The number of bijective functions $f:\{1,3,5,7, \ldots, 99\} \rightarrow\{2,4,6,8, \ldots .100\}$, such that $f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots . . f(99)$, is ____________.

Let A = {0, 1, 2, 3, 4, 5, 6, 7}. Then the number of bijective functions f : A $\to$ A such that f(1) + f(2) = 3 $-$ f(3) is equal to

Let A = {2, 3, 4, 5, ....., 30} and '$\simeq$' be an equivalence relation on A $\times$ A, defined by (a, b) $\simeq$ (c, d), if and only…

Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m,…

Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set C = {f : A $\to$ B | 2 $\in$ f(A) and f is not one-one} is…

Let $S=\{1,2,3, \ldots, 10\}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $\mathrm{R}=\{(\mathrm{A}, \mathrm{B}):…