Question

Assertion($A$) : Period of $\frac{e^x}{e^{\left[x\right]}}$ is 1.
Reason($R$) : Period of $x-\left[x\right]$ is 1.

• A. A is true , R is true. R is the correct explanation of A
• B. A is false, R is false
• C. A is true, R is true and R is not correct explanation of A
• D. A is true, R is false.

Answer 1

The correct option is A A is true , R is true. R is the correct explanation of A

Assertion (A) :

$f\left(x\right)=\frac{e^x}{e^{\left[x\right]}},\left[x\right]=x-\left\{x\right\}$
$f\left(x\right)=e^{x-\left[x\right]}$
$=e^{\left\{x\right\}}$

$\therefore$ period of $\left\{x\right\}=1$

Period of $e^{\left\{x\right\}}=1$ True.

Reason (R) :

Period of $x-\left[x\right]$ is $1$.
$x-\left[x\right]=\left\{x\right\}$
We know, period of $\left\{x\right\}=1$ True
So, $A$ is True, $R$ is True and $R$ is correct explanation of $A$.