On her vacations,Veena visits four cities ($A, B, C$,and $D$) in a random order. What is the probability that she visits $A$ either first or second?

The number of different words that can be formed from the letters of the word "$INTERMEDIATE$" such that two vowels never come together,is

$A$ linguistic club consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group including the selection of a leader (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is

Let $m$ (respectively,$n$) be the number of $5$-digit integers obtained by using the digits $1, 2, 3, 4, 5$ with repetitions (respectively,without repetitions) such that the sum of any two adjacent digits is odd. Then $\frac{m}{n}$ is equal to

The minimum value of $f(x) = |x - 1| + |2x - 1| + |3x - 1| + \dots + |119x - 1|$ occurs at $x$. Then $x$ is equal to

Suppose $a_2, a_3, a_4, a_5, a_6, a_7$ are integers such that $\frac{5}{7} = \frac{a_2}{2!} + \frac{a_3}{3!} + \frac{a_4}{4!} + \frac{a_5}{5!} + \frac{a_6}{6!} + \frac{a_7}{7!}$,where $0 \leq a_j < j$ for $j = 2, 3, 4, 5, 6, 7$. The sum $a_2 + a_3 + a_4 + a_5 + a_6 + a_7$ is: