Number of functions f:\ 1,2, , 100\ arrow\ 0,1\ , that assign 1 to...

Number of functions

f:\{1,2, \ldots, 100\} \rightarrow\{0,1\}

, that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ________. $Number of functions f:\ 1,2, , 100\ arrow\ 0,1\ , that assign 1 to exactly one of the positive integers less than or$

Correct answer

Step-by-step solution

$Number of functions f:\ 1,2, , 100\ arrow\ 0,1\ , that assign 1 to exactly one of the positive integers less than or$
392 Ans.

Practice Functions on Quantrex Academy →

More from Functions

Let ℕ denote the set of all positive integers. Consider the sets A = \ 1, 2, 3, 4, 5\ and… JEE Advanced 2026 Let f:(1,∞)→ℝ be a function defined as f(x) = (x-1)/(x+1) . Let f^ i+1 (x) = f(f^i(x))… JEE Main 2026 Let f be a polynomial function such that _2(f(x)) = ( _2(2+(2)/(3)+(2)/(9)+…∞))·… JEE Main 2026 Let f: ℝ arrow ℝ be defined as f(x) = (2x^2 - 3x + 2)/(3x^2 + x + 3) . Then f is : JEE Main 2026 Let e be the base of natural logarithm and let f: \ 1, 2, 3, 4\ arrow \ 1, e, e^2, e^3\… JEE Main 2026 Let f: R arrow R be a function such that f(x) + 3f((π)/(2) - x) = x , x ∈ R . Let the… JEE Main 2026 The sum of all the integral values of p such that the equation 3 ^2 x + 12 x - 3 = p , x… JEE Main 2026 Let A = \ 1, 2, 3, 4, 5, 6\ . The number of one-one functions f: A arrow A such that f(1)… JEE Main 2026 For the function f:[1,∞) arrow [1,∞) defined by f(x)=(x-1)^4+1 , among the two… JEE Main 2026 Let for some α ∈ ℝ , f:ℝarrowℝ be a function satisfying f(x+y)=f(x)+2y^2+y+α xy for all… JEE Main 2026 Let [·] denote the greatest integer function. If the domain of the function f(x) = ^ -1… JEE Main 2026 The number of functions f: \ 1, 2, 3, 4\ arrow \ a, b, c\ , which are not onto, is: JEE Main 2026 If the domain of the function f(x) = _ (0.6) (|(2x-5)/(x^2-4)|) is (-∞, a] \ b\ [c, d)… JEE Main 2026 Given below are two statements: Statement I: The function f: R arrow R defined by… JEE Main 2026 The sum of all the elements in the range of f(x)=Sgn( x)+Sgn( x)+Sgn( x)+Sgn( x) , x ≠ n… JEE Main 2026 If g(x)=3 x^ 2 +2 x-3, f(0)=-3 and 4 g(f(x))=3 x^ 2 -32 x+72 , then f(g(2)) is equal to: JEE Main 2026 Full Functions list Functions JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs