The sum of all three-digit numbers,formed using non-zero digits,where all the digits are perfect squares of a natural number,is:

$A$ number lock on a suitcase has $3$ wheels,each labelled with $10$ digits from $0$ to $9$. If opening the lock requires a particular sequence of $3$ digits with no repeats,how many such sequences are possible?

The value of $r$ for which $^{20}C_r \cdot ^{20}C_0 + ^{20}C_{r-1} \cdot ^{20}C_1 + ^{20}C_{r-2} \cdot ^{20}C_2 + \dots + ^{20}C_0 \cdot ^{20}C_r$ is maximum is:

When all the students in a school are made to stand in rows of $54,$ $30$ such rows are formed. If the students are made to stand in rows of $45,$ how many such rows will be formed?

$A$ company has $10$ employees. The company has decided to form a team including at least three employees and also excluding at least three employees. Then the number of ways of forming the team is

How many numbers can be formed using the digits $3, 4, 5, 6, 7, 8$ that lie between $3000$ and $4000$ and are divisible by $5$,given that repetition of digits is not allowed?