Functions PYQs - Last 5 Years

Let \(f(x)\) be a quadratic polynomial with leading coefficient 1 such that \(f(0)=p, p \neq 0\), and \(f(1)=\frac{1}{3}\). If the equations \(f(x)=0\) and \(f \circ f \circ f \circ f(x)=0\) have a common real root, then \(f(-3)\) is equal ...

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 ____________.

The number of one-one functions f : {a, b, c, d} \(\to\) {0, 1, 2, ......, 10} such
that 2f(a) \(-\) f(b) + 3f(c) + f(d) = 0 is ___________.