Let $S=\{1,2,3,4,5,6,9\}$. Then the number of elements in the set $T=\{A \subseteq S ; A \neq f$ and the sum of all the elements of...

The sum of all natural numbers ' $n$ ' such that $100< n<200$ and H.C.F. $(91, n)>1$ is :

The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple...

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of...

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed...

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are...

Let $\mathrm{P}_1, \mathrm{P}_2 \ldots \ldots, \mathrm{P}_{15}$ be 15 points on a circle. The number of distinct triangles formed by points $\mathrm{P}_{\mathrm{i}}, \mathrm{P}_{\mathrm{j}}, \mathrm{P}_{\mathrm{k}}$ such that...

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which...

Let $n$ be a non-negative integer. Then the number of divisors of the form " $4 n+1$ " of the number $(10)^{10} .(11)^{11}$. (13) $...

The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is