Question:
If \(A=\{a,b\}\), \(B=\{1,2,3\}\) then the total number of one–one (injective) functions from \(A\) to \(B\) is
If \(A=\{a,b\}\), \(B=\{1,2,3\}\) then the total number of one–one (injective) functions from \(A\) to \(B\) is
Show Hint
One–one maps from size \(m\) to size \(n\) (with \(n\ge m\)) are \(nP m=\frac{n!}{(n-m)!}\).
Updated On: Oct 17, 2025
- \(6\)
- \(8\)
- \(9\)
- none of these
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
For injective \(f:A\to B\), distinct elements of \(A\) must go to distinct elements of \(B\).
Choose an image for \(a\): \(3\) choices. Then for \(b\) only \(2\) choices remain (must be different).
Total \(=3\times2=6=P(3,2)\).
Was this answer helpful?
0
0
Top Bihar Board XII Mathematics Questions
- \(\frac{d}{dx} \left(\sec^2 x - \tan^2 x\right)\)
- \(\frac{d}{dx} \left( e^{2x} + 2e^x \right)\)
- \(\frac{d}{dx} \left[ \lim_{x \to a} \frac{x^n + a^n}{x + a} \right] \)
- \(\frac{d}{dx} \left( \sin^{-1} 2x \right)\)
- \(\frac{d}{dx} \left[ (x+2)(x^2 - 2x + 4) \right] \)
View More Questions
Top Bihar Board XII Relations and functions Questions
Top Bihar Board XII Questions
- Which metal was first used by humans?
- Where is the Harappan site called Shortughai located?
- Where has the evidence of dockyard been found from Indus Valley Civilization?
- Which is referred to as Meluhha in Mesopotamian texts?
- Where have miniature pots of faience probably used as perfume bottles been found?
View More Questions