Strange Clock

Niloy cannot wake up in the morning. He turns off the alarm on his phone and goes back to sleep. So, he buys a strange digital clock ($24$ Hours Format) to set the alarm. The alarm actually rings when his watch contains a palindrome number. For example, when the time is $01:01$, the alarm rings. So, how many times will the alarm ring on Niloy's clock in a day?

Number Theory  

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Attempt 166

Solve 61

First Solve Mesbatur_Rahman_Niloy