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JEE Main 202125 FebruaryEvening Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Evening Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2021 · 25 February · Evening Shift · Mathematics · Functions

Let x denote the total number of one-one functions from a set A...

Let xx denote the total number of one-one functions from a set AA with 33 elements to a set BB with 55 elements and yy denote the total number of one-one functions from the set AA to the set A×BA \times B. Then :

Options

  1. Ay=273xy = 273x
  2. B2y=273x2y = 273x
  3. C2y=91x2y = 91x
  4. Dy=91xy = 91x

Correct answer

C. 2y=91x2y = 91x

Step-by-step solution

Given, n(A)=3,n(B)=5n\left(A\right) = 3, n\left(B\right) = 5

⇒n(A×B)=15⇒ n\left(A \times B\right) = 15

x=C35×3!=5×4×3=60x = C3 5 \times 3 ! = 5 \times 4 \times 3 = 60

y=C315×3!=15×14×13=30×91y = C3 15 \times 3 ! = 15 \times 14 \times 13 = 30 \times 912y=60×912y = 60 \times 91

∴2y=91x∴ 2y = 91x

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