Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Mathematics
Chapter
Functions

BITSAT 2010 · Mathematics · Functions

Let (E=\ 1,2,3,4\ ) and (F=\ 1,2\ ). Then the number of onto...

Let (E=\{1,2,3,4\}) and (F=\{1,2\}). Then the number of onto functions from (E\mathrm{E}) to (F\mathrm{F}) is

Options

  1. A14
  2. B16
  3. C12
  4. D8

Correct answer

A. 14

Step-by-step solution

If set AA has mm elements and set BB has (\mathrm{n})elementsthennumberofontofunctionsfrom) elements then number of onto functions fromAtotoBis(∑r=1n(−1)n−rnCrrmis (\sum_{r=1}^n(-1)^{n-r}{ }^n C_r r^m\text{ where }1≤n≤m)Here(E={1,2,3,4},F={1,2})1 \leq n \leq m) Here (E=\{1,2,3,4\}, F=\{1,2\})m=4, n=2(∴)No.ofontofunctionsfrom(E(\therefore) No. of onto functions from (\mathrm{E}) to (\mathrm{F})$() \$(=∑r=12(−1)2−r2Cr(r)4=(−1)2C1+2C2(2)4=−2+16=14\begin{aligned}& =\sum_{r=1}^2(-1)^{2-r 2} C_r(r)^4 \\ & =(-1)^2 C_1+{ }^2 C_2(2)^4=-2+16=14 \end{aligned}$)
Practice Functions on Quantrex Academy →

More from Functions

Let [x] denote the greatest integer ≤ x . If f(x)=[x] and g(x)=|x| , then the value of f… BITSAT 2024Number of real solution of 5- _2|x| =3- _2|x| is equal to BITSAT 2024f(x)=( x)/([(2 x)/(π)]+(1)/(2)) , where x is not an integral multiple of π and [.]… BITSAT 2024The function f: R arrow R defined by f(x)= x 1+x^2 is BITSAT 2024If f: R arrow R, g: R arrow R are defined by f(x)=5 x-3, g(x)=x^2+3 , then g o f^ -1 (3)… BITSAT 2024The domain of the real valued function f(x)= (2 x^2-7 x+5)/(3 x^2-5 x-2) is BITSAT 2024If a function f: R-\ l\ arrow R-\ m\ defined by f(x)=(x+3)/(x-2) is a bijection, then 3… BITSAT 2024f(x)= x+ x, g(x)=x^2-1 , then g(f(x)) is invertible if BITSAT 2024Let the function g:(-∞, ∞) arrow (-(π)/(2), (π)/(2)) be given by g(u)=2 ^ -1… BITSAT 2024The domain of the function f(x)= x- 1-x^2 is BITSAT 2023Consider the function f in A=R-\ (2)/(3)\ defined as f(x)=(4 x+3)/(6 x-4) , then f^ -1 is… BITSAT 2023If f(x)= x 1+x^2 , then (fof of) (x) is BITSAT 2023If g(x)=x^2+x-2 and (1)/(2) g o f(x)=2 x^2-5 x+2 then f(x) is equal to BITSAT 2022The domain of the function f(x)= 1 x^ 12 -x^ 9 +x^ 4 -x+1 is given by BITSAT 2021Let [x] denote the greatest integer ≤ x . If f(x)=[x] and g(x)=|x|, then the value of f… BITSAT 2020The domain of the function f(x)= x- 1-x^ 2 is BITSAT 2020 Full Functions list Functions JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs