1
JEE Main 2022 (Online) 25th June Morning Shift
Numerical
+4
-1

Let $$f:R \to R$$ be a function defined by

$$f(x) = {\left( {2\left( {1 - {{{x^{25}}} \over 2}} \right)(2 + {x^{25}})} \right)^{{1 \over {50}}}}$$. If the function $$g(x) = f(f(f(x))) + f(f(x))$$, then the greatest integer less than or equal to g(1) is ____________.

2
JEE Main 2022 (Online) 24th June Morning Shift
Numerical
+4
-1

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 ___________.

3
JEE Main 2021 (Online) 27th July Morning Shift
Numerical
+4
-1
Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f : S $$\to$$ S
such that f(m . n) = f(m) . f(n) for every m, n $$\in$$ S and m . n $$\in$$ S is equal to _____________.
4
JEE Main 2021 (Online) 22th July Evening Shift
Numerical
+4
-1
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