COMEDK · Maths · 24. Functions
If \(n(A)=n(B)-m\), then the number of possiblc bijection from \(A\) to \(B\) is
- A \(m\)
- B \(m^{2}\)
- C \(m\) !
- D \(2 \mathrm{~m}\)
Answer & Solution
Correct Answer
(C) \(m\) !
Step-by-step Solution
Detailed explanation
If set \(A\) and \(B\) has \(m\) elements, then the number of bijections from \(A\) to \(B\) is the total number of arrangements of \(n\) distinct items taken all at a time, i.e. \(m !\).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If a set \(A\) has 4 elements, then the total number of proper subsets of set \(A\), isCOMEDK 2015 Easy
- Given that the lines \(L_1: \vec{r}=\hat{\imath}+\hat{\jmath}-\hat{k}+\lambda(3 \hat{\imath}-\hat{\jmath})\) and
\(L_2: \vec{r}=4 \hat{\imath}-\hat{k}+\mu(2 \hat{\imath}+3 \hat{k})\)
are neither skew nor parallel. Then the shortest distance between the lines isCOMEDK 2025 Medium - Evaluate : \(\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]-\cos ^{-1}\left(\sin 270^{\circ}\right)\)COMEDK 2024 Medium
- \(\text { The general solution of the differential equation } \dfrac{d y}{d x}=\dfrac{x y}{x^2+y^2} \text { is }\)COMEDK 2024 Medium
- If \(A=\left[\begin{array}{cc}1 & -3 \\ 2 & k\end{array}\right]\) and \(A^{2}-4 A+10 I=A\), then \(k=\)COMEDK 2016 Medium
- If \(R\) is a relation defined on \(N\) the set of all natural numbers defined by \(R=\{(x, y)\) if and only if \(x\) divides \(y\), for all \(x, y \in N\}\) the R isCOMEDK 2025 Easy
More PYQs from COMEDK
- Let \(P Q R\) be a right angled isosceles triangle, right angled at \(P(2,1)\). If the equation of \(Q R\) is \(2 x+y=3\), then the combined equation of the lines \(P Q\) and \(P R\) isCOMEDK 2017 Medium
- A simple pendulum is suspended from the
ceiling of a lift. When the lift is at rest its time
period is T. With what acceleration should the
lift be accelerated upwards in order to reduce
its period to T / 2 ?
(g is acceleration due to gravity)COMEDK 2018 Easy - For a cell \(2 \mathrm{M}_{(\mathrm{S})}+\mathrm{O}_2(\mathrm{~g})+4 \mathrm{H}^{+} \rightarrow 2 \mathrm{M}^{2+}(\mathrm{aq})+2 \mathrm{H}_2 \mathrm{O}_{(\mathrm{l})}\) the \(\mathrm{E}^0\) cell \(=+1.67 \mathrm{~V}\). When \(\left[\mathrm{M}^{2+}\right]\) is \(1.0 \times 10^{-3} \mathrm{M}\) and \(\mathrm{p}\left(\mathrm{O}_2\right)\) is 0.1 atm , the EMF of the cell becomes +1.57 V . Calculate the pH of the electrochemical cell.COMEDK 2025 Medium
- \(\int_\limits0^{\dfrac{\pi}{2}} \dfrac{\cos x}{1+\cos x+\sin x} d x=\)COMEDK 2024 Medium
- The angle between the curve \(y^{2}=4 a x\) and \(a y=2 x^{2}\) isCOMEDK 2015 Medium
- The probability that a randomly chosen number from one to twelve is a divisor of twelve isCOMEDK 2024 Easy