Tamil Nadu Board Solutions for Chapter: Numbers And Sequences, Exercise 12: Exercise 2.3

Find the least positive value of $x$, such that $96\equiv \frac{x}{7} (\mathrm{mod} 5)$.

Find the least positive value of $x$, such that $5x\equiv 4 (\mathrm{mod} 6)$.

If $x$ is congruent to $13$ modulo $17$, then $7x-3$ is congruent to which number modulo $17$?

If the time $100$ hours after $7 \mathrm{a}.\mathrm{m}.$ is $k \mathrm{a}.\mathrm{m}.$ then find the value of $k$.

If the time $15$ hours before $11 \mathrm{pm}$ is $k p.m.$, then find the value of $k$.

Today is Tuesday. My uncle will come after $45$ days. In which day my uncle will be coming?

Find the remainder, when $2^{81}$ is divided by $17$.

The duration of flight travel from Chennai to London through British Airlines is approximately $11$ hours. The aeroplane begins its journey on Sunday at $23:30$ hours. If the time at Chennai is four and a half hours ahead to that of London's time, then find the time in London, when will the flight lands at London Airport on Monday. If the answer is $k a.m.$ then find the value of $k$.