R. S. Aggarwal Solutions for Exercise 1: Exercise

How many 5s are there in the following number sequence which are immediately preceded by 7 and immediately followed by 6?
$7 5 5 9 4 5 7 6 4 5 9 8 7 5 6 7 6 4 3 2 5 6 7 8$
 

In the series given below, count the number of $9$'s, each of which is not immediately preceded by $5$ but is immediately followed by either $2$ or $3$. How many such $9$'s are there?
$1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8$

How many $4$'s are there preceded by $7$ but not followed by $3$ ?

$\begin{array}{llllllllllllllllllll}5& 9& 3& 2& 1& 7& 4& 2& 6& 9& 7& 4& 6& 1& 3& 2& 8& 7& 4& 1\\ 3& 8& 3& 2& 5& 6& 7& 4& 3& 9& 5& 8& 2& 0& 1& 8& 7& 4& 6& 3\end{array}$

In a school, the following codes were used during physical exercise.
'$1$' means 'start walking',
'$2$' means 'keep standing',
'$3$' means 'start running at the same spot',
'$4$' means 'sit down'.

How many times will a student who performs the following sequence without error from the beginning to the end have to sit down?

$\begin{array}{lllllllllllllllllllll}1& 2& 3& 4& 2& 3& 1& 4& 4& 3& 2& 2& 1& 2& 4& 3& 1& 4& 4& 1& 2\end{array}$

A number is greater than $3$ but less than $8$. Also, the number is greater than $6$ but less than $10$. What is the number?

If it is possible to make a number which is perfect square of a two-digit odd number with the second, the sixth and the ninth digits of the number $187642539$, which of the following is the digit in the unit's place of that two-digit odd number?

How many numbers amongst the numbers $9$ to $54$ are there which are exactly divisible by $9$ but not by $3$?

How many numbers from $11$ to $50$ are there which are exactly divisible by $7$ but not by $3$ ?