct explanation for A[x]is an integer ∀ xϵRHence, sin(π[x])=0 ∀ xϵ RHence, f(x)=0 ∀ xϵ RHence, f(x) is differentiable everywhere.The Assertion is correct and the Reason provides the correct explanation for it.

Assertion (A): $f (x) = sin (π [x])$ is differentiable every where $[]$ is greatest integer function

Reason (R): lf $x = n π \Rightarrow$ $sin x$ $= 0 \forall n \in Z$ then